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Full text of "The Ontario high school physics"

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THE ONTARIO 

HIGH SCHOOL PHYS 




AUTHORIZED SY 
THE MINISTER OF EDUCATION FOR ONTARIO 



PRICE 90 CENTS 



TORONTO 
THE COPP CLARK COMPANY LIMITf 



Digitized by tine Internet Arciiive 

in 2009 witii funding from 

Ontario Council of University Libraries 

^- .^ 

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http://www.archive.org/details/ontariohighschoolOOmerc 



THE ONTARIO 

HIGH SCHOOL PHYSICS 



BY 

F. W. MERCHANT, M.A., D.Paed., 

Director of Technical and Industrial Education 
for Ontario 



C. A. CHANT, M.A., Ph.D., 

Associate Professor of Astrophysics, 
University of Toronto 




Authorized by the Minister of Education for Ontario 
for use in the Middle School 



TORONTO 
THE COPP. CLARK COMPANY. LIMITED 



Copyright, Canada 1911, by Thb Copp, Clark Company, Limited, 
Toronto, Ontario. 

FiHOT Edition, 1911. 
Reprinted, 1911, 1912, 1912, 1913, 1914, 1914, 1915, 1917. 



PREFACE 



In the printing of tliis book two sizes of type have been 
mainly used. The portion printed in large type (§1 for 
example) is intended to cover the course in Physics at present 
prescribed for the classes of the Middle School. The sections 
in smaller type (§ 24 for example) have been included in 
order to render the treatment of the subject more complete. 

In dealing with the various branches of the subject an 
attempt has been made to illustrate its principles and laws 
by reference to numerous applications in ordinary life. Other 
illustrations are taken from tlie chief applications of Physics 
to industry and commerce, especially those to be seen in our 
own country. 

Practical questions and problems are proposed in connection 
with important topics in the text. The materials for these 
exercises have been selected with the purpose, not only of 
illustrating and applying the jirinciples discussed, but also 
of stimulating the interest of the student in the physical 
phenomena with which he is familiar. 

Attention is directed to the diagrams and other di-awings, 
of which there is an exceptionally large number. These 
have all been prepared especially for this work, and great 
pains have been taken to have them clear and easily 
understood. 



iv PREFACE 

The portraits of some of the great scientific investigators 
and the historical references which have been woven into 
almost every chapter, will, it is hoped, awaken a real human 
interest in the subject. 

Throughout the work appear concise tables of physical 
constants, which have been taken from the Smithsonian 
Physical Tables, published by the Smithsonian Institution, 
Washington, D.C. 

In the preparation of the book the authors have received 
courteous assistance from many firms and individuals regard- 
ing certain industrial applications of Physics. They are also 
indebted to many friends engaged in the practical teaching of 
the subject in secondary schools and colleges ; but they are 
especially indebted to Dr. A. L. Clark, Professor of Physics at 
Queen's University, Kingston, and to Dr. W. E. McElfresh, 
Professor of Physics at Williams College, Williamstown, Mass., 
who carefully read the proof-sheets and offered many valuable 
suggestions. 

A Laboratory Manual has been prepared to accompany 
this book. It contains a large number of exercises, with full 
instructions for the student's guidance. 

Toronto, June, 1911. 



CONTENTS 



Part T —Introduction 

CHAPTER TAQK 

I. — Measurement 1 

Part II — Mechanics of Solids 

n. — Displacement, Velocity, Acceleration 17 

III. — Inertia, Momentum, Force 33 

IV. — Moment of a Force ; Composition of Parallel FoJ-ces ; 

Equilibrium of Forces 44 

V. — Gravitation • 50 

VI. — Work and "Energy 54 

VII. — Centi-e of Gravity GO 

VIII. — Friction " . 64 

IX. — Machines C7 

Part III — Mechanics of Fluids 

X. — Pressure of Liquids 82 

XI. — Buoyancy of Fluids 92 

XII. — Determination of Density 96 

XIII. — Pressure in Gases 101 

XIV. — Applications of the Laws of Gases 119 

Part IV — Some Properties of Matter 

XV.— The Molecular Theory of Matter 131 

XVI. — Molecular Forces in Solids and Liquids . . . . 142 

XVII. — Phenomena of Surface Tension and Capillarity . . 150 



vi CONTENTS 

Part Y — Wave Motion and Hound 

CHAPTER PAGR 

XVIII..— Wave Motion 157 

XIX. — Production, Propagation, Velocity of Sound . . . 168 

XX. — Pitch, Musical Scales 179 

XXI. — Vibrations of Strings, Rods, Plates and Air 

Columns 187 

XXII. — Quality, Vibrating Flames, Beats 200 

XXIII. — Musical Instruments — The Phonograph .... 209 

Part VI — Heat 

xxiv.-^Nature and Source of Heat 214 

XXV. — Expansion through Heat 217 

XXVI. — Temperature 222 

XXVII. — Relation between Volume and Temperature . . . 229 

XXVIII. — Measurement of Heat 238 

XXIX. — Change of State 243 

XXX. — Heat and Mechanical Motion 267 

XXXI. — Transference of Heat 274 

Part VII — Light 

XXXII. — The Nature of Light; its Motion in Straight Lines 287 

XXXIII. — Photometry . 294 

XXXIV.— The Velocity of Light 300 

XXXV. — Reflection of Light : Plane Mirrors 302 

XXXVI. — Reilection from Curved Miri-ors 309 

XXXVII. — Refraction 319 

XXXVIII. — Lenses 330 

XXXIX. — Dispersion, Colour, the Spectium, Spectrum Analysis 339 

XL. — Optical Instruments 356 



CONTENTS vii 
Part VIII — Electricity and Magnetism 

CHAPTER PAOE 

XLi. — Magnetism 367 

XLii. — Electricity at Rest 380 

XLiii. — The Electric Current 39G 

XLiv. — Chemical Effects of the Electric Current .... 408 

XLV. — Magnetic Relations of the Current 419 

XLVi. — Induced Cui'rents 435 

XLVii.— Applications of Induced Currents 442 

XLViii. — Heating and Lighting Effects of the Electric Current 457 

XLix. — Electrical Measurements 462 

L. — Other Forms of Radiant Energy 479 

Answers to Numerical Problems 492 

Index 495 



TABLE OF EQUIVALENTS OF UNITS 

Length 
1 in. = 2.54 cm. 1 cm. = 0.3937 in. 
1 ft. = 30.48 cm. 1 m, = 39.37 in. = 1.094 yd. 
1 yd. = 91.44 cm. 1 km. = 0.6214 mi. 
1 mi. = 1.609 km. 1 km. = 1000 m., 1 m. = 100 cm., 

1 cm. = 10 mm. 

Surface 

1 sq. in. = 6.4514 sq. cm. 1 sq. cm. = 0. 1550sq. in. 

1 sq. ft = 929.01 sq. cm. 1 sq. m. = 10.764 sq. ft. 

1 sq. yd. = 8361.3 sq. cm. = 0.83613 sq. m. 1 sq. m. = 1.196 sq. yd. 

Volume 
1 c. in. = 16.387 c.c. 1 c.c. = 0.061 c. in. 

1 c. ft. = 28317 c.c. 11. = 1000 c.c. = 61.024 c. in. 

1 c. yd. = 0.7645 cu. m. 1 cu. m. = 1.308 c. yd. 
1 Imperial gallon = 10 lb. water at 62° F. 

= 277.274 c. in. = 4.546 1. 
1 Imperial quart = 1.136 1, 
1 U.S. gallon = 231 c. in. = 3.784 1. 
11. = 1.7598 Imperial pints. 

Mass 
1 lb. av. (7000 gr.) = 453.59 g. 1 kg. = 2.205 lb. av. 

1 oz. av. = 28.3495 g. 1 g. = 15.432 gr. 

1 gr. = 0.0648 g. 

Abbreviations 

in. = inch ; ft. = foot ; yd. = yard ; mi. = mile ; sq. = square ; 
c. or cu. = cubic ; m. = metre ; mm. = millimetre ; cm. = centimetre ; 
km. = kilometre ; c. cm. or c.c. = cubic centimetre ; 1. = litre ; lb. av. = 
pound avoirdupois ; gr. = grain ; g. = gram ; kg. = kilogram. 



PART I-INTRODUCTION 



CHAPTER I 
Measurement 

1. Physical Quantities. Tlie various operations of nature 
are continually before our eyes, and thus by the time that we 
definitely enter upon the study of physics, we have gathered 
a store of observations and experiences. 

We all admire the beauty of a water-fall, but we recognize 
that there is more than beauty in it when we see it made to 
turn our mills. In recent years the world's great water- 
powers have been used to generate electricity, which, after 
being transmitted over considerable distances, supplies motive- 
power for our great factories or our street railways. The sun 
continually sends forth immense quantities of heat and light, 
conveying to us warmth and cheer, and preserving life itself. 
We see the giant ship or the railway train, driven by the 
power of steam, transporting the commerce of the nations. 
And in the near future we shall probably see multitudes of 
aeroplanes circling about in the air and carrying passengers 
from place to place. 

When asked to describe how these various physical effects 
are produced we usually reply in vague and general terms. 
The study of physics is intended to give definiteness to our 
descriptions, and to enable us clearly to state the relations 
between successive physical events. 

In order to do this we must understand the numerous 
operations met with in mechanics, heat, electricity, and other 

1 



2 MEASUREMENT 

branches of physics ; and our knowledge of these matters can 
liardly be considered satisfactory unless we are able actually 
to measure the various physical quantities involved. We 
must not be content with saying simply that a certain sub- 
stance was present, or that a result of a certain kind was 
obtained ; but we should be able to state how much of that 
substance was present, or the precise relation of the result 
obtained to the causes producing it. 

2. Measuring a Quantity. In measuring a quantity we 
determine how many times a magnitude of the same kind, 
which w^e call a unit, is contained in the quantity to be 
measured. 

Thus we speak of a length being 5 feet, the unit chosen 
being a foot, and 5 expressing the number of times the unit is 
contained in the given lengtli. 

3. Fundamental Units. There will be as many kinds of 
units as there are kinds of quantities to be measured, and the 
size of the units may be just what we choose. But there are 
three units which we speak of as fiindainental, namely the 
units of length, mass and time. These units are fundamental 
in the sense that each is independent of the others and cannot 
be derived from tliein ; also we shall find that the measure- 
ment of any quantity, — such as the power of a steam engine, 
the speed of a rifie-bullet or the strength of an electric 
current, — can ultimately be reduced to measurement of length, 
mass and time. Hence these units are properly considered 
fundamental, 

4. Standards of Length, — the Yard. There are two 
standards of length in use in English-speaking countries, 
namel}^, the yard and the metre. 

The yard is said to have represented, originally, the length 
of the arm of King Henry I., but such a definition is not by 
any means accurate enough for present-day requirements. It 



THE METRE 




FiQ. 1.— Bronze yard, 38 in. long, 1 in. sq. in section. 
a, a are small wells in bar, sunk to mid-depth. 



is now defined as the distance between the centres of two 
transverse lines ruled on two gold pings in a bronze bar, 
which is preserved in London, England, in the Standards 
Office of the Board of Trade of Great Britain. 

The bronze bar is 38 inches long and has a cross-section one 
inch square (Fig. 1). At CrossSecUon 
a, a, wells are sunk to the 
mid-depth of the bar, and 
at the bottom of each well 
is the gold plug or pin, 
about yV inch in diameter, 
on which the line defining 
the yard is engraved. 

The other units of length in ordinary use, such as the inch, 
the foot, the rod, the mile, are derived from the yard, though 
the relations between them are not always simple. 

5. The Metre. The metre came into existence through an 
effort made in France, at the end of the 18tli century, to 
replace by one standard the many and confusing standards of 
length prevailing throughout the country. It was decided 
that the new standard should be called a metre, and that it 
should be one ten-millionth of the distance from the pole to 
the equator, measured through Paris. The system was 
provisionally established l)y law in 1793, and the standard 
bar representing the length was completed in 1799. Tliis bar 
is of platinum, just a metre from end to end, 25 millimetres 
(about 1 inch) wide and 4 millimetres (about \ inch) thick. 

As time passed, great difficulty was experienced in making 
exact copies of this platinum rod, and as the demand for such 
continually increased, it was decided to construct a new 
standard bar. 

Following the great "World's Fairs" held in London in 1851 
and in Paris in 1867, proposals were made for international 



4 MEASUREMENT 

cooperation in the production of the new standards ; and 
after several preliminary conferences, in 1875 there was 
convened in Paris an International Committee of delegates 
officially appointed by various national governments. By this 
Committee the International Bureau of Weights and Measures 
was established at Sevres, near Paris, and the different nations 
contribute annually towards its maintenance. By this bureau 
31 standard metres and 40 standard kilograms, known as 
'prototype metres and kilograms, have been constructed. 

The new metre bars are made of a hard and durable alloy 
composed of platinum 90 per cent, and 
(ffalfSize) ii'idium 10 per cent., and have tlie form 
~ ~ shown in Fig. 2. The section illustrated 
here was chosen on account of its great 
rigidity, and also in order that the cross- 
lines which define the length of the metre 
might be placed on the face which is 
just mid-way between the upper and 
lower faces of the bar. The bars are 
""sectil^lMhe^ta'daJd^^^^^^^^^^ 102 Centimetres in length over all, and 
rflTngThe'nd'ol-Jemeire 20 millimetres squarc in section. Thus 
miX^af bTtweVnVh';%o";and the liucs which define the metre are one 
bottom of the bar. centimetre from each end of the bar. 

All the bars were completed in 1889. They were made as 
nearly as possible equal in length to the original platinum one 
of 1799, but of course minute diflferences existed between 
them — perhaps one part in one hundred million. So the one 
which appeared to agree most perfectly with the old standard 
was taken as the new International Prototype Standard. 
The new kilogram (see § 11) was also chosen from all that 
had been made. These were adopted as the new international 
standards on Sept. 26, 1889, by the International Committee. 
They are kept in a special vault in tlie International Bureau 




NATIONAL STANDARDS 5 

secured by tlirce locks, the keys of which are kept by three 
different high officials. The vault is opened not oftener than 
once a year, at which time all three officials must be present. 

6. National Standards. The metre rod kept in the vault 
at Sevres is the standard for the world. Each nation con- 
tributing to the International Bureau is entitled to a 
prototype metre and kilogram. Great Britain and the 
United States have their copies. In the former country all 
the standards are kept in the Standards Office in London ; in 
the latter, they are preserved in the Bureau of Standards 
in Washington. 

In the United States the metre is taken as the primary 
standard of length, and by law 

1 yard = |g§?- of a metre. 

The standard yard and the standard metre at present in 
use in Canada are both of bronze, of the form illustrated 
in Fig. 1. They were obtained from England in 1874. 
Quite recently, however, Canada has been admitted to the 
International Committee as an autonomous nation, and so is 
entitled to receive one of the prototype metres and one of 
the prototype kilograms constructed by the International 
Bureau. No doubt these will soon be secured. The Canadian 
standards are kept in the Standards Office of the Department 
of Inland Revenue, Ottawa. 

7. The Metre Independent of the Size of the Earth. 

Great care was taken to have the original metre exactly 
one ten-millionth of the distance from the pole to the equator; 
but when once the standard had been constructed it became 
the fixed standard unit, no further reference being made to 
the dimensions of the earth. 

Indeed, later measurements and calculations have shown 
that there are more than ten million metres in the earth- 
quadrant, and hence the metre is a little shorter than it 



Q MEASUREMENT 

was intended to be. The difference, liowever, is very small 
about yV mm., which is perliaps a hair's breadth. 

8. Sub-divisions of the Metre. The metre is divided 
decimally, thus : — 

^^jj metre = 1 decimetre (dm.) 
y^y dm. = 1 centimetre (cm.) 
■^^ cm. = 1 millimetre (mm.) 
1 m. = 10 dm. = 100 cm. = 1000 mm. 

For greater lengths, multiples of ten are used, thus : — 
10 metres = 1 decametre. 

10 decametres = 1 hectometre. 
10 hectometres = 1 kilometre (km.) 
1 km. = 1000 m. 

The decametre and the hectometre are not often used. 

9. Relation of Metres to Yards. In Great Britain the 

relation between the metre and the inch is officially stated 

to be 

1 metre = 39.370113 inches ; 

in the United States, by law, 

1 metre = 39.37 inches. 
The difference between these two statements of length of the 
metre is only y^^oo^ inch, and the British and United States 
yards may be considered identical. 

The following relations hold : — 

1 cm. = 0.3937 in. 1 in. = 2.54 cm. 

1 m. = 39.37 in. = 1.094 yd. 1 ft. = 30.48 cm. 

1 km. = 0.G214 mi. 1 mi. = 1.609 km. 

Approximately 10 cm. = 4 in. 
30 cm. = 1 ft. 
8 km. — 5 mi. 



DERIVED UNITS 
In Fig. 3 is shown a comparison of centimetres and inches. 



Centimetres 

J :2 .3 ,4 .5 .6 .7 .8 

ijlijij|ij|iiilii.i|l.iiiili|ii iiii.ImiiIiiiiI|iiiIiiiiIihiIiiii|iiiiIi^ 



f> 'in '1' 



Inches 



Fig. 3. —Comparison of inches and centimetres. 

10. Derived Units, The ordinary units of surface and of 
voUnne are at once deduced from tlie lineal units. The 
imperial gallon is defined as the volume of 10 pounds of 
water at 62° F., or is equal to 277.274 cu. in. (The U.S. or 
Winchester gallon = 231 cu. in.). The litre contains 1,000 c. cm. 
The following relations hold :— 

1 sq. yd. = 0.836 sq. m. 1 c. dcm. = 61.024 c. in. 

1 sq. m. = 10.764 sq.ft. 1 gal. = 4.5461. 

1 cu. in. = 16.387 cc. 11. = 1.76 qt. 

PROBLEMS 

(For table of values see opposite page 1) 

1. How many millimetres in 2^ kilometres ? 

2. Change 186,330 miles to kilometres. 

3. How many square centimetres in a rectangle 54 x 60 metres ? 

4. Change 760 nnn. into inches. 

5. Reduce 1 cubic metre to litres and to cubic centimetres. 

6. Lake Superior is 602 feet above sea level. Express this in metres. 

7. Dredging is done at 50 cents per cubic yard. Find the cost per 
cubic metre. 

8. Air weighs 1.293 grams per litre. Find the weight of the air in a 
room 20 X 25 X 15 metres in dimensions. 

9. Which is cheaper, milk at 7 cents per litre or 8 cents per quart ? 

10. Express, correct to a hundredth of a millimetre, the difference 
between 12 inches and 30 centimetres. 

11. Standards of Mass. By the 7nass of a body is meant 
the quantity of matter in it. Matter may change its form. 



8 



MEASUREMENT 




but it can never be destroyed. A lump of matter may be 
transported to any place in the universe, but its mass will 
remain the same. 

There are two units of mass in ordinary use, namely, the 
pound and the kilogram. 

The standard pound avoirdupois is a certain piece of 
platinum preserved in the Standards Office in London, 
England. Its form is illustrated in Fig. 
4. The grain is toVo^ o^ the pound, and 
the ounce is ^\ of the pound or 437.5 
grains. 

The kilogram is the mass of a certain 
lump of platinum carefully preserved in 
Paris, and called the " Kilogramme des 
Archives." It was constructed by Borda 
(who also made the original platinum 
metre), and was intended to represent the 
mass of 1000 cubic centimetres (1 litre) of 
water when at its maximum density (at 4° C). 

Although the objection which had been raised against the 
platinum metre (namely, difficulty in reproducing it), did not 
hold in the case of the platinum kilogram ; still the platinum- 
iridium alloy is harder and more durable than pure platinum, 
and so the International Committee decided to make new 
standards out of this alloy. As already stated (in § 5), the 
International Bureau constructed 40 standard kilograms. 
These were all made as nearly as possible equal to the 
original platinum kilogram, and indeed as they do not differ 
amongst themselves by more than about one part in one 
hundred million, they may be considered identical.. 

One of these was adopted as the new International Proto- 
type kilogram, and is preserved along with the International 



Fig. 4.— Imperial Stan 
dard Pound Avoirdu 
pois. Made of platinum 
Height 1.35 inches 
diameter 1.15 inches, 
"P.S." stands for par- 
liamentary standard. 



UNIT OF TIME 



9 




Fio. 5. — Prototype 
kilogram, made of 
an alloy of plati- 
num and iridium. 
Height and dia- 
meter each 1.5 
inches. 



metre at Sevres. The others, as far as required, have 
been distributed to various nations, and are known as 
National Prototype kilograms. 

These new standards are plain cylinders, 
almost exactly 1| inches in diameter, and of 
the same height. (Figs. 5 and 6.) 

The relation of the pound to the kilogram 
is officially stated by the British government 
as follows : — 

1 kilogram (kg.) = 2.2046223 pounds avoir. 

lgram(gin.) = 15.4323564 grains. 

1 pound avoir. = 0.45359243 kg. 

1 ounce avoir. = 28.349527 grams. 

In transforming from kilograms to pounds, or the reverse, 

it will not be neces- 
sary to use so many 
decimal places as are 
given here. The equi- 
valent values may be 
taken from the table 
opposite page 1. 
Approximately 1 kg. = 2^ 
lbs. ; 1 oz. = 28j gm. 

12. Unit of Time. 
If we reckon from 
the time when the 
sun is on our meri- 
dian (noon), until it 
is on the meridian 
again, the interval is 
a solar day. But 
the solar days thus 
determined are not all exactly equal to each other. This, as 
is explained in works on astronomy, is due to two causes, 




FiQ. 6.— United States National Kilogram " No. 20, 
under two glass bell-jars at Washington. 



Kept 



10 MEASUREMENT 

(1) the earth's orbit is an ellipse, not a circle, (2) the plane 
of the orbit is inclined to the plane of the earth's equator. 
In order to get an invariable interval we take the average 
of all the solar days for an entire year, and call the day 
thus obtained a onean solar day. Dividing this into 86,400 
equal parts we call each a mean solar second. This is the 
quantity which is " ticked off" by our watches and clocks. 
It is used universally by scientific men as the fundamental 
unit of time. 

13. The English and the C. G. S. System. In the 

so-called English system of units the foot, the pound 
and the second are the units of length, mass and time, 
respectively. In another system, which is used almost 
universally in purely scientific work, the units of length, 
mass and time are 1 centimetre, 1 gram and 1 second, 
respectively. 

The former is sometimes called the F.P.S. system, the 
latter the C.G.S. system, the distinguishing letters being the 
initials of the units in the two cases. 

14. Measurement of Length. A dry-goods merchant 
unrolls liis cloth, and, placing it alongside his yard-stick, 
measures ofi" the quantity ordered by the customer. Now the 
yard-stick is intended to be an accurate copy of the standard 
yard kept at the capital of the "country, and this latter we 
know is an accurate copy of the original preserved in London, 
England. In order to ensure the accuracy of the merchant's 
yard-stick a government official periodically inspects it, 
comparing it with a standard yard which he carries with 
him. 

Suppose, next, that we require to know accurately the 
diameter of a wire, or of a sphere, or the distance between 




MEASUREMENT OF MASS 11 

two marks on a pliotographic plate. We choose the most 
suitable instrument for the purpose in view. For the wire or 
the sphere a screw gauge would be very convenient. One of 
these is illustrated in Fig. 7. A is 
the end of a screw which works in 
a nut inside of D. The screw can 
be moved back and forth by turning 
the cap G to which it is attached, 

and which slips over D. Upon D Fio. 7.— Micrometer wire gauge. 

is a scale, and the end of the cap C is divided into a number 
of equal parts. By turning the cap the end A moves forward 
until it reaches the stop B. When this is the case the 
graduations on D and G both read zero. 

In order to measure the diameter of a wire, the end A is 
brought back until the wire just slips between A and B. 
Then the scales on D and G indicate the whole number 
of turns made by the screw and also the fraction of a 
turn. Hence if we know the pitch of the screw, which is 
usually -gV inch, we can at once calculate the diameter of 
the wire. 

To measure the photographic plate the most convenient 
instrument is a microscope which can be moved back and 
forth over the plate, or one in which the stage which carries 
the plate can be moved by screws with graduated heads, much 
as in the wire gauge. 

There are other devices for accurate measurement of lengths, 
but in every case the scale, or the screw, or whatever is the 
essential part of the instrument, must be carefully compared 
with a good standard before our measurements can be of real 
value. 

15. Measurement of Mass. In Fig. 8 is shown a balance. 
The pans A and B are suspended from the ends of the beam 
GD, which can turn easily about a " knife-edge " at E, 



12 



MEASUREMENT 




This is usually a sharp steel edge resting on a steel or an 
agate plate. The bearings at G and D are made with 

very little friction, so that 
the beam turns very freely. 
A long pointer P extends 
downwards from the middle 
of the beam, and its lower 
end moves over a scale 0. 
When the pans are balanced 
and the beam is level the 
pointer is opposite zero on 
the scale. 

Suppose a lump of matter 
is placed on pan A. At 

FlO. 8.— A simple and convenient balance. When OUCC it dcSCends and equi- 

in equilibrium the pointer P stands at zero on ti • • -\ , i t, 

the scale 0. The nut n is for adjusting the llDriUm IS Clestroyea. It 

balance and the small weights, fractions of a -, ■, -i . , 

gram, are obtained by sliding the rider r along gOCS downwarcl DecaUSe the 
the beam which is graduated. The weight IT, if , ll l J.^ 

substituted for the pan 4, will balance the pan £. earth attraCtS tllC matter. 

Now put another lump on pan B. If the pan B still 
remains up we say the mass on A is heavier than that on B ; 
if the pans come to the same level and the pointer stands at 
zero the two masses are equal. 

It is the attraction of the earth upon the masses placed 
upon the pans which produces the motion of the balance. 
The attraction of the earth upon a mass is called its weight, 
and so in the balance it is the weicjhts of the bodies which 
are compared. But, as is explained in Chapter V, the 
weight of a body is directly proportional to its mass, and 
so the balance allows us to compare masses. 

16. Sets of Weights. We have agreed that the lump of 
platinum-iridiuin known as the International Prototype 
Kilogram shall be our standard of mass. (§ 11.) 



DENSITY 13 

In order to duplicate it w^e simply place it on one pan of 
the balance, and by careful filing we make another piece of 
matter which, when placed on the other pan, will just 
balance it. 

Again, with patience and care two masses can be constructed 
which will be equal to each othei', and which, taken together, 
will be equal to the original kilogram. Each will be 500 
grams. 

Continuing, we can produce masses of other denominations, 
and we may end by having a set consisting of 

1,000, 
500, 200, 200, 100 
50, 20, 20, 10 
5, 2, 2, 1 
.5, .2, .2, .1 grams 

and even smaller weights. 

If now a mass is placed on pan A of the balance, by proper 
combination of these weights we can balance it and thus at 
once determine its mass. 

The balances and the weights used by merchants throughout 
the country are periodically inspected by a government officer. 

17. Density. Let us take equal volumes of lead, aluminium, 
wood, brass, cork. These may conveniently be cylinders about 
h inch in diameter and H or 2 inches in length. 

By simply holding them in the hand we recognize at once 
that these bodies have different weights and therefore different 
masses. With the balance and our set of weights we can 
accurately determine the masses. 

We describe the difference between these bodies hy saying 
that they are of different densities, and we define density 
thus : — 

The DENSITY of a substance is the mass of unit volume of 
that substance. 



14 



MEASUREMENT 



If we use the foot and the pound as units of length and 
mass respectively, the density will be the number of pounds 
in 1 cubic foot. 

In the C.G.S. system the units of mass and volume are 
1 gram and 1 c.c. respectively, and of course the density 
wnll be the number of grams in 1 c.c. 

But 1 litre of water has a mass of 1 kilogram, 
or 1000 c.c. " " " 1000 gm., 

or 1 c.c. " " " 1 gm. 

This is the system generally used in scientific work. The 
densities of some of the ordinary substances are given in the 
following table : — 

Table of Densities 





Pounds per 
Cubic Foot. 


Grams per 
Cubic Centimetre. 


Water (at 4° C.) 


62.4 
439 to 445 

555 

658 

708 

848 

1207 

1340 

1399 

22 to 31 


1.00 


Iron 


7.03 to 7.13 


Copper 


8.90 


Silver 


10.56 


Lead 


11.34 


Mercury 


13.60 


Gold 


19.34 


Platinum 


21.50 


Iridium 


22.42 


White Pine 


0.35 to 0.50 







Note also that since the density is the mass in unit volume, 
we have the relation, 

Mass = Volume x Density. 
Thus, if the volume of a piece of cast aluminium is 150 c.c, 
since its density is 2.56, the 

Mass = 150 X 2.56 
= 384 grams. 



RELATION BETWEEN DENSITY AND SPECIFIC GRAVITY 15 

18. Relation between Density and Specific Gravity. We 

have seen that the number expressing the density of a sub- 
stance differs according to the system of units we use. 

Specific gravity is defined to be the ratio which the weight 
of a given volume of the substance bears to the weiglit of an 
equal volume of water. 

As this is a simple ratio, it is expressed by a simple 
number, and is quite independent of any system of units. 

First, however, suppose we have a cubic foot of a substance. 
Let it weigh W lbs. 

Let the weight of 1 cubic foot of water be w lbs. 

W 



Then specific gravity 



w 



density of substance 



density of water 

We see at once that this ratio is the same no matter what 
volume we use. 

Again, since in the C.G.S. system the density of water is 1, 
it follows that in this system the number expressing the 
specific gravity is the same as that expressing the density. 

For example, suppose we have 50 c.c. of cast iron. Then, 
using the balance, we find 

Weight of 50 c.c. of iron = 3G1 gm. 
But " " 50 " " water = 50 " 

Therefore the specific gravity = -W- = 7.22, which is 
simply the weight in grams of 1 c.c. of iron, or the density 
in the C.G.S. system. 



IQ MEASUREMENT 

PROBLEMS 

1. Find the mass of 140 c.c. of silver if its density is 10.5 gm. per c.c. 

2. The specific gravitj^ of sulphuric acid is 1.85. How many c.c. must 
one take to weigh 100 gm. 1 

3. A rolled aluminium cylinder is 20 cm. long, 35 mm. in diameter, 
and its density is 2.7. Find the weight of the cylinder. 

4. The density of platinum is 21.5, of iridium is 22.4. Find the 
density of an alloy containing 9 parts of platinum to 1 part of iridium. 
Find the volume of 1 kg. of the alloy. 

5. A piece of granite weighs 83.7 gm. On dropping it into the water 
in a graduated vessel, the water rises from 130 c.c. to 161 c.c. 
(Fig. 9). Find the density of the granite. 

/6/ 6. A tank 50 cm. long, 20 cm. wide and 15 cm. deep is 
130 filled with alcohol of density 0.8. Find the weight of the 
alcohol. 

7. A rectangular block of wood 5 x 10 x 20 cm. in dimen- 



m 



%> sions weighs 770 grams. Find the density. 
Fig. 9. 8. A thread of mercury in a fine cylindrical tube is 28 cm. 

long and weighs 11.9 grams. Find the internal diameter of the tube. 

9. Write out the following photographic formulas, changing the 
weights to the metric system ; — 

Developer 

Water 10 oz. 

Metol 7 gr. 

Hydroquinone 30 " 

Sulphite of Soda (desiccated) 110 " 

Carbonate of Soda (desiccated) 200 " 

Ten per cent, solution Bromide of Potassium 40 drops 

Fixing Bath 

Water 64 oz. 

Hyposulphite oJP Soda 16 " 

When above is dissolved add the following solution : — 

Water 5 " 

Sulphite of Soda (desiccated) ^ " 

Acetic Acid 3 " 

Powdered Alum 1 " 



PART II-MECHANICS OF SOLIDS 



CHAPTER II 

Displacement, Velocity, Acceleration 

19. Position of a Point. If we wish to give the position of 
a pkice on the surface of the earth, or of a star in the sky, we 
first clioose some reference hnes or points, and then state the 
distance of the place or the star from these. In geography a 
place is precisely located by stating its longitude east or west 
from a certain meridian which passes through Greenwich, in 
England, and its latitude north or south of the equator. Thus 
Toronto is said to be in longitude 79° 24' west and latitude 48° 
40' north. In astronomy a similar metliod is used, the corre- 
sponding terms being right ascension and declination. 

In the same way we can locate tlie position of a house 
by referring it to two intersecting streets or roads. 

Suppose we wish to state the position of a point 7'. Draw two 
lines of reference OX, OY. (Fig. 10.) Then if we know the 



yi 








X 


P 










y 


Q 




X 




FiQ. 10. — Locating a point by 
means of two lines of refer- 
ence. 



Fia. 11.— Locating a point by 
means of a length and an 
angle. 



lengths X, y, of the two perpendiculars from P upon OY, OX we 
know the position of the point P with respect to the lines OX, OY, 
or to the point 0. 

Again, if the length OP (Fig. 11), and the angle made with the 
line of reference OX be known the position of P is definitely fixed. 

17 



18 



DISPLACEMENT, VELOCITY, ACCELERATION 




20. Displacement. If a body is moved from to P we say 

it has suffered a displacement 
OP. (Fig. 12.) Next let it be 
displaced from P to Q. It is 
evident that if we consider 
only change of position, the 

F.a. 12. -The addition of displacements. g-j^g|g displacement OQ is equi- 
valent to the two displacements OP, PQ, though the length 
of path from to Q by way of P is greater than that from 
to Q directly. 

The displacement OQ is the residtant of the two dis- 
placements OP, PQ, each of which is called a comijonent 
displacement. 

Next let a point suffer displacements represented in direc- 
tion and magnitude by tlie lines OP, PQ, 
QR, RS; then OS is the resultant of all 
these displacements. (Fig. 13.) 

21. Velocity. Daily observation 
shows that to produce a displacement 
time is always required. When we 
travel on a railway we pay for the 
amount of our displacement but we 
are also concerned with the time 
consumed. Tliis brings us to the idea of velocity or speed. 

Velocity is tJte rate of change of j^osition, or in other words, 
the time-rate of displacement. 

Velocity involves the idea of direction. When we speak of 
the rate without reference to direction it is better to use the 
term speed. 

If we travel 300 miles in 10 hours, our average speed is 30 
miles per hour. 




Fig. 13.— The addition of four 
displacements. 



Fio. 14. — Average velocity is equal to the space divided by the time. 



UNIFORM VELOCITY IN A STRAIGHT LINE 19 

Let a body travel tlic distance AB, .s centimetres, in t 
seconds ; then 

Average velocity = '—= v centimetres per second. 

22. Uniform Velocity in a Straight Line. The velocities 
we have to deal with are usually not constant. On a long 
level track a railway train goes at an approximately 
uniform speed, though this changes when starting from, or 
approaching, a station. If the velocity is uniform in a 
straight line we have 

Space = Velocity x Time 

or s = vt. 
Thus if v = 150 centimetres per second, 

and i = 20 seconds, 
Then s = 150 x 20 = 3,000 centimetres. 

PROBLEMS 

1. Find the equivalent, in feet per second, of a speed of 60 miles 
per hour. 

2. An eagle flies at the rate of 30 metres per second ; find the speed 
in kilometres per hour. 

3. A sledge party in the arctic regions travels northward, for ten 
successive days, 10, 12, 9, 16, 4, 15, 8, 16, 13, 7 miles, respectively. 
Find the average velocity. 

4. If at the same time the ice is drifting southward at the rate of 10 
yards per minute, find the average velocity northward. 

23. Acceleration. If the velocity of a particle is not 
uniform we sa}^ that the motion is accelerated. If the velocity 
increases, the acceleration is jwsitive; if it decreases, the 
acceleration is negative. The latter is sometimes called a 
retardation. 

Let a body move in a straight line, and measure its 
velocity. At one instant it is 200 cm. j^er second ; 10 seconds 
later it is 350 cm. per second. The increase in the velocity 
acquired in 10 seconds is 150 cm. per second, and if this has 
been gained uniformly the increase per second will be 15 cm. 
per second. This is the acceleration. 



20 DISPLACEMENT, VELOCITY, ACCELERATION 

If the velocity liad decreased in 10 seconds to 50 cm. per 
second the loss of velocity would have been 150 cm. per 
second, and the loss per second would have been 15 cm. per 
second. In this case the acceleration is — 15 cm. per second 
per second. 

Observe the two time phrases " per second, per second." 
The first is used in stating the velocity gained (or lost), the 
second gives the time in which the velocity is gained (or lost). 

Acceleration is rate of change of velocity. 

PROBLEMS 

1. A railway train changes its velocity uniformly in 2 minutes from 20 
kilometres an hour to 30 kilometres an hour. Find the acceleration in 
centimetres per second per second. 

2. A stone sliding on the ice at the rate of 200 yards per minute is 
gradually brought to rest in 2 minutes. Find the acceleration in feet and 
seconds. 

3. Change an acceleration of 981 cm. per second per second into feet 
per second per second. (See Table, opposite page 1.) 

24. Uniformly Accelerated Motion. Suppose the velocity of 

a particle at a given instant to be u centimetres per second, and let 
it have a uniform acceleration + a ; i.e., it gains in each second a 
velocity of a centimetres per second. 

At the beginning, velocity v = u cm. per sec. 

At the end of 1 second, velocity v = u + a u w 

It II 2 seconds, n v = u + 2a w » 
II II 3 II II V = u + 2>a II II 

and II II t II w V — u + ta n n 

Here the gain in velocity in 1 second is a cm. per second ; tlie 
gain in t seconds is at cm. per second ; and the velocity at the end 
of the t seconds is the original velocity + the gain, i.e., 
V = u + at cm. per sec. 
The change in the velocity due to uniform acceleration is equal to 
the product of the acceleration and the time. 

If the initial velocity is zero we have u = 0, and 
V ^ at cm. per sec. 



AVERAGE VELOCITY— SPACE TRAVERSED 21 

25. Average Velocity. Let a body start from rest and move 
for 10 sec. wilh a uniform acceleration of 8 cm. per sec. per sec. 
Then the velocities at the ends of the 

1st. 2nd. 3rd. 4th. 5th. 6th. 7th. 8th. 9th. 10th. sec. 

are 8 16 24 32 40 48 56 64 72 80 cm. 

per sec, respectively. 

Thus, at the beginning the velocity is cm. per sec; at the end of 
5 sees., 40 cm. per sec; and at the end of 10 sec, 80 cm. per sec. 
The increase during the first half of the time is the same as that 
during the last half, and so the average velocity is one-half the sum 
of the initial and final velocities, i.e., J (0 + 80) or 40 cm. per sec. 

If the initial velocity had been 5 cm. per sec. the velocities at the 
ends of the successive seconds would have been, respectively, 
13, 21, 29, 37, 45, 53, 61, 69, 77, 85 cm. per. sec 
The average velocity is that possessed by the body at the middle of 
the time, or 45 cm. per sec, and this = h (5 + 85), or is equal to 
one-half the sum of the initial and final velocities, as before. 

26. Space Traversed. First, let the initial velocity be zero. 
In t seconds, with an acceleration a cm. per sec. per sec, the final 
velocity = at cm. per sec. 

The average or mean velocity = ^ (Initial + Final velocity). 

= 1(0 + at). 
= I at cm. per .«ec. 
This is the velocity when one-half the time has elapsed. 
Now the space passed over 

= average velocity x time ; 
hence if s represents space, 

s = ^ at X t = h at" cm. 
J^ext, let the initial velocity be u cm. per sec. Then we have : 
Initial velocity = ii cm. per sec. 
Final n = u + at cm. per sec. 

Average n = | (u + u + at) cm. per sec. 





= w + |- at II II 


Then space 


s = average velocity x time 




= {it + ^ at) t = ut + ^ at^ cm. 



In this expression note that nt expresses the space which would 
be traversed in time t with a uniform velocity ii, and ^^> «<- is the 
space passed over when the initial velocity = 0. The entire space 
is then the sum of these. 



22 



DISPLACEMENT, VELOCITY, ACCELERATION 



27. Graphical Representation. The relations between velocity, 
acceleration, space and time in uniformly accelerated motion can be 
shown by a geometrical figure. 

Let distance from 
along the horizontal line 
OX represent time in se- 
conds, OR representing t 
seconds, OL one half of this 
or ^t seconds. Vertical lines 
represent velocities. The 
velocity at the beginning 
7t, is represented by OM ; 
that at the end of t se- 




«o i 



^ Time in seconds 



Fig. 15. — Space traversed can be represented by an area. i i_ ti d i 

'^ ^ •" conds by EF ; and so on. 

At the middle of the time the velocity is LQ. 

The velocity at the beginning is ^i — OM. At the end of t 
seconds it is u + at = RP. Hence NP = at. The mean velocity 
is w + \ at — LQ. 

If the velocity is uniform (without acceleration), the space tra- 
versed is tit. 

Now in the figure, u = OM and t = OR, 

Hence vt = OM x OR = area of rectangle MR, and the space 
traversed is represented by the area of the rectangle. 

Again with accelerated motion the space traversed is 

(tt + ^ at) X t = tit + ^ at-, 

But tit = area of rectangle MR, 

and ^at = « triangle MNP. 

Hence the space traversed is represented by the area of the figure 
OMPR. 

28. Motion under Gravity. The most familiar illustration of 
motion with uniform acceleration is a body falling freely. Suppose 
a stone to be dropped from a height. At once it acquires a velocity 
downwards, Avhich continually increases as it falls ; and in a second 
or two it will be moving so fast that the eye can hardly follow it. 
In order to test experimentally the laws of motion we must devise 
some means of reducing the acceleration. The following is a simple 
and eflfective method of doin^ this.* 



*Devi3ed by Prof. A. W. Duff, of the Polytechnic Institute, Worcester, Mass. 



MOTION UNDER GRAVITY 



23 



In a board 5 or 6 feet long make a circular groove 4 inches 
wide and having a i-adius of 4 inches (Fig. 16). Paint the surface 

\B CX'~XZ? 




Fig. 16. — Apparatus to illustrate motion with uniform acceleration. 

black and make it very smooth. Along the middle of the groove 
scratch or paint a straight line ; and near one end of the board 
fasten a strip of brass, accurately at right angles to the length of 
the groove and extending just to the middle of it. 

Lay the board flat on the floor, and place a sphere (a steel ball 
1 in. to 1 ^ in. in diameter), at one side of the groove and let it go. 
It will run back and forth across the hollow, performing oscillations 
in approximately equal times. By counting a large number of these 
and taking the average, we can obtain the time of a single one. 

Next let one end of the board be raised and over the groove dust 
(through 4 or 5 thicknesses of muslin) lycopodium powder. Put the 
ball alongside the brass strip at one side of the groove and let it go. 
It oscillates across the groove and at the same time rolls down it, 
and the brass strip insures that it starts downwards without any 
initial velocity. By blowing the lycopodium powder away a distinct 
curve is shown like that in the upper part of Fig. 16. 

It is evident that while the ball rolls down a distance AB it rolls 
from the centre line out to the side of the groove and back again ; 
while it rolls from B to C, it rolls from the centre line to the other 
side of the groove and back again. These times are equal ; let each 
be T sec. (about J sec). In the same way CD, DE, EF and EG are 
each traversed in the same interval. 

Now, s = i at'^, where s is the space, a is the acceleration and t is 
the time (§ 26). 

Hence AB = 1 



AC ^ ^a (2t)'- = 4 X I rtT^ = 4 x AB, 
AD = la (3t)2 = 9 X 1 ar^ = 9 x AB, 
AE = ^a (4t)2 = 16 X 1 ar^ = 16 X AB, etc., 

i.e., the spaces AB, AC, AD, AE, etc., are proportional to 1, 4, 9, 
16, etc.; or the distance is proportional to the squai'e of the time. 



24 



DISPLACEMENT, VELOCITY, ACCELERATION 



By laying a metre scale along the middle of the groove these 
results can be tested experimentally. 

The following are sample measurements obtained with 1 inch and 
l;j inch balls, rolling down a board 6 feet long. In the thiid, fifth 
and seventh columns are shown the ratios of JB, AC, AD, AE, 
AF, and AG to A B. 





1 inch ball. 
End raised 20 cm. 


1^ inch ball. 
End raised 22 cm. 


1^ inch ball. 
End raised 22^ cm. 


A B 


cm. 

4.55 

18.80 

40.40 

70.28 

111.90 

161.30 


Ratio. 

1.0 

4.1 

8.9 

15.4 

24.6 

35.4 


cm. 

4.40 

18.35 

39.50 

70.90 

108.45 

157.10 


Ratio. 

1.0 

4.2 

9.0 

16.1 

24.6 

35.7 


era. 

4.45 

18.65 

40.25 

72.95 

111.00 

161.00 


Ratio. 
10 


A C 


4 2 


AD 


9 


AE 


16 4 


A F 

AG 


24.9 
36 2 







These ratios are very close to the theoretical values 1, 4, 9, 16, 
25, etc , the discrepancies being due to unavoidable imperfections 
in the board, small inaccuracies in measurement, etc. 

29. To Measure the Acceleration of Gravity. The accele- 
ration given to a falling body by the attraction of the earth is 
usually denoted by the letter g. If we gradually increase the 
height from which a body is allowed to fall until at last it just 
reaches the ground in 1 second, we find the distance is about 16 
feet. Now the measure of the acceleration is twice that of the 
space fallen through in the first second, and hence ff = 32, 
appro.ximately. 

The most accurate method of measuring the value of g is by 
means of the pendulum. In this way it is found that, using feet 
and seconds, g = 32.2; and using centimetres and seconds 
g = 981. 

These values vary slightly with the position on the earth's surface. 
At the equator g = 978.10 ; at the pole, 983.11 ; at Toronto, 980.6. 

30. All Bodies have the same Acceleration. Galileo asserted 

that all bodies, if unimpeded, fall at the same rate. Now, common 
observation shows that a stone or a piece of iron, for instance, falls 
much faster than a piece of paper or a feather. This is explained 
by the fact that the paper or the feather is more impeded by the 
resistance of the air. 



RELATION BETWEEN VELOCITY AND SPACE 



25 



From the top of the Leaning Tower of Pisa (see § 75), Galileo 
allowed balls made of various materials to fall, and he showed that 
they fell in practically the same time. Hixty 
years later, when the air-pump had been invented, 
the statement regarding the resistance of the air 
was verified in the following way. A coin and a 
feather were placed in a tube (Fig. 17) four or 
five feet long and the air was exhausted. Then, 
on inverting the tube, it was found that the two 
fell to the other end together. The more fully 
the air is I'emoved from the tube the closer to- 
gether do they fall. 

31. Relation between Velocity and Space. ^ 

We have found 



V = at, ov t = - 
a 



(§24) 



also s = h at'\ (§ 26). * 

Fio. 17.— Tube to show 
Putting in this latter equation the value of < that a coin and a feather 

e ii r 1 fall in a vacuum with 

from the former we have 



the same acceleration. 



_ J 

•I 



Va) ~^a 



Also, we have 



V = u + at, or t = ; (§ 24) 



and s = nt + h at'^. 



(§ 26). 



Putting in the latter equation the value of t from the former, we 
obtain 

V — ?/a2 



(— ) + i«(— )'• 



and on simplifying this expression Ave have 



V = u- + 



NUMERICAL EXAMPLES 

The meaning of the relations between velocity, acceleration, time and 
space, expressed by formulas in §§ 24, 26, 31, can best be comprehended 
by considering some numerical examples. 

1. A person at the top of a tower throws a stone downwards with a 
velocity of 8 m. per sec, and it reaches the ground in 3 sec. Find the 
velocity with which the stone strikes the ground, and the height of the 
tower. 



26 DISPLACEMENT, VELOCITY, ACCELERATION 

Here we have H = 800 cm. per second, 
t = 3 sec, 

a — 980 cm. per second per second. 
But v = u + at, 

that is = 800 + 980 x 3 = 3740 cm. per sec. 
Again s = ut + ^ at ^. 
that is = 800 X 3 + i X 980 X 9 = 6810 cm. (Height of tower). 

If the stone is simply dropped instead of being thrown downwards, 
and reaches the ground in 3 sec, we have 
11 = 0; 
also V = at = 980 x 3 = 2940 cm. per sec, 
and s = ^ a^2 = i X 980 X 9 = 4410 cm. 

2. A bullet is shot upwards with a velocity of 15 m. per sec. How 
high will it rise ? How long will it take to reach the ground again ? 
In this case w.= 1500 cm. per sec, 

a = - 980 (acceleration is negative). 

The bullet continues to rise until, on reaching its highest point, its 
velocity is zero. 

But i-2 = n' + 2 as (§ 31); 

and putting v = 0, it = 1500, a = - 980, 

we have 0^ = (1500)^ + 2 x ( - 980) x s ; , 

from which s = 1148 (nearly) cm. (Height of path). 

Again, the bullet loses every second 980 cm. per sec. of its velocity. 
But by the time it reaches the top of its path it has lost its ent ire velocity 
of 1500 cm. per sec. 

Hence the time going up = -VA**' — 1-53. . . seconds. 

The bullet will then begin to descend, and as it will gain 980 cm. per 
sec. during every second of its fall, it will require the same time to 
fall as it did to rise, and it will have, on reaching the ground, a velocity 
as great as it had on starting upwards, but in the opposite direction. 

Hence the time which has elapsed from its leaving the ground until it 
returns is 2 x 1.53 = 3.06 seconds. 

In both these examples the resistance of the atmosphere has been 
disregarded, tliough its effect is considerable in the case of rapidly-moving 
or light bodies. 

In all examples involving the metric system of units it will generally 
be found advisable to express all lengths in centimetres, all masses in 
grams and all times in seconds. 



NUMERICAL PROBLEMS 27 

PROBLEMS 

Unless otherwise stated, take as tlie measure of the acceleration of 
gravity, with centimetres and seconds, 980 ; with feet and seconds, 32. 

1. A body moves 1, 3, 5, 7 feet during the 1st, 2nd, 3rd, 4th seconds, 
respectively. Find the average speed. 

2. Express a speed of 36 kilometres per hour in cm. per second. 

3. A body falls freely for 6 seconds. Find the velocity at the end of 
that time, and the space passed over. 

4. The velocity of a body at a certain instant is 40 cm. per sec, and its 
acceleration is 5 cm. per sec. per sec. What will be its velocity half-a- 
minute later ? 

5. What initial speed upwards must be given to a body that it may 
rise for 4 seconds 1 

6. The Eiffel Tower is 300 metres high, and the tower of the City Hall, 
Toronto, is 305 ft. high. How long will a body take to fall from the top 
of each tower to the earth ? 

7. On the moon the acceleration of gravity is approximately one-sixth 
that on the earth. If on the moon a body were thrown vertically upwards 
with a velocity of 90 feet per second, how high would it rise, and how long 
would it take to return to its point of projection ? 

8. A body moving with uniform acceleration has a velocity of 10 feet 
per second. A minute later its velocity is 40 feet per second. Wliat is 
the acceleration ? 

9. A body is projected vertically upward with a velocity of 39.2 metres 
per second. Find 

(1) how long it will continue to rise ; 

(2) how long it will take to rise 34.3 metres ; 

(3) how high it will rise. 

10. A stone is dropped down a deep mine, and one second later another 
stone is dropped from the same point. How far apart will the two stones 
be after the first one has been falling 5 seconds ? 

11. A balloon ascends with a uniform acceleration of 4 feet per second 
per second. At the end of half-a-niinute a body is released from it. How 
long will it take to reach the ground ? 

12. A train is moving at the rate of GO miles an hour. On rounding a 
curve tlie engineer sees another train j mile away on the track at rest. 
By putting on all brakes a retardation of 3 feet per second per second is 
given the train. Will it stop in time to avoid a collision ? 



28 



DISPLACEMENT, VELOCirY, ACCELERATION 



M 



Q 



Fio. 18. — Motion in 
circle. 



32. Motion in a Circle. Let a body M be made to revolve 
uniformly in a circle with centre O and radius r. 
A familiar illustration of this motion is seen when 
a stone at the end of a string is whirled about. 

In this case the length of the line MO does not 

i alter, and yet M lias a velocity with respect to 0. 

j This arises from the continual change in the direc- 

' tion of the line MO. Every time the body 

describes a circle its direction changes through 

, 360°. 

a 

If the string were cut and M were thus allowed 
to continue with the velocity it possessed, it would move off in the 
tangent to the circle MT. This effect is well illustrated by the diops 
of water flying off from the wheels of a bicycle, or the sparks from a 
rapidly rotating emery wheel. 

We see, then, that one point has a velocity with resj)ect to another 
tvlieii the line joining them changes in magnitiide or direction. 

In the above case there is a change of velocity (being a continual 
change from motion in one tangent to motion in another), and hence 
there is an acceleration ; and as the change in the velocity is uni- 
form the acceleration is constant. The acceleration is always 
directed towards the centre of the circle. 

33. Translation and Rotation. If a body move so that all 

points have the same speed and in the 

same direction we say that it has a i | 

motion of translation. Examples : the ....■-'••■■ ] 

car of an elevator, or the piston of an 

engine. 

If, however, a body move so that all 

points of it move in circles having as 

centre a point called the centre of mass, or centre of gravity,* the 

motion is a jinre rotation. Example : a wheel on a shaft, such as 

the wheel of a sewing-machine or a fly-wheel. 

Usually, however, both motions are present, that 
is, the body has both translation and rotation. 
Examples : the motions of the planets, of a carriage 
wheel, of a body thrown up in the air. 

If a body is rotating about an axis through a 
point in it, it is evident that those points which 
are near 0, such as P, Q (Fig. 21), have smaller 
speeds than have those points such as R, S, which 
are farther away. 



-ShottinR motion of 
translation. 



Fio. 20. -Showing 
motion of rota- 
tion. 



^Explained in Chapter VII 



COMPOSITION OF VELOCITIES- LAW OF (COMPOSITION 29 



But they all (lescril)e circles about in the same time and hence 
their angular velocities are ail equal. 

Again, consider the motions of J and J] 
with lespect to each other. To a person at 
A the point B will revolve about liim in the 
same time as the body rotates about 0. 
Also, a person at B will see A revolve about 
him in the same time. 

For instance, suppose the body to rotate 
once in a second. All lines in the body will 
change their directions in the same niauner, 
turning through 3G0 degrees, and returning tu 
their former positions at the end of a second. 

34. Composition of Velocities. Suppose 

a passenger to be ti'avelling on a railway train 

which is moving on a straight track at the rate of 1 5 miles per hour, or 
22 feet per second. While sitting quietly in his seat he has a niotion 
of translation, in the direction of the track, of 22 feet per second. 

Next let the passenger rise and move directly across the car, going 
a distance of G feet in 2 seconds. His velocity across will be 3 feet 
per second. 

In Fig. 22, A is the position of the passenger at first. If the train 
were at rest, in 2 seconds he would move from A to C, 6 feet ; 




Fio. 21.— In a rotatiiiff body all 
points have the same angular 
velocity. 



FiQ. 22. — Motion of a passenger walltinjj; across a moving' railway car. 

while, if he sat still the train in its motion would carry him from A 
to y> in 2 seconds, a distance of 44 feet. It is evident, then, that if 
the train move forward and the passenger move across at the same 
time, at the end of 2 seconds he will be at D, i.e., 44 feet forward 
and 6 feet across. 

Moreover at the end of 1 second he will be 22 feet forward and 3 
feet across, that is, half way from A to D. The motions which he 
has will carry him along the line AD in 2 seconds. 

Another example will perhaps make 
clearer this principle of compound- 
ing velocities. 

Let a ring H slide with uniform 

velocity along a smooth rod AB, 

moving from yl to ^ in 1 second. 

At the same time let the rod be 

v„ yQ cv, u * ^1+ ,1 . „ moved in the direction ylC with a 

r iG. 23. — Showino: how to acid toyetlier two . i • i 

motions of a ring on a rod. uniform velocity, reaching the posi- 

tion CD in a second. The ring will be at D at the end of a second. 



35. Law of Composition. 
2 




30 



DISPLACEMENT, VELOCITY, ACCELERATION 




At the end of half-a-second from the beginning the ring will be 
half-way along the rod, and the rod will be in position (3) half-way 
between A B and CD. It is evident that between the two motions 
the ring will move uniformly along the line AD, travelling this dis- 
tance in 1 second. 

From these illustrations we can at once deduce the law of com- 
position of velocities. 

Let a particle possess two veloci- 
ties simultaneously, one represented 
in direction and magnitude by the 
line AB, the other by AC. 

Complete the parallelogram AB 

Fig. 24.— The paiallelograiu of velocities. DC. Then the diagonal AD will 

represent in magnitude and direction the resultant velocity. 

Hence to find the resultant of two simultaneous velocities we have 
the following rule : — 

Construct a parallelogram whose adja- 
cent sides represent in magnitude and 
direction the two velocities ; then the 
diagonal which lies between thetn ivill 
represent their resultant. 

Each velocity AB, AC is called a t{^ 
comjwnent; AD is the residtant. i"> 

If there are more than two com- • 
ponent velocities, such as AB, AC, 
AD, AE, proceed in the following way. 

Find the resultant oi AB and AC; 
it is AF. Next, the resultant oi AF 
and AD is AG; and finally, the re- 
sultant of AG and AE in All. Thus 
AH is the resultant of the four velocities AB, AC, AD, AE. 

36. Resolution into Components. Suppose now a body to 

have a velocity represented by the 
line AB. This may be any length we 
choose. Let us describe a parallelo- 
gram having AB a.^ its diagonal. It 
is evident that the velocity repre- 
sented by AB is the resultant of the 
velocities represented by AC, AD. 
^'f- !u~v' '^ ^■^'P'".*^' ^'^ ",?''P^"'®'^ In this way we are said to resolve the 

by the uiagonal of a parallelogram, / . . • 

the adjacent sides will represent its velocity AB into components in the 

'''""P°"^"'«- directions AC, AD 




Fig. 25.— How to combine more than 
two velocities. 




THE TRIANGLE AND THE POLYGON OP VELOCITIES 31 

NUMERICAL EXAMPLES 

1. Suppose a vessel to steam directly east at a velocity of 12 miles 
per hour, while a north wind drifts it 

southward at a velocity of 5 miles an 
hour. Find the resultant velocity. 

Draw a line AB, 12 cm. long, to 
represent the first component velocity ; 

AC, 5 cm. long, to represent the ^ _ 

second. (Fig. 27.) ^ ^ 

Completing the parallelogram, which '^\^;J^i-'"'"^"'''''"^' **"^ ""'^'°" °^ ^ 
in tliis case is a rectangle, AD will 
represent the resultant velocity. 

Here we have ZD^ = AB' + BD- = 12'-^ + 5" = 109 = 13'-. 
Hence AD = 13, i.e., the resultant velocity is 13 miles per hour in the 
direction represented by A D. 

2. A ship moves east at the rate of 7j miles per hour, and a passenger 
walks ou the deck at the rate of 3 feet per second. Find his velocity 
relative to the earth in the following three cases,, (1) when he walks 
towards the bow, (2) towards the stern, (3) across the deck. 

3. A ship sails east at the rate of 10 miles per hour, and a north-west 
wind drives it south-east at the rate of 3 miles per hour. Find the 
resultant velocity. 

To calculate the resultant accurately requires a simple application of 
trigonometry, but the question can be solved approximately by drawing 
a careful diagram. Draw a line in the easterly direction 10 inches long, 
and lay off from this, by means of a protractor, a line in the south-east 
direction, 3 inches long. Complete the parallelogram and measure care- 
fully the length of the diagonal. (13.92 miles per hour.) 

4. Find the resultant of two velocities 20 cm. per second and 50 cm. 
per second («,) at an angle of (30°, (b) at an angle of 30°. (Carefully draw 
diagrams, and measure the diagonals.) 

5. A particle has three velocities given to it, namely, 3 feet per second 
in the north direction, 4 feet per second in the east direction, and 5 feet 
per second in the south-east direction. Find the resultant. (Carefully 
draw a diagi-am.) 

37. The Triangle and the Polygon of Velocities. The law 

for compounding velocities may 
be stated in a somewhat different 
form. 

Let a particle have two velo- 



-*B 




Fio. 2S.-Repre3entation of two velocities. ^.j^-^g represented by AB, CD, 
respectively (Fig. 28). If we form a parallelogram having AB, CD 



32 



DISPLACEMENT, VELOCITY, ACCELERATION 



as adjacent sides, then we know that the diagonal represents the 
resultant. (Fig. 29.) 





Parallelogram of velocities. 



A B 

FiQ. 30. — Triangle of velocities. 



Suppose, however, that we draw the line representing the velocity 
CD, not from A but' from B (Fig. 30). Then on joining AD vfe 
form a triangle which is just one-half of the parallelogram in Fig. 29, 
and the side AD oi the triangle is equal to the diagonal of the 
parallelogram. It represents therefore the resultant of AB, CD. 

We have then the following law : 

If a body have hvo simultaneous velocities, and we represent them 
hy the two sides AB, BG of a triangle, taken in order, then the 
residtant of the two velocities will he represented hy the third side 
AC of the triangle. 

Next, let the body have several simultaneous velocities, repre- 
sented by the lines A, B, C, D. 




Fig. 31.— Polygon of velocities. 

Place lines representing these velocities end to end so as to form 
four sides of a polygon, as in Fig. 31. Then the resultant of A and 
B is c, the resultant of c and C is d, and the resultant of d and D 
is e, which is therefore the resultant of A, B, C, D. 

Hence we have the following law : 

// a hody have several simrdtuneous velocities, and we represe?it 
them as sides of a polygon, taken in order, then the closing side of the 
polygon iv.ll represent the resultant of all the velocities. 

38. Composition of Accelerations. A body may possess 

sinmltaneous accelerations, and as these can be represented in the 
same way as displacements and velocities, they may be combined in 
precisely the same way as displacements and velocities. 

In fact any physical quantities which can be represented in magni- 
tude and direction by straight lines may be combined according to 
the polygon law. Such directed quantities are known as vectors. 



CHAPTER III 

Inertia, Momentum, Force 

39. Mass, Inertia. The mass oi' a bodj^ lias been defined 
(§ 11) as the quantity of matter in it. Just what inaitei' is no 
one can say. We all understand it in a general way, but we 
cannot explain it in terms simpler than itself. We must obtain 
our knowledge regarding it by experience. 

When we see a young man kick a football high into the air 
we know that there is not much raatter in it. If it were filled 
with water or sand, so rapid a motion could not be given to it 
so easily, nor would it be stopped or caught so easily on 
coming down. A cannon ball of the same size as the foot- 
ball, and moving with the same speed, would simply plough 
through all the players on an athletic field before it would be 
brought to rest. 

In the same way, by watching the behaviour of a team 
hitched to a wagon loaded with barrels, we can tell whether 
the barrels are empty or filled with some heavy substance. 

To a person accustomed to handling a utensil made of iron 
or enamelled-ware, one made of aluminium seems singularly 
easy to move. A bottle filled with ordinary liquids is 
picked up and handled with ease, but one never fails to feel 
astonished at the effort required to pick up a bottle filled 
with mercury. 

In every instance that body which demands the expenditure 
of a great effort in order to put it in motion, or to stop it, has 
much m,atter in it, or has a great m^ass. 

Our experience thus leads us to conclude, 

First, that it requires an effort to put in motion matter 
which is at rest, or to stop matter when in motion ; 

33 



34 INERTIA, MOMENTUM, FORCE 

Second, that the amount of the effort depends on the 
amount of matter, or the mass of the body, wliicli is put in 
motion or brought to rest. 

When we say that all matter possesses inertia we mean 
just what the first of the above statements says ; while the 
second states that the inertia of a body is proportional to its 
mass. 

40. Momentum. We have seen tliat the greater tlie mass 
of a body the more difficult it is to set it in motion or to 
stop it when it is in motion. Now, very little consideration 
will lead us to recognize that we must also take into account 
the velocity which a body has. It requires a much greater 
effort to impart a great velocity to a body than to give it a 
small one ; and to stop a rapidly moving body is much harder 
than to stop one moving slowly. We feel that there is some- 
thing which depends on both mass and velocity, and which we 
can think of as quantity of motion. This is known in physics 
as momentum. It is proportional to both the mass and the 
velocity of the body, thus 

Momentum = mass x velocity, 
= mv, 
where w is tlie mass of the body and v its velocity of trans- 
lation. 

Momentum is a directed quantity, and lience (^§38) momenta can 
be compounded by tlie parallelogram or polygon law. 

QUESTIONS AND PROBLEMS 

1. Why are quoits made in the sliape of a ring and not as discs cut 
from a metallic sheet ? 

2. Why is it that in the balance wheel of a watch most of the material 
is placed near the rim ? 

3. Compare the momentum of a car weighing 50,000 kilograms and 
moving with a velocity of 30 kilometres an hour with that of a cannon ball 
weighing 20,000 grams and moving with a velocity of 50,000 cm. per 
second. 



NEWTON'S LAWS OP MOTION : THE FIRST LAW 



35 




4. A man weighing 150 jxtunds and running with a velocity of G feet 
per second collides with a boy of 80 pounds moving with a velocity of 9 
feet per second. Compare the momenta. 

41. Newton's Laws of Motion: the First Law. In his 

" Principia,"* published in 1687, Sir Isaac Newton stated, with 
a precision and clearness which 
cannot be improved, the funda- 
mental laws of motion. 

The First Law is as follows : — 

Every body continues in its 
state of rest, or of uniform inotion 
in a straiijlit line, unless it he 
compelled hy external force to 
change that state. 

This Law states what happens 
to a body when it is left to itself. 
Now, on the surface of the earth 
it is very difficult, impossible in- 
deed, to leave a body entirely to 
itself, but the more nearly we come to doing so the more 
nearly do we demonstrate the truth of the Law. 

This Law is but a statement, in precise form, of the principle 
of inertia as explained in §'39. 

42. Illustrations of the First Law. 

(a) A lump of dead matter will not move itself. 

(6) A ball rolling on the grass conies to rest. The external force 
is the friction of the ball on the grass. If we roll it on a smooth 
pavement the motion persists longer, and if on smooth ice, longer 
still. It is seen that as we remove the external foice (of friction), 
and leave the body more and more to itself the motion continues 
longer, and we are led to believe that if there were no friction it 
would continue uniformly in a straight line. 

(c) An ordinary wheel if set rotating soon comes to rest. But a 
well-adjusted bicycle wheel if put in motion will continue to move 

*The full title of the book is "Principia Mathematica Naluralis Philosophiae," i.e., "The 
Mathematical Principles of Natural Philosophj'." 



Sir Isaac Newton (1642-1727) at the 
age of S3. Ueinonst rated the law of 
gravitation. The greatest of mathe- 
matical physicists. 



36 INERTIA, MOMENTUM, FORCE 

for a long time. Here the external force — the friction at the axle — 
is made very small, and the motion persists for a long time. 

As illustrations of the law of inertia we may consider the 
following. 

(a) When a locomotive, running at a high rate of speed, leaves 
the rails and is rapidly brought to a standstill, the cars behind do 
not immediately stop, but continue ploughing ahead, and usually do 
great damage before coming to rest. 

(b) If one wishes to jump over a ditch he takes a run, leaps up 
into the air, and his body persisting in its motion reaches the other 
side. 

(c) In an earthquake the buildings tend to remain at rest while 
the earth shakes under them, and they are broken and crumble 
down. 

The evidence supporting the First Law is of a negative character; 
and since in all our experience we have never found anything con- 
trary to it, but as, on the other hand, it is in accordance with all 
our experience and observation, we cannot but conclude that it is 
exactly true. 

43. Newton's Second Law of Motion. Change ofmomen- 
tu'tii, in a given time, is proportional to the imjyressed f(/rce 
and takes place in the direction in ivhich the force acts. 

If there is a change in tlie condition of a body {i.e., if it 
does not remain at rest or in uniform motion in a straight 
line), tlien tliere is a change in its momentum, that is, in the 
quantity of motion it possesses. Any such change is due to 
some external influence which is called FORCE and the amount 
of the change in a given length of time is proportional to the 
impressed force. It is evident, also, that the total effect of a 
force depends on the length of time during which it acts. 
Again, force acts in some direction, and the change of 
momentum is in that direction. 

The word force is used, in ordinary conversation, in an 
almost endless number of meanings, but in Physics the 
meaning is definite. If there is a change of momentum, 
force is acting. 



NEWTOxN'S SECOND LAW OF MOTION 37 

Sometimes, however, a body is not free to move. In this 
case force would tend to produce a cliant^e in the momentum. 
We can include sucli cases by framing our definition thus : 

Force is that which tends to cJiavge viomentuTn. 

It is to be observed that there is no suggestion as to the 
cause or source of force. Whatever the nature of the external 
influence on the body may be, we simply look at the effect: if 
there has been a change of momentum, then it is due to force. 

It is evident, also, that the total effect of a force depends 
upon the time it acts. 

Thus, suppose a certain force to act upon a body of mass m 
for 1 second, and let the velocity generated be v, i.e., the 
momentum produced is ')nv. If the force continues for another 
second it will generate additional velocity v, or 2v in all, and 
the momentum produced will be 2mv ; and so on. 

Let us state this result in symbols. 

Let F represent the force, 

and t sec. be the time during which it acts. 
At the end of t sec. the force will have generated a certain 
momentum, which we may write mv. 

Then 

Force x time = momentum produced, 

or Ft = mv. 



Hence F = 



mv 



V 

m X ", 
t 



= ')na. 
i.e. Force = mass x acceleration. 
It should be remarked that this equation holds only when 
we choose proper units. However, F is always proportional 
to the quantity via. 



38 INERTIA, MOMENTUM, FORCE 

44. Units of Force. In further explanation of the action 

of force, consider the following arrangement. 

^ 6?* JL 



Fig. 32.— a stretched elastic cord exerting force on a mass. 

A mass of m grams rests on a smooth surface (that is, a 
surface which exerts no friction as the mass moves over it), 
and to it is attached an elastic cord the natural length of 
which is 20 cm. Let the mass be held until the cord is stretched 
to a length of 25 cm., and then let go. The force exerted on 
the mass by the stretclied cord will cause it to move. 

If the hand continually moves forward fast enough to keep 
the length of the cord always 25 cm., then the same force will 
continually act upon tyi. 

The effect of the force will be to give a velocity to m, i.e., 
to generate momentum. 

At the end of 1 second let the velocity be a cm. per second ; 
at the end of 2 seconds it will be 2(X cm. per second ; at the 
end of 3 seconds, 8a cm. per second ; and at the end of t 
seconds, at cm. per second. In this case there is given to the 
mass 7)1 an acceleration of a cm. per second per second. 

If now the mass is 1 gram and the gain in velocity every 
second is 1 cm. per second (or, in other words, the acceleration 
is 1 cm. per second per second), then the force which produced 
this is called a dyne. 

If the mass is 1 gram and the acceleration is a cm. per 
second per second, the force a dynes. ^ 

If the mass is 97i grams and the acceleration is a centi- 
metres per second per second, the force is m a dynes. If F 
represent this force, then 

F = m a, 
or Force = mass x acceleration, as obtained in § 43. 



AVERAGE FORCE 39 

• A DYNE is that force which acting on 1 gram mass for 1 
sec. will generate a velocity of 1 cm. per sec. 

If the mass is 1 pound and the acceleration is 1 foot per 
second per second the force is called a poundal. 

We can write 

1 poundal acting on 1 lb. mass for 1 sec. gives a velocity of 1 ft. per sec. 

J'pOUndals n m 1 it ir 1 n n II F „ h 

F II II M VI lbs. ii 1 II II II 



F 
m 
Ft 
m 



F K II II m II II t II II II 

Let this velocity be v feet per second. 

Then — = v, or Ft = mv, 
m 

and F = ■ — = ma, as before. 

t 

A POUNDAL is' that force wldch acting on 1 lb. mass for 1 
sec. generates a velocity of 1 ft. pe>* sec. 

45. Average Force. If the momentum generated in the 
interval t be mv, then 

Ft = mv 



and F = 



mv 
J" 

If the force has not been constant all the time tlie above 
value is the average force acting during the interval. 

PROBLEMS 

1. A mass of 400 grams is acted on by a force of 2000 dynes. Find the 
acceleration. If it starts from rest, find, at the end of 5 sec, (1) the 
velocity generated, (2) the momentum. 

2. A force of 10 dynes acts on a body for 1 min., and produces a 
velocity of 120 cm. per sec. Find the mass, and the acceleration. 

3. Find the force which in 5 sec. will change the velocity of a mass of 
20 grams from 30 cm. per sec. to 80 cm. per sec. 

4. A force of 50 poundals acts on a mass of 10 lb. for 15 sec. Find 
the velocity produced, the acceleration and the momentum. 



40 INERTIA, MOMENTUM, FORCE 

46. Gravitation Units of Force. The force with whose 
effects we are most familiar is tlie force of gravitation, and 
we shall express the dyne and poundal in terms of it. 

Take a lump of matter the mass of which is 1 gram. The 
earth pulls it downward with a force which we call a gram- 
force. 

If now it is allowed to fall freely, at the end of 1 second it 
will have a velocity of 980 (approximately) centimetres per 
second. 

We see then that 

1 gm. -force acting on 1 gin. -mass for 1 sec. gives a velocity of 980 cm. per sec; 
but 1 dyne u m 1 m n 1 .. „ t. 1 >i n 

Hence 1 dyne = g-i^ of a gram -force. 

The gram-force is a small quantity, while the dyne is -^^jy of 
this and so is a very small quantity. 

U.sing pounds and feet as units we liave 

1 pound-force acting on 1 Ib.-mass for 1 sec. gives a velocity of 32 ft. per sec.; 

but 1 poundal « n in n 1 II M Ti 1 II If 

Hence 1 poundal = ~ j)ound-force 
= I ounce-force. 

Here 980 and 82 are only approximate values of the 
acceleration of gravity ; they vary with the position on the 
earth's surface. On the other hand the dyne and the poundal 
are quite independent of position in the universe, and they are 
therefore known as absolute units of force. 

47. Composition and Resolution of Forces. Since accele- 
ration is a directed quantity, and F = 7na, it follows that force is 
also a directed quantity, and can therefore be represented in magni- 
tude and direction by a straight line. 

Just as displacements, velocities, accelerations and momenta may 
be combined and resolved according to the parallelogram or polygon 
law, so may forces. 



INDEPENDENCE OF FORCES 41 

48. Independence of Forces. It is to be observed that each 

force produces its own effect, measured by change of momentum, 
(juite independently of any others which may be acting on the 
body. 

Suppose now a person to be at the top of a tower 64 feet high. 
If he drops a stone it will fall vertically downward and will reach 
the ground in 2 seconds. Next, let it be thrown outward in a 
horizontal direction. Will it reach the ground as quickly 1 

By the Second Lara the force which gi\'es to the stone an outward 
velocity will act quite independently of the force of gravity which 
gives the dcwiuvard velocity. A horizontal velocity can have no 
effect on a vertical one, either to increase or to diminish it. Hence 
the body should reach the ground in 2 seconds, just the same as if 
simply dropped. 

This result can be experimentally tested in the following way : 

A and B are two upriglit 



M6 S jfB C 



O---^::: 



supports tlu'ough which a 
rod R can slide. 8 is a 
spring so arranged that 
when R is pulled back 
and let go it flies to the 
right. 2) is a metal sphere 
through which a hole is 
bored to allow it to slip 
over the end of R. C is , ^ 

another sphere, at the same Fio. 33.— The bail C, following a curved path reachesthe 
heijrht above the floor as D. "o*"" **' ^^^^ «*'"« t'">e as D which fails vertically. 

The rod R is just so long that when it strikes C, the sphere D is 
set free. Thus C is projected horizontally outwards while D drops 
directly down. 

By pulling R back to different distances, different velocities can 
be given to C, and thus different paths described, as shown in the 
figure. 

It will be found that no matter which of the curved paths C 
takes it will reach the floor at the same time as D. 

PROBLEMS 

1. From a window 16 ft. above the ground a ball is thrown in a hori- 
zontal direction with a velocity of 50 ft. jier second. Wliere will it 
strike the ground ? 

[It will reach the ground in 1 sec, and will therefore strike the ground 
50 feet from the house.] 



42 INERTIA, MOMENTUM, FORCE 

2. A cannon is discliarged in a horizontal direction over a lake from 
the top of a cliff 19.6 m. above the water, and the ball strikes the water 
2500 m, from shore. Find the velocity of the bullet outwards, supposing 
it to be uniform over the entire range. 

3. In problem 2 find the velocity downwards at the moment the ball 
reaches the water ; then draw a diagram to represent the horizontal and 
vertical velocities, and calculate the resultant of the two. 

49. Newton's Third Law of Motion. The Third Law relates 

to actions between bodies, and is as follows : 

To every action there is always an equal and ojyposite reaction. 

The statement of this law draws our attention to the fact that 
force is a two-sided phenomenon. If a body A acts on a body B, 
then JJ reacts upon A with equal force. 

When we confine our attention to one body we look on the other 
body as the seat of an external force ; but when we take both bodies 
into account we see the dual nature of the force. 

If one presses the table with his hand, there is an upward pressure 
exerted on the hand by the table. 

A weight is suspended by a cord : the downward pull exerted by 
the weight is equal to the upward pull exerted by the support to 
which the cord is fastened. 

In the first of these examples action and reaction are both pres- 
sures ; in the second they are tensions. 

If motion takes place the action and reaction are measured by the 
change of momentum. 

Thus, when a person jumps from a boat to the shore the momen- 
tum of the boat backward is equal to the momentum of the person 
forwaid. 

When an apple falls to the earth, the earth moves upward to 
meet the apple, the momentum in each case being the same ; but 
the mass of the earth is so great that we cannot detect its velocity 
upward. 

When a pole of one magnet attracts or repels a pole of a second 
magnet, the latter exerts an equal attraction or repulsion on the 
first. In this case we cannot detect any material cord or rod 
connecting the two poles, along which is exerted a tension or a 
pressure; but it is probable, nevertheless, that there is something 
in the space between which transmits the action. 



NEWTON'S THIRD LAW OF MOTION 



43 



The following experiment will illustrate the third law : 

A and B are two exactly similar ivory 
or steel balls, suspended side by side. A 
is drawn aside to C, and then allowed to 
fall and strike Jj. At once A comes to 
I'est, and B moves off with a velocity 
equal to that which A had. 

Here the action is seen in the forward 
momentum of B, the reaction in the equal 
momentum in opposite direction which 
just brings A to rest. Of course, if we 
call the latter the action, the former is the reaction. 

Suppose now A and B to be sticky putty balls so that when they 
collide they stick together; they will both move forward with one- 
half the velocity which A had on striking. The student can easily 
analyse the phenomenon in this case into action and reaction. 



B 

Fig. 34.— The action of il on iJ is 
equal to the reaction of Bon A. 



PROBLEMS 

1. If the sphere B (Fig. 34) has a mass twice as great as A, what will 
happen (1) when A and B are of ivory ? (2) when 
they are of sticky putty ? 

2. A hollow iron spliere is filled with gunpowder 
and exphided. It bursts into two parts, one j)art 
being one quarter of the whole. Find the relative 
velocities of the fragments. 

3. Suspend an iron ball (Fig. 35) about 3 inches 
in diameter with ordinary thread. By pulHng 
slowly and steadily on the cord below the sphere 
the cord above breaks, but a quick jerk will break 

Apply the third law to exj)lain 
tliis. 

4, A rifle weighs 8 lbs. and a bullet weighing 1 oz. leaves it with a 
velocity of 1500 ft. per sec. Find the velocity with which the rifle 
recoils. 

5. Sometimes in putting a handle in an axe or a hammer it is accom- 
plished by striking on the end of the liandle. Explain how the law of 
inertia applies hei'e. 



Fio. 35.— An iron ball sus- ;(. ],pl,.,„ t-lip l^,,!] 
pended by a thread. ^^ OtlOW tUe DaJl 



CHAPTER IV 



Moment of a Force; Composition of Parallel Forces; 
Equilibrium of Forces 



50. Moment of a Force. 




Fig. 36. — The moment of a force depends on 



In stormy weather, in order to 
keep tlie ship on her course 
the wlieelsman grasps the 
wheel at the riui (i.e., as 
far as possible from the 
axis), and exerts a force at 
right angles to the line 
joining the axis to tlie 
point where he takes hold. 
(Fig. 36.) 

From our experience we 
know that the turning 
effect upon the wheel is 

the force proportional to the force 

applied and its distance from the axis of rotation. g^ertcd and alsO to the 

distance, from the axis, of the point where the force is applied. 

Let F = the force applied, 

2? = the perpendicular distance from the axis to the 
line AB of the applied force. 

Then the product Fj:) measures the tendency of tlie wheel to 
turn, or the tendency to produce angular momentum. This pro- 
duct is the moment of the force, which is defined as follows: 

Tlie moment of a force is. the tendency of that force to 
produce rotation of a body. 

If the direction of the force F is not perpendicular to the 
line joining its point of application to the axis, the moment is 
not so great, since part of the force is spent uselessly in 
pressing the wheel against its axis. In Fig. 36, if ^C is tlie 
new direction of tlie force, then 2^', the new perpendicular, is 
shorter than p, and hence the product Fj)' is smaller. 

44 



COMPOSITION OF PARALLEL FORCES 



45 



We can experimentally 




51. Experiment on Law of Moments, 

test tlie law of moineuls in the following' 
way. 

JB is a rod which can move freely 
about a pin driven in a board at 0, and 
two cords attached to the ends A and Ji 
pass over pulleys at the edj;e of the 
board. Adjust these until the perpen- 
dicular distances from upon the sti-ings 
are 3 inches and 5 inches. Then if the 
weight P = 10 oz., the weight Q, to fig. 37.-Apparatu8 for testing the 
balance the other, must = G oz. i!^" °f inoments. 

Here moment of force 7^ is 10 x .3 = 30, 
and I! II II (> is 6 X 5 = 30. 

For equilibrium of the two moments, the products of the forces 

by the per])endicular distances must be the same, and they must 

tend to produce rotations in opposite directions. 

52. Forces on a Crooked Rod. For a body shuped as in Fig. 38, 

with forces J' and Q acting at the 
ends A and JJ, the moment of I* about 
is Pp, that of Q is Qq ; but it is to 
be observed that they turn the rod in 
opposite directions. If we call the 
first positive, the other will be nega- 
tive, and the entire tendency of the 
I'od to rotate will be 

Fp - Qq. 
If Pp - Qq = 0, the rod will be in equilibrium. 

53. Composition of Parallel Forces. The behaviour of 

parallel forces acting on a rigid body may be investigated 
experimentally in the following way : 




Fig. 38. — Balancingf forces on a rod 
wliich is not straijjht. 



A 










c 


r- 1 11 




a, 


M 


S 


ifi. 




It 1 II 


R 




A 


T 



Fio. 39. 



J/ is a metre stick (Fig. 39) with a weight W suspended at its 
centre of gravity, and two spring balances JJ^, £.„ held up by the 



46 MOMENT OF A FORCE; EQUILIBRIUM OF FORCES 

rod AC, support the stick and the weight. Be careful to have the 
Imlances lianging vertically. 

Take the readings of the balances B^, B., ; let them be P and Q, 
respectively. Also, measure the distances ^.S', ST. 

Tlien we shall find that if the weight of the stick and W together 
is U, 

P + Q =U and P X RS ^ Q X ST. 

Again, if we take moments about P we should have 
U X PS = Q X RT. 

By shifting the position of R and T, various readings of the 
balances will be obtained. 

PROBLEMS 

1. A rod is 4 feet long (Fig. 40) and one end rests on a rigid support. 
At distances 12 inches and 18 inches from that end weights of 20 lbs. 

^ and 30 lbs., respectively, are Imng. What 

W rh rS ^ force must be exerted at the other end 

30lbAA ^20im j^ ^^^^^ ^^ support these two weights? 
Fig. 40.-What Jorce^is reciuired to (j^gglect the weight of the rod.) 

2. An angler hooks a fish. Will the fish appear to pull harder if the 
rod is a long or a short one ? 

3. Astifi"rod 12 feet long, projects horizontally from a vertical wall. 
A weiglit of 20 lbs. hung on the end will bceak the rod. How far along 
the pole may a boy weighing 80 lbs. go before the pole breaks ? 

54. Unlike Parallel Forces.— Couple. Let P, P be two equal 

parallel forces acting on a body in opposite <*r \—*p 

directions (Fig. 41). The entire effect will be \\ 

to give the body a motion of rotation without y. ^ 

motion of translation. Vv 

Such a pair of forces is called a couple, and ?\ 

the moment of the couple is measured by the : \\ 

product of the force into the perpendicular „ . >\ 

distance between them. Thus if d is this dis- *-^ ^ 

tance, the magnitude of the couple is Pel. This ^'postte~paTaiie?Torces 

measures the rotating power. produce only rotation. 

Next suppose there are two unlike parallel forces P, Q and 



VERIFICATION OF THE PARALLELOGRAM LAW 



47 




that Q is greater than P. Then the forces P and Q are equivalent 

to a couple tending to cause a rotation in the 

direction in which the hands of a clock turn, W ** 

and to a force tending to produce a motion of 

translation in the direction of Q, that is, to the 

left hand (Fig. 42). 

This can be seen in the following way. Divide 
(? into two forces /'and Q - P. The portion /', 
along with P acting at the other end of the 
rod forms a couple, while the force Q — P will 
give a motion of translation to the body in 
its direction. 

55. Experimental Verification of the Parallelogram Law. 

By means of an experiment we can test the trutli of the law of the 
Par.dlelogram of Forces, which states that if two forces are 
represented in magtiitude and direction by two sides of a parallelo- 
gram, tlien their resultant will be represented, in magnitude and 
direction, by the diagonal between the two sides. 

In Fig. 43, S, S' are two spring balances liung on pins in the bar 
AB, which may conveniently be above the blackboard. Three 



Fio. 42. — Two opposite 
parallel hut unequal 
forces produce both ro- 
tation and translation. 





FiQ. 43.— How to test the law of parallelogram of forces. Fio. 44.— The triangle of forces. 

strings of unequal length are knotted together at 0, and the ends of 
two of them are fastened to the hooks of the balances. A weight, 
W ounces, attached to the third string makes it hang vertically 
downward. 

Thus three forces, namely, the tensions of the strings, pull on the 
knot 0. The magnitude of the forces acting along the strings, OS, 
OS', which we shall denote by P, Q, will be given by tlie readings on 
the balances, in ounces, let us suppose. The magnitude of the force 
acting along W is, of course, W ounces. 



48 MOMENT OF A FORCE; EQUILIBRIUM OF FORCES 



The three forces P, Q, W act upon the knot 0, and as it does not 
move, these forces must be in equilibrium. The force W may be 
looked upon as balancing tlie other forces P, Q ; and hence the 
resultant of P, Q must be equal in magnitude to W but opposite in 
sense. 

Draw now on the blackboard, immediately behind the apparatus 
or in .some other convenient place, lines piU'allel to the .strings OS, 
OS', and make OC, OD as many units long as there are ounces 
shown on ;S', S', respectively. 

On completing the parallelogram OCED it will be found that the 
diagonal OE is vertical, and that it is as many units long as there 
are ounces in W. 

56. The Triangle of Forces. A slight variation will illustrate 
the triangle of forces. 

On the blackboard, or on a sheet of paper, draw a line OD, par- 
allel to OS', to represent the force Q (Fig. 44). From 1) draw 
DC parallel to OS and representing P on the same scale. Then 
OC will be found to be parallel to W, and will represent, on the 
same scale, the force IF, but in the opposite sense. 

57. The Polygon of Forces. Next let five strings be knotted 
together or attached to a small ring, and passed over pulleys at 




a s a 




Fig. 45. — Experimental verification of the polygon of forces. 



the edge of a circular board held vertically. To these attach 
weights P, Q, R, S, T. In Fig. 45 the.se are taken to be 5, 5, 7, 
6, 4 ounces, respectively. 



THE POLYGON OF FORCES 49 

Since these forces are in e([iiilibrium we may look upon the force 
7' as balancing the other four forces; and hence tlie resultant of 
P, Q, R, S is a force equal to T but acting in the opposite direction. 

On the blackboard draw a line AB to represent P in magnitude 
and direction. From li draw BC to represent Q, from C draw CD 
to represent R, and from 1) draw DE to repiesent S. 

If the figure has been carefully drawn it will be found that the 
line joining E to A is parallel to 7' and proportional to it. 

Thus if a number of forces acting on a ))article are in equilibrium, 
they can be represented in magnitude and direction by the sides of 
a polygon taken in order. 



CHAPTER V 

Gravitation 

58. The Law of Gravitation. One of our earliest and most 
familiar observations is that a body which is not supported 
falls towards the earth. This effect we attribute to the 
attraction of the earth. 

The rates at which bodies move whilst falling were 
discovered by Galileo (1564-1642), but the general principle 
according to which the falling takes place was first demon- 
strated by Newton. 

Copernicus (1473-1543) had shown that the sun is the 
centre of our solar system, but it was Newton who gave a 
reason why the various bodies of the system move as they do. 
He showed that if we suppose the sun, the planets and their 
satellites to attract each other according to a simple law, now 
usually known as the Newtonian Law, he could account not 
only for the revolution of the planets about the sun and 
the satellites about the planets, but also for some minute 
irregularities which on close examination are found to exist 
in their motions. 

Having found his Law true for the heavenly bodies, he 
went one step further and extended it to all matter. 

59. The Newtonian Law. Let m, m' be the masses of 
two particles of matter, r the distance between them. Then 
Newton's Law of Universal Gravitation states that the 
attraction between m and m is proportional directly to tlie 
product of their masses and inversely to the square of the 
distance between them. 

50 



THE WEIGHT OF A BODY 51 



Ihua tlie l^orce is proportional to 



or 7' = a; — ;— , 
?- 

where h is a numerical constant. 

If nn, m are sniall spheres, each containing 1 gratn of 
matter and r, tlie distance between tlieir centres, is 1 centi- 
metre, tlien F = 0.0000000648 dynes. This is an exceedingly 
small quantity, and thus we see that between ordinary masses 
of matter the attractions are very small. Indeed it is only by 
means of experiments made with the utmost care and delicacy 
til at the attraction between bodies which we can ordinarily 
handle can be detected. 

It is to be remarked that though the Newtonian Law states 
tlie manner in which masses behave towards each other, it 
does not offer any explanation of the action. The reason %vhy 
the attraction takes place is one of the mysteries of nature. 

60. The Weight of a Body. Consider a mass m at A on 
the earth's surface (Fig. 46). The 
attraction of the earth on the mass 
is the weigJtt of the mass. The mass 
also attracts the earth with an equal 
force, since action and reaction are 
equal. 

If m is a pound-mass, the attraction ^'o^„ f ;-^s'o„" iliTurte'.'ndaiso 

of the earth on it is a ^JOU7U?-/orce ; if twice as far away from the centre. 

it is a gram-mass, the attraction is a gram-force. 

Now it can be shown by mathematical calculation that a 
homogeneous sphere attracts as though all the matter in it 
were concentrated at its centre. We see then that if tlie 
whole mass of the earth were condensed into a particle at C 
and a pound-mass were placed 4000 miles from it the attraction 
between the two would be 1 pound-force. 




52 



GRAVITATION 



Next, suppose the pound-mass to be placed at B, 8000 miles 
from G. Then the force is not i l:»ut i., or \ of its former value ; 
that is, the iveigJit of a pound mass 4000 miles above the earth's 
surface would be I of a pound-force. 

If it were 2000 miles from the earth's 
surface or 6000 miles from its centre, this 
distance is f ^^^ or -I of its former distance, 
and the force of attraction 




i^f 



= TT of 1 pound-force. 



Fio. 47.— Attraction of the 
sphere on a mass within it. 



-say, 




61. Attraction within the Sphere. Let 

AJJ he a liomogeneous shell (like a hollow 
rubber ball) and ni a mass within it. It can be shown that the 
attraction of the shell in any dii-ection on vi is zero. The "pull" 
exerted by the portion at the side JJ is just balanced by that at the 
side A. 

Now let us suppose the pound-mass to be some distance 
2000 miles — below the earth's surface (Fig. 48), 
and we wish to find the attraction towards the 
centre. Consider the earth divided into two 
parts, a sphere 2000 miles in radius, and a shell 
outside this 2000 miles thick. From what lias 
just been said, the attraction of the shell on the 
pound-mass is zero, and so we need only find the 
attraction of the inner sphere. 

Let us assume that the density of the earth is 
uniform. Then since the radius of the inner 
sphere is -| the earth's radius, its volume and also 
its mass is ^ that of the earth. 

Hence if the mass only were considered the attraction would be 
^ pound-force. 

But the distance also is changed. It is now 1 as great and tlie 
attraction on that account should be increased 2^ or 4 times. 

Hence, taking both of these factors into account, we find that the 
attraction towards the centre upon the pound-mass 

= 4x^ = 1 pound-force. 

Tlius, on going down half-way to the centre, the attraction is ^ 
as great. If the distance were \ the distance from the centre, the 
attraction on the pound-mass would be ^ pound-force ; and so on. 



Fig. 48. —Attraction on 
a mass halfway to 
the earth's centre is 
one half th€ attrac- 
tion at the surface. 




ATTRACTION ON THE MOON 53 

62. Attraction on the Moon. Let us calculate the weight of a 
pound-mass on the surface of the moon. 

The moon's diameter is 2163 miles and the earth's is 7918 miles, 
but for ease in calculation we shall take these numbers as 2000 and 
8000 respectively. 

Assuming, then, the radius of the moon to be ^ that of the earth, 
its volume is g^^f that of the earth, and 
if the two bodies were equally dense 
the moon's mass would also be gV ( !^^\ *v>o 

In this case the attraction on a 

pound-mass at a distance of 4000 miles 

from its centre would be ^^ of a pound Fig. 49.— Attraction on the moon is 
force one-sixth that on the eaith. 

But the distance is 1000 miles, or \ of this, and the attraction 
on this account would be 4- or 16 times as great. 

Hence, attraction = 16 x ^^ ==• ;| pound-force. 

But the density of the moon is only ^^ that of the earth ; and so 
the attraction 

= A X 1 = 5% = i approximately.* 

Hence if we could visit tlie moon, retaining our muscular strength, 
we would lift 600 pounds with the same ease that we lift 100 on the 
earth. If you can throw a base-ball 100 yards here, you could 
' throw it 600 there. 

On the surface of the sun, so immense is that body, the weight of 
a pound-mass is 27 pounds-force. 

QUESTIONS AND PROBLEMS 

1. If the earth's mass "were doubled without any change in its dimen- 
sions, how would the weiglit of a pouiid-mass vary ? 

Could one use ordinary balances and the same weights as we use now ? 

2. Find the weight of a body of mass 100 kilograms at 6000, 8000, 
10,000 miles from the earth's centre. 

3. The diameter of the planet Mars is 4230 miles and its density is 
-/(y that of the earth. Find tlie weight of a pound-mass on the surface of 
Mars. 

4. The attraction of the earth on a mass at one of its poles is ■^\^ 
greater than at the equator. Why is this ? 

5. A spring-balance would have to be used to compare the weight of a 
body on the sun or the moon with tliat on the earth. Explain wliy. 

* A more accurate calculation is 

Vms^ ^ V2le3/ ^ 10 ~ 39590 = 6.ioi' 



CHAPTER VI 
Work and Energy 

63. Definition of Work. When one draws water from a 
cistern by means of a bucket on the end of a rope ; or when 
bricks are hoisted during the erection of a building ; or when 
land is ploughed up ; or when a blacksmith files a piece of 
iron ; or when a carpenter planes a board ; it is recognized 
that work is done. 

We recognize, too, that the amount of the work done 
depends on two factors : — 

(1) The amount of water in the bucket, or the number of 
bricks lifted, or tlie force exerted to draw the plough, push 
the file or drive the plane. 

(2) Tiie distance through which the water or bricks are 
lifted or the plough, file or plane is moved. 

In every instance it will be observed that a force acts on a 
body and causes it to move. In the cases of the water and 
the bricks the forces exerted are sufficient to lift them, i.e., to 
overcome the attraction of the earth upon them ; in the other 
cases, sufficient force is exerted to cause the plough or the 
file or the plane to move. 

In physics the term work denotes the quantity obtained 
when ive multiply tJte force by the distance in the direction 
of the force tJtrough which it acts. 

In order to do work, force must be exerted on a body and 
the body must move in the direction in which the force acts. 

64. Units of Work. By choosing vai-ious units of force and 
of length we obtain dificrcut units of work. 

If we take as unit of force a pound-force and as unit of 
length a foot, the unit of work will be a foot-pound. 

54 



HOW TO CALCULATE WORK 55 

If 2000 pounds mass is raised througli 40 i'eefc the work 
done is 2000 X 40 = 80,000 foot-pounds. 

In the same way, a kilogram-metre is the work done in 
raising a kilogram througli a metre. 

If we take a centimetre as unit of length and a dyne as 
unit of force the unit of work is a dyne-centimetre. To this 
has been given a special name, erg. 

Now 1 gram -force = g dynes ; (§ 46) 

Hence 1 gram-centimetre = g ergs. 

To raise 20 grams through 80 cm. the work rccjuired is 

20 X 30 = 600 gram-centimetres = 600 g ergs = 600 X 980 

or 588,000 ergs. 

65, How to Calculate Work. A bag of flour, 98 pounds, 
has to be carried from the foot to the top of a clifl", which has 
a vertical face and is 100 feet high. 

There are three paths from the base to the summit of the 
cliff The first is by way of a vertical ladder fastened to the 
face of the cliff. The second is a zig-zag path 300 feet long, 
and the third is also a zig-zag route, 700 feet long. 

Here a person might strap the mass to be carried to his 
back and climb vertically up the ladder, or take either of the 
other two routes. The distances passed through are 100 feet, 
300 feet, 700 feet, respectively, but the result is the same in 
the end, the mass is raised through 100 feet. 

The force required to lift the mass is 98 pounds-force, and 

it acts in the vertical direction. The distance in this direction 

through which the body is moved is 100 feet, and therefore 

the 

Work = 98 X 100 = 9800 foot-pounds. 

A-long the zig-zag paths the effort required to carry the 
mass is not so great, but the length of path is greater and so 
the total work is the same in the end. 



56 WORK AND ENERGY 

PROBLEMS 

1. Find the work done in exerting a force of 1000 dynes through a 
space of 1 metre. 

2. A block of stone rests on a horizontal pavement. A spring balance, 
inserted in a rope attached to it, shows that to drag the stone requires a 
force of 90 pounds. If it is dragged through 20 feet, what is the work 
done ? 

3. The weight of a pile-driver, of 2500 pounds mass, was raised through 
20 feet. How much woi-k was required ? 

4. A coil-spring, naturally 30 centimetres long, is compressed until it 
is 10 centimetres long, the average force exerted being 20,000 dynes. 
Find the work done. Find its value in kilogram-metres (g = 980). 

5. Two men are cutting logs with a cross-cut saw. To move the saw 
requires a force of 50 pounds, and 50 strokes are made per minute, the 
length of each being 2 feet. Find the amount of work done by each man 
in one hour. 

6. To push his cart a banana man must exert a force of 50 pounds. 
How much work does he do in travelling 2 miles ? 

66. Definition of Energy. A log, known as a pile, the 
lower end of which is pointed, stands upriglit, and it is desired 
to push it into the earth. To do so requires a great force, and 
therefore the performance of great work. 

The method of doing it is familiar to all. A heavy block 
of iron is raised to a considerable height and allowed to fall 
upon the top of the log, which is tlnis pushed downwards. 
Successive blows drive the pile further and further into the 
earth, until it is down far enough. 

Here M^ork is done in thrusting the pile into its place, and 
this work is supplied by the pile-driver weight. It is evident 
then, that a heavy body raised to a height is able to do work. 

Ability to do work is called Energy. 

The iron block in its elevated position has energy. As it 
descends it gives up this higli position, and acquires volocity. 
Just before striking the pile it has a great velocity, and this 
velocity is used up in pushing the pile into the earth. It is 
clear, then, that a body in motion possesses energy. 



THE MEASURE OF KINETIC ENERGY 57 

We see, thus, tliat there are ai-e two kinds of energy : 

(1) Energy of position ov 'potential energy. 

(2) Energy of motion or Idnetic energy. 

67. Transformations of Energy. Energy may appear in 
different forms, but if closely analysed it will be fouiul that it 
is always either energy of position, i.e., potential energy, or 
energy of motion, i.e., kinetic energy. 

The various effects due to heat, light, sound and electricity 
are manifestations of energy, and one of the greatest achieve- 
ments of modern science was the demonstration of the Prin- 
ciple of the Conservation of Energy. According to this 
doctrine, the sum total of the energy in the univer.^e remains 
the same. It may change from one form to another, but 
none of it is ever destroyed. 

A pendulum illustrates w^ell the transformation „ ^ 
of energy. At the highest point of its swing tiie 
energy is entirely potential, and as it falls it 
gradually gives up this, until at its lowest 
position the energy is entirely kinetic. 

68. The Measure of Kinetic Energy. Suppose 

a mass m grams to be lifted through a lieight h 
centimetres. (Fig. 50.) 

The force required is vi grams force or vkj dynes, 
and hence the work done is mgh ergs. ^ 



Suppose now the mass is allowed to fall. Upon yio. 50.— The po- 
reaching the level A it will have fallen through a arheight fi^i^ 
space h, and it will have a velocity v such that equal to the 

kinetic energy 
V- = 2gh. (§31.) on reaching 4. 

The potential energy possessed by the body when at B is mgh 
ergs, and as this enei-gy of position is changed into energy of 
motion, its kinetic energy on reaching A must also be mgh ergs. 

But yh = 1^2 

and so the kinetic energy = ^ mv- ergs. 



58 WORK AND ENERGY 

,Hence a mass in grams moving with a velocity v cm. per second 
has kinetic energy J mv- ergs. 

If the mass is in lbs. and the velocity v ft. per sec, the kinetic 

energy = |^ 7?iv'^ ft.-poundals = h ft.-pounds, since 1 pound-force 

9 
= (/ poundals, where g = 32. (See § 46.) 

69. More General Solution. This result can be obtained in a 
somewhat more general Avay. 

Let a force F dynes act for t seconds on a mass m grams initially 
at rest. 

— 6^ -•" H) 

O V 

Fio. 51. — The calculation of kinetic energy. 

Let the velocity produced be v cm. per sec, and the space 
traversed be s cm. 

The force i^ dynes acts through a space s cm., and so does Fs ergs 
of work. The body then at the end of the time possesses Fs ergs of 
energy. 

But its velocity = v cm. per sec. 

Since, now, the velocity at first = 0, and at the end = v, the 
average velocity = ^v cm. per sec; and in time t seconds the space 
traversed, 

s = ^vt centimetres. 

Also, the force F dynes acting for t seconds generates Ft units of 
momentum. But the momentum = mv. 

Therefore Ft = mv, (See §§ 43, 44) 

, jj, mv 

and F = 

t 

But the kinetic energy = Fs, 

_ ^'^^ 1 

= |mv- ergs. 

70. Matter, Energy, Force. There are two fundamental 
propositions in science : — Matter cannot be destroyed, energy 
cannot be destroyed. The former lies at the basis of 



POWER • 59 

analytical chemistry ; the latter at the basis of physics. It is 
to be observed, also, that matter is the vehicle or receptacle 
of energy. 

Force, on the other hand, is of an entirely different 
nature. On pulling a string a tension is exerted in it, 
which disappears when we let it go. Energy is bought and 
sold, force cannot be. 

s 
Again consider the formula s = vt. Writing it thus, v = — we 

t 

say that velocity is the time-rate of traversing space. 
Similarly Work = Force x Space, 
or TT = Fs. 

^ W 
Writing this formula thus, F = ~, we can say that force is the 

space-rate of change of energy. 

71. Power. The power or activity of an agent is its rate of 
doing work. 

A horse-power (H.-P.) is that rate of doing work which 
would accomplish 33,000 foot-pounds of work per minute, or 
550 foot-pounds per second. 

In the centimetre-gram-second system the unit of power 
would naturally be 1 erg per second. 

But this is an extremely small quantity, and instead of it 
we use 1 watt which is defined thus : 

1 watt = 10,000,000 ergs per second. 

It is found that 

746 watts = 1 H.-P. ; 

and if 1 kilowatt = 1000 watts, then 

746 
j^^K.W.=lH.-P. 



CHAPTER VII 

Centre of Gravity 




72. Definition of Centre of Gravity. Eacli particle of a 
body is acted on by the force of gravitation. The line of 
action of each little force is towards the centre of the earth, 
and hence, strictly speaking, they are not absolutely parallel. 
But tlie angles between them are so very small that we 
usually speak of the weights of the various particles as a set 
of parallel forces. 

These forces have a single resultant, as can be seen in the 
following way. 

Consider two forces F^, F.,, acting Sit A,B, 
respectively (Fig. 52). These will have a 
resultant acting somewhere in the line AB 
which joins the points of application. 

Next, take this resultant and another 
force ; they will have a single resultant. 

Continuing in this way, we at last come to the resultant of 
all, acting at some definite point. 

The sum of all these forces is the weight of the bod}'^, and 
the 2>oint G where the tueight acts is called the centre of 
GRAVITY of the body. If the body be supported at this point 
it will rest in equilibrium in any position, that is, if the body 
is put in any position it will keep it. 

73. To find the Centre of Gravity Experimentally. 

Suspend the body by a cord attached to any point A 

of it. 

60 



Fio. 52.— The weight of 
a body acts at its centre 
of gravity. 



CENTRE OF GRAVITY OF BODIES OF SIMPLE FORM Ql 




Kio. 53.— How to 
find the centre 
of gravity of 
a body of any 
form. 



Then tlie ■\vei<;ht actiii": at G and the tension of tlie strinof 
acting upwards at A will rotate the body until 
the point G conies directly beneath A, and the 
line GW is coincident with the direction of the 
supporting cord (Fig. 53). 

Thus if the body is suspended at A, and 
allowed to come to rest, the direction of the 
supporting cord will pass through the centre 
of gravity. 

Next let the body be supported at B. The 
direction of the supj^orting cord will again pass through the 
centre of gravity. That point is, therefore, where the two 
lines meet. 

In the case of a flat body, such as a sheet of metal or a thin 

board, let it be supported at A 
(Fig. 54(t) by a pin or in some 
other convenient way. Have a 
cord attached to A with a small 
weight on the end of it. 

Chalk the cord and then snap 
it on the plate : it will make a 
white line across it. 

Next, support the body from 
B (Fig. 545) and obtain another chalk line. At G, the point 
of intersection of these two lines, is the centre of gravit}^ 

74. Centre of Gravity of some Bodies of Simple Form. 

The centre of gravity of some 

bodies of simple form can often be a g q 




Fio. 54(1 Fig. 54 ?> 

How to find the centre of gravity of a flat 
body. 



deduced from e'eometrical consider 
ations. 



Fig. 55.— Centre of gravity of a 
uniform rod 



(1) For a sti'aight uniform bar AB (Fig. 55), the centre of 
gravity is midway between the ends. 



62 



CENTRE OF GRAVITY 



(2) For a parallelogram, it is at the intersection of the 
diagonals. (Fig. 50.) 




Fig. 56. — Centre of gravity of a parallelogram and a triangle. 

(3) For a cube or a sphere, it is at the centre of figure. 

(4) For a triangle, it is where tlie three median lines 
intersect. (Fig. 56.) 

75. Condition for Equilibrium. For a body to rest in equili- 
brium on a plane, the line of action of the weight niu.st fall within 




Fig. 57. — A and C are in stable equilibrium ; B is not, it will topple over ; 
D is in the critical position. 

the supporting base, which is the space within a cord drawn about 

the points of support. (See Fig. 57.) 

The famous Leaning Tower of Pisa is 
an interesting case of stability of equili- 
brium. It is circular in plan, 51 feet in 
diameter and 172 feet high, and has eight 
stages, including -the belfry. Its con- 
struction was begun in 1174. It was 
founded on wooden piles driven in boggy 
ground, and when it had been carried up 
35 feet it began to settle to one side. 
The tower overhangs the base upwards of 
13 feet, but the centre of gravity is so 
low down that a vertical through it falls 
within the ba.se and hence the equilibrium 
is stable. 

76. The three States of Equili- 
brium. The centre of gravity of a body 
Fig. 53.— The Leaning Tower of ^^'i'^ always descend to as low a position 
Pisa. It overhangs its base more as possible, or the potential energy of a 

than 13 feet, but it is stable, t t j_ t \ ^ • ■ ^"^ 

(Drawn from a photograph.) body tends to beconie a minimum. 





THE THREP] STATES OF EQUILIBRIUM 63 

Consider a body in equilibrium, and suppose tbafc by a slight 
motion this equilibrium is disturbed. Then if the body tends to 
return to its former position, its equilibrium is said to be stable. In 
this case the slight motion raises the centre of gravity, and on 
letting it go the body tends to return to its original position. 

If, however, a slight disturbance lowers the centre of gravity the 
body will not return to its original position, but will take up a new 
position in which the centre of gravity is lower than before. In 
this case the equilibrium is said to be unstable. 

Sometimes a body rests equally well in any position in which it 
may be placed, in which case the equilibrium is said to be neutral. 

An e^g standing on end is in unstable equilibrium ; if resting on 
its side the equilibrium is stable as 
regards motion in an oval section and 
neutral as regards motion in a circular 
section. A uniform sphere rests any- 
where it is placed on a level surface ; f,«. 59. -Stable, unstable and neutral 
its equilibrium is neutral. (Fig. 59.) equilibrium. 

A round pencil lying on its side is in neutral equilibrium ; 
balanced on its end, it is unstable. A cube, or a brick, lying on a 
face, is stable. 

The amount of stability possessed by a body resting on a hori- 
zontal plane varies in different cases. It increases with the distance 
through which the centre of gravity has to be raised in order to 
make the body tip over. Thus, a brick lying on its largest face is 
more stable than when lying on its smallest. 

QUESTIONS AND PROBLEMS 
1. Why is a pyramid a very stable structure ? 

2. Why is ballast used in a vessel ? Where should it 
be put ? 

3. Why should a passenger in a canoe sit on the 
bottom 1 

4. A pencil will not stand on its point, but if two 
pen-knives are fastened to it (Fig. 60) it will balance on 
one's finger. Explain why this is so. 

5. A uniform iron bar weighs 4 pounds per foot of its 
length. A weight of 5 pounds is hung from one end, and 

^'?v;„^'~^M^'^ the rod balances about a point which is 2 feet from that 

the pencil in ^ 

equilibrium? end. Tind the length of the bar. 

6. Illustrate the three states of equilibrium by a cone lying on a 
horizontal table. 




CHAPTER VIII 
Friction 

77. Friction Stops Motion. A stone thrown along the ice 
will, if " left to itself," come to rest. A railway-train on a 
level track, or an ocean steamboat will, if the steam is shut off, 
in time come to rest. Here much energy of motion disappears 
and no gain of energy of position takes its place. In the same 
way all the machinery of a factory when the " power " is 
turned off soon comes to rest. 

In all these cases the energy simply seems to disappear and 
be wasted. As we shall see later, it is transformed into energy 
of another form, namely, heat, but it is done in such a way 
that we camiot utilize it. 

The stopping of the motion in every instance given is due 
to friction. Wiien one body slides or rolls over another there 
is always friction, which acts as a force in opposition to the 
motion. 

It may be observed, however, that if there were not friction 
between the rails and the wheels of the locomotive, the latter 
could not start to move. 

78. Every Surface is Rough. The smoothest surface, when 
examined with a powerful microscope, 
is seen to have numerous little pro- 

FiG. 61.— Roughness of a surface jections and cavities on it (Fig. 61), 

as seen under a microscope. tt i i <> i 

Hence when two surfaces are pressed 
together there is a kind of interlocking of these irregularities 
which resists the motion of one over the other. 

64 



LAWS OF SLIDING FRICTION 65 

79. Laws of Sliding Friction. Friction depends upon the 
nature of the substances and the roughness of the surfaces in 
contact; and as it is impossible to avoid irregularities in surfaces, 
accui-ate experiments to determine the laws of friction are very 
difficult. By means of the apparatus shown in Fig. 62, the laws 
of sliding friction can be investigated. 

M is a flat block resting on a / yy- \ p 

plane surface. A cord is at- ^ I > / I ^ =: 

tached to it and passes over a 

pulley. On the end of the cord p,^ 62. -Experiment to find the 

is a pan holding weights. coefficient of friction. pj 

Let the entire weight on the 
pan be F ; then the tension of the cord, which is the force 
tending to move the block AI, is equal to F. 

Now let F be increased until the block M moves uniformly over 
the surface. The friction developed just balances the force F. If 
F were greater than the friction it would give an acceleration to M. 

Suppose that tlie weight on the block is doubled. In order to 
give a uniform motion to M we shall have to add double the weight 
to the pan. 

Thus the ratio FjW is constant ; it is called the coefficient of fric- 
tion between the block M and the surface. 

For dry pine, smooth surfaces, the coefficient is about 0.25, i.e., 
a 40-pound block would require a 10-pound force to drag it over a 
horizontal pine surface. 

For iron on iron, smooth but not oiled, the coefficient is about 
0.2 ; if oiled, about 0.07. This shows the use of oil as a lubricant. 

The following laws have been established by experiment : 

(1) Friction varies directly as the pressure between the surfaces 
in contact. 

(2) Friction is independent of the extent of the surfaces. 

(3) Friction is independent of the rate of motion. 

(4) The friction at the instant of starting is greater than in a 
state of uniform motion. 

80. Rolling" Friction. When a wheel or a sphere rolls on a 
plane surface the resistance to the motion produced at the point of 
contact is said to be due to rolling friction. This, however, is very 
different from the friction just discussed, as there is no sliding. It 
is also very much smaller in magnitude. 



66 



FRICTION 



After a rain, when some rust has formed on the rails, the power 
requii-ed to draw a train over- them is considerably greater than 
when they are dry and smooth, since the coefficient of friction is 
higher. 

In ordinary wheels, however, sliding friction is not avoided. In 
the case of the hub of a carriage (Fig. 03) there is sliding friction 
at the point C. 



Fig 64. — Section of the crank 
of a bicvcle. The cup 
which holds the balls and 
the cone on which they 
run are shown separately 
below. Here the balls 
touch the cup in two 
points and the cone in 
one; it is & "three-point" 
bearing. 




Fi0. 63. —Section 
throug-h a carriage 
hub, showing an 
ordinary bearing. 




In ball-bearings (Fig. 64), which are much nsed in bicycles, 
automobiles and other high-class bearings, the sliding friction is 
almost completely replaced by rolling friction, and hence this kind 
of bearing has great advantages over the other. 



QUESTIONS AND PROBLEMS 

1. Explain the utility of friction in 

(a) Locomotive wheels on a railway track. 

(b) Leather belts for transmitting power. 

(c) Brakes to stop a moving car. 

2. The current of a river is less rapid near its banks than in mid-stream. 
Can you explain this ? 

3. Wliat horizontal force is required to drag a trunk weighing 150 
pounds across a floor, if the coefficient of friction between trunk and floor 
is 0.3? 

4. Give two reasons why it is more difficult to start a heavily-laden cart 
than to keep it in motion after it has started. 

5. A brick, 2x4x8 inches in size, is .slid over ice. Will the distance 
it moves dei)end on what face it rests upon ? 



CHAPTER IX 
Machines 

81. Object of a Machine. A machine is a device by which 
energy is transferred from one place to another, or is trans- 
formed from one kind to another. 

Tlie six simplest machines, usually known as the 'nieclianical 
powers are, the lever, the pulley, the wheel and axle, the 
inclined plane, the wedge and the screw. All other machines, 
no matter how complicated, are but combinations of these. 

Since energy cannot be created or destroyed, but simply 
changed from one form to another, it is evident that, neglect- 
ing friction, the amount of work put into a machine is equal 
to the amount which it will deliver. 

82. The Lever; First Class. The lever is a rigid rod 
movable about a fixed axis called the fulcrum. Levers are of 
three classes. 

First Class. In Fig. 65 ^5 is a rigid rod which can turn 




B 

-Lever of the first class. 

about 0, the fulcrum. By applying a force i^at J. a force TTis 
exerted at B against a heavy body, which it is desired to raise. 

AO, BO are called the arms of the lever. 

Then by the principle of moments, the moment of the force 
F about is equal to the moment of the force W about 0, 
that is, F X AO = W X BO, 

W AO 

F=m 

Force obtained y j.- (• i i.i p 

or -; — -— = inverse ratio ot lengths or arms. 

l^orce applied 

This is called the Law of the Lever, and the ratio W jF 

is called the mechanical advantage. 

(57 



68 



MACHINES 



rpi W AO 

F BO 



Suppose, for instance, AO = 3G inches, BO — 4 inches. 
on 

~ — 9, the mechanical advantaii'e. 
4 " 

There are many examples of levers of the first class. 

Among them are, the common balance, a pump handle, a pair 

of scissors (Fig. 66), a claw-hammer (Fig 67). 





Fio. 66.— Shears, lever of the first class. Fig. 67 



-Claw-hammer, used as a lever 
of the first class. 



The law of the lever can be obtained by applying the 
principle of energy. 

Suppose the end A (Fig. 68) to move through a distance a 



% 







It is evident that 



Fig. 68. 

and the end B through a distance h. 

a _A0 
h~BO 
Now the work done by the force F, acting through a distance 
a is ^ X a, while the work done by W acting through a dis- 
tance h\^ W X h. 

Neglecting all considerations of friction or of the weight of 
the lever, the work done by the applied force F must be equal 
to the work accomplished by the force W. 
Hence Fa = Wh, 

, . . , W a AO 

and the mechanical advantage ~v — J = 'Un' 

which is the law of the lever. 

83. The Lever; Second Class. In levers of the second 

class the weight to be lifted is jilaced between the point where 

the force is applied and the fulcrum. 



THE LEVER; SECOND CLASS 



69 



As before, the force F is applied at A (Fig. 09), but the 
force produced is exerted at B, between A and the fulcrum 0. 



-A 



w 



B 







Fig. 70.— Theory of the lever of the 
second class. 



Fig. 69.— Lever of the second class. 

Here we have, by the principle of moments, 

F X AO = W X BO, 

W AG . , 
and the mechanical advantage -r? = -jrj:, which in levers of 

this class is always greater than 1. 

Or, by applying the principle of enei'gy (Fig. 70), work done 

by F is Fa, by W is Wh. 

Hence Fa — Wh, 

W _ a 
or 



-- — , the law of the lever. 
BO 



F b 

Examples of levers of the second class : nut-crackers (Fig. 
7l), trimming board (Fig. 72), safety-valve (Fig. 73), wheel- 
barrow, oar of a row- 
boat. 





Fig. 71. — Nutcrackers, lever of the 
second class. 



Fig. 72. — Trimming board for cutting paper or 
cardboard ; lever of the second class. 





Fig. 73.— a safety-valve of a steam boiler. (Lever of the second class.) L is the lever arm, V 
the valve on which the pressure is exerted, W the weight which is lifted, F the fulcrum. 



70 



MACHINES 



84.— The Lever ; Third Class. In tliis case the force F 

is applied between the fulcrum and 
]^| M the weight to be lifted. (Fig. 74.) 

As before, we have 

F X AO = W X BO, 



J 



4 

Fig. 71.— a lever of the third class. 



or — — — , the law or tlie lever. 
F BO 

Notice that the weight lifted is always less than the force 
applied, or the mechanical advantage is less than 1. 

Examples of levers of this class : sugar-tongs (Fig. 75), the 
human forearm (Fig. 76) ; treadle of a lathe or a sewing 
machine. 





Fig. 75. —Sugar-tongs, lever of the third 
class. 



Fio. 76. — Human forearm, lever of the 
third class. One end of the biceps 
muscle is attached at the shoulder, the 
other is attached to the radial bone near 
the elbow, and exerts a force to raise the 
weight in the hand. 



PROBLEMS 

1. Explain the action of the steelj'ards 
(Fig. 77). To which chiss of levers does 
it belong ? If the distance from B to 
is Ij inches, and the sliding weight P 
when at a distance 6 inclies from 
balances a mass of 5 lb. on the hook, 
what must be the weight of P ? 

If the mass on the hook is too great 
to be balanced by P, what additional 
attachment would be required in order 
to weigh it ? 




Fig. 77.— The steelyards. 



THE PULLEY 



71 




^ 2. A hand-barrow (Fig. 78), with the mass loaded on it weighs 210 

pounds. The centre of gravity of tlie barrow and load is 4 feet from the 

front handles and 3 

feet from the back 

ones. Find the 

amount each man 

carries 

3. To draw a nail 
from apiece of wood 
requires a pull of 
200 pounds. A 
claw-hammer is 
used, the nail being 
1^ inches from the 
fulcrum (Fig. 67) 
and the hand being F'"- ^^-^^ hand-barrow. 

8 inches from 0. Find what force the hand must exert to draw the nail. 

4. A cu])ical block of granite, whose edge is 3 feet in length and which 
weighs 4500 lbs., is raised by thrusting one end of a crowbar 40 inches 
long under it to the distance of 4 inches, and then lifting on the other end. 
What force must be exerted ? 

85. The Pulley. The pulley is used sometimes to change the 
direction in M^liich a force acts, sometimes to gain mechanical 
advantage, and sometimes for both purposes. We shall neglect 
the weight and friction of the pulley and the rope. 

A single fixed pulley, such as is shown in Fig. 79, can 
change the direction of a force but cannot give a 
mechanical advantage greater than 1. F, the force 
applied, is equal to the weight lifted, W. 

By this arrangement a lift is changed into a pull 
in any convenient direction. It is often used in 
raising materials during the construction of a 
building. 

By inserting a spring balance, S, in the rope, be- 




Fig. 79. -a fixed 

EhingeTthe twccu the hand and tlie pulley, one can show that 

di recti 
force. 



direction of ^^^ f^^,^^ ^ -^ ^^^^^ ^.^ ^J^^ Weight W. 



72 



MACHINES 




Then each 



Suppose the Imnd to move through a distance a, then the 
weight rises through the same distance. 
Hence F x a = W x a 
ovF= W, 
as tested by the spring balance. 

86. A Single Movable Pulley. Here the weight 
W (Fig. 80) is supported by the two portions, 
B and C, of the rope, and lience each portion 
supports half of it. 
F,o 80 -With a Thus the force F is equal to h W, and the 
thef<^ce^e^^t:| mechanical advantage is 2. 
great^as^ the " This result caii also be obtained from the 

weight lifted. ..»,(. 

pnnciple oi energy. 

Let a be the distance through which W rises, 
portion, B and C, of the rope will be shortened 
a distance a, and so F will move through a 
distance 2a. 

Then, since 

F X 2a = W X a 

W/F = 2, the mechanical advantage. 

For convenience a fixed pulley also is 
generally used as in Fig. 81. 

Here when the weight rises 1 inch, B and C 
each shorten 1 inch and hence A lengthens 2 ^antfam^abie^puiiey 
inches. That is, F moves through twice as Jn'^dlrectioirarTdTJ! 
far as W, and W/F = 2, as before. duced one-haif. 

87. Other Systems of Pulleys, Various combinations of 
pulleys may be used. Two are shown in Figs. 82, 83, the 
latter one being very commonly seen. 

Here there are six portions of the rope supporting W, 
and hence the tension in each portion is ^ W. 




OTHER SYisTEMS OF PULLEYS 



73 



Hence F = i W, 

or a force equal to ^ W will hold up 
neglects friction, which in 
such a system is often con- 
siderable, and it therefore 
follows that to prevent W 
from descending, less than ^ 
W will be required. On the 
other hand, to actually lift W 
the force F must be greater 
than ^ W. In every case fric- 
tion acts to prevent motion. 

Let us apply the principle 
of energy to this case. If W 
rises 1 foot each portion of 
the rope supporting it nmst 
shorten 1 foot and the force F will move 6 feet. 

Then, work done on W = W X 1 foot-pounds 
„ „ by i^ =:^ F X G " 

These are equal, and hence 
W = 6F 
or W/F ~ 6, the mechanical advantage. 



W. This entirely 



w 



Fio. 82. —Combination 
of 6 pulleys ; 6 times 
the force lifted. 



Fig. 83. — A familiar 
combination for 
multiplying the force 
6 times. 



PROBLEMS 

1. A clock may be driven in two ways. First, the weight may be 
attached to the end of tlie cord ; or secondly, it may be attached to a 
pulley, movable as in Fig. 80, one end of the cord being fastened to 
the framework, and the other being wound about the barrel of the driving 
wheel. Compare the weights required, and also the length of time the 
clock will run in the two cases. 

2. Find the mechanical advantage of the system shown in Fig. 84. 
This arrangement is called the Spanish Barton. 



74 



MACHINES 



3. Wliat fraction of his weiglit must the man shown in Fig. 85 exert in 
order to raise himself ? 



m 




Fig. 84. — The Spanish Barton. 







a 



Fig. 85.— An easy method 
to raise one's self. 



Fig. 86. — Find the pressure 
of the feet on the floor ? 



4. A man weighing 140 pounds pulls up a weight of 80 pounds by 
means of a fixed pulley, under which he stands (Fig. 86). Find his 
pressure on the floor. 

88. The Wheel and Axle. This machine is shown in Figs. 

87, 88. It is evident that in one 
complete rotation the weight F will 
descend a distance equal to tlie cir- 
cumference of the wheel, while the 
weight W will rise a distance equal 
to the circumference of the axle. 

Hence F x circumference of 
wheel = W X circumference of 
axle. Let the radii be R and r, respectively; the circumfer- 
ences will be 27rR and 27rr, and therefore 
F X 27rR = W X 27rr, 
or FR = Wr, 
R 




Fig. 87.— The wheel 
and axle. 



Fig. 88.— "Diagram 
to explain the 
wheel and axle. 



1 ^ 

and — = 
F 



, the mechanical advantage. 



This result can also be seen from Fig. 88. The wheel and 
axle turn about the centre C. Now W acts at B, a distance r 
from C, and F acts at -<4, a distance R from G. 

Then, from the principle of the lever 

F X R ^ W X r, as before. 



EXAMPLES OF WHEEL AND AXLE 



75 



89. Examples of Wheel and Axle. The windlass (Fig. 89) 
is a common example, but, in place of a 
wheel, handles are used. Forces are 
applied at the handles and the bucket 
is lifted by the rope, which is wound 
about the axle. 

11 F = applied force, and W = weiglit 
lenpth of crank 



lifted, - 
F 



radius of axle 





Fia. 90.— Raising the ship's anchor by a 
capstan. 



FlQ. 89. — Windlass used in draw- 
ing water from a well. 

The capstan, used on board ships for raising the anchor, 
is another example (Fig. 90). 

The sailors apply the force by 
pushing against bars thrust into 
holes near the top of the capstan. 
Usually the rope is too long to be 
all coiled up on the barrel, so it is 
passed about it several times and 
the end A is held by a man who 
keeps that portion taut. The 
friction is sufScient to prevent 

the rope from slipping. Sometimes the end B is fastened to a 

post or a ring on the dock, and by turning the capstan this 

portion is shortened and the shij) is drawn into the dock. 
90. Differential Wheel and Axle. This machine is shown 

in Fig. 91. It will be seen that the rope 

winds off one axle and on the other. 

Hence in one rotation of the crank the 

rope is lengthened (or shortened) by an 

amount equal to the difference in the 

circumferences of the two axles ; but 

since the rope passes round a movable 

pulley, the weight to be lifted, attached 

to this pulley, will rise only one-half Fie. 9i.-Differentiai wheel 

the difference in the circumferences. 




76 



MACHINES 



Thus by makinjr the two drums which form the axles 
nearly equal in size we can make the difference in tlieir 
circumferences as small as we please, and the mechanical 
advantage wnll be as great as we desire. 

91. Differential Pulley. This is somewhat similar to the 

, , last described machine. (Figs. 

92, 93.) 

Two pulleys, of different radii 
(Fig. 92), are fastened together 
and turn with the same angular 
velocity. Grooves are cut in the 
pulleys so as to receive an end- 
less chain and prevent it from 
slipping. 

Suppose the chain is pulled at 
F until the two pulleys have 

Fio. 92. — Explana- , , . _, Fiq o-? _Thp artiial 

tion of the action made a Complete rotation. Tlien appearance of the 
of^^the differential ^ ^.^^ have mOVed thrOUgha <ii«-ntial pulley. 

distance equal to the circumference of A, and it will have 
done work 

= F X circumference of ^. 

Also, the chain between the upper and the lower pulley 
will be sliortened by the circumference of A but lengthened 
by the circumference of B, and the net shortening is the 
difference between these two circumferences. 

But the weight W will rise only half of this difference. 
Hence w^ork done by W 

= W X I difference of circumferences of A and B, 

W circumference of A 




and therefore 



F ^ difference of circumferences of A and B 



THE INCLINED PLANE 



77 



PROBLEMS 
1. A mail weighing IGO pounds is drawn up out of a well by means of a 
windlass, the axle of which is 8 inches in diameter, and the crank 24 
inches long. Find the force required to be applied to the handle. 




Fig. 94.— Windlass, with gearing, such as is usta uiUi a pile-driver. 

2. Calculate the mechanical advantage of the windlass .shown in Fig. 
94. The length oi the crank is 16 inches, the small Avheel has 12 teeth 
and the large one 120, and the diameter of the drum about which the rope 
is wound is 6 inches. 

If a force of 60 pounds be applied to each crank how great a weight 
can be raised ? (Neglect friction.) 

92. The Inclined Plane. Let a lieavj- mass, such as a barrel 
or a box, be rolled or dragged up an 
inclined plane AC (Fig. 95) whose 
length is I and height /^, by means of 
a force F, parallel to tlie plane. Tlie 
work done is i^ X ^. 

Again the weight is raised throntrli 
a height Ji and so, neglecting friction, 
the work done = W X h. , 

Hence Fl = Wh, 

and — - _ -, 
F h' 

that is, tlie mechanical advantage is the ratio of the length to 
the height of the plane. 




Fig. 95. — Theory of the incHned 
plane. 



78 



MACHINES 



The inclined plane, in the form of a plank or a skid, is used 
in loading goods on a wagon or a railway car. 

Takinof friction into account, the mechanical advantacre is 
not so great, and to reduce the friction as much as possible 
the body may be rolled up the plane. 

93. The Wedge. The wedge is designed to overcome great 
R iAD resistance through a small space. 
Its most familiar use is in splitting 
wood. Knives, axes and chisels are 
also examples of wedges. 

The resistance W (Fig. Q6) to be 

Fig. 96. — The wedere, an application of , j. „•„! i. i„„ j.^ 

the inclined plane ovcrcome acts at right angles to 

the slant sides BC, DC, of the w^edge, and when the wedge has 
been driven in as shown in the figure, tlie work done in 
pushing back one side of the split block will be W x AE, and 
hence the work for both sides is W X 2 AE. 

But the applied force F acts through a space AC, and so 
does work F X A G. 

Hence W x 2AE = F x AC, 




and -p- 



AC 
2AE' 



This is the mechanical advantage, which is evidently greater 
the thinner the wedge is. 

Tliis result is of little practical value, as 
we have not taken friction into account, 
nor the fact that the force F is applied as 
a blow, not as a steady pressure. Both of 
these factors are of great importance. 

94. The Screw. The screw consists of a 
grooved cylinder which turns within a 
hollow cylinder or nut which it just fits. 
The distance from one thread to the fi<j. 97 
next is called the pitch. 




-The jackscrew. 



THE SCREW 



79 



or 



The law of the screw is easily obtained. Let I be the 
length of the handle by which the screw is turned (Fig. 97) 
and F the force exerted on it. In one rotation of the screw 
the end of the handle describes the circumference of a circle 
with radius I, that is, it moves through a distance l-wl, and 
the work done is therefore 

F X 2irl. 
Let W be the force exerted upwards as the screw rises, and 
d be the pitch. In one rotation the work done is 

W X d. 
Hence W x d = F x l-wl, 
W_27rl 
1 ~ d ' ■ 

or the mechanical advantage is equal to the ratio of the 
circumference of the circle traced out by the end of the 
handle to the pitch of the screw. 
In actual practice the advantage 
is much less than this on account of 
friction. 

The screw is really an application 
of the inclined plane. If a tri- 

ino-nlar nippp of mnpr iq in Fin- Fio. 98.— Diagram to show that the 
angular piece or papei, as in rig. screw ia an application of the in- 

98, is wrapped about a cylinder «»n«d plane. 

(a lead pencil, for instance), the hypotenuse of the triangle 

will trace out a spiral like the thread of a screw. 





FiQ 99. — The letter press. 



Fio. 100.— The mechanic's vice. 



Examples of the screw are seen in the letter press (Fig 99), 
and the vice (Fig. 100). 



80 



MACHINES 



ILLUSTRATIVE PROBLEMS 

1. Why should shears for cutting metal have short blades and long 
handles ? 

2. In the driving mechanism of a self-binder, shown in Fig. 101, the 

driving-wheel A 
has a diameter 
of 3 feet, the 
sprocket-wheels 
B and C have 
40 teeth and 10 
teeth, respec- 
tively. The large 
gear-wheel D 
has 37 teeth and 
the small one E 
has 12 teeth, and 
the crank G ia 3 

in. long. Neg- 

Fia. 101.— The driving part of a self-binder. The driving-wheel A is i„„f,-„„ fT-;of;r.ti 
drawn forward by the horses. On its axis is the sprocket-wheel B, i«^<-''i"g iiicbioii, 
and this, by means of the chain drives the sprocket-wheel C. The what pull On the 
latter drives the cog-wheel D which, again, drives the cog-wheel £, . i i 

and this causes the shaft F with the crank G on its end to rotate. driving-wheel 

will be required to exert a force of 10 pounds on the crank G ? 




3. Explain the action of the 
levers in the scale shown in 
Fig. 102. 

If HF^ = 12 ft., FW^ = 4 
inches, 3IN = 36 inches, KM 
= 3 inches, what weight on N 
would balance 2000 pounds of 
a load (wagon and contents)? 
In the scale E^F^ = E'F', and 
7^2)1 = p2i)\ so the load is' 
simply divided equally between 
the two levers. 



fe' 



rT"r°^ . 




Fio. 102.— Diagram of multiplying levers in a scale 
for weighing hay, coal and other heavy loads. 
In the figure is shown one half of the system of 
levers, as seen from one end. The platform P 
rests on knife-edges Z)', D-, the former of which 
is on a long lever, the latter on a short one. The 
knife-edges F', F'' at the ends of these levers are 
supported by suspension from the brackets C, C 
which are rigidly connected with the earth. 



THE SCREW 



81 




Fig. 103.— Train of wheels used 
in a standard clock. One end 
of the weight-cord is fastened 
to the frame of the clock and 
the other is wound on the 
barrel B ; this drives the 
trreat wheel O, which has 
144 teeth ; this turns the 
pinion c, which drives the 
centre wheel C, having 96 
teeth ; this turns the pinion 
t which drives the third wheel 
T, having 91) teeth ; this turns 
the pinion e which drives tlie 
escape- wheel E, with 30 teeth. 
All the pinions have 12 leaves, 
or teeth. 



4. In the train of 
wheels shown in Fig. 
103, let the diameter 
of the barrel jS be 2 
inches and that of the 
escape- wheel .B be 1| 
inches, and let the 
weight Wbe 10 pounds. 
Neglecting friction, 
what force must the 
fingers exert to pre- 
vent the escape-wheel 
from turning ? If fric- 
tion consumes half the 
power, what force will 
be required 1 



PART III-MECHANICS OF FLUIDS 



CHAPTER X 




Fio. 104. — Pressure applied 
to the piston transmitted 
in all directions by the 
liquid within the globe. 



Pressure of Liquids 

95. Transmission of Pressure by Fluids. One of the most 

cliaracteristic properties of matter is its power to transmit 
force. The liarness connects the horse 
with its load; the piston and connecting 
rods convey the pressure of the steam 
to tlie driving wlieels of the locomotive. 
.Solids transmit pressure only in the line 
of action of the force. Fluids act differ- 
ently. If a glohe and cylinder of the 
form shown in Fig. 104, is filled with 
water and a foi'ce exerted on tlie water 
by means of a piston, it will be seen that 
the pressure is transmitted, not simply 
in the direction in which tlie force is 

applied, but in all directions; because jets of water are 

thrown with velocities which are apparently equal from all 

the apertures. If the conditions are modi- 
fied by connecting U-shaped tubes partially 

filled with mercuiy with the globe, as shown 

in Fig. 105, it will be found that when the 

piston is inserted, the change in level of the 

mercury, caused by the transmitted pressure, 

is the same in each' tube. This would show 

that the pressure applied to the piston is 

transmitted equally in all directions by tlie 

water. 

This principle, which is true of gases as 

well as liquids, may be stated as follows : — 

82 




Fig. 105. — Transmission 
shown to be equal in 
all directions by pres- 
sure gauges. 



PRACTKJAL APPLICATIONS OF PASCAL'S PRINCIPLE 88 




S^zJ 



:5^^ 



Pressure exerted anywhere on the mass of a fluid is trans- 
mitted undiminished in all directions, and acts with the 
same force on all equal surfaces in a direction at right angles 
to tJtem. The principle was first enunciated by Pascal, and is 
generally known as Pascal's Law.* 

96. Practical Applications of Pascal's Principle. Pascal 
himself pointed out how it was possible, b}' the application 
of this princijjle, to multiply 

force for pi'actical purposes. 
By experimenting with j^is- 
tons inserted into a closed 
vessel filled with water, he 
showed that the pressures ex- 
erted on the pistons when 
made to balance were in tlie 
ratio of their areas. Thus if 
the area of piston A (Fig. 
106) is one square centimetre, 
and that of B ten times as great, one unit of force applied 
to A will transmit ten units to B. It is evident that this 
principle has almost unlimited application. Pascal remarks, 
" Hence it follows that a vessel full of water is a new principle 
of Mechanics and a new machine for multiplying forces any 
degree we choose." Since Pascal's time the "new machine" 
lias taken a great variety of forms, and has been used for a 
great variety of purposes. 

97. Hydraulic Press. One of the most common forms is 
that known as Bramah's hydraulic press, which is ordinarily 
used whenever great force is to be exerted through short 
distances, as in pressing goods into bales, extracting oils from 
seeds, making dies, testing the strength of materials, etc. Its 
construction is shown in Fig. 107. A and B are two cylinders 

*It appears in Pascal's Traite de I'equilibre des liqueurs, written in 1653 but first published 
in 1663, one year after the author's death 



Fio. 106. 



-Force multiplied by transmission of 
pressure. 



84 



PRESSURP] OF LIQUIDS 



0^ 




Fig. 107. — Krainah's hjdraiilic press. 



connected with each other and Avith a water cistern by 

pipes closed by valves 7^ and Y^. In tliese cylinders work 

pistons Pj and F<i through water-tight collars, Pj being 

moved by a lever. The bodies 
to be pressed are held between 
plates G and D. When P^ is 
raised by the lever, water flows 
up from the cistern through 
the valve Y^ 
and fills the 
cjdinder A. 
On the down- 
stroke the 
valve Y^ is 
closed and the 

water is forced through the valve Y^ into tlie 

cylinder B, thus exerting a force on the piston 

P2, which will be as many times that applied 

to Pj as the area of the cross-section of P.^ is 

that of the cross-section of P^. It is evident 

that by decreasing the size of P^ and in- 
creasing that of P2, an immense force may 

be developed by the machine. While this is 

true, it is to be noted that the upward 

movement of P., will be very slow, because 

the action of the macliine must conform 

to the law enunciated in |81, that is, 

the force acting on P^ x the distance through 

which it moves = the force acting on P., x the 

distance through which it moves. ^'^ 

Fig. 108.— Hydraulic 

98. The Hydraulic Elevator. Another elevator. 

important application of the multiplication of force through 
the principle of equal transmission of pressure by fluids is 
the liydraulic elevator, used as a means of conveyance from 



THE HYDRAULIC ELEVATOR 



85 



floor to floor in buildings. In its simplest form it consists of 
a cage A, supported on a piston P, which works in a long 
cylindrical tube C. (Fig. 108.) The tube is connected with 
the water mains and the sewers by a three-way valve D 
which is actuated by a cord E passing through the cage. 
When the cord is pulled up by the operator, the valve takes 
the position shown at D, and the cage is forced up by the 
pressure on P of the water which rushes into C from the 
mains. When the cord is pulled doM^n, the valve takes the 
position shown at F (below), and the cage descends by its 
own weight forcing the water out of C into the sewers. 

When a higher lift, or increased speed is i-equired, the cage 
is connected with the piston by a system of pulleys which 
multiplies, in the movement of the cage, the distance travelled 
by the piston. 




FiQ. 109.— Hydraulic lift-lock at Peterborougrh, Out., capable of lifting a 140-foot 
steamer 65 feet. 



86 



PRESSURE OF LIQUIDS 




Fio. 110.— Principle of the lift-lock. 



99. Canal Lift-Lock. The hydraulic lift-lock, designed to 
take the place of ordinary locks where a great difference of 
level is found in short distances, is another application of the 
principle of equal transmission. Fig. 109 gives a general view 
of the Peterborough Lift Lock, the largest of its kind in the 

world, and Fig. 110 is a simple 
diagrammatic section showing its 
principle of operation. The lift- 
lock consists of two immense 
hydraulic elevators, supporting on 
their pistons P^ and. P^ tanks A 
and B in which float the vessels 
to be raised or lowered. The 
presses are connected by a pipe 
containing a valve R which can 
be operated by the lockmaster in 
his cabin at the top of the central tower. To perform the 
lockage, the vessel is towed into one tank and the gates at 
the end leading from the canal are closed. The upper tank is 
then made to descend by being loaded with a few inches 
more of water than the lower. On opening the valve the 
additional weight in the upper tank forces the water from its 
press into the other, and it gradually descends while the other 
tank is raised. The action, it will be observed, is automatic, 
but hydraulic machinery is provided for forcing water into 
the presses to make up pressure lost through leakage. 

100. Pressure due to Weight. Our common experiences 
in the handling of liquids give us evidence of force within 
their mass. Wlien, for example, we pierce a hole in a water- 
pipe or in the side or the bottom of a vessel filled with water, 
we find that the water ruslies out with an intensity which we 
know, in a general way, to depend on the height of the water 
above the opening. Again, if we hold a cork at the bottom 



RELATION BETWEEN PRESSURE AND DEPTH 



87 




Fio. 111.— Pressure gauge. 



of a vessel containing water, and let it go, it is forced up to 
the surface of the water, where it remains, its weight being 
supported by the pressure of the li(iuid on its under surface. 

101. Relation between Pressure and Depth. Since the 
lower layers of the liquid support the upper layers, it is to be 
expected that this force within the mass, due to the action 
of gravity, will increase with the depth. To investigate this 
relation, prepare a pressure gauge of the 
form shown in Fig. Ill by stretching a 
rubber membrane . over a thistle-tube A, 
which is connected by means of a rubber 
tube with a U-shaped glass tube 7?, partially 
filled with M^ater. The action of tlie gauge is shown by 
pressing on the membrane. Pressure transmitted to the 
water by the air in tlie tube is measured by the difference in 
level of the water in the branches of the U:tube. 

Now place ^ in a jar of water (which should be at the 
temperature of the room), and gradually push it downward 
(Fig. 112). The changes in the level of the water in the 
branches of the U-shaped tube indicate an increase in pressure 
with the increase in depth. Careful experiments have shown 
that this pressure increases from the surface downward in 
direct 'proportion to tlte depth. 

102. Pressure Equal in -all Directions at the same Depth. 
If the thistle-tube A is made to face in different directions 

while the centre of the membi'ane is 
kept at the same depth, no change in 
the difference in level of the water in 
the U-shaped tube is observed. Evi- 
dently the magnitude of the force at 
any point within the fluid mass is 
independent of the direction of pres- 
sure. The tip ward, dmvnward, and 
lateral pressures are equal at the 




Fig. 112.— Investigation of pres- 
sure within the mass of a liquid 
by pressure gauge. 



same depth. 



88 



PRESSURE OF LIQUIDS 




Fig. 113. — Pressures on the bottoms of vessels of 
different shapes and capacities. 



103. Magnitude of Pressure due to Weight. The down- 
ward pressure of a liquid, say water, on tlie bottom of a vessel 
with vertical sides is obviously the weight of the liquid. But, 

if the sides of the vessel 
are not vertical, the mag- 
nitude of the force is not 
so apparent. The appa- 
ratus shown in Fig. 113 
may be used to investi- 
gate the question. A, B, 
G, and D are tubes of 
different shapes but made 
to fit into a common base. 
^ is a movable bottom 
held in position by a lever 
and weiglit. Attach the 
cj'lindrical tube to the 
base, and support the bottom E in position. Now place any 
suitable weight in the scale-j^an and pour water into the tube 
until the pressure detaches the bottom. If the experiment be 
repeated, using in succession the tubes A, B, C, and D, and 
marking with the pointer the height of the water when the 
bottom is detached, it will be found that the height is the 
same for all tubes, so long as the weight in the scale-pan 
remains unchanged. The pressure on the bottom of a vessel 
filled with a given liquid is, therefore, dependent only on the 
depth. It is independent of the form of the vessel and of 
the amount of liquid which it contains. Tliis conclusion, is 
sometimes known as the hydrostatic paradox, because it 
would seem impossible that a small quantity of liquid, like 
that contained in tube D, could exert the same force on 
the bottom as that exerted by the larger quantity con- 
tained in B. 



EXPLANATION OF THE PARADOX 



89 




FlQ. 114. — Explanation of the hydro- 
static paradox. 



104. Explanation of the Paradox. By an arrangement very 

similar to that just described Pascal fifst 

demonstrated the truth of his Principle, 

and also showed how to apply it to ex- 
plain the apparent contradiction. 

Take, for example, the case of a 

vessel of the form D (Fig. 113). The 

pressure on the bottom DF (Fig. 114) 

is equal to the weight of the water in 

CDFU, together with the pi-essure due 

to the water in LABK. Now on the 

lower faces of CK and BE there is an 

upward pressure (which is that due to 

a depth AB oi the water), and the.se 

surfaces exert upon the water a reaction downwards, wliich is 

transmitted to the base. If the spaces HK and AM were filled 

with water the pressure downwards on GK and BE would just 

balance the upward pressure on them. 

Hence the entire pressure on tlie bottom is equal to the weight 

of the water in HDFG, or the pressure on the bottom is the same 

as if the vessel had vertical sides. 

Now take the case of the funnel- 
shaped vessel B (Fig. 113). Since the 
pressure at any point in the wall is 
perpendicular to the wall, it may have 
a vertical component which is balanced 
by the reaction of the wall at the point 
(Fig. 115). Hence the weight of the 
water is supported in part by the sides 
of the vessel, the bottom supporting only 
the vertical column BCDE. 

105. Surface of a Liquid in Con- 
necting Tubes. If a liquid is poured 
into a series of connecting tubes 
to the same horizontal plane in all 




C D 

Fio. 115. — Explanation of hy- 
drostatic paradox, r, pressure 
of liquid at .4 ; p, vertical 
component ; q, horizontal com- 
ponent. 

(Fig. 116), it will rise 
the tubes. The reason is 
apparent. Consider, for ex- 
ample, the tubes A and B. 
Let a and h be two points in 
the same horizontal plane. 
The liquid is at rest only 
on the condition that the 




Fig. 116. — Surface of a liquid in connecting tubes 
in the same horizontal plane. 

pressure at a in the direction 



90 



PRESSURE OF LIQUIDS 



ab is equal to the pressure at b in the direction ba ; but 
since the pressure at either of these points varies as its depth 
only, and is independent of the shape of the vessel, or of the 
quantity of the liquid in the tubes, the height of the liquid in 
A above a must be tlie same as the height in B above 6. 

This principle, that " water seeks its own level," is in a 
variety of ways, of practical importance. Possibly the common 
method of supplying cities with water furnishes the most 
striking example. Fig. 117 sliows the main features of a 





Fia. 117. — ^Water supply system. A, source of water supply; B, pumping station; C, stand- 
pipe ; D, house supplied with water ; E, fountain ; F, hydrant for fire hose. 

modern system. While there are various means by whicli 
the water is collected and forced into a reservoir or stand- 
pipe, the distribution in all cases depends on the principle 
that, however ramified the sj^stem of service pipes, or however 
high or low they may be carried on streets or in buildings, 
there is a tendency in the water which they contain to rise 
to tlie level of the water in the original source of supply 
connected with the pipes. 

C_ _ c 




Fig. 118. — Artesian basin. A, impermeable strata. B, permeable stratum. C, C, points where 
permeable stratum reaches the surface. W, artesian well. 

106. Artesian Wells. The rise of water in artesian wells 
is also due to the tendency of a liquid to find its own level. 



ARTESIAN WELLS 



91 



These wells are bored at tlie bottom of cup-shaped basins 
(Fig. 118), which are frequently many miles in width. The 
upper strata are impermeable, but lower down is found a 
stratum of loose sand, gravel, or broken stone containing water 
which has run into it at the points where the permeable stratum 
reaches the surface. When the upper strata are pierced the 
water tends to rise with a force more or less great, depending 
on the height of the head of water exerting the pressure. 



PROBLEMS 

1. A closed vessel is filled with licjuid, and two circular pistons, whose 
diameters are respectively 2 cm. and 5 cm. inserted. If the pressure on 
the smaller piston is 50 grams, find the pressure on the larger piston 
when they balance each other. 

2. The diameter of the large piston of a hydraulic press is 100 cm. and 
that of the smaller piston 5 cm. What force will be exerted by the press 
when a force oi 2 kilograms is applied to the small 

piston ? 

3. The diameter of the piston of a hydraulic 
elevator is 14 inches. Neglecting friction, what load, 
including the Aveight of the cage, can be lifted when 
the pressure of the water in the mains is 75 pounds 
per sq. inch ? 

4. What is the pressure in grams per sq. cm. at a 
depth of 100 metres in water ? (Density of water one 
gram per c.c.) 

5. The area of the cross-section of the piston P 
(Fig. 119), is 120 sq. cm. What weight must be 
placed on it to maintain equilibrium when the water 
in the pipe B stands at a height of 3 metres above "*' 
the height of the water in A ? 

6. The water pressure at a faucet in a house supplied with water by 
pipes connected with a distant reservoir is 80 pounds per sq. inch when 
the water in the system is at rest. What is the vertical height of the 
surface of the water in the reservoir above the faucet ? (1 lb. water = 
27.73 c.c. ; see Table opposite page 1.) 




CHAPTER XI 

Buoyancy of Fluids 

107. Nature of Buoyancy. When a body is immersed in a 
liquid every point of its surface is subjected to a pressure 
which is perpendicular to the surface at that point, and which 
varies as the depth of that point below the surface of the 
liquid. When these pressures are resolved into horizontal 
and vertical components, the horizontal components balance 
each other ; and since the pressure on the lower part of the 
body is greater than that on the upper part, the resultant of 
all the forces acting upon the body must be vertical and act 
upward. This force is termed the resultant vertical pressure 
or buoyancy of the fluid. 

Consider, for example, the resultant pressure on a solid 
in the form of a cube, whose edge is 1 cm., immersed 
in water with its upper face horizontal at 
a depth of, say, 1 cm. below the surface. 
(Fig. 120). Obviously the pressures on 
the vertical sides balance. The resultant 
force, which is vertical, is. the difference 
between the pressure on the top and that 
on the bottom ; but the pressure on the 
top is the weight of a column of water 1 
sq. cm. in section and 1 cm. long, and the 
pressure on the bottom is the weight of a similar column 2 cm. 
long (§102). Hence the cube is buoyed up with a force which 
is the weight of a column of water 1 sq. cm. in section and 
1 cm. long, or the weight of water equal in volume to the 
solid, that is, 1 gram. 

92 




Fio. 120.— Buoyant force of 
a liquid on a solid. 



BUOYANT FORCE WHICH A LIQUID EXERTS 



93 




108. To determine experimentally the amount of the 
Buoyant Force which a Liquid exerts on an Immersed 
Body. Take a brass cylinder A, which fits exactly into a hollow 
socket B. Hook _^ 

the cylinder to the "-^ ■' '- " ' ^ ' 

bottom of the socket 
and counterpoise 
tiiem on a balance. 
Surround the cylin- 
der with water(Fig. 
121). It will be 
found that the cy- 
linder is buoyed up 
by the water, but 
that equilibrium is 
restored when the 

socket is filled with *'"*• 121 —r^etemiination of buoyant force. 

water. Hence the buoyant force of the water on the cylinder 
equals the weight of a volume of water equal to the volume of 
the cylinder. 

In general terms, the buoyant force exerted by a fluid wpon 
a body immersed in it, is equal to the weight of the fluid 
displaced by tlie body ; or a body wJien weighed in a fluid 
loses in apparent weiglit an amount eqmd to tlte weight of 
the fluid which it displaces. This is known as the Principle 
OF Archimedes. 

Archimedes had been asked by Hiero to determine whether 
a crown which had been made for him was of pure gold or 
alloyed with silver. It is said that the action of the water 
when in a bath suggested to him the principle of buoyancy as 
the key to the solution of the problem. The story is that he 
leaped from his bath, and rushed through the streets of 
Syracuse, crying " Eureka ! Eureka ! " (I have found it, I have 
found it.) 



94 BUOYANCY OF FLUIDS 

109. Principle of Flotation. It is evident that if the 
weight of a body immersed in a liquid is greater than the 
weight of tlie liquid displaced by it, that is, greater than the 
buoyant force, the body will sink ; but if the buoyant force is 
greater, it will continue to rise until it reaches the surface. 
Here it will come to rest when a portion of it has risen above 
the surface and the weight of the. liquid displaced by the 
immersed portion equals the weight of the body. For 
example, consider again the cube referred to in Fig. 120. If 
its weight is less than one gram, for definiteness say 0.6 gram, 
it will float in water. In this case the downward pressure on 
the top has disappeared and the weight of the cube alone is 
supported by tlie pressure on the bottom, which equals the 
weight of a column of water 1 sq. cm. in section and 0.6 cm. 
deep. 

The conditions of flotation may be demonstrated experi- 
mentally by placing a light body, a piece of wood for example, 
on the surface of water in a graduated tube (Fig. 123). If 
the volume of water displaced is noted and its weight calcu- 
lated, it will be found to be equal to the weight of the body. 

PROBLEMS 

i . A cubic foot of marble which weighs ICO pounds is immersed in 
water. Find (1) the buo^-ant force of tlie water on it, (2) the weight of 
the marble in water, (1 c. ft. water = 62.. 3 lbs. § 17). 

2. Twelve cubic inches of a metal weigh 6 pounds in air. What is the 
weight when immersed in water ? 

3. If 3,500 c.c. of a substance weigh 6 kg., what is the weight when 
immersed in water ? 

4. A piece of aluminium whose volume is 6.8 c.c. weighs 18.5 grams. 
Find the weight when immersed in a liquid twice as heavy as water. 

5. One cubic decimetre of wood floats with i of its volume immersed 
in water. What is the weight of the cube ? 

6. A cubic centimetre of cork weighs 250 mg. What part of its 
volume will be immersed if it is allowed to float in water ? 



PRINCIPLE OF FLOTATION $5 

7. The cross-section of a boat at the water-line is 150 s({. ft. What 
additional load will sink it 2 inches ? 

8. A piece of wood whose mass is 100 grams floats in water with | 
of its volume immersed. What is its volume 1 

9. Why will an iron ship float on water, while a piece of the iron of 
which it is made sinks ? 

10. A vessel of water is on one scale-pan of a balance and couriter- 
poised. Will the equilibrium be disturbed if a person dijjs liis fingers 
into the water without touching the sides of the vessel 1 Explain. 

11. A piece of coal is placed in one scale-pan of a balance and iron 
weights are placed in the other scale-pan to balance it. How would the 
e(iuilibrium be affected if the balance, coal and weights were now placed 
under water ? Why ? 

12. What is the least force which must be applied to a cubic foot of 
wood whose mass is 40 lbs. that it may be wholly immersed in water ? 

13. Referring to Fig. 110, answer the following question : If the depth 
of the water in the press A is the same as that in the press B which 
contains the vessel, which press will be the heavier? 



CHAPTER XII 
Determination of Density 

110. Determination of the Density of a Solid Heavier than 
Water. To determine the density of a body it is necessary to 
ascertain its mass and its volume. 

The mass is determined by weighing. The volume is, as a 
rule, most easily and accurately found by an application of 
Archimedes' Principle. 

For example, if a body whose mass is 20 gi-ams, weighs 16 
orams in water, the mass of the water displaced is 20 — 16 = 
4 grams. But the volume of 4 grams of M^ater = 4 c.c. The 
volume of the body is, therefore, 4 c.c. Hence the density, or 
mass per unit volume, of the substance must be 20 ^ 4 = 5 
grams per c.c. 

Next, let W/ grams = weight or mass of a body in air, 
and 771^ " = its weight in water. 
Then m — m-^ " = loss of weight in w^ater, 

= wt. of water equal in vol. to body. 

Now, mass of a body — its volume X its density ; and since 
in the C.G.S. system the density of water = 1, 

in — m-^ c.c. = vol. of water equal in vol. to body, 
= volume of body. 
That is, the volume of a body is numerically equal to its loss 
of weight in water. 

Hence, density {in gms. per c.c.) 

mass {in grams) 
~ loss of wt. in water {in gms.) 

The number thus obtained also expresses the specific gravity 
of the body. (§18.) 

If the solid is soluble in water its density may be obtained 

by weighing it in a liquid of known density, in which it is 

not soluble, and determining, as above, the ratio of its mass to 

that of an equal volume of the liquid, and then multiplying 

the result by the density of the liquid. 

90 



DENSITY OF A SOLID LIGHTER THAN WATER 97 

111. Determination of the Density of a Solid Lighter than 
Water. If a solid is lio-litcr tliau water, iis density may be 
determined by attaching to it a lieav.y body to cause it to sink 
beneath the surface. 

The following metliod may be used : — 

1st. Weigh the body in air. Let this be m grams. 

2nd. Attach a sinker and weigh both, vnfli the sinker only 

in water. Let this be ni^^ grams. 
3rd. Weigh both, with both in water. Let this be ni.^ 
grams. 
Now the only difference between the second and third 
operations is that in the former case the body is weighed 
in air, in the latter in water. The sinker is in the water 
in both cases. 

Hence ni-^ — m, = buoyancy of the water on the body, 

n% 
and the density (in grams per c.c.) 



m, — m, 



1 ""2 



The number thus obtained expresses also the specific 
gravity of the body. 

112. Density of a Liquid by the Specific Gravity Bottle. 

As in the case of solids, the problem is to determine the 
volume and the mass of the liquid. 

The volume of a sample of the liquid may be oljtained by 
pouring it into a bottle so constructed as to 
contain at a specified temperature a given 
volume of liquid, usually 100 c.c. at 15° C. 
To render complete filling easy, the bottle 
is provided with a closely-fitting stopper per- 
forated with a fine bore through which excess ^ „ .„ 

„ ,. . ° Fig. 122.— Specific 

oi liquid escapes (Fig. 122). gravity bottle. 

The mass of the liquid is obtained by taking the diflference 
between the weights of the bottle when filled with the liquid, 
and when empty. 




98 



DETERMINATION OP DENSITY 



If VI denotes the mass of tlie liquid and v the volume of 



the bottle, density of liquid = 



m 



If the volume of the bottle is not given, it may be found 
by taking the difference between its weight when empty 
and when filled with water. 

113. Density of a Liquid by Archimedes' Principle. 

Archimedes' Principle may also be applied to determine the 
densities of liquids. 

Take a glass sinker whose mass is, say m grams, and weigh 
it first in the liquid whose density is to be determined, and 
then in water. If irii grams denotes the weight of the sinker 
in the liquid and m.^ grams its weight in water, 

m — mj^ grams = mass of liquid displaced by sinker, 
m — m.2 grams = mass of water displaced by sinker. 
Hence volume of the sinker = on — m., c.c, 



and density of liquid (in grams per c.c.) 



tn 



m-i 



TTh — m^ 
114. Density of a Liquid by means of the Hydrometer. 

The hydrometer is an insti-ument designed to indicate directly 
the density of the liquid by the depth at which it floats in it. 
The principle underlying the action of this 
instrument may be illustrated as follows. Take 
a rectangular rod of wood 1 sq. cm. in section 
and 20 cm, long, and bore a hole in one end. 
After inserting sufficient shot to cause the rod to 
float upright in water (Fig. 123) plug up the 
hole and dip the rod in hot paraffin to render 
it impervious to water. Mark off on one of the 
long faces a centimetre scale. Now place the 
rod in water, and suppose it to sink to a depth 
of 16 cm. when floating. Then the weight of 
'tnition^' of'"the the rod = Weight of water displaced = 16 grams. 

principle of the . . . . i i p 1 1;^ 

hydromeier. Agam, supposc it to Sink to a depth 01 12 

cm. in a liquid whose density is to be determined. 



i!T~ . 



KiQ. 123.— Illus- 



DENSITY OF A LIQUID BY MEANS OF HYDROMETER 99 



Tlien, since tlie weight of liquid displaced equals weight of 

the rod, -^2 C.C. of the liquid = 16 grams, 

And density of the liquid = if gram per c.c. 

^ , . ,. , T ■ 1 vol. of water displaced by a floating body 

Or, density of the liquid = — z — j—r — t-- — n"^^ — i n. — Ti ^ — i — T 

vol. or the liquid displaced by the same body 

A hydrometer for commercial purposes is usu- 
ally constructed in tlie form shown in Fig. 124. 
The weight and volume are so adjusted that 
the instrument sinks to the division mark at 
the lower end of the stem in the densest liquid 
to be investigated and to the division mark in 
the upper end in the least dense liquid. The 
scale on the stem indicates directly the densities 
of liquids between tliese limits. The float A is 
usually made much larger than the stem to give 
sensitiveness to the instrument. 

As the range of an instrument of this class no. i-24.-The 

. , 1 • • , 1 • 1 • J 1 hydrometer. 

IS necessarily J united, special instruments are 
constructed for use with different liquids. For example, one 
instrument is used for the densities of milks, another for 
alcohols, and so on. 

PROBLEMS 

(For table of densities see § 17) 

1. A body whose mass is 6 grams has a sinker attached to it and the 
two together weigh 16 grams in water. The sinker alone weighs 24 
grams in water. What is the density of the body ? 

2. A body whose mass is 12 grams has a sinker attached to it and the 
two together displace when submerged 60 c.c. of water. The sinker alone 
displaces 12 c.c. What is the density of the body ? 

3. A body whose mass is 60 grams is dropped into a graduated tube 
containing 150 c.c. of water. If the body sinks to the bottom and the 
water rises to the 200 c.c. mark, what is the density of the body ? 

4. If a body when floating in water displaces 12 c.c, what is the density 
of a liquid in which when floating it displaces 18 c.c. ? 




100 DETERMINATION OF DENSITY 

5. A piece of metal whose mass is 120 grams weighs 100 grams in water 
and 104 grams in alcohol. Find the volume and density of the metal, 
and the density of the alcohol. 

6. A hydrometer floats with f of its volume submerged when floating 
in water, and J of its volume submerged when floating in anotlier liquid. 
What is the density of the other liquid ? 

7. A cylinder of wood 8 inches long floats vertically in water with 5 
inches submerged, (a) What is the specific gravity of the wood ? (6) What 
is the specific gravity of the liquid in which it will float with 6 inches 
submerged ? (c) To what depth will it sink in alcohol wliose specific 
gravity is 0.8 ? 

8. The specific gravity of pure milk is 1.086. What is tlie density of a 
mixture containing 500 c.c. of pure milk and 100 c.c. of water? 

9. How much silver is contained in a gold and silver crown whose mass 
is 407.44 grams, if it weighs 385.44 grams in water? (Density of gold 
19.32 and of silver 10.52 grams per c.c.) 



CHAPTER XIII 
Pressure in Gases 



115. Has Air Weight ? This question puzzled investigators 
from the time of Plato and Aristotle down to the seventeenth 
century, when it was answered by Galileo and Guericke. 

Galileo convinced himself that air had weight by proving 
that a glass globe filled with air under high pressure weighed 
more than the same globe when filled with air under ordinary 
conditions. Guericke, the inventor of the air-pump, showed 
that a copper globe weighed more when filled with air than 
when exhausted. 

The experiments of Galileo and Guericke may be repeated 
with a glass flask (Fig. 125) fitted with a stop-cock. If the 
flask is weighed when filled with air under 
ordinary pressure, then weighed when the 
air has been compressed into it with a 
bicycle pump, and again when the air has 
been exhausted from it with an air-pump, 
it is found that the first weight is less than 
the second but greater than the third. 

Since the volume of a mass of air varies 
with changes in temperature and pressure, 
the weight of a certain volume will be 
constant only at a fixed temperature and 
pressure. Exact quantitative experiments have shown that 
the mass of a litre of air at 0" C. and undep normal pressure of 
the air at sea level (760 mm. of mercury) is 1.293 grams. 

116. Pressure of Air. It is evident that since air has 

weight it nmst, like liquids, exert pressure upon all bodies 

with which it is in contact. Just as the bed of the ocean 

sustains enormous pressure from the weight of the water 

resting on it, so the surface of the earth, the bottom of the 

101 




Fio. 125, 



Glolie for 
weighing air. 




102 PRESSURE IN GASES 

aerial ocean in. which we live, is subject to a pressure due to 
the weight of the air supported by it. This pressure will, of 
course, vary with tlie depth. Thus the pressure of the 
atmosphere at Victoria, B.C., on the sea-level is gi*eater than 
at points on the mountains to the east. 

The pressure of the air may be shown by many simple 
experiments. For example, tie a piece of thin sheet rubber 
over the mouth of a thistle-tube (Fig. 126) 
and exhaust the air from the bulb by 
suction or by connecting it with the air- 
pump. As the air is exhausted the i-ubber 
is pushed inward by the pressure of the 
outside air. 

Again, if one end of a straw or tube is 
^branl^ToS^nward; thrust iuto Water and the air witlidrawn 

• by pressure of the air. ^^.^^^ -^ ^^ sUCtiou, the Water is forced Up 

into the tube. This phenomenon was known for ages but did 
not receive an explanation until the facts of the weight and 
pressure of the atmosphere were establislied. It was explained 
on the principle that Nature had a horror for empty space. 

The attention of Galileo was called to this problem of the 
horror vacui* in 1640 by his patron, the Grand Duke of 
Tuscany, wlio had found that water could not be lifted more 
than 32 feet by a suction pump. Galileo inferred that 
"resistance to vacuum" as a force had its limitations and 
could be measured ; but although he had, as we have seen, 
proved that air has weight, he did not see the connection 
between the facts. After his death the problem was solved 
by his pupil, Torricelli, who showed definitely that the 
resistance to a vacuum was the result of the pressure of the 
atmosphere due to its weight. 

117. The Torricellian Experiment. Torricelli concluded 
that since a water column rises to a height of 32 feet, and 
since mercury is about 14 times as heavy as water, the 

•Horror of a vacuum. 



THE TORRICELLIAN EXPERIMENT 



103 



corresponding mercniy cohimn should be ^^ as long as the 
water column. To confirm his inference an experiment similar 
to the following was performed under his direction by 
Vincenzo Viviani, one of his pupils. 

Take a glass tube about one metre long (Fig. 127), closed at 
one end, and fill it with mercury. Stopping the open end 
with the finger, invert it and 
place it in a vertical position, 
with the open end under the 
surface of the mercury in another 
vessel. Remove the finger. The 
mercury will fall a short dis- 
tance in the tube, and after 
oscillating will come to rest with 
the surface of the mercury in 
the tube between 28 and 30 
inches above the surface of the 
mercury in tlie outer vessel. 

Torricelli concluded rightly 
that the column of mercury was 
sustained by the pressure of the 
air on the surface of the mer- 
cury in the outer vessel. This 
conclusion was confirmed by 

Pascal, who showed that the length of the mercury colunni 
varied with the altitude. To obtain decisive results he asked 
his brother-in-law, P^rier, who resided at Clermont in the 
south of France, to test it on the Puy de Dome, a near-by 
mountain over 1,000 yards high. Using a tube about 4 ft. 
long, which had been filled with mercury and then inverted 
in a vessel containing mercury, Pdrier found that while at the 
base the mercury column was 26 in. 3| lines* high, at the 
summit it was only 23 in. 2 lines, the fall in height being 3 in., 

^The French inch then use4 = 2§ cm., and 1 line = -^ inch. 




Fig. 



127. — Mercury column sustained by 
the pressure of the air. 



104 



PRESSURE IN GASES 



1| lines (over 8 cm.). This result, he remarks, "ravished 
us all with admiration and astonishment."* Later, Pascal 
tried the experiment at the base and the summit of the tower 
of Saint- Jacques-de-la-Boucherie, in Paris, which is about 150 
ft. high. He found a difference of more than 2 lines (about 
I cm.). 

QUESTIONS AND PROBLEMS 

1. Fill a tumbler and hold it inverted in a dish of water as shown in 
Fig. 128. Why does the 
water not run out of the 
tumbler into the dish ? 

2. Fill a bottle with 
water and place a sheet 
of writing paper over its 
mouth. Now, holding the 
paper in position with the 
palm of the hand, invert 
the bottle. (Fig. 129.) 
Why does 'he water re- 
main in the bottle when the hand -^ removed from the paper ? 

3. Take a bent-glass tube of the form shown 
in Fig. 130. The upper end of it is closed, the lower 
open. Fill the tube with water. Why does the 
water not run out when it is held in a vertical 
position 1 

4. Why must an opening be made in the upper 
part of a vessel filled with a liquid to secure a 
proper flow at a faucet inserted at the bottom ? 

5. Fill a narrow-necked bottle with water and 
hold it mouth downward. Explain the action of 
the water. 

6. A flask weighs 280.60 gm. when empty, 284.19 
gm. when filled with air and .3060.60 gm. when filled^ 
with water. Find the weight of 1 litre of air. 





Fig. 128. 



FiQ. 129. 



*"Ce qui nous ravit tous d'adiiiiration et d'etoiinement." This account is taken from 
Perier's letter to Pascal, dated September 22, 1648. 



THE CISTERN BAROMETER 



105 



Barometer. Torricelli pointed out that the object 
•iuieiit was " not simply to produce a vacuum, but 
to make an instrument which shows the muta- 
tions of the air, now Jieavier and dense, now 
lighter and thin."'* The modern mercury baro- 
meter designed for this purpose is the same in 
principle as that constructed by Torricelli. With 
this instrument the pressure of the atmosphere 
is measured by the pressure exerted by the 
column of mercury which balances it, and 
changes in pressure are indicated by correspond- 
ing changes in the heiglit of the mercury column. 
Two forms of the instrument are in common 



use. 



119. The Cistern Barometer. This 
form applies directly to the original 
Torricellian experiment. The vessel 
or cistern and tube are permanently 
mounted, and an attached scale meas- 
ures the height of the surface of the 
mercury in the tube above the surface 
of the mercury in the cistern. 

A convenient form of this instru- 
ment is shown in Figs. 181, 132. The 
cistern has a flexible leather bottom 
which can be moved up and down by section of 

ri • 1 1 T i. i.1 the cistern. 

a screw (J in order to adjust the 
mercury level. Before taking the reading, the surface of the 
mercury in the cistern is brought to a fixed level indicated by 
the tip of the pointer P, which is the zero of the barometer 
scale. The height of the colunm is then read directly from 
a scale, engraved on the case of the instrument, A vernierf 

* Extract from letter written Tjy Torricelli, in 1644, to M. A. Ricci, in Rome, first published 
in 1063. 

tAn explanation of the vernier is given in the laboratory Manual designed to accompanj 
this book. 




Fio. 131.— The cis- 
tern barometer. 



106 



PRESSURE IN GASES 




is usually employed to determine the reading with ex- 
actness. 

120. The Siphon Barometer. This barometer 
consists of a tube of the proper length closed at 
one end and bent into U -shape at the otiier. 
(Fig. 133.) When filled and placed upright the 
mercury in the longer branch is supported by 
tlie pressure of the air on the surface of the 
mercury in the shorter, A scale is attached 
to each branch. The upper scale gives the 
height of the mercury in the closed branch 
above a fixed point, and the lower scale the 
distance of the mercury in the open branch 
below the same fixed point. The sum of the 
two readings is the height of the barometer 

Fig. 133.— Siphon ° ° 

barometer. columU. 

121. Aneroid Barometer. As its name implies,* this is a 
barometer constructed without liquid. (Fig. 134.) In this form 
the air presses against the flexible corrugated cover of a cir- 
cular, air-tight, metal box A, from which the air is partially 
exhausted. The cover, which is usually supported by a 
spring S, responds to the pressure of the atmosphere, being 
forced in when the pressure is increased, and springing out 
when it is decreased. The 
movement of the cover is 
multiplied and transmit- 
ted to an index hand B by 
a system of delicate levers 
and a chain or by gears. 
Tlie circular scale is gradu- 
ated by comparison with 
a mercury barometer. 

The aneroid is not so accurate as the mercury barometer, 
but, on account of its portability and its sensitiveness, is 

•Greek, a=not, iteros=wet. 




FiQ. 134. — Aneroid barometer. 



PRACTICAL VALUE OF THE BAROMETER 107 

joining into very connnon use. It is specially serviceable for 
determining readings to be used in computing elevations. 

122. Practical Value of the Barometer; Atmospheric 
Pressure. By the barometer we can determine the pressure 
of the atmosphere at any point. For example, to measure the 
pressure per sq. cm. of the air at a point where the mercury 
barometer stands at 76 cm., we have but to find the weight of 
the colunni of mercury balanced by, the atmospheric pressure 
at this point; that is, we have to find the weight of a column 
of mercury 1 sq. cm. iu section and 76 cm. high. The volume 
of the column is 76 c.c, and taking the density of mercury as 
13.6 gram per c.c, this weigiit will be 

76 X 13.6 = 1033.6 grams. 

In general terms, if a is the area pressed, and h the 
height of a barometer, using a liquid whose density is d, 

alt — volume of liquid in barometric column, 

ahd = weight of liquid in barometric colunni, 

= pressure of atmosphere on area a, 

and Jul = pressure of atmosphere on unit area. 

123. Variations in Atmospheric Pressure. By continually 
observing the height of the barometer at any place we learn 
that the atmospheric pressure is constantly changing. Some- 
times a decided change takes place within an hour. 

Again, by comparing the simultaneous readings of barometers 
distributed over a large stretch of country we find that the 
pressure is different at different places. 

124. Construction of the Weather Map. The Meteorological 

Service has stations in all parts of the country at which observers 
regularly record at stated hours of each day the prevailing meteoro- 
logical conditions. Twice each day these simultaneous observations 
are sent by telegraph to the head otlice at Toronto. These I'eports 
include :— The barometer leading, the temperature, the direction and 



108 PRESSURE IN GASES 

velocity of the wind, and the rainfall, if any. The information thus 
received is entered upon a map, such as that shown in Fig. 135. 
Places having equal barometric pressures are joined by lines called 
isobars* the successive lines showing difference of pressure due to yts 
inch of mercury. The circles show the state of the sky and the 
arrows indicate the direction of the wind. 

The Map given shows the conditions existing at 8 p.m., February 
15th, 1910. It will be seen that there were certain areas of low 
and of high pressure enclosed by the isobars. For instance a "low " 
was central over Michigan while a " high " was central over Dakota 
and southern Saskatchewan. In all weather maps there are found 
sets of these areas, but no two maps are ever quite the same. 

On account of the difference in pressure there is a motion of the 
air inwards towards the centre of the "low," and outwards from the 
centre of the "high." But these motions are not directly towards 
or away from the centre. An examination of the arrows on the 
map will show that there is a motion about the centre. In the case 
of the "low" this motion is contrary to the direction of motion of 
the hands of a clock, while in the case of the " high " the motion is 
with the hands of the clock. Through a combination of the motions 
the air moves spirally inwards to the centre of low pressure and 
spirally outwards from the centre of high pressure. The system of 
winds about a centre of low pressure is called a cyclone ; that about 
a centre of high pressure, an anti-cyclone. Tiie disturbance in the 
cyclone is usually much greater than in the anti-cyclone. 

At the centre of low pressure the barometer is low because at that 
place there is an ascending current of air, which rises until it reaches 
a great height, when it flows over into the surrounding regions. In 
the case of the area of high pressure there is a flow of air from the 
upper levels of the surrounding atmosphere into the centre of high 
pressure, thus raising the barometer. 

It will be observed, also, that while the air in an area of low or 
high pressure may 1)0 only three or four miles high, these areas 
are hundreds of miles across. 

Now it has been found that within the tropics, in the trade-wind 
zones, the drift of the atmosphere is towards the west and south, 
and disturbances are infrequent ; but in higher latitudes the general 
drift is eastward, and disturbances are of frequent occurrence, 
especially during the colder months. Thus in Canada and the 



•Greek, isos = equal, haros = weight, 



CONSTRUCTION OF THE WEATHER MAP 



109 



X ¥ ¥ 




i S ' " 




\j^ 


X'-'\^' 


j^-^ZJ^ /mWS/— vSK>v^CY\/^^ 9-'l \ \ \ \ 






^^^K^^^^^^A \ \ U-V 




\ S \ o 


£^^^^^^ — . \--A\^ \ 










s f >-"~- ^^P^^xl^-^^r^ 




\ \ 












\^l--^ J \ 


'A--' ■<::X^^^--..-^^^m 


^^^^S ^""\~^ /S 


■ ''\y^^^^ \ ^ /'^^-55==<C''^ 


^^^r'*^^^^£s\ \ ,— -2^K^ 






KvsV I ^^^""^^^^3^ o 


o ^<^ \ \ ^ — y^'^/Sri^KX >A ^ 




\§vX;!J^>\_^ \ ^'!!^^^^^^^^^!S * 


^ ■•• \ ^A^"/^ / fc^T^^^^— ^ \^ '^ ^ ' ^ 






\ 3,-V- 


is^-*^!^^^^^,^^?^'^ jJsWy 


\ ^-^' \ -o / W J? vȴV' ^\ \ . 


L-^C— VT 


N^ ^^^^^^^^^^ f^^^r 


^;-;^-<; , ^V'"/w4'Sj^^^ ^ ^ 


\v ^^l ^_^,^^^V'^ 




V \ \JJV 


^^""^T^^^^/^ 


^^^^^m^\il S S^Xi I 


lAv4 


"^^^"^P^'" 


JC5— Hnr^^ffl 


^UJM 


5 W \ 


X^"^\ 


""'^Jii ^ '^ ^^^»\ 


^^^ 


-^/^Vh 


a — :Nj— 


^}^ " 


'^^ 


: \i^ 


t* 




>x^ 




[ i__ 


« ^"''^ \ 


■-,..« ^ ^"~~^ 


p:?< 


\ \ /Y 


1 ^ 


\fei=^" 


,,~~'~vf^'''^^if9 ^"^ — 






/-TS^-. 


\ \^ L 






§-_____ 1 „'*=*^.4?=^2i»' n 


h0»7^v 


\ A V 




jS^^^""""*^ 




\ c a 


«> 




,^_.A[;^0^ 


ffh-in 




///fe^ 


/ ^ T' 




^ / 1 / / s 


t / 




E/ )/ /J 


,=—-, -1, 










fT'~~'~'~iU^^/^ A / ^ M 






s 


/^^Ac / /TiHi 








' ■^^r-s^:^ ^-1^.7^7/^(1] 


^^ 


V \/ 


^-i 


1 s 




3 


^=J 


1 1 1 1 1 8 


O ? y S.>^ >^*^ y#^ X3CV \ ^^^sL \ i^ 






c- « rt rt rt ■ 


= U.3^il!8A^<^^^^f / ^ /^"^x 




:^^^S^ 


S o tj « o 


^^^^^Iw^^^^^^^^^^ 1 \ / § 






^ ^ ^ ^ ^ 


'^^^^"^^^^^^^k 


^^pn/ 


s 


c c c fl c 


O © • © @ 






>( . s 






C.2 






jVo<e,— The storm indicated in the area of low pressure, at the centre nf the map, developed during February 
14th over the extreme northwestern States and moved southeast to Nebraska, wliere it was cei]tre<l cm tlie 
nifjht of the 14th. It then moved in a more easterly direction, and at the time of the map w.as centred in the 
State of Michigan, whence it moved eastward along the St. Lawrence Valley. The high to the west of it, 
extended to the Yukon Territory and Mackenzie River Valley. 

Forecast.— Light snowfall with strong east winds during night of 15th, followed on the morning of 16th by 
strong northwest winds, and a change to much colder weather. 



110 PRESSURE IN GASES 

United States the areas of high and low pressure move eastward ; 
the latter, however, travel faster than the former. 

125. Elementary Principles of Forecasting. In using the 

weather map the chief aim is to foresee the movement of the areas 
of high and low pressure, and to predict their positions at some 
future time, say 36 liours hence. It is also essential to Judge rightly 
what changes will occur in the energy of the areas shown on the 
map, as these changes will intensify or otherwise modify the 
atmospheric conditions. 

As the cyclone moves eastward, the first indication of its approach 
will be the shifting of the wind to the eastward. The direction in 
which the wind will veer depends on whether the storm centre 
passes to the northward or the soiithward ; and the strength of the 
wind will depend on the closeness of the isobars. If they are close 
together, the wind will be strong. If the centre passes nearly over 
a place, the wind will chop round to the westward very suddenly ; 
while if the centre is at a considerable distance the change will be 
more gi'adual. 

The precipitation (rain or snow) in connection with a cyclonic 
area is largely dependent on the energy of the disturbance, and on 
the temperatnie and moisture of the air towards which the centre is 
advancing. It must, of course, be remembered that rain cannot fall 
unless there is moisture, and moisture will not be precipitated unless 
the volume of the air containing it is cooled below the dew-point 
(§ 295). This cooling is caused by the expansion of the air as it 
ascends. 

Occasionally we have a rain with a northerly wind succeeding the 
passage of a centre of low pressure. In this case the colder and 
heavier air flows in under the warmer air, lifting it to a height 
sufficient to cause the condensation of its moisture. 

The duration of precipitation, and of winds of any particular 
direction, depends on the rate of movement of the storms and of the 
areas of high pressure. Temperature changes in any given region 
can be arrived at only by an accurate estimation of the distance and 
direction from which the air which passes over has been transferred 
by wind movement. 

Abnormally warm weather results from the incoming of warm 
air from more southern latitudes ; and cold waves do not develop 
in lower middle latitudes (such as Ontario), but are the result 
of the rapid How southward of air which has been cooled in high 
latitudes. 



DETERMINATION OF ELEVATION 



111 



1 



. 5^ 
o 

10 .Sf 

a 

.15 

SO 



126. Determination of Elevation. Since the pressure of 
the air decreases oi-;ulnally with increase in height above 
the sea-level, it is *" 
evident that the 
barometer may be 
utilized to deter- 
mine changes in 
elevation. If the 
density of tlie air t 
were uniform, its ^ i5 
pressure, like that ^ 
of liquids, would « ^^ 
vary directly as 
tlie depth. But 
on account of the 
compressibility of 
air, its density is 
not uniform. The 

lower layers, which Fig. 136.— Atmospheric pressure at different heights. 

sustain the greater weight, are denser than those above them. 
For this reason the law giving tlie relation between the 
barometric pressure and altitude is somewhat complex. For 
small elevations it falls at an approximately uniform rate 
of one inch for every 900 feet of elevation. Fig. 136 shows 
rouglily the conditions of atmospheric pressure at various 
heights. 

127, The Height of the Atmosphere. We have no means 
of determining accurately the lieiglit of the atmosphere. 
Twilight effects indicate a height of about fifty miles ; above 
this the air ceases to reflect light. But it is known that air 
must extend far beyond this limit. Meteors, which consist of 
small masses of matter, made incandescent by the heat 
produced by friction witli tlie atmosphere, have been known 
to become visible at heights of over 100 miles. 



DEEPEST SEA SOUNBIWGS 



112 



PRESSURE IN GASES 



sg* 



128. Compressibility and Expansibility of Air. We have 
already referred to the well-known fact that air is m 
compressible. Experiments might be multiplied 
indefinitely to sliow that the volume of air, 
or of any gas, is decreased by pressure. The 
air within a hollow rubber ball may be 
compressed by the hand. If a tightly- 
fitting piston be inserted into a tube closed 
at one end (Fig. 137) the air may be 
so compressed as to take up but a small 
fraction of the space originally occupied 
by it. 

Again, if mercury is poured into a U-tube 
closed at one end (Fig. 138) it will be found Fia.iss.— 
that the higher the column of the mercury in 
the open branch, that is, the greater the 
pressure due to the weight of the mercury, 

FiQ 137 

Aircom- the Icss the volume of the air shut up in 

pressed 

within a the closcd branch becomes. 

cl osed 

p"essu^re ^^^ ^^^^ othcr hand gases manifest, under all 
to^'pTs'- conditions, a tendency to expand, 
ton- Whenever the pressure to which a 
given mass of air is subjected is lessened, its 
volume increases. The com- 
pressed rubber ball takes 
its original volume and 
shape when the hand is 
withdrawn, and when the 
applied force is removed fig 
the piston shoots outwards. 
If a toy balloon, partially 
Fio. 139.— Expansion of filled with air, is placed under the receiver 

air when pressure is „ . . -, ^^rw i i • • 

removed. ot an air-jDump (r ig 139) and the air is ex- 

hausted from the receiver, the balloon swells out and if its 



pressed 
within a 
closed 
tube by 
w e i g' h t 
of mer- 
cury in 
tlie long 
branch. 





140. — Water forced 
out of the closed bol tie 
by the expansion ot the 
air above it. 



RELATION BETWEEN VOLUME AND PRESSURE OF AIR II3 

walls are not strong it bursts. When a bottle partly filled 
with water, closed with a perforated cork, and connected 
by a bent tube with an uncorked bottle, as shown in Fig-. 
140, is placed under the receiver of the air-pump, and 
the air exhausted from the receiver, the water is forced 
into the open bottle by the pressure of the air shut up 
within the corked bottle. This tendency of the air to 
expand explains why frail hollow vessels are not crushed 
by the pressure of the air on their outer walls. The pres- 
sure of the air within counterbalances the pressure of the 
air without. 




Fig. 141. 



Fig. 142. 




QUESTIONS AND PROBLEMS 

1. Arrange apparatus as shown 
in Fig. 141. By suction remove 
a portion of tlie air from the 
flask, and keeping the rubber 
tube closed by pressure, place 
the open end in a dish of water. 
Now open tlie tube. Explain 
the action of the water. 

2. Guericke took a pair of hemi- 
spherical cups (Fig. 142) about 
1.2 ft. in diameter, so constructed that tliey formed a hol- 
low air-tight sphere when their lips were placed in contact, ^"'- l*^- 
and at a test at Regensburg before the Emperor Ferdinand III and the 
Reichstag in 1654 showed that it required sixteen horses (four pairs on 
each hemisphere), to pull the hemispheres apart when the air was 
exhausted by his air-pump. Account for this. 

3. If an air-tight piston is inserted into a cylindrical vessel and the 
air exhausted through the tube (Fig. 143) a heavy weight may be lifted 
as the piston rises. Explain this action. 

129. The Relation between the Volume and the Pressure 
of Air — Boyle's Law. The exact relation between the ^'olume 
of a given mass of gas and the pressure upon it was first 



114 



PRESSURE IN GASES 



determined by Robert Boyle (1627-1691), born at Lismore 
Castle, Ireland, who devoted a great deal of attention to 
«» the study of the mechanics of the air. In 

endeavouring to show that the phenomenon of 
the Torricellian experiment is explained by " the 
spring of the air," he hit upon a method of in- 
vestigation which confirmed the hypothesis he 
had made, that the volume of a given quantity 
of air varies in- 
versely as the pres- 
sure to which it 
is subjected. He 
took a U-tube of 
the form shown in 
Fig. 144, and by 
pouring in enough ( , 
mercury to fill the 
bent portion, in- 
closed a definite 
portion of air in 
the closed shorter 
arm. By manipu- 
lating the tube he 
adjusted the mercury so as to stand at the same height in 
each arm. Under these conditions the imprisoned air was at 
the pressure of the outside atmosphere, which at the time of 
the experiment would support a column of mercury about 29 
inches high. He then poured mercury into the open arm 
until the air in the closed arm was compressed into 
one-half its volume. "We observed," he says, "not without 
delight and satisfaction, that the quicksilver in that longer 
part of the tube was 29 inches higher than the other." 
This difierence in level gave the excess of pressure of the 
inclosed air over that of the outside atmosphere. It was 




Fig. 144.— Boole's 
apparatus. 



ROBKRT BOTIK (1C27-1691). PublUlied liis 
Law in 1662. One of the earliest of En^'lish 
scientists basing their investigations upon 
experiment. 



RELATION BETWEEN VOLUME AND PRESSURE OF AIR 115 

clear to him, therefore, that the pressure sustained by the 
inclosed air was doubled when the volume was reduced to one- 
half. Continuing his experiment, he showed, on using a great 
variety of volumes and their corresponding pressures, that 
the product of the pressure by the volume was appi'oximately 
a constant quantity. His conclusion may be stated in general 
terms thus : — 

Let Vi, Vo, F3, etc., represent the volumes of the inclosed air, 

and Pj, P2, P3, etc., represent corresponding pressures ; 

Then Fj P^ = V^ P^ = V^ P.^ = K, a constant quantity. 

That is, 

If the temperature is kept constant, the volume of a given 
mass of air varies inversely as the pressure to which it is 
subjected. This relation is generally known as Boyle's Law. 
Li France it is called Mariotte's Law, because it was inde- 
pendently discovered by a Fi-ench physicist named Mariotte 
(1G20-1684), fourteen years after Boyle's publication of it in 
England. 

PROBLEMS 

1. A tank whose capacity is 2 cu. ft. has gas forced into it until the 
pressure is 250 pounds to tlie sq. inch. What volume would the gas 
occupy at a pressure of 75 pounds to the sq. inch 1 

2. A gas-holder contains 22.4 litres of gas when the barometer stands 
at 760 mm. What will be the volume of the gas when the barometer 
stands at 745 mm. ? 

3. A cylinder whose internal dimensions are : length 3G in., diameter 
14 in., is filled with gas at a pressure of ^00 pounds to the sq. inch. 
What volume would the gas occupy if allowed to escape into the air when 
the barometer stands at 30 in.? (For density of mercury see page 14.) 

4. Twenty-five cu. ft. of gas, measured at a pressure of 29 in. of 
mercury, is compressed into a vessel whose capacity is Ig cu. ft. What 
is the pressure of the gas ? 



llg PRESSURE IN GASES 

5. A mass of air whose volume is 150 c.c. when the barometer stands 
at 750 mm. has a volume of 200 c.c. when carried up to a certain height 
in a balloon. What was the reading of the barometer at that height ? 

6. A piston is inserted into a cylindrical vessel 12 in. long, and forced 
down within 2 in. of the bottom. What is the pressure of the inclosed 
air if the barometer stands at 29 in. ? 

7. Tlie density of the air in a gas-bag is 0.001293 grams per c.c. when 
the barometer stands at 760 mm. ; find its density when the barometric 
height is 740 mm.? 

8. An open vessel contains 100 grams of air when the barometer stands 
at 745 mm. What mass of air does it contain when the barometer stands 
at 755 mm.? 

9. Oxygen gas, used for the ' lime-light,' is stored in steel tanks. The 
volume of a tank is 6 cii. ft., and the pressure of the gas at first was 15 
atmospheres. After some had been used the pressure was 5 atmospheres. 
If the gas is sold at 6 cents a cu. ft., measured at atmospheric pressure, 
what should be charged for the amount consumed ? 

130. Buoyancy of Gases. If we consider the cause of 
buoyancy we must recognize that Archimedes' principle applies 
to gases as well as to liquids. If a hollow metal or glass globe 
A (Fig. 14-5), suspended from one end of a short balance beam 
and counterpoised by a small weight B at the other end, is placed 
under the receiver of an air-pump and the air 
exhausted from the receiver, the globe is seen 
to sink. It is evident, tlierefore, that it was 
supported to a certain extent by the buoyancy 
of the air. 




A gas, like a liquid, exerts on any body 

immersed in it, a buoj^ant force which is equal 

to the w^eight of the gas displaced by the 

Fig. i45.-Buoyancy body. If a body is lighter than the weiglit 

°' "•"'■ of the air equal in volume to itself, it will rise 

in the air, just as a cork, let free at the bottom of a pail of 

water, rises to the surface. 



BALLOONS 



117 



131. Balloons. The use of air-ships or balloons is made 
possible by the buoyancy of the air. A balloon is a large, 
light, gas-tight bag filled with some gas lighter than air, 
usually hydrogen or illuminating gas. Fig. 146 shows the 
construction of an air-ship devised by Count Zeppelin in 
Germany. By means of propellers it can be driven in any 
desired direction. 

A balloon will continue to rise so lonor as its weijrht is less 
than the weight of the air which it displaces, and when there 




FiO. 146. ^Zeppelin's air-ship, over 400 ft. long and able to carry 30 passengers. 



is a balance between the two forces it simply floats at a 
constant height. The aeronaut maintains his position by 
adjusting the weight of the balloon to the buoyancy of the air. 
When he desires to ascend he throws out ballast. To descend 
he allows gas to escape and thus decreases the buoyancy. 



118 PRESSURE IN GASES 



QUESTIONS AND PROBLEMS 

1. Why should the gas-bag be subject to an increased strain from the 
pressure of the gas within as the balloon ascends ? 

2. Aeronauts report that balloons have greater buoyancy during the 
day when the sun is shining upon them than at night when it is cold. 
Account for this fact. 

3. If the volume of a balloon remains constant, where should its 
buoyancy be the greater, near the earth's surface or in the upper strata 
of the air ? Give reasons for your answer. 

4. The volume of a balloon is 2500 cu. m. and the weight of the gas- 
bag and car is 100 kg. ; find its lifting power when filled with hydrogen 
gas, the density of which is 0.0000895 grams per c.c. while that of air is 
0.001293 grams per c.c. 




Fig. 147.— Common form of air-pump. AB, cylin- 
drical barrel of pump ; R, receiver from which air 
is to be exhausted ; C, pipe connecting,' l)arrel with 
receiver ; P, piston of pumi) ; K, and V„, valves 
opening upwards. 



CHAPTER XIV 

Applications of the Laws of Gases 

132. Air-Pump. Fig. 147 shows the construction of one of 
the most coininon forms of pumps used for exhausting air 
from a vessel. When the r-p || jlll 

piston P is raised, the 
valve Vi is closed by its 
own weiglit andtlie pres- 
sure' of the air above it. 
The expansive force of 
the air in the receiver lifts 
the valve V^ and a portion 
of the air flows into the 
lower part of the barrel. 
When the piston descends, the valve V^ is closed and the 
air in the barrel passes up througli the valve Fj. Tlius at 
each double stroke, a fraction of the air is removed from the 
receiver. The process of exhaustion will cease when the 
expansive force of the air in the receiver is no longer sufficient 
to lift the valve V.,, or when the pressure of the air below 
the piston fails to lift tlie valve V^. It is evident, therefore, 
that a partial vacuum only can be obtained with a pump 
of tliis kind. To secure more complete exhaustion, pumps 
in which the valves are opened and closed automatically by 
the motion of the piston are frequently used, but even with 
these all the air cannot be removed from the receiver. 
Theoretically, a perfect vacuum cannot be obtained in this 
way, because at each stroke the air in the receiver is reduced 

only by a fraction of itself, x 

119 



120 



APPLICATIONS OF THE LAWS OF GASES 




Fig. 148.— An oil air-pump with two 
cylinders. 



133. The Geryk or Oil Air-Pump. This is a very efficient 
pump recentl}^ invented but widely used. (Figs. 148, 149.) Its 

action is as follows. The piston 
J, made air-tight by the leather 
washer G and by being covered 
with oil, moves up-and-down in 
the barrel. The tube A, opening 
into the chamber B surrounding 
the barrel, is connected to the 
vessel from which the air is to be 
removed. On rising the piston 
pushes before it the air in the 
barrel, and on reaching the top it 
pushes up O about \ inch, thus 
allowing the imprisoned air to 
escape through the oil into the 
upper part of the cylinder, from which it passes out by the 
tube D. 

When the piston descends the spring K, 
acting upon the packing /, closes the upper 
part of the cylinder, and the piston on reaching 
the bottom drives whatever oil or air is beneath 
out through the tube F, or allows it to go up 
through the valve E, into the space above the 
piston. 

Oil is introduced into the cylinder at L. 
When the pump has two cylinders they are 
connected as shown in Fig. 149. With one 
cylinder the pressure of the air can be reduced 
to \ mm. of mercury, while with two a reduc- 
tion to -^^-fj mm. can be quickly obtained. These 
pumps are used for exhausting electric light p,g ^^^ _ vertical 
bulbs and in some cases for X-ray tubes. oran°oii'Lir-pump.^'^ 




MERCURY AIK-PUMP-BUXSEN JET PUMP 



121 




134. Mercury Air-Pump. When the highest possible 
vacuum is required, use is made of some 
form of the mercury air-pump devised by 
Sprengel. The principle of its action may 
be understood by reference to Fig. 150. 
As the mercury which is poured into tlie 
reservoir A falls in a broken stream 
through the nozzle N into the tube B, it 
carries air with it because each pellet of 
mercury acts as an air-tight piston and 
bears a small portion of air before it. 
The density of the air in G and R is 
thus gradually decreased. The mercury 
which overflows into D is poured back 
into A. A vacuum as high as 0.000,007 
mm", has been obtained with a mercury 
pump. It requires a good pump of the 
valved type to give an exhaustion of 1 mm. 

135. Bunsen Jet Pump. Bunsen devised a simple and con- 
venient form of pump, which is much used in 
laboratories where a moderate exhaustion 
is required, as for hastening the process of 
filtration. In this pump (Fig. 151) water 
under a pressure of more than one atmos- 
phere is forced into a jet through a tube 
nozzle N. The air is carried along by the 
water and is thus withdrawn from any 
vessel connected with the offset tube A. 

136. The Hydraulic Air-Compressor. An 
application of the principle involved in the 
instruments just described is to be seen in 
the great air-compressor at Ragged Chutes, 
on the Montreal River, eight miles south-west from Cobalt, 
the centre of the great mining region in northern Ontario. 



Fio. 15C. — Sprengel air- 
pump. A, reservoir into 
which mercury is poured. 
JS, {jlass tube of small 
bore, about one metre 
lon^ ; B, vessel from 
which air is to be drawn. 




Fig. 151.— Bunsen jet 
pump. 



122 



APPLICATIONS OF THE LAWS OF GASES 



A cement dam 660 feet long across the river raises the level 
of the water. By a large tube A (Fig. 152) the water is led 
into two vertical pipes P (only one 
shown in the figure), 16 feet in dia- 
meter, into each of which is fitted a 
framework holding 66 intake pipes 
a, a, 14 inches in diameter. The 
water-line is about 10 or 12 inches 
above the top of the nest of intake 
pipes. In descending the water forms 




c 



^}i^ ^fyam/mmm'^/m^^^ 



^rf 



i'l 



i 



Fig. 152.— Taylor air-compressor at Ragged Chutes on Montreal River (section). 

a vortex in the mouth of each pipe through which air is 
drawn down into the shaft below. Thus air and water are 
mixed together. At 6 the pipe is reduced to 9 feet and near 
the bottom, at c, is enlarged to Hi feet in diameter. 

The water drops 350 feet, falling on a steel-covered cone B, 
from wliich it ru.shes into a horizontal tunnel over 1000 feet 
long, the farther end d of which is 42 feet high. In this large 
channel the water loses much of its speed and the air is 
rapidly set free, collecting in the upper part of tlie tunnel. 
At e the tunnel narrows and tlie water races past and enters 
the tail-sliaft T, 300 feet high, from which it flows into the 
river again. 

The air entrapped in the tunnel is under a pressure due to 
about 300 feet of water, or about 125 pounds per square inch. 
From d a 24-inch steel pipe leads to tlie surface of the earth 
and from here the compressed air is piped off to the mines. 

Other air-compressors on the same principle are to be 
found at Magog, Quebec; at Ainsworth, B.C.; at the lift-lock 
at Peterborough (see § 97); and at the Victoria Mines in 
Michigan ; but the one near Cobalt is the largest in existence. 



AIR CONDENSER— USES OF COMPRESSED AIR 



123 




Fia. iri,"?.— Air-compres8or. P, piston ; R, tank or 
receiver ; Vi inlet valve ; V.,, outlet valve. 



137. Air Condenser. It is obvious that the air-pump 
could be used as an air-compressor or condenser if the 
valves were made to 
open inwards instead 
of outwards; but a 
pump with a solid 
piston is commonly 
employed for this 
purpose. Fig. 153 
shows the arrange- 
ment of the valves. When the piston is raised, tlie inlet valve 
Fj opens and the barrel is filled with air from the outside, and 
when the piston is pushed down the inlet valve is closed and 
the air is forced into the tank through the outlet valve V^, 
which closes on the up-stroke and thus retains the air within 
the tank. Hence at each double stroke a barrelful of air is 
forced into the tank. For rapid compression a double-action 
pump of the form shown in Fig. 159 is used. 

Exercise. — Obtain a small bicycle pump, take it apart, and study its 
construction and action. 

138. Uses of Compressed Air. The air-brakes and diving 
apparatus are described in the next two sections. Another 
useful application is the pneumatic drill, used chiefly for boring 
holes in rock for blasting. In it the steel drill is attached to a 
piston which is made to move back and forth in a cylinder by 
allowing compressed air to act alternately on its two faces. 
The pneumatic hammer, which is similar in principle, is used 
for riveting and in general foundry work. Steam could be 
used, but the pipes conveying it would be hot and water would 
be formed from it. By means of a blast of sand, projected by 
a jet of air, castings and also discoloured stone and brick walls 
are cleaned. Figures on glass are engraved in the same way. 
Tubes for transmitting letters or telegrams, or for carrying 
cash in our large retail stores, are operated by compressed air. 
Many other applications cannot be mentioned here. 



124 



APPLICATIONS OF THE LAWS OF GASES 



139. Air- Brakes. Compressed air is used to set the brakes 
on railway cars. Fig. 154 shows the principal working parts 
of the Westinghouse air-brakes in common use in this country. 
A steam-driven air-compressor pump A and a tank B for com- 
pressed air are attached to the locomotive. The equipment on 
each car consists of (a) a cylinder C in which works a piston P 
directly connected, by a piston-rod D and a system of levers, 




Fig. 154. — Air brakes in use on railway trains. 

with the brake-shoe, (6) a secondary tank E, and (c) a system 
of connecting pipes and a special valve F which automatically 
connects B with E when the air from B is admitted to the 
pipes, but which connects E with the cylinder C when the 
pressure of the air is removed. 

When the train is running, pressure is maintained in the 
pipes, and the brakes are free, but when the pressure is 
decreased either by the engineer or the accidental breaking of 
a connection, the inrush of air from E to C forces the piston P 
forward and the brakes are set. To take off the brakes, the 
air is again turned into the pipes when B is connected with 
E and the air in C is allowed to escape, while the piston P is 
forced into its original position by a spring. 

140. Diving Bells and Diving Suits. Compressed air is 
also used as a reserve supply for individuals cut off from 
the atmosphere, as in the case of men engaged in submarine 



DIVING BELLS AND DIVING SUITS 



125 



work. The diving 
bells and pneumatic 
caissons used in 
laying the founda- 
tions of bridges, 
piers, etc., are sim- 
ply vessels of var- 
ious shapes and 
sizes, open at the 
bottom, from which 
the water is kept 
out and workmen 
within supplied 
with air by com- 
pressed air forced 
in through pipes 
from above. (Fig. 
155.) The air tills 
the tank complete- 
ly, thus excluding 
the water, and es- 
capes at the lower 
edges. 




Fig. 155.— Section of a Pneumatic Caisson. The sides of the 
caisson are e.xtended upward and are stroni;!}' braced to keep 
baclithe water. Masonry or concrete, C, D, placed on top of 
the caisson, press it down upon the bottom, while compressed 
air, forced through a pipe P, drives the water out of the 
working chamber. To leave the caisson the workman climbs 
up and passes through the open door B into the airlock L. 
The door B is then closed and the air is allowed to escape 
from L until it is at atmospheric pressure. Then door A 
is opened. In order to enter, this process is reversed. 
Material is hoisted out in the same way or is sucked out 
by a mud pump. As the earth is removed the caisson sinks 
until the rock is reached. The entire caisson is then filled 
with solid concrete, and a permanent foundation for a dock 
or bridge is thus obtained. 



The modern diver is incased in an air-tight weighted suit. 
(Fig. 156.) He is supplied with air from above 
through pipes or from a compressed-air reservoir 
attached to his suit. The air escapes through a 
valve into the water. Manifestly the pressure of 
the air used by a diver or a workman in a caisson 
must balance the pressure of the outside air, and 
the pressure of the water at his depth. The 
deeper he descends, therefore, the greater the 
pressure to which he is subjected. The ordinary 
limit of safety is about 80 feet ; but divers have 
worked at depths of over 200 feet. 




Fio. 156. — Diver'a 
suit. 



126 



APPLICATIONS OF THE LAWS OF GASES 



141. Water Pumps. From very early times pumps were 
employed for raising water from reservoirs, or for forcing it 
through tubes. It is certain that the suction pump was in 
use in the time of Aristotle (born 384 B.C.). The force- 
pump was probably the invention of Ctesibius, a mechanician 
who flourished in Alexandria in the second century B.C. 
To Ctesibius is also attributed the ancient fire-engine, 
whicli consisted of two connected force-pumps, spraying 
alternately. 

142. Suction or Lift-Pump. The construction of the com- 
mon suction-pump is shown in Fig. 157. During the first 

strokes the suction-pump acts as an 
air-pump, withdrawing the air from 
the suction pipe BG. As the air 
below the piston is removed its 
pressure is lessened, and the pressure 
of the air on the surface of the 
water outside forces the water ujd tlie 
suction pipe, and through the valve 
V^ into the barrel. On the down- 
stroke the water held in the barrel 
by the valve F^ passes up through 
the valve V^, and on the next up- 
stroke it is lifted up and discharged 
tlirough the spout G, while more 
water is forced up through the valve 
Fj into the barrel by the external 
pressure of the atmosphere. It is 
evident that the maximum lieight 
to which water, under perfect con- 
ditions, is raised by the pressure of tlie atmosphere cannot be 
greater than the height of the water column which the air 
will support. Taking the relative density of mercury as 13.6 
and the height of the mercury barometer as 30 inches, this 




Fio. 157. — Suction-pump. AB, cvlin- 
drioal barrel ; BC, suction-pipe ; P, 
piston ; V^ and (',, valves opening 
upwards ; R, reservoir from which 
water is to be lifted. 



FORCE-PUMP 



127 



height would be {^ X 13.6 = .34 feet. But an ordinary 
suction-pump will not work satisfactorily for heights above 
25 feet. 

143. Force-Pump. When it is necessary to raise water to a 
considerable heioht, or to drive it with force throufj^h a nozzle, 
as for extinguishing fire, a force-pump is used. Fig. 158 
shows the most common form 
of its construction. On the up- 
stroke a partial vacuum is formed 
in the barrel, and the air in the 
suction tube expands and passes 
up through the valve Vy As 
the plunger is pushed down the 
air is foi'ced out through the 
valve Fg. The pump, therefore, 
during the first strokes acts as 
an air-pump. As in the suction- 
pump, the water is forced up into 
the suction pipe by the pressure 
of the air on the surface of the 
water in the reservoir. When it 
enters tlie barrel it is forced by 
the plunger at each down-stroke 
through the valve V^ into the 
discharge pipe. The flow will 
obviously be intermittent, as the 
outflow takes place only as the plunger is descending. To 
produce a continuous, stream, and to lessen the shock on the 
pipe, an air chamber, F is often inserted in the discharge pipe. 
When the water enters this chamber it rises above the outlet 
G which is somewhat smaller than the inlet, and compresses 
the air in the chamber. As the plunger is ascending the 
pressure of the inclosed air forces the water out of the 
chamber in a continuous stream. 




158 —Force-pump. AB, cylindrical 
barrel ; BC, suction-pipe ; P, piston ; F, 
air chamber ; V, , valve in suction-pipe ; 
Tj, valve in outlet pipe; G, disnharg:e 
pipe ; R, reservoir from which water is 
taken. 



128 



APPLICATIONS OF THE LAWS OF GASES 



144. Double Action Force-Pump. In Fig. 159 is shown 
the construction of tlie double-action force-pump. When the 

piston is moved forward in the 
direction of the arrow, water is 
drawn into the back of the cylin- 
der through the valve Fj, while 
the water in front of the piston 
is forced out through the valve V^. 
On the backward stroke water is 
drawn in through the valve Fg 
and is forced out through the 
valve V^. Pumps of this type are 
used as fire engines, or for any 
purposes for which a large con- 
tinuous stream of water is required. They are usually 
worked by steam or other motive power. 




Fig. 159. — Double-action force-pump 
P, piston ; V,, V^, inlet valves ; F3 
F,, outlet valves." 



QUESTIONS AND PROBLEMS 

1. The capacity of tlie receiver of an air-pump is twice that of the 
barrel ; what fractional part of the original air will Ite left in the receiver 
after («) the first stroke, (h) the third stroke ? 

2. The capacity of the barrel of an air-pump is one-fourth 
that of the receiver ; compare tlie density of the air in the 
receiver after tlie first stroke with the density at first. 

3. The capacity of the receiver of an air-compressor is ten 
times that of the barrel ; compare the density of the air in 
the receiver after the fifth stroke with its density at first. 

4. How high can alcohol be raised by a lift-pump 
when the mercury barometer stands at 760 mm. if the 
relative densities of alcohol and mercury are 0.8 and 13.6 
respectively I 

5. Connect a glass model pump with a flask, as shown in 
Fig. 160. Fill the flask (a) full, (b) partially full of water, 
and endeavour to pump the water. Account for tlie result 
in each case. 




Fig. 160. 



SIPHON-THE ASPIRATING SIPHON 



129 




145. Siphon. If a bent tube is filled with water, placed 
in a vessel of water and the ends unstopped, the water will 
flow freely from the tube, so long as 
there is a difference in level in the water 
in the two vessels. A bent tube of this 
kind used to transfer a liquid from one 
vessel to another at a lower level is 
called a siphon. 

To understand ihe cause of the flow 
consider Fig. 161. 

The pressure at A tending to move ^lo. lei.-The siphon, 
the water in the siphon in the direction AG 

= the atmospheric pressure — the pressure due to the 
weight of the water in AC ; 
and the pressure at B tending to move the water in the siphon 
in the direction BD 

= the atmospheric pressure — the pressure due to the 

weight of the water in BD. 

But since the atmospheric pressure is the same in both cases, 

and the pressure due to the weight of the water in ^C is less 

than that due to the weight of the water in BD, 

the force tending to move the water in the 

direction AG is greater than the force tending 

to move it in the direction BD ; consequently 

a flow takes place in the direction AGDB. 

This will continue until the vessel from which 

the water flows is empty, or until the water 

comes to the same level in each vessel. 




146. The Aspirating Siphon. When the 
liquid to be transferred is dangerous to 
handle, as in the case of some acids, an 
aspirating siphon is used. This consists of 
an ordinary siphon to which is attached an offset tube and 



Fio. 1G2.— The aspira 
ting siphon. 



130 



APPLICATIONS OF THE LAWS OF GASES 



stopcock, as shown in Fig. 162, to facilitate the process of 
filling. The end B is closed by the stopcock and the liquid 
is drawn into the siphon by suction at the mouth-piece A. 
The stopcock is then opened and the flow begins. 





Fio. 1G3. 



Fio. 164. — An intermittent spring. 



QUESTIONS AND PROBLEMS 

1. Upon what does the limit of tlie height to wliich a liquid can be 
raised in a siphon 
depend ? 

2. Over what 
height can (o) 
mercury, (6) 
water, be made 
to flow in a 
siphon ? 

3. How high 
can sulphuric acid 
be raised in a 

siphon when the mercury barometer stands at 29 in., 
taking the specific gravities of sulphuric acid and 
mercury as 1.8 and 13.6 respectively ? 

4. Upon what does the rapidity of flow in tlie 
siphon depend ] 

5. Arrange apparatus as shown in Fig. 1G3. Let 
water from a tap run slowly into the bottle. What 
takes place ? Explain. 

6. Natural reservoirs are sometimes found in the 
earth, from which the water can run by natural 
siphons faster than it flows into them from above 
(Fig. 1(34). Explain why the discharge through the 
siphon is intermittent. 

7. Arrange apparatus as shown in Fig. 165, Fill 
the flask A partly full of water, insert the cork, and 

then invert, placing the short tube in water. Explain the cause of the 
phenomenon observed. 




Fig. 165. 



PART IV— SOME PROPERTIES OF MATTER 



CHAPTER XV 
The Molecular Theory of Matter 

147. Why we make Hypotheses. In order to account for 
tlie observed behaviour of bodies the human mind finds 
satisfaction in making hypotheses as to the manner in which 
material bodies are built up. In this way we attempt to 
" explain " and to trace a connection between various natural 
plienomena. But it must be remembered that our hypotheses 
are only methods of picturing to ourselves what we know of 
the behaviour of substances. Of the real nature of matter we 
still remain in complete ignorance. 

We are all familiar with matter in its three ordinary forms 
— solid, liquid, gaseous — and a multitude of observations have 
led to the universal belief that it is composed of minute 
separate particles. These particles are called miolecules. The 
molecules of some elements and of compound substances can 
be still further divided into atoms, but in this way the 
nature of the substance is altered, — in other words this is 
not a physical subdivision but a chemical change. Thus, 
the oxygen molecule has two atoms, and the water molecule 
consists of two atoms of hydrogen and one of oxygen. 

148. Evidence suggesting Molecules. Water will soak 
into wood, or into beans, peas or other such seeds. On 
mixing 50 c.c. of water with 50 c.c. of alcohol the resulting 

131 



132 THE MOLECULAR THEORY OF MATTER 

volume is not 100 c.c, but only about 97 c.c. When copper 
and tin are mixed in the ratio of 2 of copper to 1 of tin, 
which gives an alloy used for making mirrors of reflecting 
telescopes, there is a shrinkage in volume of 7 or 8 per 
cent. 

Again, various gases may be inclosed in the same space, 
and gases may be contained in liquids. Fish live by the 
oxygen which is dissolved in the water. 

A simple explanation of these phenomena is that all bodies 
are made up of molecules with spaces between, into which 
the molecules of other bodies may enter. As we shall see, 
the molecules and the spaces between are much too small 
to be observed with our most powerful microscopes. The 
magnifying power would have to be increased several 
thousand times, but even though this requisite magnification 
were obtained it is probable that the molecules could not then 
be seen, since there are good grounds for believing that they 
are constantly moN-ing so rapidly that the eye could not follow 
them. 

That there are pores or channels between the molecules was 
neatly proved by Bacon,* who filled a leaden shell with 
water, closed it, and then hammered it, hoping to compress 
the water within. But the water came through, appearing 
on the outside like perspiration. Afterwards the scientists of 
Florence tried the experiment with a silver shell, and also 
with the same shell thickly gilded over, but in both cases the 
water escaped in the same way. Many other illustrations of 
porosity could be given.f 

*Franci3 Bacon, 1561-1626. 

fSee Tail's " Properties of Matter," §§ 98-100. 



DIFFUSION OF GASES 



133 




149. Diffusion of Gases. Tlxe intermingling of molecules 
is best illustrated in the behaviour of gases. In order to 
investigate this question the French 
chemist, Berthollet, used apparatus like 
that illustrated in Fig. 166. It con- 
sisted of two glass globes provided 
with stopcocks, which could be securely- 
screwed together. The upper one was 
filled with hydrogen and tlie lower with 
carbonic acid gas which is 22 times as 
dense. They were then screwed together, 
placed in the cellar of the Paris Observa- 
tory and the stopcocks opened. After 
some time the contents of the two globes 
were tested and found to be identical,^ 
the gases had become viniforudy mixed. 
When the passage coiniecting the two 
vessels is small, hours may be required for 
perfect mixing; but when it is large a few minutes will suffice. 
A simpler experiment on diffusion is the following. Fill 
one wide-mouthed jar wnth hydrogen and a similar one with 
oxygen, which is 16 times as heavy, covering the vessels 
with glass plates. Then put them together as 
shown in Fig. 167 and withdraw the glass 
plates. After allowing them to stand for some 
minutes separate them and apply a match. 
At once there will be a similar explosion from 
each, showing that the two gases 
have become thoroughly mixed.* 

It is through diffusion that the 
proportions of nitrogen and oxygen 
in the earth's atmosphere are the 
same at all elevations. Thouirh 



Fio. 166.— Two glass globes, 
one filled with hydrogen, 
the other with carbonic 
acid p:as. The two gases 
mix until the contents of 
the two globes are identi- 
cal. 




Fio. 167. — Hydrogen in one vessel 
quickly mixes with oxygen in 
the other. 



oxygen is 
there is no excess of it at low levels. 



the heavier constituent 



*In performing this experiment wrap a cloth about each jar for safety. 



134 THE MOLECULAR THEORY OF MATTER 

150. Diffusion of Liquids and Solids. Liquids diffuse into 
each other, though not nearly so rapidly as do gases. 

If coloured alcohol (density 0.8) is carefully poured on the 

top of clear water in a tumbler (or if water be introduced 

under the alcohol), the mixing of the 

^ rrnram,^ two wiU be secu to commence at once 

and will proceed quite rapidly. 

Let a wide-mouthed bottle a (Fig. 168) 
be filled with a solution of copper sul- 
phate and then placed in a larger vessel 
Fig. 16S. -Copper sulphate Containing clear water. The solution is 
fn'a^vessd o^'watlr.^'!:! denser than the water but in time the 
Seads'^lii^through'^the colour will be distributed uniformly 
throughout the liquid. 
Diffusion takes place also in some metals, though very 
slowly at ordinary temperatures. Roberts-Austen found that 
the diffusion of gold through lead, tin and bismuth at 550° C. 
was very marked ; and that even at ordinary temperatures 
there was an appreciable diffusion of gold through solid lead. 
In his experiments discs of the different metals were kept in 
close contact for several weeks. 

151. Motions of the Molecules ; the Kinetic Theory. An 
explanation of such results as these is the hj^pothesis that all 
bodies are made up of molecules which have considerable 
freedom of motion, especially so in the case of gases. 

The laws followed by gases, which are much simpler than 
those of solids and liquids, are satisfactorily accounted for by 
these molecular motions. 

The distinguishing feature of a gas is its power of indefinite 
expansibility. No matter what the size of the vessel is into 
which a certain mass of gas is put, it will at once spread out 
and occupy the entire space. The particles of a gas are 
practically independent of their neighbours, moving freely 
about in the enclosure containing the gas. 




EXPLANATION OF BOYLE'S LAW 135 

A gas exerts pressure against the walls of the vessel con- 
taining it. This can be well illustrated as follows. Place a 
toy balloon or a half-inflated football 
rubber under the receiver of an air-puinp 
and work the pump. (Fig. 169.) As the 
air about the bag is continually removed 
the bag expands ; and when the air is 
admitted again into the receiver the bag 
resumes its original volume. 

We may consider the bag as the seat 

of two contending factions, the troops ^'remove7flom"lhe1-eceher 

of molecules within endeavouring to keep '^' '°^' ^""°°" ''""''"^'• 
back the invading hosts of molecules without. Incessantly 
they rush back and forth, continually striking against the 
surface of the bag. As the enemies are withdrawn by the 
action of the pump, the defenders within gain the advantage 
and, pushing forward, enlarge their boundary, which at last 
however becomes so great that it is again held in check by 
the outsiders. 

Or, we may comj^are the motion of the molecules of a gas 
to the motions of a number of bees in a closed vessel. They 
continually rush from side to side, frequently colliding with 
each other. The never-ceasino; striking of the molecules of 
the gas against a body gives rise to the pi'essure exerted by 
the gas. This view of a gas is known as the Kinetic Theory. 

152. Explanation of Boyle's Law. According to Boyle's 
Law (§ 129), when a gas is compressed to half its volume the 
pressure which it exerts against the walls of the vessel con- 
taining it is doubled. This is just what we would expect. 
When the gas is made to occupy a space half as large, the 
particles in that space will be twice as numerous, the blows 
against its sides will be twice as numerous as before, and con- 
sequently the pressure will be doubled. 



136 THE MOLECULAR THEORY OF MATTER 

153. Effect of a Rise in Temperature. If we j^lace the 
rubber hug used in § 151 in an oven it expands, showing that 
the pressure of the gas is increased by tlie appHcation of heat. 
Evidently when a gas is heatsd its molecules are made to 
move with greater speed, and this produces a greater pressure 
and causes the gas to expand. 

154. Molecular Velocities. On account of numerous col- 
lisions the molecules will not all have the same velocity, but 
knowing the pressure which a gas exerts and also its density, 
it is possible to calculate the mean velocity of the molecules. 
In the following table the mean velocity,* at atmospheric 
pressure and freezing temperature, is given for some gases. 

Table of Molecular Velocities 



Hydrogen 


1843 m. or 604G ft. 


per 


second. 


Nitrogen 


493 m. or 1618 ft. 




t( 


Oxygen 


462 m. or 1517 ft. 




(( 


Carbon Dioxide 


393 m. or 1291 ft. 




( 1 



It will be seen that the hydrogen molecules move fastest of 
all, being about four times as rapid as the molecules of 
nitrogen and oxygen, the chief constituents of the atmosphere. 
This is because it is much lighter. Each gas, by means of the 
bombardment of its molecules, is able to produce a pressure as 
great as that of any other gas, and hence as hydrogen is much 
lighter its molecular velocity must be much higher. The 
velocity is inversely proportional to the square root of the 
density of the gas. 

•strictly speaking it is the square root of the mean square velocity which is given here. 



PASSAGE OF HYDROGEN THROUGH A POROUS WALL 137 



155. Passage of Hydrogen through a Porous Wall. As 

the velocities of the hydrogen molecules are so great, they 
strike much more frequently against the walls of the vessel 
which contains them than do the molecules of other gases. 
Hence, it is harder to confine hydrogen in a vessel than 
another gas, and it diffuses more rapidlj^ This is well 
illustrated in the following experiment. 

An unglazed earthenware cup, A, (such as is used in 
galvanic batteries) is closed with a 
rubber or other cork impervious to air, 
and a glass tube connects this with a 
bottle nearly full of water (Fig. 170). 
A small glass tube B, drawn to a point, 
also passes through the cork of the 
bottle and reaches nearly to the bottom 
of the bottle. 

Now hold over the porous cup a 
bell-jar full of dry hydrogen, or pass 
illuminating gas by the tube G into 
the bell-jar. Very soon a jet of water 
will spurt from the tube B, sometimes 
with considerable force. After this ac- 
tion has ceased remove the bell-jar, and bubbles will be seen 
entering the water through the lower end of the tube B. 

At first the space within the porous cup and in the bottle 
above the water is filled with air, and when the hydrogen is 
placed about the porous cup its molecules pass in through the 
walls of the cup much faster than the air molecules come out. 
In this way the pressure within the cup is increased, and this, 
when transmitted to the surface of the water, forces it out in 
a jet. When the jar is removed the hydrogen rapidly escapes 
through the porous walls and the air rushing in is seen to 
bubble up through the water. 




Fig. 170. — Experiment showing 
rapid passage of hydrogen 
through a porous wall. 



138 THE MOLECULAR THEORY OF MATTER 

156. Molecular Motions in Liquids. In liquids the motions 
of the molecules are not so unrestrained as in a gas, but one 
can hardly doubt that the motions exist, however. Indeed, 
some direct evidence of these motions has been obtained. 
Brown, an English botanist, in 1827, with the assistance of a 
microscope, observed that minute particles like spores of 
plants when introduced into a fluid were always in a state of 
agitation, dancing to and fro in all directions with considerable 
speeds. The smaller the particle the greater was its velocity, 
and the motions were apparently due to these particles being 
struck by molecules of the liquid. More recently a method 
has been devised for demonstrating the presence of particles 
which are too small to be seen with a microscope, and by means 
of it the particles obtained on making an emulsion of gamboge 
in water (which are too small to be observed with a micro- 
scope) have been shown to have these same Brownian motions. 
It is natural to infer that these motions are caused by the 
movement of the molecules of the liquid. 

The spaces between the molecules are much smaller than in 
a gas and so the collisions are much more frequent. Moreover 
the molecules exert an attractive force on each other, the force 
of cohesion, but they glide about from point to point through- 
out the entire mass of the liquid. Usually when a molecule 
comes to the surface its neighbours hold it back and prevent 
it from leaving the liquid. The molecules, however, have not 
all the same velocity, and occasionally when a quick-moving 
one reaches the surface the force of attraction is not sufficient 
to restrain it and it escapes into the air. We say the liquid 
evaporates. 

When a liquid is heated the molecules are made to move 
more rapidly and the collisions are more frequent. The result 
is that the liquid expands and the evaporation is more rapid. 

In the case of oils the molecules appear to have great 
difficult}'- in escaping at the surface, and so there is little 
evaporation. 



OSMOSIS— MOLECULAR MOTIONS IN SOLIDS 



139 




Fi8. 171.— Osmosis. 



157. Osmosis. Over the openinj^ of a thistle-tube let us tie 
a sheet of moistened parchment or other animal membrane 
(sucli as a piece of bladder). Then, having filled the funnel 
and a portion of the tube with a strong 

solution of copper sulphate, let us support 
it as in Fig. 171 in a vessel of water so 
tliat the water outside is at the same level 
as the solution within the tube. 

In a few minutes the solution will be 
seen to have risen in the tube. The water 
will appear blue, showing that some of 
the solution has come out, but evidently- 
more water has entered the tube. The rise 
in level continues (perhaps for two or three 
hours) until the hydrostatic pressure due 
to the difference of levels stops it. 

This mode of diffusion through mem- 
branes is called osmosis, and the difference of level thus 
obtained is called osmotic pressure. 

Substances such as common salt and others which usually 
form in crystals are called crystalloids. These diffuse through 
membranes quite rapidly. Starch, gelatine, albumen and 
gummy substances generally, which are usually amorphous 
in structure, are called colloids. These difluse very slowly. 

Osmosis plays an important part in the processes of nature. 

158. Molecular Motions in Solids. As has been stated in 
§ 150, evidences of the diffusion of the molecules of one solid 
into another have been observed, but the effect is very 
slight. 

If a lumj) of sugar is dropped into a cup of tea it soon 
dissolves, and in time its molecules spread to every part of the 
liquid, giving sweetness to it. In this instance the molecules 
of water enter into the lump of sugar and loosen the bonds 



140 THE MOLECULAR THEORY OF MATTER 

which hold the molecules of sugar together. The molecules 
thus set free spread throughout the liquid. 

Drop a minute piece of potassium permanganate into a 
quart jar full of water and shake the jar for a moment. The 
solid disappears and the water soon becomes of a rich red 
colour, showing that the molecules of the solid have spread to 
every part. 

Again, ice gradually disappears even when below the freez- 
ing point. Camphor and iodine when gently heated readily 
pass into vapour without melting. Indeed, if a piece of 
camphor is cut so as to have sharp corners the w^asting 
away at ordinary temperatures will be seen by the rounding 
of the corners in a very few days. This change from solid 
to vapour is called suhliviation. 

The motions of the molecules of a solid are much less free 
than those of a liquid. They vibrate back and fortli about 
their mean positions, but as a rule are kept well to their 
places by their neighbours. When heated, the molecules are 
more vigorously agitated and the body expands, and if the 
heating is intense enough it becomes liquid. 

Since when a solid changes to a liquid its volume is not 
greatly changed we conclude that in the two states of matter 
the molecules are about equally close together. But in gases 
they are much farther apart. A cubic centimetre of water 
when turned into steam occupies about IGOO c.c, 

159. Viscosity. Tilt a vessel containing water ; it soon 
comes to its new level. With ether or alcohol the new level 
is reached even more quickly, but with molasses much more 
slowly. 

Although the molecules of a liquid or of a gas move 
with great freedom amongst their fellows some resistance is 
encountered when one layer of the fluid slides over another. 
It is a sort of internal friction and is known as viscosity. 



DISTINCTION BETWEEN SOLIDS AND LIQUIDS 141 

Ether and alcohol have very little viscosity ; they flow very 
freely and are called mobile liquids. On the other hand, tar, 
honey and molasses are very viscous. 

Stir the water in a basin vigorously and then leave it to 
itself. It soon comes to rest, showing that water has viscosity. 
The viscosity of gases is smaller than that of liquids, that of 
air being about J^ that of water. 

160. Distinction between Solids and Liquids. We readily 
agree tliat water is a li(][uid and that glass is a solid, but it is 
not easy to frame a definition which will discriminate between 
the two kinds of bodies. A liquid offers no 'permanent resis- 
tance to forces tending to change its shape. It will yield to 
even the smallest force if continuously applied, but the rate of 
yielding varies greatly with different fluids, and it is this 
temporary resistance which constitutes viscosit3^ 

Drive two pairs of nails in a wall in a warm place, and on 
one pair lay a stick of sealing-wax or a 

paraffin candle, on the other a tallow C^^^^^^^^^^Jk 

candle or a strip of tallow (Fig. 172). ( ^ u 

After some days (perhaps weeks), the fig. 172. -a paraffin candle 

tallow will still be straight and unyield- ^^^^ s^^aVht!""''' °"' 
inef while the wax will be bent. 

Lord Kelvin describes an experiment which he made many 
years ago. On the surface of the water in a tall jar he placed 
several corks, on these he laid a large cake of shoemakers' 
wax about two inches thick, and on top of this again were 
put some lead bullets. Six months later the corks had risen 
and the bullets had sunk half through the cake, while at the 
end of the year the corks were floating in the water at the 
top and the bullets were at the bottom of the vessel. 

These experiments show that at ordinary temperatures wax 
is a liquid, though a very viscous one, while tallow is a true 
solid. 



CHAPTER XVI 
Molecular Forces in Solids and Liquids 

161. Cohesion and Adhesion. When we attempt to sepa- 
rate a solid into pieces we experience difficulty in doing so. 
The molecules cling together, refusing to separate unless com- 
pelled by a considerable effort. This attraction between the 
molecules of a body is called cohesion, and themolecules must 
be very close together before this force comes into play. The 
fragments of a porcelain vessel may fit together so well that 
the eye cannot detect any cracks, but the vessel falls to j)ieces 
at the touch of a finger. 

Some substances can be made to weld together much more 
easily than others. Clean surfaces of metallic lead when 
pressed together cohere so that it requires considerable force 
to pull them apart; and powdered graphite (the substance 
used in ' lead ' pencils), when submitted to very great pressure, 
becomes once more a solid mass. 

Cohesion is the natural attraction of the molecules of a 
body for one another. If the particles of one body cling to 
those of another body there is said to be adhesion between 
them. The forces in the two cases are of the same nature, 
and tliere is really no good reason for making a distinction 
between them. 

The force of cohesion is also present in liquids, but it is 

much weaker tlian in solids. If a clean glass rod is dipped in 

water and then withdrawn a film of water will be seen 

clinging to it ; but if dipped in mercury no mercury adheres. 

This shows that the adhesion between glass and water is 

greater than the coliesion between the molecules of water, but 

the reverse holds in the case of mercury and glass. 

142 



HOW TO MEASURE ELASTICITY 



143 



1 



162. Elasticity. When a body is altered in size or shape 
in any way, so that tlie relative positions of its parts are 
changed, it is said to be strained. A ship may be tossed 
about by the waves and suffer no harm, but if it runs on 
a sand-bar and one portion is moved with respect to the rest 
it becomes strained and very serious results are sure to follow. 
Let us strain a bo<ly, bend it, for instance. It exerts a 
resistance, and on setting it free, (if the strain has not been 
too great), it returns to its original shape. This resisting 
force is due to the elasticity of the body. We apply an 
external force and thus strain the body, and this strain arouses 
an internal force which is precisely equal in magnitude and 
opposite in direction to the external force. The internal 
forces in a body are called stresses, and the stress is 
'proportional to tlie strain which accomjjanies it. 
Strain is of two kinds, — change of form and 
change of volume, and there are corresponding 
elasticities of form and of volume. Solids have 
both kinds of elasticity, while liquids and gases 
have only elasticity of volume, — they offer no 
resistance to change of form. 

Steel, glass and ivory are solids which strongly 
resist change of form and are said to have high 
elasticity ; on the other hand, india rubber, while 
easily stretched, has small elastic force. 

163. How to Measure Elasticity. From a 
strong bracket placed high on a wall hang near 
together two wires A, B (Fig. 173). To the end 
of A attach a weight to keep the wire taut, and to 
the end of B attach a hook on which weights 
may be laid. On B a cardboard scale is fastened 
and on A a piece of cardboard bearing a mark 
(or preferably a vernier), by which any change 
in the lenirth of B can be measured. 



B 




Fig. 173. — Ap- 
paratus to test 
Hooke's Law. 



144 MOLECULAR FORCES IN SOLIDS AND LIQUIDS 

First place on B a weight sufficient to keep the wire taut, 
and take the reading on the scale. Then add X kilos and 
take the reading again. Let the increase in length be x mm. 
Then add another X kilos, and find the new extension. It 
will be found to be x mm. By continuing the process we 
shall find that the extension is 'proportional to the stretching 
force. This is known as Hooke's Law from its discoverer, 
Robert Hooke (1635-1703), a contemporary of Newton. 

The object of having the wire A to hold the index mark is 
to eliminate any change in the wires through a change in 
temperature, or any error arising through any ' give ' in the 
support as weights are added to B. As both wires will change 
in the same way the extension will be given by reading the 
scale. 

Hooke's Law holds also in the case of a coiled spring (such 
as used in spring balances), and also in tlie bending of a bar. 
The amount of tlie bending is proportional to the force 
producing it. 

In performing experiments on elasticity the weights used 
must not be too large, otherwise the body will not return to 
its original condition, but will take a permanent 'set.' In 
this case the body will have been strained beyond the limits 
of perfect elasticity. 

164. Elasticity of Various Metals. Steel has the greatest 
elasticity of all the metals, and hence it is used very exten- 
sively in bridges and other structures. To stretch a rod of 
steel 1 m. long and one sq. cm. in section so that it is 1 m.m. 
longer {i.e., to increase its length by yoVo) requires 20 kilos. 
Steel is perfectly elastic within comparatively large limits. 
Suppose a connecting rod 10 ft. long and 1 sq. inch in section 
to be exposed to a tension of 10,000 pounds ; the extension 
would be -s-V inch. For copper a like extension would be 
produced with y*^ of this force. 



OTHER PROPERTIES DEPENDING ON COHESION 145 

165. Shearing Strain. In building a bridge tlie ends of 
the braces are held in place l>y bolts 
or rivets; and besides the fear of a rod (^ 

being stretched beyond its elastic limit, P" 



there is danger of the bolt or rivet being C 

cut right across its section (Fig. 174). 

In this case a section slides past the [_J 

neighbouring section, and the strain is '— JU 

said to be a sJtear. When we cut a sheet m 

of paper with scissors we shear it. For ^'the''e.l'T'A'iacet 

steel the resistance to shearing is very high. 



sheared. 



166. Other Properties Depending on Cohesion. A body is 
said to be plastic when it can be readily moulded into any 
form. The more plastic the body, the smaller is the elastic 
force exerted to recover its form. Clay and putty are good 
examples of plastic bodies. 

A tnalleable body is one which can be beaten into thin 
sheets and still preserve its continuity. Gold is -the best 
example. The gold leaf employed in ' gilding ' is extremely 
thin. Between the fingers it crumples almost to nothing. 

Tlie process of making it demands much patience and skill. First, 
a piece of gold, by means of powerful smooth rollers, is rolled into a 
thin sheet, 1 ounce making a ribbon 1^ inches wide and 10 feet 
long. Its thickness is then about xsV^ inclv, thinner than the 
thinnest writing paper. The ribbon is cut into about 75 pieces, 
which are then placed between leaves of vellum or of a special 
tough paper, and are beaten with a heavy mallet until their 
area is multiplied about 6 times. Then each sheet is cut into 4 
pieces, which are placed between sheets of gold-beaters' skin and 
beaten until the area is about 7 times as great. Each sheet is 
again cut into 4 pieces, and these, on being placed between gold- 
beaters' skin, are beaten until they are about 3^ inches square. In 
the end the leaf is ordinarily about ^stjochj inch thick, though gold 
has been beaten until but ^^tVtto inch thick. Silver and aluminium 
are also very malleable, but being less valuable, they are not made 
so thin as gold. 



146 MOLECULAR FORCES IN SOLIDS AND LIQUIDS 

A ductile substance is one which can be drawn out into fine 
wires. Platinum, gold, silver, copper and iron are all very 
ductile. By judicious work platinum can be drawn into a 
wire 2"oV"o ^^^^^^- i^ diameter. Glass is very ductile when 
heated, as also is quartz, though to soften the latter a much 
higher temperature is required. 

A friable or brittle substance is one easily broken under a 
blow. Glass, diamond and ice are brittle substances. 

Relative hardness is tested by determining which of two 
bodies will scratch the other. The following is the scale of 
hardness given by Mohs,* and generally adopted : — 1. Talc, 
2. Gj^psum, 8. Calcite, 4. Fluorspar, 5. Apatite, 6. Feldspar, 
7. Quartz, 8. Topaz, 9. Sapphire, 10. Diamond. A substance 
with hardness 7 J would scratch quartz and be as easily 
scratched by topaz. 

167. The Size of Molecules. The pi^oblem of determining the 
size of the molecules of matter is one of great interest, but also one 
of extreme difficulty. The question has been approached in various 
ways, and the fact that the results obtained by processes entirely 
different from each other agree satisfactorily is evidence that they 
are somewliere near the truth. 

According to Avogadro's Law all gases when under the same 
pressure and temperature have the same number of molecules in 
equal volumes ; hence if we know the number of molecules in a 
cubic centimetre of one gas we have the number for all gases, and 
if we know, in addition, the density of the gas we can at once 
calculate the mass of a single molecule. 

Experiments have been made to find out the very smallest amount 
of matter which can be detected by our senses of sight, smell and 
taste; and it is astonishing what small quantities of some substances 
can be recognized. 

On dissolving magenta dye it has been found that ^p^^^Q^ of a 
grain or 3.5 x 10"^ grams can be detected by the eye; and 
3 X 10"^^ grains or 1 x 10"i2 grams of mercaptan, a very 
strong-smelling substance, can be recognized. 

Glass when softened in a flame can be drawn out into fine 
threads ; and Prof. C. V. Boys, an English physicist, has succeeded 

•German mineralogist (1773-1839). 



THE SIZE OF MOLECULES 147 

in obtaining very fine threads of quartz. First he melted some 
quartz in an oxy-hydrogen flame. Then he fastened another piece 
to an arrow, dipped it into the molten quartz, some of which 
adhered to it, and then shot the arrow from a cross-bow. This 
drew out a fibre of quartz so fine that its smallest portion could not 
be seen with the best microscope. Boys estimated that its diameter 
was not greater than ^ J^ ^^ inch. One cubic inch of quartz would 
make over 20,000,000 jniles of such fibre. If we supposed this to 
be wound on a reel and then unwound by an express train moving 
at the rate of a mile a minute, over 38 years would be required. It 
is quite certain that a section of this fibre must contain a large 
number of molecules, but for simplicity let us suppose the fibre to be 
comjiosed of a single row of molecules in contact. A sphere Yimlm 
inch in diameter made from quartz would weigh 3.5 x 10"^^ grains or 
1.23 X 10"^" grams. The molecule of quartz must weigh less than this. 
But the molecule of quartz is 60 times as heavy as that of hydrogen, 
and so the latter must weigh less than 2 x 10^^^ grams. Now 1 c.c. 
of hydrogen weighs 0.00009 or 9 x 10"^ grams. Hence the number 
of hydrogen molecules in 1 c.c. must be greater than (9 x 10"^) -i- 
(2 X 10"^'-') = 4.5 X 10^*. As we shall see presently, there are likely 
100,000 times as many. 

In recent years a wonderful property has been discovered to 
belong to certain substances, which has been named radio-activity 
(see v^ 582). Substances which are radio-active are able to fog a 
sensitive photographic plate even though it be securely packed in a 
box, they can discharge an electrified body and do other extra- 
ordinary things. Uranium and thorium are two of these substances, 
but i-adium and polonium appear to be the most powerful of them. 
These substances are exceedingly scarce and hence are extremely 
expensive. 

The radiation which radium is continually giving out has been 
most carefully investigated by Rutherford,* and has been found to 
consist of three parts, which he named the Alpha, Beta and Gamma 
Jiai/sj Further examination has shown that the Alpha rays are 
made up of small particles, or corpuscles, travelling at a very great 
speed, each carrying a small charge of electricitj^, and when these 
corpuscles are collected in a vessel they are found to be the gas 
helium. Each coi'puscle is a molecule of helium charged with elec- 
tricity ! 

*Novv of the University of Manchester, England. For ten years Professor of Physics at McGill 
University, Montreal. 

t a (alpha), |3 (betal v (gamma), are the first three letters of the Greek alphabet. 



148 



MOLECULAR FORCES IX SOLIDS AND LIQUIDS 



Now Rutherford and Geiger liave devised a method by which the 
passage of a single Alpha corpuscle into a suitable receiving vessel 
can be detected, and by actual count and calculation they have 
found that 1 gram of radium sends out 13.6 x 10^^ particles per 
second. But it has also been found that 1 gram of radium produces 
0.46 c. mm. of the gas helium per day which is 5.32 x 10"*^ c. mm. 
per second. It follows then that in 5.32 x 10~*^ c. mm. of helium 
gas there are 13.6 x 10^^ molecules 

Hence, 

f.i. . • 13.6 X 1010 X 103 

1 c.c. of the gas contains — — — — r— ^ = 2. Ob x 10^'' 

" 5.32 X 10"^ 

molecules, and from Avogadro's Law this is the number of molecules 
in 1 c.c. of all gases at standard pressure and temperature. 

Since 1 c.c. of helium weighs 0.00000174 or 1.74 x 10"^ grams, we 
at once deduce that 1 molecule of helium Aveighs 6.8 x lO"-*^ grams. 
Also, the average distance apart of the molecules = 3.4 x 10^ cm. 

Rutherford has given several other methods of calculating the 
number of molecules, and taking the avei'age of them all he finds 
1 c.c. of gas at ordinary pressure and temperature 
contains 2.77 x 10^'' molecules. 
Lord Kelvin has also calculated in several ways the size of 
molecules, and he gives the following illustration. "Imagine a 

rain-drop, or a globe of glass as 
large as a pea, to be magnified up 
to the size of the earth, each con- 
stituent molecule being magnified 
in the same proportion. The magni- 
fied structure would be more 
coarse-grained than a heap of 
sms^ll shot, but probably less 
coarse-gi'ained than a heap of 
cricket balls.' 

168. Nature of the Molecule. 
In tlie discussion given above, 
molecules have been treated as 
simple bits of matter, like grains 

Sir Joseph Thomson. Born in Manchester, p wlio.;if in a bncbpl niPiQiirp 
1856. Cavendish Professor of Experimental Ol Wlieat 111 a UUSIiei meabUie, 
Physics at Cambridge University. England, ^j^^^ J^ reaSOnS haVB been given 

for believing that they are in motion. The view ordinarily 




NATURE OF THE MOLECULE I49 

held has been that a conipound body is made up of molecules, 
and that each molecule can be broken up into elementary 
atoms (§ 147). 

But in recent years the investigations of various physicists, 
the most distinguished of whom is Sir Joseph Thomson, have 
led to the belief that the atom itself is a complex organization. 
According to this theory the atom of a substance has a certain 
amount of positive electricity as its nucleus, and about this a 
large number of very minute negatively-charged corpuscles or 
electrons revolve. Indeed the construction of the atom has 
been compared to that of our solar system, which has the sun 
as its centre and the planets revolving about it. Though the 
evidence in favour of some such view is undisputed, the theory 
is at present in a speculative stage and need not be considered 
further in a book like this. 



CHAPTER XVII 



Phenomena of. Surface Tension and Capillarity 



169. Forces at the Surface of a Liquid. 

water out of 




o 

Fig. 175. — A drop of water assumes 
the globular form. 



On slowly forcing 
a medicine dropper 
we see it gradually gather at the 
end (Fig. 175), becoming more 
and more globular, until at last it 
breaks off and falls a sphere. 
When mercury falls on the floor it 
breaks up into a thousand shining 
globules. Why do not these flatten 
out ? If melted lead be poured 
through a sieve at the top of a 

tower it forms into drops which harden on the way down and 

finally appear as solid spheres of shot. 

A beautiful way to study these phenomena was devised by 

the Belgian physicist Plateau.* By mixing in the proper 

proportions water and alcohol (about 60 water to 40 alcohol), 

it is possible to obtain a mixture of the same density as olive 

oil. By means of a pijjette now introduce 

olive oil into the mixture (Fig. 176). At 

once it assumes a globular form. In this 

case it is freed from the distorting action 

of gravity and rests anywhere it is put. 
When the end of a stick of sealing-wax 

or of a rod of glass is heated in a flame it 

assumes a rounded form. 




Fio. 176.— A sphere of 
olive oil in a mixture 
of water and alcohol. 



These actions are due to cohesion. A little consideration 
would lead us to expect the molecules at the surface to act in 



*Born 1801, died 1883. 
in 1843. 



From 1829 his eyesight gradually deteriorated, and it failed entirely 
150 



SURFACE TENSION IN SOAP FILMS 



151 




FiQ. 177.— Behaviour of 
molecules within the 
liquid and at its sur- 
face. 



a manner somewhat different from those in the interior of a 
hquicl. Let (X be a molecule well within 
the liquid (Fig. 177). The molecule is at- 
tracted on all sides by the molecules very 
close to it, within its sphere of action 
(which is extremely small, see § 161), and 
as the attraction is in all directions it will 
remain at rest. Next consider a molecule 
b which is just on the surface. In this case there will 
be no attraction on b from above, but the neighbouring 
molecules within the liquid will pull it downwards. Thus 
there are forces pulling the surface molecules into the liquid, 
bringing them all as close togetlier as possible, so that the 
area of the surface will be as small as possible. It is for this 
reason that the water forms in spherical drops, since, for a 
given volume, the sphere has the smallest surface. 

The surface of a liquid behaves precisel}^ as though a rubber 
membrane were stretched over it, and the phenomena 
exhibited are said to be due to surface tension. 

170. Surface Tension in Soap Films. The surface tension 
of water is beautifully shown by soap bubbles and films. In 
these there is very little matter, and the force of gravity does 
not interfere with our experimenting. It is to be observed, 
too, that in the bubbles and films there 
is an outside and an inside surface, each 
under tension. 

In an inflated toy balloon the rubber 
is under tension. This is shown by 
pricking with a pin or untying the 
mouthpiece. At once the air is forced 
out and the balloon becomes flat. A 
similar effect is obtained with a aoap 
bubble. Let it be blown on a funnel, 
and the small end be held to a candle flame (Fig. 178). The 




Fig. 178.— Soap-bubble blow- 
ing out a candle. 



152 PHENOMENA OF SURFACE TENSION AND CAPILLARITY 




Fio. 179.— A loop of thread 
on a soap film. 



outrushing air at once blows out the flame, which shows that 
the bubble behaves like an elastic bag. 

There is a difference, however, between the balloon and the 
bubble. The former will shrink only to a certain size; the latter 
first shrinks to a film across the mouth of the funnel and then 
runs up the funnel handle ever trying to reach a smaller area. 
Aoain, take a ring; of wire about two inches in diameter 
with a handle on it (Fig. 179). To two points on the ring tie 
a fine thread M'ith a loop in it. Dip the 
ring in a soap solution and obtain a film 
across it with the loop resting on the 
film. Now, with the end of a wire or 
with the point of a pencil, puncture the 
film within the loop. Immediately the 
film which is left assumes as small a sur- 
face as it can, and the loop becomes a perfect circle, since b^' so 
doing the area of the film becomes as small as possible. 

171. Contact of Liquid and Solid. The surface of a liquid 
resting freely under gi-avity is hori- 
zontal, but where the liquid is in 
contact with a solid the surface is 
usually curved. Water in contact 
with clean glass curves upward, mer- 
cury curves downward. Sometimes when the glass is dirty 
the curvature is absent. 

These are called capillary phenomena, for a reason which 
will soon appear. The angle of contact A (Fig. 180) betAveen 
the surfaces of the liquid and solid is called the capillary 
angle. For 2)eKf^cfly pure water and clean glass the angle is 
zero, but with slight contamination, even such as is caused by 
exposure to air the angle may become 25° or mcfi-e. For pure 
mercury and clean glass the angle is about 148", but slight 
contamination reduces this to 140° or less. For turpentine it 
is 17°, and for petroleum 26°. 




Fig. 180. — Water in a glass vessel 
curves up.mercury curvesdown. 



LEVEL OF LIQUIDS IN CAPILLARY TUBES 



153 



172. Level of Liquids in Capillary Tubes. In § 105 it was 

stated that in uny number of com- 
municating vessels a liquid stands at 
the same level. The following ex- 
periment gives an apparent exception 
to this law. Let a series of capillary* 
tubes, whose internal diameters range 
from say 2 mm. to the finest obtainable, 
be held in a vessel containing water 
(Fig. 181). It will be found that in 
each of them the level is above that of 
the water in tlie vessel, and that the 
finer the tube tlie higher is the level. With alcohol tlie li(]uid 
is also elevated, (though not so much), but with mercury the 




Fia. 181.— Showing the elevation 
of water in capillary tubes. 





\ 







Fio. 182. — Contrasting the be- Fig. 183. — Water rises between the two 

haviour of water (left) and mer- plates of glass which touch along one 

cury (right). edge. 

liquid is depressed. The behaviour of mercury can con- 
veniently be shown in a U-tube as in Fig. 182. 

Another convenient method of showing capillary action is 
illustrated in Fig. 183. Take two square pieces of window 
glass, and place them face to face with an ordinary match or 
other small object to keep them a small distance apart along 
one edge while they meet together along the opposite edge. 
They may be held in this position by an ela.stic band. Tlien 
stand the plates in a dish of coloured water. The water at 
once creeps up between the plates, standing highest wdiere the 
plates meet. 

* Latin, Capillus, a hair. 



154 PHENOMENA OF SURFACE TENSION AND CAPILLARITY 



When a glass rod is withdrawn from water some water 
clings to it, and the liquid is said to wet the glass. If 
dipped in mercury, no mercury adheres to the glass. Mercury 
does not wet glass. 

The following are the chief laws of capillary action : — 

{1) If a liquid wets a tube, it rises in it ; if not, it 

falls in it. 
(2) The rise or depression is inversely proportional to 
the diaTneter of the tube. 
173. Explanation of Capillary Action. Capillary pheno- 
mena depend upon the relation between the cohesion of the 
liquid and the adhesion between the liquid and the tube. 

In all cases the surface of a liquid at rest is perpendicular 
to the direction of the resultant force which acts on it. 
Usually the surface is horizontal, being perpendicular to the 
plumb-line, which indicates the direction of the force of 
gravity. In the case of contact between a solid and a liquid 
the forces of adhesion and cohesion must be taken into 
account, since the force of gravity acting on a particle of 
matter is negligible in comparison with the attraction of 
neighbouring particles upon it. 

Consider the forces on a small particle of the liquid at 0. 

(Fig. 184.) The force of 
adhesion of the solid will 
be represented in direction 
and magnitude by the line 
A, that of the cohesion of 

Fio. 184. — Diagrams to explain capillary action. flip rpst of the lifiuid bv 

the line G. Compounding A and G by the parallelogram law 
(§ 55) the resultant force is R. The surface is always perpen- 
dicular to this resultant. When G greatly exceeds A the 
liquid is depressed ; if A greatly exceeds G, it is elevated. 

In the case of capillary tubes the column of liquid which is 
above the general level of the liquid is held up by the adhesion 





SURFACE TENSION AND CAPILLARITY 



155 



of the glass tube for it. Tlie total force exerted varies directly 
as tiie length of the line of contact of the liquid and the tube, 
which is the inner circumference of the tube ; while the 
quantity of liquid in tlie elevated (or depressed) colunni is 
proportional to the area of the inner cross-section of the tube. 
If tlie diameter of the tube is doubled the lifting force is 
doubled and so the quantity of liquid lifted is doubled ; but as 
the area is now four times as great the height of the column 
lifted is one-half as great. 

Hence the elevation (or depression) varies inversely as the 
diameter of the tube. 

174. Interesting Illustrations of Surface Tension and 
Capillarity.* It is not easy to pour water from a tumbler into 

a bottle without spilling it, but by holding 

a glass rod as in Fio;. 185, the water runs 

down into the bottle and none is lost. The 

glass rod may be inclined 

but the elastic skin still 

holds the water to the rod. 
Water may be led from 

the end of an eave-trough 

into a barrel by means of a 
Fig. 185.-HOW to utilize pole aluiost as Well as by 

surface tension in pour- ,^,o)-ol fnl-,o Fia. 186. —Surface 

ing a liquid. a meCdl LUUe. tension holds the 

When a brush is dry the hairs spread out together. 
as in Fig. 186tt, but on wetting it they cling together (Fig. 
186c). This is due to the surface film which contracts and 
draws the hairs togetlier. That it is not due simply to being 
wet is seen from Fig. 186&, which shows the brush in the 
water but with the hairs spread out. 

A wire sieve is wet by water, but if it is covered with 
paraffin wax the water will not cling to it. Make a dish out 

* Many beautiful experiments are described in "Soap Bubbles and the Forces which Mould 
Them," by C. V. Boys. 





156 PHENOMENA OF SURFACE TENSION AND CAPILLARITY 

of copper gauze having about twenty wires to the incli ; let 
its diameter be about six inches and height one inch. Bind it 
with wire to strengthen it. Dip it in melted paraffin wax, 
and while still hot knock it on the table so as to shake the 
wax out of the holes. A good sized pin will still pass through 
the holes and tliere will be over 10,000 of them. On the 
bottom of the dish lay a small piece of paper and pour water 
on it. Fully half a tumblerful of water can be poured into 
the vessel and yet it will not leak. The water has a skin 
over it which will suffer considerable stretching before it 
breaks. Give the vessel a jolt, the skin breaks and the water 
at once runs out. A vessel constructed as described will also 
float on the surface of water. 

Capillary action is seen in the rising of water in a cloth, or in 
a lump of sugar when touching the water ; in the rising of oil 
in a lamp- wick and in the absorption of ink by blotting paper. 

175. Small Bodies Resting on the Surface of Water. 

By careful manipulation a needle may be laid 
on the surface of still water (Fig. 187). Tlie 
surface is made concave by laving the needle 

Fig. 187.— Needle on ^ ^ a 

the surface of water q^ {\^ and in the cudeavour to contract and 

kept up by surface 

tension. smootli out tlic hollow, Sufficient force is 

exerted to support the needle, though its density is 7^ times 
that of water. When once the water has wet the needle the 
water rises against the metal and now the tendency of the 
surface to flatten out will draw the needle downwards. 

If the needle is magnetized, it will act when floating like a 
compass needle, showing the north 
and soutli direction. 

Some insects run over the surface 
of water, frequently very rapidly 
(Fig;. 188). These are held up in the Fia. m-insect stipported by the 

^ f> ■> ^ surface tension of the A-ater. 

same way as the needle, namely, by 

the skin on the surface, to rupture which requires some force. 




PART V WAVE MOTION AND SOUND 



CHAPTER XVIII 
Wave Motion 

176. Characteristic of Wave-Motion. It is very interes- 
ting to stand on tlie shore of fl, large body of water and 
watch the waves, raised by a stiff breeze, as they travel 
majestically along. Steadily they move onward, until at last, 
crested with foam, they roll in upon the beach, breaking at 
our feet. The great ridges of water appear to be moving 
bodily forward towards us, but a little observation and con- 
sideration will convince us that such is not the case. 

By watching a log, a sea-fowl or any other definite object 
floating on the surface, we see that, as the waves pass along, it 
simply moves up and down, not coming appreciably nearer to us. 

We see, then, that the motion of the water is handed on but 
not the water itself. In the case of a flowing stream the water 
itself moves and, perhaps, turns our water-wheels. Equally 
certain it is, however, that energy (that is, ability to do work), 
is transmitted by waves. A small boat, though at the distance 
of several miles from the course of a great steamer, will, some- 
time after the latter has passed, experience a violent motion, 
produced by the " swells " of the large vessel. The water has 
not moved from one to the other, but it is nevertlieless the 
medium by which considerable energy has been transmitted. 

The motion of each particle of water is similar to that of a 

pendulum. It is drawn aside, then swings through its mean 

position, s^ which place its motion is most rapid, and its 

momentum carries it forward to the farthest part of its course. 

Here it comes to rest and then it returns through its mean 

position to its starting-point. 

157 



158 WAVE MOTION 

A peculiar characteristic of wave-motion is that, while the 
particles of water, or other medium, never move far from 
their ordinary positions of equilibrium, yet energy is trans- 
mitted from one place to another by means of the motion. 

When, further, we learn that the sound of the rolling and 
breaking waves is conveyed to our eai's by a wave-motion in 
tlie atmosphere about us ; and that the light by which we see 
tliese and other wonderful things, is also a wave-motion, of a 
kind still more difficult to comj)rehend, produced in a medium 
called the ether, which is believed to fill all space, penetrating 
even between the particles of ordinary matter, our interest is 
increased ; and we realize how necessary it is to understand 
the laws of wave-motion. The subject, however, is a very 
extensive one, and only the simplest outline of it will be 
given here. 

177. Cause of Waves on Water. Water in a state of 
equilibrium assumes the lowest possible level. If then an 
elevation or a depression in the surface be produced at any 
point, waves will be excited and will si:)read out from that point. 

Let a stone be thrown into the water. It makes an opening 
in tlie water, at the same time elevating the surface of the 
water surrounding it. At once the neighbouring water rushes 
forward to fill up the vacant space, but on arriving there its 
momentum does not allow it to come to rest at once. The 
water, coming in from all sides, now raises a heap where the 
stone entered. Tiiis falls back, and the motion continues, 
until at last it dies away through friction. 



Fio. 189.— The water from the troughs has been raised into the crests, thuFincreasing 
the potential energy and causing wave-motion. 

Suppose SS (Fig. 189) to be the natural level surface of the 
water when in equilibrium. It is evident, when there is such 



Cause of waves on water 159 

a wave-motion as liere illustrated, that by some means the 
water has been taken out of the 'troughs' BG, DE, etc., and 
raised into the 'crests' AB, CD, EF, etc., and thus the 
potential energy has been increased. At once the crests begin 
to fall, but on account of their momentum they will sink 
below the position of equilibrium, and thus an oscillation is 
produced. In this case the continued motion is due to the 
force of gravity. 

However, there is another source besides gravity which 
produces motion of the surface of a liquid. In § 169 it was 
stated that a liquid behaves as though there is an elastic skin 
stretched over its surface, which tends to reduce the surface 
to as small dimensions as possible. This skin gives rise to 
the phenomena of surface tension. 

Consider now liquid at rest in a vessel, — a cup of tea, for 
instance. If any object is touched to that surface its area 
will be increased and surface tension will endeavour to 
prevent this. Now it is evident that if by a current of air 
(or in any other way) the surface which is naturally level as 
SS (Fig. 190) is given the 

wavy form shown in the ■^^^BmM^^^miifl^MMmf^& 
figure, the area of the „ ,„„ c. „ • , ,• -^ ^ 

° Fig. 190. — Small waves, or ripples, on a liquid, due 

surface is increased, and chiefly to surface tension. 

surface tension will strive to reduce this and to bring about 
equilibrium again. 

Thus surface tension as well as gravity is competent to 
produce waves on the surface of a liquid. Indeed it has been 
found that in the case of short waves surface tension is much 
more effective than gravity, while in large waves the reverse 
holds. 

These small waves, chiefly due to surface tension, are known 
as ripples. 



160 WAVE MOTION 

178. Definition of Wave-length. A continuous series of 
waves, such as one can produce by moving a paddle back-and- 
forth in the water, or by lifting up and down a block 
floating on the water, is called a wave-train. The number 
of waves in such a train is indefinite; there may be few or 
many. 

If now we look along such a train we can select portions 
of it which are in exactly the same stage of movement, 
that is, which are moving in the same way at the same time. 
The distance between two successive similar points is called 
a wave-length. It is usual to measure from one crest to 
the next one, but any other similar points may be chosen. 

Particles which are at the same stage of the movement at 
the same time are said to be in the same pha.se ; and so we 
can define a wave-length as the shortest distance between any 
two particles whose motions are in the same phase. 

179. Speed of Waves on Water. We have seen that the 
circumstances of tlie motion on the surface of a liquid depend 
on gravity and on surface tension. If the wave-length is 
great the surface tension may be neglected, while if the waves 
are very small it is all-important and the action of gravity 
may be left out of account. 

Now for long gravity waves the speed of transmission is 
liigher, the greater the wave-length, the speed being propor- 
tional to the square-root of the wave-length. 

On the other hand, for small waves under surface tension, 
the speed of transmission increases as the wave-length 
diminishes. 

180. Wave-length for Slowest Speed. On the deep sea, 

waves which are 100 feet from crest to crest travel at the rate of 
15 miles per hour. Those with wave-length 300 feet will therefore 
move at the rate of 15 ^^3 or 26 miles per hour, and so on. 
Atlantic storm waves are often 500 or 600 feet long, and these 
travel at the rate of 34 and 38 miles per hour, respectively. 



SPEED DEPENDENT ON DEPTH 



161 





FlQ. 191. — Ripple8 formed on moving 4 
wire through water ; (a) low-speed, (6; 
high-speed ripples. 

if shorter, surface tension 



If a wire — a knitting needle, for instance— is moved through 
water, ripples are formed before it 
(Fig. 191), and the faster the 
motion of the wire, the closer are 
the ripples together (Fig. 1916), 
i.e., the shorter is the wave-length. 

It is evident that for every liquid 
there is some critical wave-length 
for which the waves travel most 
slowly. For water this is 0.68 inch 
and the speed of travel is 9 inches 
a second. If the waves are longer, 
gravity will make them travel faster 
will cause them to move faster. 

181. Speed Dependent on Depth. That waves in deep 
water travel faster than in shallow can be shown experi- 
mentally in the following way. 

Take two troughs (Fig. 192) each about 6 feet long and 1 

foot wide and deep. 
At one end of each 
trougli an empty 
tin can or a block 
of wood is held in 
such a way that it 
can rise and fall 
but not move along 
the trough. 

Let one trough 




Fio. 192. — Apparatus to show that waves travel faster in deep 
than in shallow water. 



be filled to the depth of 6 inches, the other to the depth of 3 
inches. By means of a double paddle, as shown in the figure, a 
solitary wave is started in each trough at the same instant. The 
float on the deeper water will easily be seen to rise first, thus 
showing tliat the wave has travelled faster in the deeper water. 
182. Motion of the Particles of Water. It may be remarked 

that in water waves the particles do not simply move up and down. 
In deep water they move in circles, but as the water becomes 
shallow these circles are flattened into ellipses with the long axes 
horizontal. 



162 



WAVE MOTION 



Also, the oscillatory motion of the particles rapidly diminishes 
with the depth. At the depth of a wave-length it is less than s^js 
of that at the surface. At a few hundred feet down — a distance 
small compared with the depth of the ocean — the water is quite still, 
even though the surface may be in very violent motion under fearful 
storms. A submarine boat, by descending a hundred feet, could 
pass from the midst of a terrific tempest to a region of perfect quiet. 

183. Refraction of Water Waves. It has often been 
observed that when waves approach a shallow beach the crests 

„:■.--■-::::;■-.... are usually approxi- 

mately parallel to the 
shore line. In Fig. 193, 
A,B,G, etc., represent the 
successive positions of a 
wave approaching the 
shore. The dotted lines 
indicate the depth of 
water. It is seen that the 
end of the wave nearest 
the shore reaches shallow 
water first, and at once 
travels more slowly. 
This continues until at 




12 



4 6 8 10 
inches deep 

Fig. 193.— Diagram illustrating how a wave changes its last the Wave is alniOSt 
direction of motion as it gets into shallower water, n i . .1 i t 

and is refracted. parallel to tlie shore line. 

This changing of the direction of the motion of the waves 
througli a change in their velocity is called refraction. 

184. Reflection of Waves. If, however, a train of water 
waves strike a precipitous shore or ^~^, \^C 



>S</. 



-4c, 



>< 



r 



B 



a long pier, they do not stop there, 

but start off again in a definite 

direction. This is illustrated in 

Fig. 194. The waves advance along 

AB, strike the pier and are reflected 

in tlie direction BG, the lines AB, BG making equal angles 

with BD the perpendicular to the pier. In sound and light 

we meet with many illustrations of reflection and refraction. 



Fio. 194. — Water waves striking a long 
pier are reflected. 



STUDY OF WAVES IN A CORD 1C3 

185. Study of Waves in a Cord, Let one end of a light 
chain or rubljor tube, 8 feet or more in length, be fastened to 
the ceiling or the wall of a room. Then, by shaking from side 
to side the free end, waves will be formed and w^ill pass freely 
along the tube. A rope or a length of garden hose lying on the 
floor may be used, but tlie results will not be so satisfactory. 

We shall examine this motion more closely. Let us staH 

with the tube ^ - (^^ 

straight as o__ 

shown in (a), ^' v^/ 

Fig. 195. The f b-rz:::-j2 . (,) 

end A is quick- 



ly drawn aside A:—-^^^ ^^^^ 

throug-h the . ^^ ~-\5 

spacers. The ^ ^ ^^^ 

■"• , Fio. 195.— Diagram to show how a wave is formed and travels 

end particles along a cord. 

drag the adjacent ones after them ; these drag the next ones, 
and so on; and when the end ones have been pulled to B the 
tube then has the form shown in (6). 

Instead of keeping the end at B, however, let it be quickly 
brought back to A , that is, the motion is from A to B and B 
to A without waiting at B. Now the particles between B and 
P have been given an upward movement, and their inertia will 
carry them further, each pulling its next neighbour after it, 
until when the end is brought back to A the tube will have 
the form J.Q, shown in (c). 

Suppose, next, that the motion did not stop at A, but that 
it continued on to B. On arriving there the tube will have 
the form (tZ). Immediately let the end be brought back to A, 
thus completing the ' round trip.' The tube will now have the 
form shown in (e). 

Notice (1) that the end has made a complete vibration, (2) 
that one wave has been formed, and (3) that the motion has 
travelled from A to /S, which is a wave-length. 



Ig4 WAVE MOTION 

If the motion of the end ceased now, the wave would simply 
move forward along the tube. If, however, the end continued 
to vibrate, waves would continue to form and move along the 

M 



Fia. 196. — Three waves in a cord. 

tube, as seen in Fig. 196, where three full waves are shown, 
movino; in the direction of the arrow. 

186. Relation between Wave-length, Velocity and Fre- 
quency. The time in which the end A executes a complete 
vibration is called its period, and the number of periods in a 
second is called its frequency, or vihration-nuiiiber. 

We have just seen that during one period the wave-motion 
travels one wave-length. 

Let the frequency be n per second ; then the period T will 
be \Jn. second. 

If I = wave-length, 

and V — velocity of transmission of the wave-motion ; 

then I == vT, 

or V = nl. 

This is a very important relation. 

The amplitude of a vibration is the range on one side or 
the other of the middle point of the course. Thus AB ov AD 
(Fig. 195) is the amplitude of the motion of the particle A. 

187. Transverse and Longitudinal Waves. In the wave- 
motion just considered the direction of the motion of the 
particles is across, or at right angles to, the direction of propa- 
gation. Such are called transverse waves. In addition to 
the illustrations of these waves which have already been 
given, it may be remarked that in an earthquake disturbance 
the motions which do the great damage are long, transverse 
waves which travel along the earth's crust at the rate of from 
1.6 to 4 km. per second.* 

* In the destructive Messina earthquake, December 28, 1908, the speed of transmission 
areraged 3.3 km. (or 2 mi.) per second. 



TRANSVERSE AND LONGITUDINAL WAVES 



165 



-A wave consists of a condensation B, and a 
rarefaction A. 



Let us now consider a long spiral spring (Fig. 197). The 
spiral should be 2 or 3 ni. long and 
the diameter of the coils may l)e 
from 3 to 8 cm. One end may be 

securely attached to the bottom of Fio. lO-.— Portion ot a spiral aiirinfr to 
/ 1 11 1 illustrate the transmission of a wave. 

a light box (a chalk-crayon box), it should be 2 or 3m. lon^; if of no. 

'=' , > 22 wire the coils may he 3 or 4 cm. in 

Then, holding" the other end firmly diameter; if of heavier wire the colls 
" _ _ "^ should be lart'er. 

in the hand, insert a knife-blade 

between the turns of the wire and quickly rake it along the 

spiral towards the box. 

In this way the turns of wire at B, Fig. 198, in front of 

^ B^ C the hand are crowded 

together, and the 
turns behind, for about 
the same distance, are 
pulled wider apart. 
The crowded part of the spiral may be called a condensation, 
the stretched part a rarefaction. 

Now watch closely and you will see the condensation, fol- 
lowed by the rarefaction, run with great speed along the spiral, 
and on reaching the end it will give a sharp thump against the 
box. Here it will be reflected, and will return to the hand from 
which it may be reflected and again return to the box. 

If a light object be tied to the wire at any place, it will be seen, 
as the wave passes, to receive a sharp jerking motion forward 
and backward in the direction of the length of the spiral. 

On a closer examination we find that the following is what 
takes place. 

By applying force with the hand to the spiral we produce 
a crowding together of the turns of wire in the section B, and 
a separation at A. Instantly the elastic force of the wire 
causes B to expand, crowding together the turns of wire in 
front of it (in the section C), and thus causing the condensa- 
tion to be transmitted forward. But the coils in B do not 



166 



WAVE MOTION 



stop when they have recovered their original position. Like 
a pendulum they swing beyond the position of rest, thus pro- 
ducing a rarefaction at B where immediately before thei'e was 
a condensation. Thus the pulse of condensation as it moves 
forward will be followed by one of rarefaction. 

Such a vibration is called longitudinal ; the motions of the 
particles are parallel to the direction of transmission. 

188. Length and Velocity of Waves in a Cord. Let us 

experiment further with the stretched rubber tube. 

Make the 'end to vibrate faster; the waves produced are 
shorter. Stretch the tube more ; the waves become longer, 
and travel faster. 

Notice, also, that on reaching the farther end the wave is 
reflected as it was in the long spiral. 

189. Nodes and Loops. Next, let us keep the end of the 
rubber tube in continual vibration. A train of waves will 
steadily pass along the tube, and being reflected at the other 
end, a train will steadily return along it. These two trains 
will meet, each one moving as though it alone existed. 

As the tube is under the action of the two sets of waves, the 
direct and reflected trains, it is easy to see that while a direct 
wave may push downward any point on the tube a reflected 
one may lift it up, and the net result may be that the point 
will not move at all. The two waves in such a case are said 
to interfere. 

That is just what does happen. By properly timing the 

vibrations of the end 
■■■■■■■K:^ of the tube the direct 
and reflected trains 
interfere and certain 
points will be con- 

Fio. 199. -standing waves in a cord. At ^. C, D, E, B mre ^mually at rCSt. 

7wdes; midway between are ioops. jr; .i i a ('Fip" 

199) is vibrated slowly the tube will assume the form (a). 




METHOD OF STUDYING STANDING WAVES 167 

On doubling the frequency of vibration, it will take the form (b). 
By increasing the frequency other forms, such as shown in (c) 
and (c^) may be obtained. In these cases the points A,B, G, D, 
E, are continually at rest and are called nodes. The portion 
between two nodes is called a ventral segment, and the middle 
point of it we shall call a loojj. The distance between two 
successive nodes is half a wave-length. 

Such waves are called stationary or standing waves As 
we have seen, they are caused by continual interference 
between the direct and the reflected waves. 

190. Method of Studying Standing Waves. The most 
satisfactory method of producing the vibrations in a cord is to 
use a large tuning-fork, so arranged that tlie cord (which 
should be of silk, light and flexible) may be attached to one 
prong. In the absence of this the arrangement shown in 



^<5 



^O 



FiQ. 200. — A cordis attached to the armature of an electric bell, and to the other 
end which passes over a pulley are added weights. By adjusting the length 
and the tension standing waves are produced. 

Fig. 200 may be used. The gong and the hammer of a large 
electric bell are removed. One end of the cord is attached to 
the armature and the other passes over a pulley and has a 
pan to hold weights attached to it. In this way the length 
and the tension of the coi'd can be varied and the resulting 
standing waves studied. 

The following law has been found to hold : — The numher of 
loops is inversely proportional to the square root of the tension. 

Instead of having the string pass over a pulley, it might be 
allowed to hang vertically with the weight tied on the end, the 
electric vibrator then being turned so that the armature is verti- 
cal. This arrangement, however, is not quite so satisfactory. 



CHAPTER XIX 

Production, Propagation, Velocity of Sound 

191. Sound arises from a Body in Motion. The sensation 
of sound arises from various kinds of sources, but if we take 
the trouble to trace the sound to its origin, we always find 
that it comes from a material body in motion. 

A viojin or a guitar string when emitting a sound has a hazy 
outline, which becomes perfectly definite when the sound dies 
away. A bit of paper, doubled and hung on the string, is at 
once thrown off". On placing the hand upon a sounding bell 
we feel the movement, which, however, at once ceases, as also 
does the sound. On touching the surface of water with the 
prong of a sounding tuning-fork the water is formed into 
ripples, or splashes up in spray. A light ball or hollow bead 
suspended by a fine thread, if held against the sounding bell 
or tuning-fork is thrown off vigorously. 

All our experience leads us to conclude that in every case 
sound arises fro^m matter in rapid vibration. 

192. Conveyance of Sound to the Ear. In order that a 
sound may be perceived by our ears it is evident that some 
sort of medium must fill the space between the source and the 
ear. Usually air is this medium, but other substances can 
convey the sound quite as well. 

By holding the ear against one end of a wooden rod even a 

light scratch with a pin at the far end will be heard distinctly. 

One can detect the rumbling of a distant railway train by 

laying the ear upon the steel rail. The Indians on the western 

plains could, by putting the ear to the ground, detect the 

tramping of cavalry too far off to be seen. If two stones 

be strupk together under water, the sound perceived by an 

168 



VELOCITY OF SOUND IN AIR 



169 




ear under water is louder than if the experiment had been 
performed in the air. 

Thus we see that solids, liquids and gases all transmit 
sound. Further, we can show that some one of these is 
necessary. 

Under the receiver of an air-pump place an electric bell, 
supporting it as shown in Fig. 201. At first, 
on closing the circuit, the sound is heard 
easily, but if the receiver is now exhausted 
by a good air-pump it becomes feebler, con- 
tinually becoming weaker as the exhaustion 
proceeds. 

If now the air, or any other gas, or any 
vapour, is admitted to the receiver the sound 
at once gets louder. 

In performing this experiment it is likely 
that the sound Avill not entirely disappear, as 
there will always be some air in the receiver, 
and in addition, a slight motion will be transmitted to the 
pump by the suspension ; but we are justified in believing 
that a vibrating body in a perfect vacuum will not excite the 
sensation of sound. 

In this respect sound differs from light and heat, which 
come to us from the sun and the stars, passing freely through 
the perfect vacuum of space. 

193. Velocity of Sound in Air. It is a common observation 
that sound reciuires an appreciable time to travel from one 
place to another. If we watch a carpenter working at a 
distance we distinctly see his hammer fall before we hear the 
sound of the blow. Also, steam may be seen coming from the 
whistle of a locomotive or steamboat several seconds before 
the sound is heard, and we continue to hear the sound for the 
same length of time after the steam is shut oflf. 



Fio. 201. -Electric bell 
in a jar connected 
to an air-pump. On 
exhausting the air 
from the jar the sound 
became weaker. 



170 PRODUCTION, PROPAGATION, VELOCITY OF SOUND 

Some of the best experiments for determining the velocity 
of sound in air were made in 1822 by a commission appointed 
by the French Academy. The experiments were made 
betweeen Moutlh^ry and Villejuif, two places a little south of 
Paris and 18.6 kilometres (or 11.6 miles) apart. 

Each station was in charge of three eminent scientists and 
provided with similar cannons and chronometers. It was 
found that the interval between the moment of seeing the 
flash and the arrival of the sound was, on the average, 54.6 
seconds. This gives a velocity of 340.9 m. or 1118.15 ft. per 
second. Now the temperature was 15°.9 C, and as the 
velocity increases about 60 cm. per second for a rise of 1° C, 
this velocity would be 331.4 m. per second at 0° C. Other 
experimenters have obtained slightly different results. 

Velocity of Sound in Air 



Temperature. 


Velocity, Per Second. 


0° a = 32° F. 


332 m. = 1089 ft. 


15° G. = 61° F. 


341 m. = 1119 ft. 


20° C. = 68° F. 


344 m. = 3129 ft. 


-45.6° a = -50° F. 


305.6 m. = 1002 ft. 



The velocity at —50° F. was determined by Greely during 
his explorations in the arctic regions, 1882-3. 

194. Nature of a Sound-Wave. The vibrations in sound- 
waves are longitudinal, the nature of which is explained 
in § 187. 

Let a flat strip of metal be clamped in a vice or be otherwise 
held in a rigid support. Draw it aside, and let go. As it 
moves forward it condenses the air before it, and on its return 
the air is rarefied. With each complete vibration a wave of 
condensation and rarefaction is produced, and during that time 



AN AIR-WAVE ENCIRCLING THE EARTH 



171 



the sound will have travelled one wave-length, I. If the strip 
vibrates n times a second the space traversed in one second 
will be 

nl = V, the velocity of sound per second. 

The sound, however, does not go in just one direction as 
shown in Fig. 202, but it spreads out in all directions, as 



D 

Pia. 202. — As the strip vibrates the air is alternately condensed and rarefied. 

illustrated in Fig. 203, where spherical waves move out from 
the sounding bell as their centre. 
195. An Air-Wave Encircling the Earth. A wonderful 

example of the spread of an air-wave occurred in 1883. Krakatoa is 

a small island between 

Java and Sumatra, in 

the East Indies, long 

known as the seat of 

an active volcano. 

Following a series of 

less violent explosions, 

a tremendous eruption 

occurred at 10 a.m. of 

August 27. The 

effects were stupendous. Great portions of the land, above the sea 

and beneath it, were displaced, thus causing an immense sea-wave 

which destroyed 36,000 human 'hves, at the same time producing 

a great air-wave, which at once began to traverse the earth's 

atmosphere. It spread out circularly, gradually enlarging until it 

became a great circle to the earth, and then it contracted until it 

came together at the antipodes of Krakatoa, a point in the northern 

part of South America. It did not stop there, however, but enlarging 

again, it retraced its course back to its source. Again it started 

out, went to "the antipodes and returned. A third time this course 

was taken, and indeed it continued until the energy of the wave 

was spent. 

The course taken by the wave was traced by means of self- 
registering barometers located at various observing stations through- 
out the world. As the wave passed over a station there was a rise 




Fio. 203.— Illustrating 



the transmission of sound in spherical 
waves. 



172 PRODUCTION, PROPAGATION, VELOCITY OF SOUND 

and then a fall in the barometer, and this was recorded by photo- 
graphic means. In many places (Toronto included) there were four 
records of the wave as it moved from Krakatoa to the antipodes, 
and three of its return. In Fig. 204 is shown the rise in the baro- 
meter at Toronto caused by the second outward trip of the wave 



Midn ight 



53 







August 29, 18\83 



Fig. 204.— a portion of the photographic record of the height of the barometer at 
Toronto for August 29, 1SS3. To obtain the record, light is projected through 
the barometer tube above the mercury against sensitized paper which is on a 
drum behind the barometer. Every two hours the light is cut off and a white 
line is produced on the record. Shortly after 2 a.m., August 29, there was a 
rise, and at about 4.40 there was another. The former was due to the passage 
over Toronto of the wave on the second journey from Krakatoa to the 
antipodes; the latter was due to the second return from the antipodes to 
Toronto. (From the records of the Meteorological Service, Toronto.) 

and the second return. The time required to go to the antipodes 
and return to Krakatoa was approximately 36 hours. 

The sound of the explosion was actually heard, four hours after 
it happened, by human ears at Rodriguez, at a distance of over 
2,900 miles to the south-west. At the funeral of Queen Victoria, 
on February 1, 1901, the discharges of cannon were heard 140 miles 
away. 

196. Intensity of Sound. The intensity of sound depends 
on three things : — 

(1) The Density of the Mediwrn in which it is produced. 
It is found that workmen in a tunnel, in wliich the air is 
under pressure, though conversing naturally, appear to each 
other to speak in unusually loud tones, while balloonists and 
mountain climbers have difficulty in making themselves 
heard when at great heights. The denser the medium, the 
louder is the sound. 

(2) The Energy of the Vibrating Body. The amount of 
energy radiated per second is proportional to the square of 
the amplitude of the vibrating body. 



TRANSMISSION BY TUBES 



173 




Fig. 205.— Diagram to show that the 
intensity of sound diminishes with 
the distance from the source. 



(3) The Distance of the Ear from the Sounding Body. 
Suppose the sound to be radiating 
from (Fig. 205) as centre, and 
let it travel a distance OA in one 
second. The energy will be dis- 
tributed amongst the air particles 
on the sphere whose centre is 
and radius OA. 

In two seconds it will reach a 
distance OB, which is twice OA, 
and the energy which was on the 
smaller sphere will now be spread 
over the surface of the larger one. But this surface is four 
times that of the smaller, since the surface of a sphere is 
proportional to the square of its radius. Hence the intensity 
at B can be only one-fourth that at A, and we have the law 
that the intensity of a sound varies inversely as the square of 
tJie distance from the source. 

197. Transmission by Tubes. If, however, the sound is 
confined to a tube, especially a straight and smooth, one, it 
may be transmitted great distances with little loss in intensity. 
Being prevented from expanding, the loss of the energy of the 
sound-waves is caused chiefly by friction of the air against 
the sides of the tube. 

198. Velocity of Sound in Solids by Kundt's Tube. 

Having determined the velocity of sound in air we can determine it 
in other gases and in solids by a method devised by Kundt in 1865. 

A _ B JtC 



,.«m-_.Ttt1a..<ff»>^tt 



D 



^ 



Fig. 206.— The Httle heaps of powder in the tube are produced by the vibrations of the disc B. 

BD (Fig. 206) is a brass rod about 80 or 100 cm. long and 8 or 
10 mm. in diameter, securely clamped at the middle. To the end B 
is attached a disc of cork or otlier light substance which fits loosely 
into a glass tube about 30 or 35 mm. in diameter, yl is a rod on 
the end of which is a disc which slides snugly in the tube, thus 



174 PRODUCTION, PROPAGATION, VELOCITY OF SOUND 

allowing the distance between A and B to be varied. Dried pre- 
cipitated silica, or simply powder made by filing a baked cork, is 
scattered along the lower side of the tube. 

Now with a dry cloth or piece of chamois skin, on which is a 
little powdered rosin, stroke the outer half of the rod. With a little 
practice one can make the rod emit a high musical note. At the 
same time the powder in the tube is agitated, and by careful adjust- 
ment of A, the powder will at last gather into little heaps at regular 
intervals. 

We must now carefully measure the length of the rod and also 
the distance between the heaps of powder, taking the average of 
several experiments. 

By stroking the half CD of the rod we make it alternately lengthen 
and shorten, and the half BO elongates and shortens in precisely the 
same way. Thus the mid-point of the rod remains at rest, while 
all other portions of the rod vibrate longitudinally, the ends having 
the greatest amplitude. 

It is evident that the middle of the rod is a node and the ends 
loops (§ 189), and hence if we had a very long rod and each part of it 
of length BD were vibrating in the same way we would have standing 
waves in the brass I'od and BD would be one-half the wave length. 

Again, as the piston at B moves forward it compresses the air in 
front of it and as it retreats it rarefies the air. These air-waves 
travel along the tube and are reflected at A and return. The two 
sets of waves thus meet and interfere producing stationary waves as 
explained in § 189. The powder gathers at the nodes, and hence the 
distance between the nodes is one-half the wave-length in air of the 
note emitted by the brass rod. 

Let Z = length of brass rod, 

V = velocity of sound in brass, 
n = frequency of note emitted, 

then 22/ = wave-length, and V = n x 1L. 
Again, if ^ = length between the heaps of powder, 
and V = velocity of sound in air, 
then n = frequencj?^, and v = n x 21. 

V 71 X 2L L 



Hence 



X 21 I 



and r = — X V. 
I 

By measuring L, I, and knowing v we can at once deduce V, the 
velocity in brass. 

Note that 2L = wave-length in brass, 21 = wave-length in air, 
where I = length between adjacent heaps. 



VELOCITY IN DIFFERENT GASES 



175 



On using rods of other metals we can find the velocity in each of 
them. 

199. Velocity in Different Gases. The same apparatus can be 

used for different gases. To do so it is arranged as shown in 



m 



Fii 



Fio. 207.— Kuiidt's method of finding the velocity of sound in different gases. 

207. For this purpose a glass rod is preferable. It vibiates 



more easily by using a damp woollen cloth. It is waxed into the cork 
through wliich it passes. The piston D must be reasonably tight. 

As before, measure the distance between adjacent heaps when the 
tulje is filled witli air. Let it be a. Now fill it with carbonic acid 
gas and let the distance be c. 

Then we have, velocity in air = iV x 2 a, 
and velocity in carbon dioxide = iV^ x 2 c. 

TT velocity in carbon dioxide _ JV x 2 c c 

velocity in air JV x 2 a a 

and velocity in carbon dioxide = - x v. 



Velocity 


OP Sound in Solids, Liquids 


and Gases 


Substance. 


Temper- 
ature. 


Velocity. 


Substance. 


Temper- 
ature. 


Velocity. 


Aluminium 

Brass 

Copper.. . . 
II 

Iron 

Maple 


100 

20 


111. per ft. per 
Pec. sec. 
5104 16740 
3500 11480 
3560 11670 
3290 10800 
5130 16820 
4110 13470 


Water 

Carbon diox- 
ide 

Illuminating 
gas 

Oxygen 


-c. 

9 








ni. per ft. per 
sec. sec. 
1435 4708 

261.6 858 

490.4 1609 
317.2 1041 



200. Reflection of Sound. Everyone has heard an echo. 
A sharp sound made before a large isolated building or a 
steep cliff, at a distance of 100 feet or more, is returned as an 
echo. The sound-waves strike the flat surface and are 
reflected back to the ear. 

When there are several reflecting surfaces at different dis- 
tances from the source of sound a succession of echoes is heard. 
This phenomenon is often met with in mountainous regions 



176 PllODUCTION, PROPAGATION, VELOCITY OF SOUND 

In Europe there are many places celebrated for the number 
and beauty of their echoes. An echo in Woodstock Park 
(Oxfordshire, England) repeats 17 syllables by day and 20 by 
night. Tyndall says : " The sound of the Alpine horn, echoed 
from the rocks of the Wetterhorn or the Jungfrau [in Switzer- 
land] is in the first instance heard roughly. But by successive 
reflections tlie notes are rendered more soft and flute-like, the 
gradual diminution of intensity giving the impression that 
the source of sound is retreating farther and farther into the 
solitude of ice and snow." 

The laws of reflection of sound are the same as those of 
light (see § 346). Let a watch be hung at the focus of a large 

concave mirror (Fig. 208). 
The waves strike the mirror 
and are returned as shown 
in the figure, being brought 

Fig. 208.— a watch is held in the focus of one ^^ ^ lOCUS agaui by a SCCOud 

concave reflector and the ticking is heard at niivvnr On linlrlino- fl^- fliic 

the focus of the other. (The foci can be UllllOl. VJU IlOlUnig ai WllS 

located by means of rays of light.) f^^^^ ^ f^^^^^^j f^.^^^^ ^^^j^-^j^ ^ 

rubber tube leads to the ear the sound may be heard, even 
though the mirrors are a considerable distance apart. 

In the Whisperir^g Gallery of St. Paul's Cathedral in London, 
England, the faintest sound is conveyed from one side of the 
dome to the other, but is not heard at any intermediate point. 

The Mormon Tabernacle at Salt Lake City, Utah, is an 
immense auditorium, elliptic in shape, 250 feet long, 150 feet 
wide and 80 feet high, with seating accommodation for 8000 
people. A pin dropped on a wooden railing near one end, or 
a w^hisper there is heard 200 feet away at the other end with 
remarkable distinctness. 

The bare walls of a hall are good reflectors of sound, though 
usually the dimensions are not great enough to give a distinct 
echo, but the numerous reflected sound-waves produce a rever- 
beration which appears to make the words of the speaker run 




THE SUBMARINE BELL 



177 



into each other, and thus prevents them being distinctly heard. 
By means of cushions, carpets and curtains, which absorb the 
sound which falls upon them instead of reflecting it, this 
reverberation can be largely overcome. The presence of an 
audience lias the same effect. Hence, a speaker is heard nmch 
better in a well-filled auditorium than in an empty one. 

201. The Submarine Bell. A valuable application of the fact 
that water is a good conductor of sound is made in a method 
recently introduced for 
warning ships from dan- 
gerous places. Light- 
houses and fog-horns 
liave long been used, but 
the condition of the at- 
mosphere often renders 
these of no avail. Sub- 
marine signals, however, 
can be depended upon 
in all kinds of weather. 
The submarine bell, 
which sends out the 
signals (Fig. 209), is 
hung from a tripod rest- 
ing at the bottom of the 
water or is suspended 
from a lightship or a 
buoy. The striking me- 
chanism is actuated by compressed air 
or electricity supplied from the shore or 
the lightship. 

The receiving apparatus is carried by the ship. Two iron tanks 
are located in the bow of the vessel, one on each side (Fig. 210). 
These tanks are filled with salt water, and the ship's outer skin 
forms one side of the tank. Suspended in eacii tank are two micro- 
phones (§537), which are connected to two telephone receivers up in 
the pilot-house. The officer on placing these to his ears can hear 
sounds from a bell even when more than 15 miles away ; and by 
listening alternately to the sounds from the two tanks he can 
accurately locate the direction of the bell from him. Signal stations 
are to be found on the shores of various countries, several being 
located in the lower St. Lawrence and about the maritime provinces 
of Canada. 




Fio. 209. — Subma- 
rine bell, worked 
by compressed air 
supplied from the 
shore. The mecha- 
nism for moving 
the hammer of the 
bell is contained 
in the upper cham- 
ber. 





. 11 . . ^7 


l:lt=q 




i? 


\'\^^3 


^'^ 


> 


A')^^*^^: J 


i 


\ \\\\\Hu *^\mlr — ' 


\ 




\^ 


^\r — ^ 



Fig. 210.— The sound from the bell is 
received by two tanks placed in the 
forepeak of the ship, one on each 
side. The tank is filled with salt 
water, and the ship's outer skin 
forms one of its sides. In the water 
are two microphones, which are 
connected by wires A , A to two tele- 
phone receivers up in the pilot- 
house. 



178 PRODUCTION, PROPAGATION, VELOCi;rY OF SOUND 



QUESTIONS AND PROBLEMS 

1. Calculate the velocity of sound in air at 5°, 10°, 40° C. (See § 193.) 

2. An air-wave travelled about the earth (diameter 8000 miles) in 36 
hours. Find the velocity in feet per second. 

3. A thunder-clap is heard 5 seconds after the lightning flash was seen. 
How far away was the electrical discharge ? (Temperature, 15° C.) 

4. The velocity of a bullet is 1200 feet per second, and it is heard to 
strike the target 6 seconds after the shot was fired. Find the distance of 
the target. (Temperature, 20° C.) 

5. At Carisbrook Castle, in the Isle of Wight, is a well 210 feet deep 
and 12 feet wide, the interior being lined with smooth masonry. , A pin 
dropped into it can easily be heard to strike the water. Explain. 

Find the interval between the moment of dropping the pin and that of 
hearing the sound. (Temperature, 15° C, g = 32.) 

6. Why does the presence of an audience improve the acoustic pro- 
perties of a hall ? 

7. Explain the action of the ear-trumpet and the megaphone or 
speaking-trumpet. 

8. If all the soldiers in a long column keep time to the music of a 
band at their head will they all step together ? 

9. A man standing before a precipice shouts, and 3 seconds afterwards 
he hears the echo. How far away is the precipice ? (Temperature, 15° C.) 

10. In 1826 two boats were moored on Lake Geneva, Switzerland, one 

on each side of the lake, 44,250 

feet apart. One was supplied 

with a bell B (Fig. 211a), placed 

under water, so arranged that at 

the moment it was struck a torch 

m lighted some gunpowder in 

the pot P. The sound was heard 

at tlie other boat by an observer 

with a watch in his hand and 

his ear to an ear-trumpet, the 

bell of which was in the water. 
The sound was heard 9.4 seconds after the flash was seen. Calculate the 
velocity of sound in water. 

11. In a Kundt's tube a brass rod is 1 m. long, and five of the intervals 
between the dust-heaps equal 49.5 cm. Find the velocity of sound in brass. 

12. When a Kundt's tube is filled with hydrogen the dust-heaps are 3.8 
times as far apart as with air. Find the velocity of sound in hydrogen. 
(Temperature, 20° C.) 





Flo. 211a. — Apparatus for 
producing the sound, in 
Lake Geneva. 



Fig. 2116. — Listening 
to the sound from 
the other side of 
the Lake. 



CHAPTER XX 

Pitch, Musical Scales 

202. Musical Sounds and Noises. The slam of a door, the 
fall of a luiuimer, the crack of a rifle, the rattling of a 
carriage over a rough pavement, — all such disconnected, 
disagreeable sounds we call noiftes ; while a 
note, such as tliat yielded by a plucked guitar 
string or by a flute, we at once recognize as 
musical. 

A musical note is a continuous, uniform and 
pleasing sound ; while a noise is a shock, or 
an irregulai" succession of shocks, received by 
the ear. 

Against the teeth on a rotating disc (Fig. 
212) hold a card. When the speed is slow we 
hear each separate tap as a noise, but as it is 
increased these taps at last blend into a clear 
musical note. 




Fig. 212. — Toothed 
wheels on a rotating' 
niaohine. On hold- 
ingf a card against 
the teeth a musical 
sound is heard. 




The same result, with a rather more pleasing effect is 
obtained by sending a current of air through holes regularly 
spaced on a circle near the circumference 
® -v-.^ of a rotating disc (Fig. 213). The little 

"ir^-"" — puffs through the holes blend into a 

FiQ 213.-Air is blown through pleasing^ UOte. 
the holes in the rotating- plate. ^ o 

It is possible for a number of musical notes to be so 

jumbled together that the periodic nature is entirely lost, 

and then the result is a noise. If the holes in the disc (Fig. 

213) are irregularly spaced we get a noise, not a musical note. 

179 



180 PITCH, MUSICAL SCALES 

A musical tone is due to raiiid periodic motion of a 
sonorous body ; a noise is due to non-jjeriodic motion. 

203. Pitch. There are three features by which musical 
tones are distinguished from each other, namely: — 

(1) Intensity or Loudness, (2) Pitch, (3) Quality. 

The intensity of a sound depends on the amplitude of the 
vibrations of the air particles at the ear, and has already been 
discussed (§ 196). 

The pitch of a sound depends on the number of vibra- 
tions per second, or what amounts to the same thing, upon 
the number of sound-waves which enter the ear in a 
second. 

This can be tested very easily by means of the toothed 
wheel or the perforated disc just described. When the speed 
of rotation is slow, and hence the number of vibrations per 
second few, the pitch is low, and when it is increased the 
pitch becomes higher. 

204. Determination of Pitch. The number of vibrations 
corresponding to any given pitch may be determined by 
various devices. One is the toothed wheel shown in Fig. 212. 
Suppose we wish to find the number of vibrations of a tuning- 
fork. The speed of rotation is increased until the sound 
given by the wheel is the same as that by the fork. Then 
the speed is kept constant for a certain time — say half a 
minute — and the number of turns of the crank in this time is 
counted and the rotations of the wheel deduced. Then on 
multiplying this number by the number of teeth on the wheel 
we can at once deduce the number of vibrations per second. 
The perforated disc may be used in the same way. 

A more satisfactory instrument is that shown in Fig. 214 
and known as a siren. It was invented by Cagniard de la 
Tour in 1819. 



LIMITS OF AUDIBILITY OF SOUNDS 



181 




A perforated metal disc B rotates on a vertical axis, just 
above a cylindrical air-chamber G. The 
upper end of the chamber and also the disc 
are perforated at equal intervals along a 
circle which has as centre the axis of rota- 
tion. The upper and lower holes correspond 
in number, position and size, but they are 
drilled obliquely, those in tlie disc sloping 
in a direction opposite to those in the end 
of the chamber. The tube D is connected 
with a bellows or other blower. 

When the air is forced into the chamber fio- 2i4.-The siren. Air 

enters the chamber C by 

and passes up through the holes, the disc is way of the pipe /> andon 

r L o ' escaping causes the disc 

made to rotate by the air-current striking ^ '^ rotate, 
against the sides of the holes in the di«c, and the more power- 
ful the air-current the more rapid is the rotation. 

Vibrations in the air are set up by the puffs of air escaping 
above the disc as the holes come opposite each other ; and by 
controlling the air supply we can cause the disc to rotate at 
any sj^eed, and thus obtain a sound of any desired pitch. 

Having obtained this sound, a mechanical counter, in the 
upper part of the instrument, is tin-own in gear and, keeping 
the speed constant for any time, this will record the number 
of rotations. Tlie number of vibrations is obtained at once by 
nuiltiplying the number of rotations by the number of holes in 
the disc and dividing by the number of seconds in the interval. 

A method depending on the principle of resonance is 
described in § 221. 

205. Limits of Audibility of Sounds. Not all vibrations, 
even though perfectly periodic, can be recognized as sounds, 
the power of detecting these varying widely in different 
persons. For ordinary ears the lowest frequency which causes 
tlxe sensation of a musical tone is about 30 per second, the 
highest is between 10,000 and 20,000 per second 



182 PITCH, MUSICAL SCALES 

In music the limits are from about 40 to 4000 vibrations per 
second, the piano liaving approximately this range. The 
range of the human voice lies between 60 and 1300 vibrations 
per second, or more than 4 J octaves ; a singer ordinarily has 
about two octaves. 

206. Musical Combinations or Chords. A musical note is 
pleasing in itself, but certain combinations of notes are 
especially agreeable to the ear. These have been recognized 
amongst all nations from the earliest times, having been 
developed purely from the aesthetic or artistic side. The older 
musicians knew nothing about sound waves and vibration 
numbers ; they only knew what pleased the heart and 
expressed its emotions. 

But on measuring the frequencies of the notes of the pleasing 
combinations, we find that the ratios between tliem are 
peculiarly simple, and indeed that the more pleasing any 
combination is the simpler are the ratios between the 
frequencies of the notes. 

207. The Octave. Pitch depends only on the number of 
vibrations per second ; but as we compare notes of different 



!ll!llllllll!m.lJIHIIJI 



Fio. 215. — Central part of a piano key-board. The notes marked 
C;, Ci, C, C, C, go up by octaves. 

pitch with one another — for instance the notes on a piano — 
we are struck with the fact that when we have gone a certain 
distance upwards or downwards, the notes appear to repeat 
themselves. Of course the pitch is different but there is a 
wonderful similarity between the notes. 

On investigation, a remarkable relation between the 
vibration-frequencies of the notes is revealed. Thus one note 
appears to be the repetition of another when their vibration- 
frequencies are as 2 to 1, and one is said to be an octave above 



INTERVALS OF THE MAJOR DIATONIC SCALE 183 

the other. The combination of a note and its octave is the 
most pleasing of all. 

between the note and its octave custom lias introduced six 
notes, the eight notes thus obtained usually being designated 
in music thus : — 

G D E F G A B C. 
As we pass from G to G' by these interpolated notes we do so 
by steps which are universally recognized as the most pleasing 
to the ear. This series of notes is called the natural or "major 
diatonic scale. 

208. Intervals of the Major and Minor Diatonic Scales. 

By actual experiment it has been found that, whatever the 
absolute pitch may be, — whether high up in the treble, or low 
down in the bass, — the ratios between the vibration-frequencies 
of the different notes are constant. 

Suppose the note G has a frequency 256. The entire scale 
is as follows : — ■ 

G D E F G A B G' 
256 288 320 8411 334 426S 480 512, 
the ratios being 1 I f | t f -w 2. 

These ratios hold, whatever the absolute frequency may be. 
By international agreement the frequency of middle G of the 
piano is taken as 261, that of the A string of a violin being 
435 vibrations per second. The numbers for the scale are 
then, 

261 293.6 326.2 348 391.5 435 489.4 522. 
The interval between two notes is measured by the im- 
proper fraction obtained on dividing their frequencies. 
Thus the interval C to D is HI = | 

" " X> to ^ is III = V- ; and so forth. 
Hence the intervals between the successive notes of the scale 
are : — 

G D E F G A B G' 



184 PITCH, MUSICAL SCALES 

This scale is called the Major Diatonic Scale. Another 
scale is also used in music, known as the Minor Scale. In it 
the ratios and intervals are : — 

A^ B, C D E F G A 

1 964 3 890 



As a matter of fact, in modern music tlie minor scale is not 
always used in precisely this form, the principal difference 
being in the sharpening of the 7th or leading note. The 
major scale has a cheerful exciting tendency ; the minor, to 
most hearers, is melancholy and pathetic, 

209. Musical Chords. Two or more notes sounded simul- 
taneously constitute a chord. If the effect is agreeable it is 
called concord; if disagreeable, discord. 

The most perfect concord is G, G', the interval between the 
notes being f or 2. The next is C, G, the interval being f . It 
will be observed that in expressing these intervals we use 
only the small numbers 1, 2, 3. 

When the notes G, E, G are sounded together the effect is 
extremely pleasing. This combination is called the Major 
Triad, and when G' is added to it we get the Major Chord. 
The frequencies of the triad have the ratios : 

C : ^ : (^ = 4 : 5 : 6. 
A close examination of the Major Scale shows that it is made 
up of repetitions of this triad. Thus 0, E, G, F, A, G' and 



GDEFGABG'D' 



G, B, D' are all major triads. 

210. The Scale of Equal Temperament. In musical com- 
position G is not always used as the first or key-note of the 
scale, but any note may be chosen for that purpose. On 
calculating the frequencies of the different notes of the major 



THE HARMONIC SCALE 185 

scale when C, D and E are key-notes (taking C = 256), we 
find them to be as follows : — 

C D E F G A B C ly E' F' G' 

Key of C | 256 288 320 3411 334 426| 480 512 I 576 640 682§ 768 
Key of D 270 1288 324 364 380 432 480 540 576|648 720 7G0 
Key of E 266§ 300|320 360 400 426f 480 533^ 600 640 1720 800 

Comparing the first two scales together, we see that the 
second requires 5 notes not in the first ; the third scale 
requires 3 notes not found in either of the others. With each 
new scale additional notes are required. To use the minor 
scale still more would be needed. Indeed, so many would 
have to be introduced that it would be quite impracticable to 
construct an instrument with fixed notes, such as the piano or 
organ, to play in all these keys. 

The difficulty is overcome by tempering the scale, i.e., by 
slightly altering the intervals. In the scale of equal tempera- 
vient, which is the one usually adopted, the octave contains 
13 notes, the intervals between adjacent notes all being equal. 
Each is equal to 'i72 = 1.059, and is called a semi-tone. On 
multiplying the frequency of a note by this ratio, the note 
next above is obtained. From the chromatic scale of 13 
notes thus obtained, the intervals of the major scale are : — 
Between the 1st and 2nd, 2nd and 3rd, 4th and 5th, 5th and 
6th, .6th and 7th, each two semi-tones or a whole tone, i.e., 
(1.059)" ; between the 3rd and 4th and the 7th and 8th, each 
a semi-tone. 

The following table shows the difference between the true 
or natural and the tempered scale : — 

C D E F G ABC 

True 256 288 320 3411 SM 426f 480 512 

Tempered 256 287.3 322.5 341.7 388.6 430.5 483.2 512 

The natural scale is more agreeable than the equally- 
tempered. On a violin an accomplished performer can obtain 



186 PITCH, MUSICAL SCALES 

true intervals by properly placing his fingers ; and a choir of 
picked voices, when singing unaccompanied, uses true intervals, 

211. The Harmonic Scale. When a note is sounded on 
certain musical instruments a practised ear can usually detect, 
in addition to the fundamental or principal tone, tones of 
other frequencies. These are much less intense than the prin- 
cipal "tone. If tho frequency of a tone is represented by 1, 

those tones with frequencies, corresponding to 2, 3, 4, 5 

are said to be harmonics of the tone 1 which is called their 
fundamental. The entire series is known as the Harmonic 
Scale. 

The tones which are present in a note are members of such 
a harmonic scale, but they are not necessarily harmonics of 
the lowest note heard. Their fundamental may be a still 
lower tone. They are often referred to as overtones of the 
fundamental. 

In the piano these harmonics are prominent. In the tuning- 
fork when properly vibrated, the harmonics almost instantly 
disappear, leaving a pure tone. 

QUESTIONS AND PROBLEMS 

1. From what experience would you conclude that all sounds, no 
matter what the pitch may be, travel at the same rate ? 

2. If the vibration number of G is 300 find those for F and A. 

3. Tlie wave-length of a sound, at temperature 15° C, is 5 inches. 
Find its frequency. 

4. Why does the sound of a circular saw fall in pitch as the saw enters 
the wood ? 

5. Find the wave-length of D'^ {i.e., four octaves above D) in air at 
0° C, taking the frequency of C as 261. 

6. Find the vibration numbers of all the Cs on the piano, taking 
middle G as 261. 

7. If the frequency of A were 452 what would be that of CI 

8. Which note has 3 times the number of vibrations of 0? Which 
has 5 times ? 

9. Find the wave-lengths in air at 20° C. of the fundamental notes of 
the yioliii G^j, D, A, E'. {A = 435 vibrations per second.) 



CHAPTER XXI 

Vibrations of Strings, Rods, Plates and Air Columns 

212. The Sonometer. Tlie vibrations of strings are best 
studied by means of the sonometer, a convenient form of 
which is shown in Fig;. 216. Tlie strings are fastened to steel 




TIT 



Fig. 216. — A sonometer, consisting of stretched strings over a thin wooden box. 
By means of a bridge we can use any part of a string. 

pins near the ends of the instrument, and then pass over 
fixed bridges near them. The tension of a strino- can be 
altered by turning the pins with a key, or we may pass the 
string over a pulley and attach weights to its end. A movable 
bridge allows any portion of a string to be used. The 
vibrations are produced by a bow, by plucking or by striking 
with a suitable hammer. 

The thin wooden box which forms the body of the instru- 
ment strengthens the sound. If the ends of a string are 
fastened to massive supports, stone pillars for instance, it 
emits only a faint sound. Its surface is small and it can put 
in motion only a small mass of air. When stretched over the 
light box, however, the string communicates its motion to the 
bridges on which it rests, and these set up vibrations in the 
wooden box. The latter has a considerable surface and 
impresses its motion upon a large mass of air. In this way 

the volume of the sound is multiplied many times. 

187 



188 VIBRATIONS: STRINGS, RODS, PLATES, AIR COLUMNS 

The motions Avliich the bridges and the box undergo are 
said to be forced vibrations, while those of the string are 
called free vibrations. 

213. Laws of Transverse Vibrations of a String. First 
take away the movable bridge and pluck the string. It 
vibrates as a whole and gives out its fundainental note. TJien 
place the bridge under the middle point of the string, and 
pluck again, thus setting one-half of the string in vibration. 
The note is now an octave above the former note.* We thus 
obtain twice the number of vibrations by taking half the 
length of the string. 

If further we take lengths which are f , f , f , f , f, y\ of the 
full length of the string we secure six notes which, with the 
fundamental and its octave, comprise the major scale. Now 
from § 208 we see that the relative frequencies of the notes of 
the scale are proportional to the reciprocals of these fractions, 
and hence we deduce the following important 

Law of Lengths. — Tfie number of vibrations of a string 
is inversely lyroportional to its length. 

Next, let the tension of one of the strings be so altered that 
it emits the same note as does that one with the weight on the 
end of it. Then let us keep adding to the weiglit until the 
string gives a note which is one octave higher, that is, the note 
now obtained is in unison with that obtained from the other 
string Avhen the movable bridge is put under its middle point. 

It will be found that the new weight is four times the old 
one. Thus we see that in order to obtain twice the number of 
vibrations we had to multiply the tension 4 times. In order 
to obtain 3 times the number of vibrations we must multiply 
the tension 9 times ; and so on. In this way we obtain the 
second important law, namely, the 

Law of Tensions. — The number of vibrations is i^ro- 
portional to the square root of the stretcldng lueigJd. 

* By runniriff up the successive notes of the scale the ear will recogriize the octave when the 
String is just half the entire length. 



NODES AND LOOPS IN A VIBRATING STRING 189 

Now let us see what is the effect of making tlie string 
thicker. Let us use a string of tlie same material but of 
twice the diameter. We find that the number of vibrations 
obtained is one-half as great. If the diameter is made three 
times as great, the number of vibrations is reduced to one- 
third ; and so on. In this way we obtain the 

Law of Diameters. — The number of vibrations is inversely 
proportional to the diameter of the string. 

Finally, on testing strings of different materials we would 
reach the 

Law of Densities. — The number of vibrations per second 
is inversely proportional to tlie square root of the density. 

For example: — The density of steel wire is 7.86 and of 
platinum wire is 2L50 g. per c.c. Hence if we take wires of 
steel and platinum of the same diameter, length and under the 
same tension, the number of vibrations executed by the steel 
wire will be VV# ~ ^-^^ times that by the platinum. 

214. Nodes and Loops in a Vibrating String. The pro- 
duction of nodes and loops in a vibrating string can be 
beautifully exhibited on the sonometer. 

Place five little paper riders on the wire at distances 
h h h h> I of the wire's 
length from one end. 
Then while a tip of tlie 
finger or a feather is 
gently lield against tlie 
string at a distance ^ 

of the leno"th from ■''"'*'• ^^'^' — obtaining nodes and loops in a vibrating 
to string. The paper riders stay on at the nodes, but 

the other end, carefully ^''^ ''*'''°'^" °^ ^"^ *^^ '°°p^- 
vibrate the string with a bow. The string will break up into 
nodes and loops, as shown in the figure, the little riders 
keeping their places at the nodes but being thrown off" at the 
loops. The note emitted will be 2 octaves above the funda- 
mental, with a frequency 4 times that of the latter. 




100 VIBRATIONS: STRINGS, RODS, PLATES, AIR COLUMNS 




lilllini*- (a) 

(h) 
(c) 



Fio. 218. — How a string vibrates when 
giving (a) its fundamental, (h) its first 
harmonic, (c) both of these together. 



In the same way, though somewhat more easily, tlie string 
can be made to break up into 2 or 3 segments. To obtain 2 
segments, touch the string at the middle-point ; for 8 segments, 
touch it ^ of the string's length from the end. In both cases, 
of course, tlie paper riders must be properly placed. 

215. Simultaneous Production of Tones. Wlien a string 

vibrates as a whole, as shown in 
Fig. 218«, it emits its funda- 
mental tone. To emit its first 
harmonic or overtone it should 
assume the form shown in (6). 
In the same way the forms as- 
sumed when giving the higher overtones can easily be drawn. 

Now it is practically impossible to vibrate the string as a 
whole without, at the same time, having it divide and vibrate 
in segments. Thus with the fundamental tone of the string 
will be mingled its various harmonics. 

The relative strengths of these harmonics will depend on 
the manner in which the string is put in vibration, — whether 
by a bow, by plucking or by striking it at some definite point. 
The sound usually described as " metallic " is due to the 
prominence of higher harmonics. 

In Fig. 218c is shown the actual shape of the string obtained 
by combining (a) and (b), that is, by adding the first harmonic 
to the fundamental. 

216. Vibrations of Rods. The 

vibration of a rod clamped at its 
middle and stroked longitudinally has 
been desci-ibed in § 198, in connection 
with Kundt's tube. 

But a rod may vibrate transversely 
also. Let it be clamped at one end, and the other end be 
drawn aside and let go. Ordinarily it will vibrate as in 



\b 



Mr 



□ □ □ 



Fig. 



219.— Vibrations of a rod 
clamped at one end. 



THE TUNING-FORK 



191 



Fig. 219a, in whicli case ifc produces its fundamental tone. 
But it may vibrate as illustrated in (h) and (c), emitting 
its overtones. 

The vibi-ations are due to the elasticity of the rod. The 
investigation into these transverse vibrations is somewhat 
complicated and difficult, but the following simple law has 
been found to be true. 

Law of Transverse Vibrations of Rods : — llie number 
of vibrations varies inversely as the square of tlte length of 
the rod and directly as its thickness. 

The triangle and musical boxes are examples of the trans- 
verse vibrations of rods. 

217. Tuning-Fork. A tuning-fork may be considered as a 
rod which is bent and held 
at its middle point. When 
it vibrates the two prongs 
alternately approach and re- 
cede, while the stem has a 
slight motion up and down. 
Why this is so may be seen 
from Fig. 220. In 7, N, N 
represent the nodes when the straight bar is made to vibrate. 
As the bar is bent more and more the nodes approach the 
centre, and when the fork is obtained (as in //) the nodes are 
so close together that the motion of the stem is very small. 
That it exists, however, can be readily shown. 

If a fork, after being set in vibration, is held in tiie hand it 
will continue in motion for a long time. It gives up its energy 
slowly and so the sound is feeble. But if the stem is pressed 
against the table the sound is much louder. Here the stem 
produces forced vibrations in the table, and a large mass of air 
is thus put in motion. In this case the energy of the fork is 
used up rapidly and the sound soon dies awa3^ 




N N 

Fig. 220.— How a tuning-fork vibrates. 



192 VIBRATIONS: STRINGS, RODS, PLATES, AIR COLUMNS 



Tuniuf-forks are of great importance in the study of sound. 
When set in motion by gentle bowing, the overtones, if present 
at all, die away very rapidly. 

With a rise in temperature the elasticity of the steel is 
diminished and the pitch is slightly lowered. 

218. Vibrations of Plates. The plates used in the study 
of sound are generally made of brass or glass, and are ordi- 
narily square or circular in shape. The plate is held by a 
suitable clamp at its centre, and is made to vibrate by a 
violin bow drawn across the edge. 

Let us scatter some sand over a square plate, and while a 

finger-nail touches it at the 
middle of one side draw 
the bow across the edge 
near one corner. At once 
a clear note is given, and 
the sand takes up the figure 
shown in Fig. 221a. If 
the corner is damped with 
the finger-tip and the bow 
is applied at the middle of 
a side, the form shown in h 

is assumed, and the note is higher than the former. By 

damping with two finger-tips the form c is obtained and a 

much higher note is produced. 

The sand is tossed away from certain parts of the surface 

and collects along the nodal lines, that is, those portions which 

are at rest. 

Some of the forms assumed by the sand when a circular 

plate is vibrated are shown in d, e, f. The sand-figures always 

reveal the character of the vibration, and the more complicated 

the figure, the higher-pitched the note. 




Fio. 221.— Sand-figures showing nodal lines in 
vibrating plates. 



VIBRATIONS OF AIR COLUMNS; RESONANCE 



198 




Fio. 222.— Aircoluim 
in resonance with j 
tuning-forli. 



219. Vibrations of Air Columns ; Resonance 
a tube about 2 inclies iu diameter and 18 
inches long with its lower end in a vessel con- 
taining water (Fig. 222) ; and over the open 
end hold a vibrating tuning-fork. Suppose 
the fork to make 256 vibrations per second. 

By moving the tube up and down we find 
that when it is at a certain deptli, the sound 
we hear is greatly intensified. This is due to 
the air column above the water in the tube. 
It must have a definite length for each fork. 
On measuring it for this one we find it is ap- 
proximately 13 inclies. With higher-pitched 
forks it is smaller than this, being always 
inversely proportional to tlie frequency of 
the fork. 

The air column is put in vibration by the 
fork, its period of free vibration being tha 
same as that of the fork. The air column 
is said to be in resonance with the fork. 

220. Explanation of the Resonance of the 
Air Column. The tuning-fork prong vibrates 
between the limits a and h (Fig. 223). As it 
moves forward from a to 6 it produces a con- 
densation which runs down the tube and is 
reflected from the bottom. When the fork retreats from 
6 to a a rarefaction is produced which also travels down the 
tube and is reflected. 

Now for resonance the tube must have such a length that in 
the time that the prong moves from a to 6 the condensation 
travels down the tube, is reflected, and arrives back at h ready 
to start up, along with the fork, and produce the rarefaction. 
Thus the vibrations of the fork and of the air column are 
perfectly synchronous; and as the fork continues to vibrate 



Fig. 223.— Diagrram to 
explain resonance 
in a closed tube. 



194 VIBRATIONS: STRINGS, RODS, PLATES, AIR COLUMNS 

the motion of the air in the tube accumulates and spreads 
abroad in the room, producing the marked increase of sound. 

221. Determination of the Velocity of Sound by Resonance. 

From the explanation given of the resonance of the air column 
in a tube, it is seen that the sound-waves travel from A to B 
and back again while the fork is making half of a vibration. 
During a complete vibration of the fork the waves will travel 
four times the length of the air column ; but we know that 
while the fork is making one vibration the sound-waves travel 
a wave-length. Thus the length of the air column is one- 
fourth of a wave-length of the sound emitted by the fork.* 

If we know the frequency of the fork we can, by measuring 
the length of the resonance column, at once deduce the velocity 
of sound. Also, if we know the length of the resonance 
column and the velocity of sound we can deduce the pitch. 

For example, using tlie values just obtained, 

Frequency it = 2.56 per second, 
Wave-length i = 4 x 13 = 52 inches ; 
Then v = nl = 256 x 52 

= 1109 feet per second. 

222. Forms of Resonators. A resonator is a hollow vessel 

tuned to respond to a certain defi- 
nite pitch. Two forms are shown 
in Fig. 224. In each case there is 

Fio 224.-TWO forms of resonators a large Opening, to be placed near 

The one on the right can be adjusted tort)' r 

for different tones. ^]^q source of the sound, while the 

smaller opening is either placed in the ear, or a rubber tube 
leads from it to the ear. The volume is carefully adjusted so 
as to be in resonance with a tuning-fork (or other body) 
vibrating a definite number of times per second. 

These resonators are used to analyse a compound note. We 
can at once test whether there is present a tone corresponding 

*More accurately the quarter wave-length of the sound is equal to the distance from the 
surface of the water to the top of the tube + 0.8 of the radius of the tube. 




RESONANCE OF AN OPEN TUBE 195 

to tliJit of the resonator, by simply liolding the instrument 
near the sounding body ; if tlie air in the resonator responds, 
tliat tone is present, if it does not respond, tlie tone is absent. 

The spherical form was used largely by the great German 
scientist Helmholtz ; the other, ■which can be adjusted to 
several tones, was introduced by Koenig. They are usually 
made of glass or brass, but quite serviceable ones can be made 
in cylindrical shape out of heavy paper. (See also § 234.) 

Tuning-forks which are used in acoustics are generally 
mounted on a light box of definite size (see Fig. 238). This 
is so constructed that the air within it is in resonance with 
the fork. If a fork is held with its stem resting on the table, 
the table is forced to vibrate in consonance with the fork. 

223. Resonance of an Open Tube. Let us take two tubes, 

about two inches in diameter, one of 

them slipping closely over the other, n _ 

Each may be 15 or 18 inches long. 

'' ° Fio. 225.— The length of an open tube 

ISTnw viVirofp +1ta fnvV ■urlmuA fro when in resonance with a tunintr- 

INOW VlDrare tne IOIK W nose Iie- ^^^^ j^ o„g.haif the wave-length Sf 

quency is 256 per second and hold the sound 

it over the end of the tube, varying the length at the same time. 

At a definite length the air within the tube vigorously 
responds, and there is a marked increase in the sound. On 
measuring the length of the tube we find it is 26 inches, just 
twice the length of the tube when one end is closed. 

But we found that the closed tube was one-fourth the wave- 
length of the sound to which it responded ; hence an open tube 
is one-half the wave-length of the sound given by it. 

The relation between the notes emitted by an open and a 
closed pipe of the same length can easily be illustrated by 
blowing across the end of a tube (say ^ inch in diameter and 
2 inches long), and observing the note produced when the tube 
is open and when a finger is held over one end of it. The 
former note is an octave hioher than the latter. 



196 VIBRATIONS: STRINGS, RODS, PLATES, AIR COLUMNS 



224. Mode of Vibration in an Open Tube. When a rod is 
clamped at the middle and one half is stroked, 
as in §198, we find that both halves lengthen 
and shorten. In this case there is a node 
at the* middle, which is always at rest, and a 
loop at each end. 

The air in an open tube vibrates quite 
similarly' ; indeed it behaves like two closed 
tubes placed end to end. (Fig. 226.) 

The Isiyer of air across the middle of the 

open tube remains at rest while those on each 

side of it crowd up to it and then separate 

from it again. The layers at either end swing 

without appreciably approaching those next 



Pia. 226.— Explaining 
how an open pipe 
vibrates. 

back and forth 
to them. 



There is the greatest change of 
density at the middle of the tube, 
or the bottom of the closed tube, 
— i.e., at the node, — while the 
air particles execute the greatest 
swing back -and -forth (without 
change in the density of the air), 
at the open ends. There is a loop 
at each end. 

225. Organ Pipes. The most 
familiar application of the vibra- 
tions of air columns is in organ 
pipes. They are made either of 
wood or metal. If of wood, pine, 
cedar or mahogany is used ; if of 

metal, tin (with some lead in it) or zinc. 

In Fig. 227 is shown a section of a rectangular wooden 

pipe ; in Fig. 228 is a metallic cylindrical pipe. Sometimes 

the pipes are conical in shape. 



Fio. 227. — Section of 
a wooden organ 
pipe. 



Fig. 228. -A me- 
tallic org^an 
pipe. 



OVERTONES (OR HARMONICS) IN AN ORGAN PIPE 197 



Air is blown through the tube T into the chamber C, and 
escaping from this by a narrow slit it strikes against a thin 
lip D. In doing so a periodic motion of the air at the lip is 
produced, and this sets in motion the air in the pipe, which 
then gives out its proper note. 

Organ pipes are of two kinds, — open and closed. In some 
open pipes reeds are used (^ 238.) From the discussion in 
§ 223 it will be clear that the note yielded by an open pipe 
is an octave higher than that given by a closed pipe of the 
same leno-th. 



The 
been 



226. Overtones (or Harmonics) in an Organ Pipe. 

vibrations of the open and closed pipes which have 
described in § 219 are the 
simplest which the air- 
column can make, and they 
give rise to the lowest or 
fundamental notes of the 
pipes. In order to obtain the 
fundamental the pipe must 
be blown gently. If the 
strength of the air-current 
is gradually increased, 
other tones, namely, the figs. 229, 230, 231, 232, 233, 234. 

1 C 4-1 • "ll Showing the nodes and loops in open and 

overtones or tne pipe, will closed orj^an pipes with different strengths 

1111 of air-currents. 

also be iieard. 

In Figs. 229, 280, 231 are represented the divisions of the 
air column in a stopped pipe corresponding to different 
strengths of the air-current. In Fig. 229 we have the funda- 
mental vibration; here the column is undivided. The only 
node present is at the closed end, and there is a loop at the 
lip-end. In Fig. 230 is shown the condition of the air column 
corresponding to the first overtone of the pipe. There is a 
node at the closed end, and another at a distance \ of the 



1 — ' — 1 

(: 

! '; 
■ i 


' ,K 


v/ 

/ \ 




"K" 


i \ 

■ 


/ 

/ \ 


j ■ 


1 \ 






\ 


--){•■■ 


i \ 




I \ 


"7V 

/ \ 










Sr 


hr 


hr 




'^^ 


nr 


nr 



198 VIBRATIONS: STRINGS, HODS, PLATES, AIR COLUMNS 

length of the pipe from the lip-end. Thus the distance from 
a node to a loop is ^ that in Fig. 229, and the wave-length of 
the note is -3- that of the fundamental. This is called the third 
harmonic, the fundamental being considered the first. 

In Fig. 231 there are three nodes and three loops, in the 
places indicated. From a node to a loop the distance is \ of 
the length of the pipe, and hence the wave-length of the 
sound is 4 that of the fundamental. This is the ^fifth har- 
monic. The next harmonics produced would be the seventh, 
the ninth, etc. Thus we see that in a closed pipe the even 
harmonics are absent, the odd ones only being present. 

Next consider the open pipe. For the fundamental the air 
column divides as shown in Fig, 232, with a node at the 
middle and a loop at each end. With stronger blowing there 
is a loop "at the middle as well as at each end and nodes half- 
way between (Fig. 233). In this case the wave-length is | 
that of the fundamental, and the harmonic is the second. 

In Fig. 234 is shown the next mode of division of tlie air 
column. It will be seen that the wave-length is ^ that of the 
fundamental and the harmonic is the third. By using still 
stronger currents of air we get the fourth, fifth, sixth, etc., 
harmonics. Thus in an open pipe all the harmonics (or 
overtones) can be produced ; in the closed pipe only the odd 
harmonics of the series are possible. 

QUESTIONS AND PROBLEMS 

1. Why is it advisable to strike a piano-string near the end rather 
than at the middle ? 

2. As water is poured into a deep bottle the sound rises in pitch. 
Explain why. 

3. A stopped pipe is 4 feet long and an open one 12 feet long. Compare 
the pitch and the quality of the two pipes. 

4. What would be the effect on an organ pipe if it were filled with 
carbonic acid gas ? What with hydrogen ? 



STRINGS, RODS AND PIPES 199 

5. Find the length of a stopped pipe whose fundamental has a frequency 
of 522. (Temperature, 20° C.) 

6. A glass tube, 80 cm. long, held afc its centre and vibrated with a 
wet cloth gives out a note whose frequency is 2540. Calculate the velocicy 
of sound in glass. 

7. If the tension of a string emitting the note A is 25 pounds, find 
that re(|uired to. produce C. 

8. What effect will a rise in temperature have on the notes of a pipe 
organ ? 

9. One wire is twice as long as another (of the same material and 
diameter), and its tension is twice as great. Compare the vibration 
numbers. 

10. Find the length of an air column in resonance with E. (Tempera- 
ture, 20 C. ; (7 = 261.) 



CHAPTER XXII 



Quality — Vibrating Flames — Beats 

227. Quality of Sound. It is a familiar and remarkable 
fact that though sounds having- tlie same pitch and intensity 
may be produced on the piano, the organ, the cornet, or with 
the human voice, the source of the sound in each case can be 
easily recognized. That peculiarity of sound which allows us 
to make this distinction is called quality. 

The cause of this was not explained until, in quite recent 
times, Helmholtz showed that it depends on the co-existence 
with the fundamental of secondary vibrations which alter the 
forms of the sound waves-. These secondary vibrations are 
the overtones or harmonics, and their number and prominence 
determine the peculiar characteristics of a note. 

In general, those notes m which the fundamental is relatively 

strong and the overtones few and 
feeble are said to be of a ' mellow ' 
character ; but when the overtones 
are numerous the note is harsher 
and has a so-called metallic sound. 
If a musical string is struck with 
a hard body tlie high harmonics 
come out prominently. 

When a violin string is bowed 
the first seven overtones are pres- 
ent, and give to the sound its 

is shown separately above" On speak- piercino' character. lu the CaSe of 
ing into the funnel the flame dances •■■ ~ 

rapidly up and down, and this motion the piaUO the Ist, 2nd and 3rd over- 
is observed in the square mirror which •■■ 
is rotated bv hand. 




Fio. 235.— The manometric flame and 
mirror. A section of the gas chamber 



4th, 5th and 6th 



tones are fairly strong while the 
are more feeble. 



228. Vibrating Flames. The cause of quality was investi- 
gated by Helmholtz by means of spherical resonators (Fig. 224). 
But a very beautiful and simple way of investigating the 

200 



VIBRATING FLAMES 



201 



complex natui-e of sound-waves is by means of tlie mano- 
metric, or iiressure-'tneasuring, flame devised by Koenig. 

A convenient form of the apparatus is shown in Fig. 235. 
A small chamber is divided into two compartments by a 
thin membrane* m. Gas enters one compartment as shown 
in the figure, and is lighted on leaving by a fine tip. The 
other compartment is connected by means of a rubber tube 
with a funnel-shaped mouthpiece. 

The sound-waves enter the funnel and their condensations 
and rarefactions produce variations in the density of the air 
beside the membrane. This makes the membrane vibrate 
back and forth, and the gas-flame dances up and down. But 
these motions are so rapid that the eye cannot follow them, 
and in order to separate them they are viewed by reflection in 
a rotating mirror. 

The appearance of various images of the flame is given in 
Fig. 236. When the mirror (.4) 
is at rest the image is seen 
as at J.. If now the mirror 
is rotated wliile the flame 
is still, the image is a band' 
of lio-ht, B. On sin^ino; 
into the conical mouthpiece 
the sound of oo as in tool, 
or on holding before it a 
vibrati)ig mounted tuninof- 
fork the gas-jet's motion 
appears in the mirror like 
C. If the note is sung an 
octave higher there will be 

twice as many little tongues no. 236.-Flame pictures seen in the rotating 

11 -r\ TTT1 mirror. A, when mirror is at rest; B, when 

ni the same space, V. W hen flame is at rest and mirror rolating ; C, when a 

111/ tuning-fork is held before the mouthpiece ; D, 

tnese two tones are sung same as C but an octave higher ;£, when C and 

1,1. • T-» Dare combined; P, obtained witli vowel e at 

tOgetJier images as \nh are pitch C ; G, with vowel O at the same pitch. 




*This may be very thin mica or rubber or gold-beater's skin. 



202 



QUALITY— VIBRATING FLAMES— BEATS 



r-.. 




given. On singing the vowel e at the pitcli C we obtain 
imao-es as at F\ and G is obtained on singing o at the 
same pitch. 

From the figures it will be seen that the last three notes are 
'complex sounds. These dancing images have been success- 
fully photographed on a moving film by Nichols and Merritt. 

A simple form of the above apparatus can be constructed by 
anyone (Fig. 237). Hollow out a piece of 
wood or a cork (2 inches in diameter), 
A, and across the opening stretch the 
membrane, M, keeping it in place by 
screwing or pinning a ring B against it. 
Gas enters by the tube C and leaves by 
the tube D. No mouthpiece is necessary 
but a funnel, shaped as shown in the 

Fia. 237.— A simple form of man- •^^ • ,i rr j. t 

ometricfiame capsule. AA\^ dotted line. Will lucrcase the eiiect. in 

a cork hollowed out, M is the . . • e. 

thin membrane. placc of the rotating mirror a piece oi 

mirror 6 by 8 inches square, held in the hand almost vertical 
and given a gentle oscillatory motion will give good results. 

229. Sympathetic Vibrations. Let us place two tuning- 
forks, v.diich have the same vibration numbers, with the open 
ends of their resonance boxes 
facing each other and a short 
distance apart (Fig. 238). Now 
vibrate one of them vigorously 
by means of a bow or by striking 
with a soft mallet (a rubber 
stopper on a handle), and after 
it has been sounding for a few 

seconflq brino- it to rest bv Fia. 238.— Two tunins-forks arranged to 
SeCOnUb Uling lU W xebU uy show sympathetic vibrations. When one 

placing the hand upon it. The is vibrated the other responds. 

sound will still be heard, but on examination it will be 
found to proceed from the other fork. 




ILLUSTHATIONS OF SYMrATHETIC VIBRATIONS— BEATS 203 

This ilhistrates tlie plienomenon of sympathetic vibrations. 
The first fork sets up vibrations in tlie resonance box on wliich 
it is niounted, and tliis produces vibrations in tlie inclosed 
air column. The waves proceed from it, and on reaching the 
resonance box of the second fork its air column is put in 
vibration. The vibrations are communicated to the box and 
then to the fork, which, having considerable mass, continues its 
motion for some time. 

A single wave from the first fork would have little effect, 
but when a long series comes in regular succession each helps 
on what the one next before it has started. Thus the effect 
accumulates until the second fork is given considerable motion, 
its sound being heard over a large room. 

For this experiment to succeed the vibration numbers of 
the two forks must be accurately equal. 

230. Illustrations of Sympathetic Vibrations. The pen- 
dulum of a clock has a natural period of vibration, depending 
on its length, and if started it continues swinging for a while, 
but at last comes to rest. Now the works of the clock are so 
constructed that a little push is given to the pendulum at each 
swing and these, being properly timed, are sufficient to keep 
up the motion. 

Again, it is impossible by a single pull on the rope to ring a 
large bell, but by timing the pulls to the natural period of the 
bell's motion, its amplitude continually increases until it rings 
properly. 

When a body of soldiers is crossing a suspension bridge they 
are usually made to break step for fear that the steady tramp 
of the men might start a vibration agreeing with the free 
pei'iod of the bridge, and which, by continual additions, might 
reach dangerous j^i'oj^ortions. 

231. Beats. We shall exjseriment further with the two 
unison forks (Fig. 238). Stick a piece of wax* on each prong 

*The soft modelling wax sold as "plasticine" is very convenient. 



204 QUALITY— VIBRATING FLAMES— BEATS 

of one fork ; we cannot get sympathetic vibrations now, but 
on vibrating tlie two forks at tlie same time a peculiar wavy 
or throbbing sound is heard, caused by alternate rising and 
sinking in loudness. Each recurrence of maximum loudness 
is called a heat. 

"We at once recognize that this effect is due to the inter- 
action of the waves from the two forks, resulting in an 
alternate increase and decrease in the loudness of the sound. 

Each fork produces condensations and rarefactions in the 
air, and since in a condensation the air particles have a 
forivard motion while in the rarefaction the motion is 
backward, it is evident that if a condensation from one 
fork reaches the ear at the same time as a rarefaction from 
the other they will oppose tlieir effects and the ear-drum 
will have little motion — the sound will be faint. If, however, 
a condensation from each or a rarefaction from each, arrives 
at the same time, the action on the ear-drum will be increased 
and the sound will be louder. 

Consider the curves in Fig. 239. Between A and B are 8 
complete waves, and between C and D, taking up the same 

distance, are 9 waves. 

A f^ "A 'T\"A" /A'- /^ A "^^ ^^^® beginning at A 

"^ \j \y^X/.\/AX^M \J \J^ and (7, the waves are in 

(^\l\f\J\J\J\[\f\J\jD the same phase; this is 
^ ^ the case also at the end, 

at B and D. But half- 
way between, at il/andiV, 

Fio. 239. — Illustrating the production of beats. The fl,^ -nlTjcoo qi-o r>T->-r.r>oif q 

coiiil.inaion of AB with CD gives EF. The dotted '^'^^ pnahLb aie opposite, 
curve in ^B is the same as the curve CD. At 3/ the -p^ - ,. , 

motion is up, at N it is down, and these added give By adding the motlOnS 

us motion as at P. , i • a 

represented m AB to 
those represented in CD we obtain the motion illustrated 
by EF. 

These curves can represent the motions in sound-waves if 
we agree that a crest in the figure shall correspond to a 




INTERFERENCE OF SOUND-WAVES 205 

condensation in the sound-wave, and lienee a trougli sliall 
correspond to a rarefaction. 

For simplicity let us suppose that one fork in a second gives 
out the 8 waves in AB while the other gives the 9 waves in 
CD. The combined effect, as shown in EF, will move to the 
ear. At first the effect will be intense, then it will be a mini- 
mum (corresponding to P), then intense again ; and so on during 
the next second. Thus there would be one beat per second. 

If the forks gi\e 8 and 9 vibrations, respectively, in one- 
half second, i.e., 16 and 18 per second, there will be one beat 
each half-second or two per second. To produce beats the 
forks should not differ greatly in pitch. 

We arrive then at the simple law that the number of beats 
per second due to two simple tones is equal to the difference of 
their respective vibration numbers. 

232. Tuning by Means of Beats. Suppose we wish to tune 

two strings to unison. Even the most unmusical person can do it. 
Simply vary the tension, or the length, of one of them until as they 
approach unison the beats are fewer per second. If one beat per 
second is heai'd, there is a ditierence of only one vibration per second 
in their frequencies. Let us alter a little more until the beats are 
entirely gone. The strings are then in unison. 

In the same way other sounding bodies, for instance two organ 
pipes, or a pipe and tuning-fork, may be brought to unison. 

233. Interference of Sound- Waves. The production of 
beats is but one of the many phenomena "*, 

due to the interference of sound-waves. '\ ,.-' 

Let us consider two others. 

In Fig. 240 are shown the extremities ^ fPff^ c 

of the two prongs of a tuning-fork. /*~ ■"*•. 

They vibrate in such a way that they 

move alternately towards and away from g / e >,A 

each other. Thus while they produce ' 

, . . . , , 1 , F'O' 240.— Interference with a 

a condensation m the space a between tuning-fork. 

them, they produce a rarefaction at b and c on the opposite 



206 



QUALITY— VIBRATING FLAMES— BEATS 



sides. In this way each prong starts owt two sets of waves, 
which are in opposite pliases. These waves travel out in all 
directions, and it is evident that we can find points such that 
when the two sets of waves arrive there they will be in 
opposite phases and so, at each point, will counteract each 
other's effects. Such points are located on two curved surfaces, 
of which fg, hk are horizontal sections. 

This can be demonstrated by holding a vibrating fork near 
the ear and then rotating it slowly. When the ear is in the 
positions b, c, d, e the sound is heard clearly ; while if it is on 
either of the curved surfaces fg, hk no sound is heard. 

234. Interference with Resonators. Another interesting 
experiment can be performed with two wide-mouthed (pickle) 
bottles. Vibrate a tuning-fork (256 vibrations) over the mouth 
of one of the bottles, and slip a microscope slide over the mouth 
until the air in the bottle responds vigorously. Fasten with 
wax the glass in the position when the bottle resounds most 
loudly. The bottle is then a resonator tuned to the fork. 

Tune the other bottle in the 
same way and then arrange 
them, with their mouths close 
too^ether, as shown in Fig. 241. 
Make the fork vibrate, and 
then, holding it horizontally, 
bring it down so that the space 
between the prongs is opposite 
the mouth of the upright bottle. 
As it is brought into place you 
will observe that the sound first 
increases,and then suddenly fades 
away or disappears entirely. 

The reason for this is easily understood. The air in one 
bottle is put in vibration by the air from between the prongs, 




Fio. 241. — Interference with two 
resonators. 



DOPPLER'S PRINCIPLE 207 

while that in the other is put in vibration by the air on the 
other side of tlie prongs ; and these, as we have seen, are in 
opposite phases. Hence they interfere and produce silence. 

If a card is slipped over the mouth of one of the bottles, 
that bottle's vibrations are shut off and the other sings out 
loudly. 

235. Doppler's Principle. Suppose a body at A to be emitting 
a note of ti vibrations per second. Waves will be excited 'in the 
surrounding air, and an observer at B will receive n waves each 
second. He will recognize a sound of a certain pitch. 

Next suppose that the observer approaches the sounding body ; 
he will now receive more than n waves in a second. In addition to 
the n waves which he would receive if he were stationary he will 
meet each second a certain number of weaves, since he is nearer the 
sounding body at the end of a second than he was at its beginning. 
He will receive those waves which at the commencement of the 
second occupied the space he has moved. As he will now receive 
more than n waves per second the pitch of the sound will appear to 
be higher than when there was no motion. 

If the observer moves away, the number of waves received will be 
smaller and the pitch will be lowered. 

If the observer remains at rest while the sounding body ap- 
proaches or recedes similar results will be obtained ; and if we can 
determine the change in pitch we can calculate the speed of the 
motion. This phenomenon is known as the Doppler etlect and the 
explanation given is known as Doppler's principle. 

The Doppler effect can be observed when a whistling locomotive 
is approaching or receding at a rapid rate. An automobile sounding 
its horn is a still better illustration as its motion makes less noise. 
AVheti the machine is approaching the sound is distinctly higher in 
pitch than when it is travelling away. Doppler's effect is referred 
to again in § 406. 

QUESTIONS AND PROBLEMS 

1. What are the fourth and fifth overtones to 0? 

2. A tuning-fork on a resonance box is moved towards a wall, and a 
' wavy ' sound is heard. Explain the production of this. 

3. Hold down two adjacent bass keys of a piano. Count the beats per 
second and deduce the difference of the vibration-frequencies. 



208 QUALITY— VIBRATING FLAMES— BEATS 

4. If a circular plate is made to vibrate in four sectors as in d. Fig. 221, 
and if a cone-shaped funnel is connected with tlie ear by a rubber tube, 
and the other ear is stopped with soft wax, no sound is heard wlien the 
centre of the mouth of the cone is placed over the centre of the plate ; 
but if it is moved outward along the middle of a vibrating sector, a sound 
is heard. Explain these results. (For a plate 6 inches in diameter 
the mouth <;{ the funnel should be 2| inches in diameter. Try the 
experiment.^ 



CHAPTER XXIII 
Musical Instruments — The Phonograph 



236. Stringed Instruments. In the piano tliere is a sepa- 
rate string, or a set of strings, for eacli note. The strings are 
of steel wire, and for the bass notes tliey are overwound witli 
other wire, being in this way made nioi-e massive witliout 
losing their flexibility. When a key is depressed a combina- 
tion of levers causes a soft hammer to strike the string at a 
point about ^ of the length of the string from the end. If 
the instrument gets out of tune it is repaired by re-adjusting 
the tensions of tlie strings. 

The harp is somewhat similar in principle to the j)iano, but 
it is played by plucking 
the strings with the 
fingers. By pressing 
pedals tlie lengths of the 
strings may be altered 
so as to sharpen or flat- 
ten any note. 

The guitar has six 
strings, the three lower- 
pitched ones being of silk 
over-wound with fine 
wire. The strings are 
tuned to 

E„ A„ D, G, B, E\ 
where D is the note next 
above middle C and has 293.6 vibrations per second. There 
are little strips across the finger-board called ' frets,' and by 
pressing the strings down by the fingers against these they 
are shortened and give out the other notes (Fig. 242). 

209 




Fia. 242.— The guitar. With the left hand the strings 
are shortened by pressing them against tlie 'frets,' 
while the note is obtained by plucking with the right 
hand. 



210 



MUSICAL INSTRUMENTS 



There are only four strings on the violin, and tliey are 
tuned to 

G,, D, A, E', 

where D is next above middle C {A = 435 vibrations per 
second). The other notes are obtained by shortening the 
strings by means of the fingers, but as 
there are no * frets ' to guide the performer, 
he must judge tlie correct positions of the 
fingers himself. 

237. Pipe Organ and Flute. The action 
of organ pipes has been explained in 
§§ 225, 226. In large organs they vary 
in length from 2 or 3 inches to about 20 
feet, and some of them are conical in 
shape. 

In Fig. 243 is shown a flute. This is an 
instrument of great antiquity, though the 
modern form is quite unlike the old ones. 
By driving a current of air across tlie thin 
edge of the opening, M'hich is near one end, 
the air column within is set in vibration 
much as in an organ pipe. In the tube 
there are holes which may be opened oT 
closed by the player, opening a hole being 
equivalent to cutting off the* tube at that 
place. The overtones are also used, being 
obtained by blowing harder. 

The fife and the piccolo resemble the 
flute, both being open at the further end. 
Whistles, on the other hand, are usually 
closed. 

238. Reed Instruments. In the ordinary organ, the mouth- 
organ, the accordion and some other instruments the vibrating 



REED INSTRUMENTS 



21] 




Fig. 245. — An organ reed. The tongue 
A moves in and out of the oponitijj. 
This is called a, free reed. 



body is a reed, such as is shoAvn in Fig. 245. The tongue A 

vibrates in and out of an opening 

which it accurately fits, the motion 

being kept up by the current of 

air which is directed through the 

opening. 

In some organ pipes reeds are 
placed, but the note produced is due chiefly to the air column 
in the pipe, the reed simply serving to set it in vibration. 

In Fig. 244 is shown a clarinet. This instrument has holes 
in the tube which are covered by keys or by the fingers of the 

pla^^er. The air 

in the tube is put 

in vibration by 

means of a reed 

made of cane 

shown in Fig. 

246. The reed 

is very flexible, 
_ „ ^ and the note 

Fig. 246.-Mouth- 

piece of the heard is that of 

clarinet. The 

reed R covers the air column, 

the opennig. 

not of the reed. 
In this case the reed simply 
covers and uncovers the 
opening in the mouthpiece, being too large to pass into the 
opening. It is called a striking reed, that in the organ 
(Fig. 245) being a free reed. 

A reed is used in a similar way in the mouthpiece of the 
oboe, saxophone and other instruments of that class. 

In the automobile 'honk' (Fig. 247) a striking reed is used. 
It is inserted at r, where the flexible tube joins on the brass 
portion. On pressing the bulb the reed sets in vibration the 
air column in the brass portion. 





Fig. 247. — Automobile 'honk.' The reed R is 
shown separately above. It is inserted at r, 
where the flexible and brass tubes unite. 



212 



MUSICAL INSTRUMENTS 




FlQ. 248.— The Bufjle. 



239. Instruments in Which the Vibrations are Produced 
by Player's Lips. These all consist essentially of an open 
conical tube, the larger end terminating in a bell while at the 
smaller end is a cup, carrying a rounded edge, against which 
the tense lips of the player are steadily pressed. The lips thus 
constitute a reed and by their vibrations waves are set up in 
the air within the tube. 

In this way the fundamental and the various harmonics of 

the air column in the tube are 
produced, and all but the ex- 
treme bass sounds are used in 
the scale. 

In the French horn the total 
length of tube is about 17 feet, 
and hence the fundamental 
note is very deep. The pro- 
duction of the harmonic series depends entirely on the varied 
tension of the lips. 

The bugle is illustrated in Fig. 248. The length of tube is 
fixed, and the notes producible are the fundamental and about 
5 overtones. Its 
compass is much 
smaller than that 
of the French horn. 
In the cornet, 
by means of 
three valves a, h, c 
(Fig. 249), the air 
column may be 
divided into differ- 
ent lengths, and a 
series of overtones is obtained with each length. 

In the trombone, on the other hand, besides obtaining over- 
tones by suitable blowing, the pitch is varied by altering the 




Fio. 249.— By the valves a, b, c, the air column is divided into 
different lengths. 



THE PHONOGRAPH 



213 



length of the tube. This is done by means of a U-shaped 
portion, AB (Fig. 250), which can slide with gentle friction 





FiQ. !51. — The phonograph. C is the cylinder on 
which the spiral groove is made. A cylinder ia 
shown (enlarged) beside the instrument. 



FiQ. 250.— A slide trombone. 

upon the body of the instrument. 

240. The Phonograph. This instrument, now so familiar, was 

invented by Edison in 1877. Its construction, like that of the tele- 
phone receiver, is extremely 

simple, and one is astonished 

that such wonderful results 

can be obtained in so simple 

a manner. 

A cylinder (C, Fig. 251), of 

comparatively hard wax is 

made (usually by clockwork), 

to rotate and at the same 

time move parallel to its axis. 

Resting on tliis is a sharp 

steel point (P, Fig. 252), at- 
tached to a thin diaphragm, 

which covers the lower end 

of tlie cone, J?. In this way, as the cylinder rotates, a long spiral 

groove is scratched on its surface. 

Sounds are spoken or sung into the cone, which collects them and 

leads them to the diaphragm. The varying pressures of the waves 
cause this to move back and forth, alternately 
increasing and decreasing the pressure of the 
point upon the wax. In this way hollows of 
different depths and forms are carved at the 
bottom of the groove. 

If now the point* is made to run along the 
groove again the diaphragm will execute precisely 
the same motions once more, the motion will be 

imparted to the air and thus the original sound will be reproduced 

with surprising fidelity. 

In place of the cylinder a disc may be used ; and by suitable 

processes duplicates of the cylinder or the disc can be made in 

more permanent substance than the original wax. 
* Different cones and points are used for recording and reproducing the sounds. 




Fio. 252.— Point and 
diaphragm of the 
phonograph. 



PART VI-HEAT 



CHAPTER XXIV 
Nature and Source of Heat 

241. Nature of Heat. It is a matter of every day experience 
that when motion is cheeked by friction or collision, heat is 
developed in the bodies concerned. Thus if a button is rubbed 
vigorously on a piece of cloth it may be made too hot to be 
handled. A drill used in boring steel quickly becomes heated. 
A leaden bullet shot against an iron target may be melted by 
the impact. The aborigines obtained fire by rubbing two dry 
sticks together. 

From very early times such effects were supposed to be due 
to a subtle imponderable fluid which entered the bodies, and 
produced the various phenomena of heat. Although certain 
philosophers, notably Descartes, Boyle, Francis Bacon and 
Newton, evidently had in a vague way anticipated the theory 
of heat as a mode of motion, yet the conception of heat as a 
material agent was generally accepted up to the beginning of 
the nineteenth century. 

The first serious attack upon the theory was made by 
Count Rumford,* in 1798, In this he was supported by 
Sir Humphry Davy and others during the early years of the 
last century, but it was near the middle of the century before 
the modern dynamical theory of heat was firmly established. 
It was then shown by Joule that a definite amount of 
mechanical work corresponds to a definite quantity of heat, 
from which it is manifest that heat must be a form of 
energy. 

♦Benjamin Thompson was born at Wohurn (near Boston, Mass.) in 1753. In 1775 he went to 
England and in 1783 to Austria. He was created Count Rumford by the Elector of Bavaria. 
While engaged in boring cannon at Munich he made his experiments on heat. He died in 
France in 1814. 

214 



HEAT FROM FRICTION, PERCUSSION, COMPRESSION 215 

There would appear to be in each of the illustrations given 
above a loss in energy due to the loss in velocity of the body 
whose motion is checked, but, according to the modern view of 
heat, the loss is only apparent, not real. The energy which 
disappears as onward motion re-appears as increased molecular 
motion. To be definite, heat is a form of energy possessed by 
a body in virtue of the motion of its 'molecules. 

242. Sources of Heat. Since heat is a form of energy it 
must be derived from some other form of energy. The process 
of the development of heat is a transformation of energy. 

243. Heat from Friction, Percussion and Compression. 

We have already noted that heat is produced when on\\ard 

motion is arrested through friction or percussion. 

It is also developed by compression. If a piece 

of dry tinder is placed in a tube closed at one 

end containing air, and a closely-fitting piston 

is pushed quickly into the tube (Fig. 253), the 

tinder may be lighted by the heat developed 

by the compression of the air. The cylinders of 

air-compressors (a bicycle pump for instance) 

become heated by the repeated compression of 

the air drawn into them. 

Conversely, if a compressed gas is allowed to 
expand its temperature falls. The steam which 
has done work by its expansion in driving 
forward the piston of a steam engine escapes 
from the cjdinder at a lower temperature than 
that at which it entered it. "syringe. "^^ 

244. Heat from Chemical Action. The potential energy 
of chemical separation is one of our most common sources of 
heat. Combustible bodies, such as coal and wood, possess 
energy of this kind. When raised to the ignition point they 
unite chemically with the oxygen of the air, and their union 



216 NATURE AND SOURCE OF HEAT 

is accompanied by the development of heat. So far this has 
been tlie chief source of artificial heat used for cooking our 
food and warming our dwellings. 

245. Heat from an Electric Current. When an electric 
current is made to pass through a conductor whicli offers 
resistance to it, heat is developed. For example, if the 
terminals of a battery consisting of three or four galvanic 
cells joined in series are connected with a short piece of fine 
platinum or iron wire, it will be heated to a white heat. 
Electric lamps also furnish examjjles of this transformation of 
energy, the source of the radiation in them being bodies heated 
to incandescence by an electric current. Electric heaters and 
electric cookers in their simplest forms are but coils of resis- 
tance wire heated by an electric current. 

246. Heat from Radiant Energy. " The sun is our source 
of natural heat," but the heat is natural only in the sense tliat 
it comes from our most abundant source of supply. The heat 
does not, as we might at first suppose, come unchanged from 
the sun to the eartli. The air extends to but a relatively 
short distance above the earth, and it is certain that matter, 
as we understand it, constituted of molecules, cannot extend 
throughout space. The direct transference of molecular 
motion from tlie sun to the earth is, therefore, an impossibility. 
To account for tlie transmission of energy the physicist 
assumes tlie existence of a medium called the ether, which he 
conceives to pervade all space, intermolecular as well as inter- 
stellar." The vibrating molecules of a hot body cause distur- 
bances in tlie ether, which are transmitted in all directions by 
a species of wave-motion. When the ether waves fall upon 
matter, they tend to accelerate the motion of its molecules. 
According to this theory the heat of the sun is first changed 
into radhiut energy, or the energy of ether vibration, and the 
ether *^'aves which fall upon the earth are transformed into 
heat The subject is further discussed in §§ 325, 326. 



CHAPTER XXV 



Expansion Through Heat 

247. Expansion of Solids by Heat. In discussing the 
molecular constitution of matter we saw (§ 153) that one effect 
of the application of heat to a body is to 
cause it to expand. The theoretical ex- 
planation was discussed at some lengtli, 
and need not be again referred to here. 
Moreover, examples of the expansion of 
bodies through heat are so numerous and 
so commonly observed that fulness in 





tn^^d 



Fia. 



254. — Expansion of 
ball by heat. 



Fio. 255. — Expansion of rod by heat. 



illustration is unnecessary. If a brass ball (Fig. 254) which 
can just pass through a ring when cold is heated it will then 
be found to be too large to go through. If we heat a metal 
rod which is fixed at one end while the other is made to press 
against the short arm of a bent lever 
(Fig. 255) an elongation of the rod is 
shown by a movement of the end of 
the long arm over a scale. When a 
compound bar, made by riveting to- 
gether strips of copper and iron (Fig. 
256) is heated uniformly it bends into the form of an arc of a 

circle with the copper on the convex side, because the copper 

217 




Fio. 256. — Bendinj; of compound 
bar by unequal expansion of its 
parts. 



218 



EXPANSION THROUGH HEAT 



expands more than the iron. If placed in a cold bath it curves 
in the opposite direction. 

These experiments illustrate a very general law. Solids 
with very few exceptions expand when lieated and contract 
when cooled, but different solids have different rates of 
expansion. 

248. Expansion of Liquids and Gases by Heat. Liquids 
also expand when heated. The amount of expansion varies 

with the liquid, but on the 
whole, it is much greater than 
that of solids. Let us enclose 
a liquid within a flask and 
connected tube, as shown in 
Fig. 257, and heat the flask. 
The liquid is seen to rise in 
the tube 

The same apparatus may be 

used to illustrate the expansion 

of gases. When the flask and 

tube are filled with air only, 

insert the open end of the 

tube into water (Fig. 258), and 
heat the flask. A portion of the air is seen 
to bubble out through the water. If the 
flask is cooled, water is forced by the pressure of the outer 
air into the tube to take up the space left by the air as it 
contracts. 

Unlike solids and liquids, all gases have, at the ordinary 
pressure of the air, approximately the same rates of 
expansion, 

249. Applications of Expansion— Compensated Pendulums. 

A clock is regulated by a pendulum, whose rate of vibration 
depends on its length. The longer the pendulum, the 




Fio. 257. — Expan- 
sion of liquids by 
heat. 




Fio. 258.— Expansion 
of gas by heat. 



CHRONOMETER BALANCE WHEEL 



219 



slower tlie beat ; and tlie sliorter, the faster. Changes in 
temperature will therefore cause irregularities 
in the running of the clock, unless some pro- 
vision is made for keeping the pendulum con- 
stant in length through varying changes in 
temperature. Two forms of com- I 

pensation are in common use. The 
Graham pendulum (Fig. 259) is pro- 
vided with a bob consisting of a jar 
of mercury. Expansion in the rod 
lowers the centre of gravity of the 
bob, while expansion in the mercury 
raises it. The quantity of mercury 

Fig. 259.-Graham is SO adjusted as to keep the centre 
of gravity* always at tlie same level. 

In the Harrison, or gridiron pendulum (Fig. 260) 
the bob hangs from a framework of brass and steel 
rods, so connected that an increase in length of the 
steel rods (dark in the figure), tends to lower the 
bob, while an increase in the length of the brass ones 
tends to raise it. The lengths of the two sets are ^son^penduimT 
adjusted to keep the resultant length of the pendulum constant. 

250. Chronometer Balance Wheel. A watch is regulated 
by a balance wlieel, controlled by a hair- 
spring (Fig. 261). An increase in tempera- 
ture tends to increase the diameter of tlie 
wheel and to decrease tlie elasticity of the 
spring. Botli efi'ects would cause the watch 
to lose time. To counteract the retarding 
effects, the rim of the balance wheel in 
chronometers and high-grade watches is 
constructed of two metals and mounted in sections, as shown 





Fia. 261.— Balance wheel 
of watch. 



•Strictly speaking-, it is a point called the centre of oscillation (which nearly coincides with 
the centre of gravity) whose distance from the point of suspension should be kept constant. 



220 



EXPANSION THROUGH HEAT 



in Fig. 261. The outer metal is the more expansible, and the 
effect of its expansion is to turn the free ends of the rim 
inwards, and thus to lessen the effective diameter of the 
wheel. 

251. Thermostats. The fact that a bar composed of two 
metals having unequal expansion tends to curl up with 
increased temperature finds practical application also in the 
construction of thermostats. 

Thermostats are used mainly for controlling the temperature 
in buildings heated by hot-air furnaces or boilers. In most 
systems of control, dampers 
or steam valves are opened 
and closed by electricity or 
compressed air. The object 
of the thermostat is to set 
free the current of elec- 
tricity or the compressed 
air to close the valves or 
dampers when the tempera- 
ture reaches a certain point. 
Fig. 262 shows an electric 
thermostat and Fig. 263 
shows a pneumatic thermostat. The 
essential part of each is the same, 
the compound bar b. On the electric 
thermostat, the bending of the bar by 
heat closes the electi'ic current at a. 
On the pneumatic thermostat, the bend- 
ing of the bar closes a small aperture at 
a through which the compressed air 
escapes slowly by a by-pass. The air thus held back enters 
tlie bellows c, which on expanding opens a valve and this 
allows tlie main current of compressed air to have access 
to the regulators in the furnace room. 




FI0.2C2.— Anelec 
trie thermostat. 




Fig. 263. — A pneumatic 
thermostat. 



THERMOSTATS 221 

QUESTIONS 

1. A glass stopper stuck in tlie neck oi a bottle may be loosened by 
subjecting the neck to fi'iction by a string. Explain. 

2. Boiler plates are put together with red-hot rivets. What is the 
reason for this ? 

3. Why does a bhicksmith heat a wagon-tire before adjusting it to the 
wheel ? 

4. Why are tlie rails of a railroad track laid with the ends not cjuite 
touching ? 

5. Why does change in the temperature of a room affect the tone of a 
piano ? 

6. Glass vessels are liable to l)reak wlien suddenly heated or cooled in 
one part only. Give the reason. 



CHAPTER XXVI 

Temperature 

252. Nature of Temperature. When the blacksmith throws 
the red-hot iron into a tub of cold water to cool it, the iron 
evidently loses heat, while the water gains it. Wiien two 
bodies like the iron and water are in such a condition that one 
grows warmer and the other colder when they are brought in 
contact, they are said to be at different temperatures. The 
body which gains heat is said to be at a lower temperature 
than the one which loses it. If neither grows warmer when 
the bodies are brought together, tliey are said to be at the 
same temperature. TeniiDeratwre, therefore, may be defined as 
the condition of a body considered with reference to its power 
of receiving heat from, or communicating heat to, another 
body. 

253. Temperature and Quantity of Heat. A pint of water 
taken from a vat is at the same temperature as a gallon taken 
from the same source. Tliey will also be at the same tempera- 
ture when both are brought to the boiling point, but if they 
are heated by the same gas flame, it will take much longer to 
bring the gallon up to the boiling point than to raise the pint 
to the same temperature. The change in temperature is the 
same in each, biit the quantity of heat absorbed is diflTerent. 
A large radiator, filled with hot water may, in cooling, supply 
sufficient lieat to warm up a room, but a small pitcher of water 
loses its heat with no apparent effect. The quantity of heat 
possessed by a body evidently depends on its mass as well as 
its temperature. 

254. Determination of Temperature. Up to the time of 
Galileo, no instrumental means of determining temperature 
had been devised. Differences in the temperature of bodies 
were estimated by comparing the sensations resulting from 



GALILEO'S THERMOMETER 



223 



contact with them. But simple experiments will show that 
our temperature sense cannot be relied upon to determine 
temperature with any deoree of accuracy. Take three vessels, 
one containing water as hot as can be borne by the hand, one 
containing ice-cold water, and one with water at the tempera- 
ture of the room. Hold a finger of one hand in. the cold 
water and a finger of the other in the hot water for one or 
two minutes, and immediately insert both fingers in the third 
vessel. To one finger the water will appear to be hot, and to 
the other, cold. The experiment shows that our estimation of 
temperature depends, to a certain extent, on the temperature 
of the sensitive part of the body engaged in making the 
determination. Our ordinary experiences confirm this con- 
clusion. If we pass from a cold room into one moderately 
heated, it appears warm, while the room at the same tempera- 
ture appears cold when we enter it from one that has been 
overheated. 

Again, our estimation of the temperature of a body depends 
on the nature of the body as well as upon its temperature. It 
is a well-known fact that on a very cold day 
a piece of iron exposed to frost feels much colder 
than a piece of wood, although both may be at 
the same temperature. 

255. Galileo's Thermometer. So far as known, 
Galileo was the first to construct a thermometer. 
He conceived that since changes in the tempera- 
ture of a body are accompanied by changes in 
its volume,, these latter changes might be made 
to measure, indirectly, temperature. He selected 
air as the body to be employed as a thermometric 
substance. 

His thermometer consisted simply of a glass 
bulb with "a long, slender, glass stem made to dip into water, 
as shown in Fig. 264. By warming the bulb, a few bubbles 




Fio. 264.— Galileo's 
air thermometer. 



224 TEMPERATURE 

of air were driven out of the stem, and on cooling the bulb 
the water rose part way up the stem. Any increase in 
temperature was then shown by a fall of the water in the 
tube, and a decrease by a rise. Such a thermometer is 
imperfect, as the height of the column of liquid is affected 
by changes in the pressure of the outside air, as well as by 
changes in the temperature of the air within the bulb. 
According to Viviani, one of Galileo's pupils, 1593 was the 
date of the invention of the instrument. 

256. Improvements on the Thermometer. About forty 
years later, Jean Rey, a French physician, improved the 
instrument by making use of water instead of air as the 
expansible substance. The bulb and a part of the stem were 
filled with water. Further improvements were made by the 
Florentine academicians, who made use of alcohol instead of 
water, sealed the tube, and attached a graduated scale. The 
first mercury thermometer was constructed by the astronomer, 
Ismael Boulliau, in 1659. 

257. Construction of a Mercury Thermometer. Alcohol is 
still used to measure very low temperatures, but mercury is 
now found in most thermometers in common use. This liquid 
has been selected for a variety of reasons. Among others, the 
following may be noted. 

It can be used to measure a fairly wide range of tempera- 
tures, because it freezes at a low temperature and boils at a 
comparatively high temperature. At any definite tempera- 
ture it has a constant volume. Slight changes in temperature 
are readily noted, as it expands rapidly with a rise in 
temperature. It does not wet the tube in which it is enclosed, 
' To construct the thermometer a piece of thick-walled glass 
tubing with a uniform capillary bore is chosen, and a bulb is 
blown at one end. Bulb and tube are then filled with 
mercury. This is done by heating the bulb to expel part of 



THE GRADUATION OF THE THERMOMETER 



225 



the air, and then dipping the open end of the tube into 
mercuiy. As the bulb cools, mercury is forced into it by 
the pressure of the outside air. The liquid within the bulb 
is boiled to expel the remaining air, and the end of the tube 
is again immersed in mercury. On cooling, the vapour con- 
denses and bulb and tube are completely filled with mercury. 
The tube is then sealed off. 

258. Determination of the Fixed Points. Since we can 
describe a particular temperature only by stating how much 
it is above or below some temperature assumed as a standard, 
it is necessary to fix upon standards of temperature and also 
units of difierence of temperature. This is most conveniently 
done by selecting two fixed points for a thermometric scale. 
The standards in almost Universal use are the "freezing 
point " and the " boiling point " of water. 

To determine the freezing 
point, the thermometer is 
surrounded with moist pul- 
verized ice (Fig. 265), and the 
point at which the mercury 
stands when it becomes sta- 
tionary is marked on the 
stem. 

The boiling point is deter- 

mined by exposing the bulb 

dl and stem to steam rising from 

pure water boiling under a 

pressure of 76 cm. of mercury 

(Fig. 266). As before, the height of the mercury is marked 

on the stem. 

259. The Graduation of the Thermometer. Having marked 
the freezing and boiling points, the next step is to graduate 
the thermometer. Two scales are in connnon use, the Centi- 
grade scale and the Fahrenheit scale. 





Fio. 265. — Determina 
tion of freezinj; point. 



FiQ. 266.— Determina- 
tion of boiling point. 



226 



TEMPERATUEE 



Fig. 2G7.— Thermometer 
scales. 



The Centigrade scale, first proposed by Celsius, a Swedish 
scientist, in 1740, and subsequently modified 
by his colleague Marten Stromer, is now 
universally employed in scientific work. 
The space intervening between the freezing 
point and the boiling point is divided into 
one hundred equal divisions, or degrees, and 
the zero of the scale is placed at the freezing 
point, the graduations being extended both 
above and below the zero point.* 

The Fahrenheit scale is in common use 
among English-speaking people for house- 
hold purposes. It was proposed by Gabriel 
Daniel Faln^enheit (1686-1736), a German 
instrument maker. The space between the freezing point and 
the boiling point is divided into one hundred and eiglity equal 
divisions, each called a degree, and the zero is placed thirty- 
two divisions below the freezing point. The freezing point, 
therefore, reads 32° and the boiling point 212° (Fig. 267). Tliis 
zero point was chosen, it is said, because Fahrenheit believed 
this temperature, obtained from a mixture of melting ice and 
ammonium chloride or sea-salt, to be the lowest attainable. 

260. Comparison of Thermometer Scales. If the tempera- 
ture of the room at the present moment is 68°, the temperature 
is 68 — 32, or 36 degrees above the freezing point ; but 
since 180 Fahrenheit degrees =100 Centigrade degrees, or 9 
Fahrenheit degrees = 5 Centigrade degrees, the temperature 
of the room is |- of 36, or 20 Centigrade degrees above the 
freezing point ; that is, the Centigrade thermometer will 
read 20°. 

The relation between corresponding readings on the two 
thermometers may be obtained in tlie following way. Let a 

•Celsius at first marked the hoiling-point zero and the freezing-point 100. It is said that the 
great botanist Linnaeus proocpted Celsius and Stromer to invert the seal*. 



MAXIMUM AND MINIMUM THERMOMETERS 227 

certain temperature be represented by F° on the Fahrenheit 
and C'° on tlie Centigrade scale. Then this temperature is 
F — 32 Fahrenheit degrees above the freezing point, and it is 
also G Centigrade degrees above the freezing point. Hence 

{F — 32) Fahr, degrees correspond to C Cent, degrees. 

But 9 Fahr. degrees correspond to 5 Cent, degrees, 

Therefore ^ {F - 32) = C. 

261. Maximum and Minimum Thermometers. A maximum 

tliermoineter is one which records the highest temperature reached 

during a certain time. One ^ ^ 

form is shown in Fig. 268. It /' ^ |^f « M'ai>'i a »>.<> «, ' ''.'«. »>.'?.?, ' a ^ 

is a mercu ry thermometer with l[^^^l( |^ ^^~~z: ~"~ "___ _°J 1 

a constriction fixed in the tube ^ 

just above the bulb (c, Fig. Fiu. 26S.— A maximum thermometer (as used in 
2G8). As the temperature the Meteorolo^ncal Service). 

rises the mercury expands and goes past the constriction ; V>ut when 
it conti'acts the thread breaks at the constriction, that portion below 
it contracting into the bulb, while the mercury in the tube remains 
in the position it had when the temperature was highest. By gently 
tapping or shaking the thermometer the mercury can be forced past 
the constriction, ready for use again. 

The clinical thermometer, with which the physician takes the 
temperature of the body, is constructed in this way. 

In another kind of maximum thermometer a small piece of iron is 
inserted in the stem a])ove the mercury (Fig. 2G9), and is pushed 

forward as the mercury expands. 
When the mercury contracts the iron 
is left behind and thus indicates the 
Fig. 269.— The iron index is pushed highest point reached by the mercury. 

forward by the mercury. . . , , . , 

In the minimum thermometer, which 
registers the lowest temperature reached, alcohol is used. Within 
the alcohol a small glass index 
is placed (Fig. 270). As the 
alcohol contracts, on account 
of its surface tension (S 169) 

., , ii • 1 1 1 1 i. F'8. 270. -A minnnum thermometer (as used in 

It drags the index back, but the Meteoroloaical Service). It is hung in a 

when it expands it flows past horizontal position. 

the index which is thus left stationary and shows the lowest tempera- 
ture reached. By tilting the thermometer the index slips down to 
the surface of the alcohol column, ready for use again. 




228 TEMPEEATURE 

PROBLEMS 

1. To how many Fahrenheit dei^rees are the following Centigrade 
degrees equivalent : — 5, 18, 27, Co ? 

2. To how many Centigrade degrees are the following Fahrenheit 
degrees equivalent : — 20, 27, 36, 95 ? 

3. How manj' Fahrenheit degrees above freezing point is 05° C. ? 

4. How many Centigrade degrees above freezing point is GO" F.? 

5. Convert the following readings on the Fahrenheit scale to Centi- 
grade readings :—0°, 10°, 32°, 45°, 100", -25°, and -40°. 

6. Convert the following readings on the Centigrade scale to Fahrenheit 
readings :— 10°, 20°, 32', 75°, -20^ -40°, and -273°. 

7. Find in Centigrade degrees the difierence between 30° C. and 16° F. 

8. In the Reaumur scale, (which is used for household purposes in some 
countries of Europe), the freezing point is marked 0' and the boiling 
point 80°. Express 

(a) 12° C, - 10° C, 5° F., 36' F. in the Reaumur scale. 

(b) 16° R., 25'^R., -6°R. in both the Centigrade and the Fahren- 

heit scale. 



CHAPTER XXVII 
Relation between Volume and Temperature 

262. Coefficient of Expansion of Solids. We have seen 
(§ 247) tliat a rise in the temperature of a body is usually 
accoinpaiiied by an increase in its dimensions, and that 
different substances have different rates of expansion. In 
the case of solids we are usually concerned with change in 
length, while with liquids and gases it is chiefly change of 
volume which we have to consider. 

The coefficient of linear expansion may be defined as 
the increase in length experienced by a rod of unit length 
when its temjyeratare is raised one degree. 

Let li be the first length of a rod and 1^° its temperature. 
Raise the temperature to 1.,° and let the length then be l.,. The 
total increase in length is L — l^ for a rise of t^ — t^ degrees in 

temperature, and so the increase for one degree = ;= — -'• But 

2 1 

this is the increase in length of a rod whose length at first was l^. 

Hence the increase per unit length per degree = — ^- — y^* 

This is the coefficient of linear expansion, and to determine 

it we must measure ^j, l.^, t^, t.^ and put them in this expression. 

As the change in length is always small it must be measured 

with accuracy. Tiiis may be done as follows: — A long, 

straight bar of the substance, M'hose coefficient is to be 

determined, is taken and a fine line drawn across it near eacli 

end. The bar is then supported in a bath, the temperature of 

which can be determined, and changed at will. By means of a 

micrometer-microscoj^e and a scale, the distance between the 

marks is measured when the bar is at the initial temperature. 

The bath is then heated. When the temperature of the whole 

is again steady, the distance between the marks is again 

measured and the temperature noted. Data are thus furnished 

for calculating the coefficient of linear expansion of the metal. 

229 



230 RELATION BETWEEN VOLUME AND TEMPERATURE 



The following table gives the coefScients of linear expansion 
of some common substances. The volume coefficient of expan- 
sion of a solid is usually determined by a calculation from the 
linear coefficient. 

Coefficients of Lineak Expansion for 1° C. 



Substance. 



Coefl&cient. 



Ahxminium ' 0.00002313 

Bra.ss ' 0.00001900 

Copper ; 0.00001678 

Glass ; 0.00000899 

Gold , 0.00001443 

Iron (soft) 0.00001210 



j Substance. 

1 


Coefficient. 


Nickel 


0.00001279 


Platinum 


0.00000899 


Silver 


0.00001921 


Steel 


0.00001322 


Tin 


0.00002234 


Zinc 


0.00002918 







An alloy of nickel and steel (86 per cent, of nickel) known 
as " invar," has a coefficient of expansion only one-tenth that 
of platinum. 

263. CoefBcient of Expansion of Liquids. Like solids, 
different liquids expand at different rates. Many liquids also 
are very irregular in their expansion, having different coeffi- 
cients at different temperatures. 

The coefficient of expansion of a liquid may 
be determined with a fair degree of accuracy 
by a modification of the experiment described 
in § 248. The liquid is enclosed in a bulb 
and graduated capillary tube, shown in 
Fig. 271. The bulb is heated in a bath, and 
the position of the surface of the liquid in 
the tube corresponding to various tempera- 
tures is noted. Now, if the volume of 
the bulb in terms of the divisions of the 
stem is known, the expansion can be calcu- 
To be accurate, corrections should be made for changes 



Fio. 271.— Determinaiion 
of the coefficient of ex- 
pansion of a liquid. 



lated. 



, PECULIAR EXPANSION OF WATER 231 

in the capacities of the bulb and tube through changes in 
temperature. 

264. Peculiar Expansion of Water ; its Maximum Density. 
If the bulb and tube shown in Fig. 271 is filled with water at 
the temperature of the room — say 20° C. — and the bulb 
placed in a cooling bath, the water will regularly contract in 
volume until its temperature falls to 4° C, and then it will 
expand until it comes to the freezing point. Conversely, if 
water at 0° C. is heated it will contract in volume until it 
reaches 4° C, and then it will expand.* Hence, a given mass 
of w^ater has minimum volume and maximum density when it 
is at 4° C. 

An experiment devised by Hope shows in a simple manner 
that the maximum density of water is at 4" C A metal 
reservoir is fitted about the middle of a tall ^^ 
jaj", and two thermometers are inserted, one Bli. 

at the top and the other at the bottom, as <^^^^^& 
shown in Fig. 272. The jar is filled with |||| |||P 
water at the temperature of the room, and fela 
a freezing mixture of ice and salt is placed ' qW, , r 

in the reservoir. The upper thermometer J| |^ 
remains stationary and the lower one con- „ „-„ „ . 

•^ _ Fig. 272.— Hope's ap- 

tinues to fall until it indicates a temperature paratua. 

of 4° C The lower one now remains stationary and the upper 
one begins to fall and continues to do so until it reaches the 
freezing point. 

The experiment shows that as the water about the centre 
of the jar is cooled it becomes denser and continues to descend 
until all the water in the lower part of the jar has reached the 
maximum density. On further cooling the water in the 
middle of the jar it becomes lighter and ascends. 

The experiment illustrates the behaviour of large bodies of 
w^ater in cooling as winter approaches. As the surface layers 

* Jn an actual expeiimeut the contraction of the glass must be allowed for. 



232 RELATION BETWEEN VOLUME AND TEMPERATURE 

cool they become denser and sink, while the warmer water 
below rises to the top. This process continues until the whole 
mass of water reaches a uniform temperature of 4° C. The 
colder and lighter water then remains on the surface, where 
the ice forms, and this protects the water below. 

PROBLEMS 

1. A steel piano wire is 4 feet long at a temperature of 16° C. What is 
its length at 20° C? 

2. A brass scale is exactly one metre long at 0° C. What is its length 
atl8°C.? 

3. A pane of glass is 12 inches long and 10 inches wide at a temperature 
of 5° C. What is the area of its surface at 15° C? 

4. The bars in a gridiron pendulum are made of iron and copper. If 
the iron bars are 80 cm. long, what should be the length of the copper bars ? 

5. The height of the mercury column in a barometer was 7G0 mm. when 
the temperature was 0" C. What would be the height at 20° C, being 
given that the volume-coefficient of expansion of mercury is 0.000187 ? 
If the height was observed by means of a brass scale which was correct at 
0° C, what would be the apparent reading on the scale ? 

6. At temperature 15° C. the barometric height is 763 mm. as indicated 
by a brass scale which is correct at 0° C. Wliat would be the reading if 
the temperature fell to 0° C. ? 

7. Explain where the ice would form and what would happen if water 
continued to contract down to 0° C, (1) if solidification produced the same 
expansion as it does now ; (2) if contraction accompanied freezing. 

265. Coefficient of Expansion of Gases— Charles' Law. It 

has been shown by the experiments of Charles, Gay-Lussac, 
Regnault,* and other investigators, that under constant pressure 
all gases expand equally for equal increases in temperature. In 
other words, all gases have approximately the same coefficient 
of expansion. Further, it was shown by Charles, that under 
constant pressure the volume of a given mass of gas increases 
by a constant fraction of its volume at 0° C. for each increase 
of 1° C. in its temperature. Charles roughly determined 
this ratio, which was afterwards more accurately measured 
by Gay-Lussac, whose researches were published in 1802. 

♦Charles (17461823), Gay-Lussac (1778-1850), Eegnault (1810-1878) were all French scientists. 



COEFFICIENT OF EXPANSION OF GASES 



233 



The general statement of the principle is usually known as 
Charles' Law, but sometimes as Oay-Lussacs Law, It is 
given in the following statement : — The 
volume of a given mass of any gas at 
constant pressure increases for each rise 
of r G. by a constant fraction {about 
2Tii) ^f ^^^ volume at 0° C. 

It has also been shown that if the 
volume remains constant, the pressure 
of a given mass of gas increases by the 
same constant fraction (about ^^ya) of 
its pressure at 0^ C. for each rise in 
temperature of 1° C. That is to say, 
the volume-coefficient, and the pressure- 
coefficient of a gas are numerically equal. 
Practically, this is but a statement, in 
other terms, of the fact that, in obeying 
Charles' Law, gases also obey Boyle's 
Law. 

The volume-coefficient and the pres- 
sure-coefficient may be determined ex- 
perimentally by the apparatus devised 
by Regnault (Fig. 273). The gas is 
inclosed in the bulb N, whose volume 
is known. The bulb is placed first in melting ice, and then in 
steam rising from boiling water, the pressure being kept con- 
stant by keeping constant the difference in level of the mercury 
in the tubes A and />. The increase in volume is calculated by 
the change in height in the mercury column in A. Given the 
volume of the bulb and the tube, and having determined the 
increase in volume for a change in tempei'ature from 0° to 100°, 
the expansion-coefficient is found by a simple calculation. 

To determine the pressure-coefficient the bulb, as before, is 
placed alternately in melting ice, and in steam. The volume 




Fig. 273. — Regnault's apparatus 
for finding the coefficient o( 
expansion of a gas. 



234 RELATION BETWEEN VOLUME AND TEMPERATURE 

is kept constant by keeping the surface of the mercury in the 
tube J. at a fixed level a. This is done by adjusting the 
height of the mercury column in B. The increase in pressure 
is measured by the increased difference in the level in the 
mercury columns in A and B. 

266. Gas Thermometer. The Regnault apparatus is used 
as a gas thermometer. The bulb is filled with a gas, usually 
hydrogen. The position of the mercury level in B is marked 
0° when the bulb is in melting ice and the surface of mercury 
in J. is at a fixed point a; it is marked 100° when the bulb is 
in steam and the mercury level in A is at the same fixed 
point. The space between 0" and 100° is divided into 100 
equal divisions, and these are continued below 0° and above 
100°. To use the instrument the tube B is adjusted to bring 
the mercury level in A to the fixed point a, and the tempera- 
ture is read directly from the scale placed behind B. 

In the gas thermometer changes in temperature are 
measured, not as in the thermometers already described, by 
the changes in volume, but by the corresponding changes in 
pressure when the volume is kept constant. 

The nitrogen gas thermometer is the most perfect instru- 
ment of its kind. It has been chosen by the International 
Bureau of Weights and Measures as the standard for tempera- 
ture measurement. For convenience, mercury thermometers 
are employed for most purposes. The gas thermometer is 
used mainly for standardizing mercury thermometers and 
for measuring very low and very high temperatures. 

267. Absolute Temperature. In the gas thermometer the 
volume of the gas is kept constant, wliile a change in the 
temperature is determined by the change in the pressure 
which the gas exerts. 

Let the gas at first be at 0° C. If its temperature is raised 
to 1° C. its pressure will increase -g^-j, that is, at 1° C. the 



FURTHER STATEMENT OF CHARLES' LAW 



235 



pressure will be |I| of that iit 0^ C. At 2° C. tlie pressure 
exerted by the gas will be f^% ; at 100° C. the pressure will 
be llf of that at 0° C. ; and so on. 

Again, at — 1° C. the pressure will be diminished ^ra' t-hat is, 
the gas will exert a pressure f ^f of that at 0° C. ; at — 2" C. 
the pressure will be |f ^ ; at — 20"^ C. it will be ||^^ ; and so on. 

If we could continue lowering 
the temperature and reducing the 
pressure in this same way, then 
at —273° C. the pressure would 
be nothing. But before reaching 
such a low temperature the gas 
will change to a liquid, and our 
method of measuring temperature 
by the pressure of the gas would 
then fail. 

However, calculations based 
on the kinetic theory of gases 
(§ 151) lead to the conclusion 
that at —273° C. the rectilinear 
motions of the molecules would 
cease ; which would mean that the substance was completely 
deprived of heat and at the lowest possible temperature. 
This point is hence called the absolute zero, and temperature 
reckoned from it is called absolute temperature. Thus a 
Centigrade reading can be converted into an Absolute reading 
by adding 273 to it. 

The method of measuring temperature on an absolute scale 
was proposed by Lord Kelvin in 1848. 

268. Further Statement of Charles' Law. Let V^, V^, V^, 
etc., represent the volumes of a given mass of gas, under con- 
stant pressure, at temperatures, respectively, 0°, 1°, 2°, etc., C, 




Lord Kelvin (Sir William Thomson) 
(1824-1907). Made important investigations 
in almost every branch of physics. Famous 
as electrician of Atlantic cables. 



236 RELATION BETWEEN VOLUME AND TEMPERATURE 

that is, 273^ 274°, 275'', etc., Absolute, then according to 
Charles' Law 

V • V • V • etc — ^^s V • 5i* V • 2.J.I V • etc 

•^ • '^ 1 • '^ 2 • tJtU., — 273 *^0"273 '0-277 'O* ^'^^^ 

= 273 : 274 : 275 : etc. 

Stating this result in words, tJie volume of a given mass of 
gas at a constant 'pressure varies directly as the absolute 
temperature. 

This manner of stating the law is often convenient for 
purposes of calculation. 

PROBLEMS 

1. If the absolute temperature of a given mass of gas is doubled while 
the pressure is kept constant, what change takes place in («) its volume, 
(6) its mass, (c) its density ? 

2. The pressure of a given mass of gas was doubled while its volume 
remained constant. What change must have taken place in (a) its 
absolute temperature, (6) its density 1 

3. The pressure remaining constant, what volume will a given mass of 
gas occupy at 75° C. if its volume at (f C. is 22.4 litres ? 

4. If the volume of a given mass of gas is 120 c.c. at 17° C, what will 
be its volume at - 13° C. ? 

5. A gauge indicates that the pressure of the oxygen gas in a steel gas 
tank is 150 pounds per scpiare inch when the temperature is 20° C. 
Supposing the capacity of the tank to remain constant, find the pressure 
of the gas at a temperature of 30° C. 

6. An empty bottle, open to the air, is corked when the temperature 
of the room is 18° C. and the barometer indicates a pressure of 15 pounds 
per square inch. Neglecting the expansion of the bottle, find the pressure 
of the air within it after it has been standing for some time in a water 
bath whose temperature is 67° C. 

7. An uncorked flask contains 1.3 grams of air at a temperature of 
— 13° C. What mass of air does it contain at a temperature of 27° C. if 
the pressure remains constant ? 

8. The volume of a given mass of gas is one litre at a temperature of 
5° C. The pressure remaining constant, at what temperature will its 
volume be («) 1100 c.c, (h) 900 c.c? 



EXPANSION OF GASES 237 

9. At what temperature will the i)ressure of the air in a Vjicycle tire 
be 33 pounds to the square inch, if its pressure at 0° C. is 30 pounds 
per square inch ? (Assume no change in volume.) 

10. A certain mass of hydrogen gas occupies a volume of 380 c.c. at a 
temperatui'e of 12° C. and 80 cm. pressure. What volume will it occupy 
at a temperature of - 10° C. and a pressure of 76 cm. ? 

(1) Change in volume for change in temperature. 

Since the volume varies directly as the absolute temperature and 
the temperature is reduced from 12° C. to -10° C. the volume 
will be reduced to become fff lH or |f| of the original volume. 

(2) Change in volume for change in pressure. 

Since the volume varies inversely as the pressure, and the 
pressure is reduced from 80 cm, to 7fi cm. the volume will 
be increased to become f§ of the original volume. 

Hence, taking into account the changes for both temperature and 
pressure, the volume required will be, 

380 X Iff X fg = 369.12 CO. 

11. A mass of oxygen gas occupies a volume of 120 litres at a tempera- 
ture of 20° C. when the barometer stands at 74 cm. What volume will it 
occupy at standard temperature and pressure ? (0° C. and 76 cm. 
pressure.) 

12. The volume of a certain mass of gas is 500 c.c. at a temperature of 
27° C. and a pressure of 400 grams per sq. cm. What is its volume at a 
temperature of 17° C. and a pressure of 600 grams per sq. cm. ? 

13. The weight of a litre of air at standard temperature and pressure 
is 1.29 grams. Find the weight of 800 c.c. of air at 37° C. and 70 cm. 
pressure. 

14. The density of hydrogen gas at standard temperature and pressure 
is 0.0000896 grams per c.c. Find its density at 15° C. and 68 cm. 
pressure. 



CHAPTER XXVIII 

Measurement of Heat 

269. Unit of Heat. As already pointed out (§ 253), the 
temperature of a body is to be distinguished from the 
quantity of heat which it contains. The thermometer is used 
to determine the temperature of a body, but its reading does 
not give the quantity of heat possessed by it. A gram of 
water in one vessel may have a higher temperature than a 
kilogram in another, but the latter will contain a greater 
quantity of heat. Again, a pound of water and a pound of 
mercury may be at the same temperature, but we have reasons 
for believing that the water contains more heat. 

In order to measure heat we must choose a suitable unit, 
and by common consent, the amount of heat required to raise 
by one degree the temperature of a unit mass has been selected 
as the most convenient one. The unit, will, of course, have 
different magnitudes, varying with the units of mass and 
temperature-difference chosen. In connection with the metric 
system the unit called the calorie has been adopted for 
scientific purposes. It is the ainouv t of heat required to raise 
a mass of one gram of water one degree Centigrade in 
temjjerature. 

For example, 

to raise 1 gram of water through 1° C. requires 1 calorie, 
to raise 4 grams of water through 5' C. requires 20 calories, 

and to raise m grams of water from ti° to t.,° C. requires m (io - tj) 

calories. 

In engineering practice, the British Thermal Unit (designated 

B. T. U.) is in common use in English-speaking countries. It 

is tlie quantity of heat required to raise one pound of water 

one degree Fahrenheit in temperature. 

238 



THERMAL CAPACITY- SPECIFIC HEAT 



239 



PROBLEMS 

1. How many calories of heat must enter a mass of 65 grams of water 
to change its temperature from 10° C. to 35° C? 

2. How many calorics of heat are given out by the cooling of 120 grams 
of water from 85° C. to G0° C? 

3. If 1400 calories of heat enter a mass of 175 grams of water what 
will be its final temperature, supposing the original to be 15° C? 

4. A hot water coil containing 100 kilograms of water gives oflF 1,000,000 
calories of heat. Neglecting the heat lost by the iron, find the fall in 
temperature in the water. 

5. On mixing 65 grau)s of water at 76° C. with 85 grams at 60° C, what 
will be the temperature of the mixture ? 

270. Thermal Capacity — Specific Heat. The amount of 
heat required to change a unit-mass of a substance through 
one degree in temperature varies with different substances. 
To ilhistrate, if we place equal masses of turpentine and water 
at the same temperature in similar beakers and add to each 
the same mass of hot water we shall find, on determining the 
temperature of the mixture with a thermometer, after stirring, 
that, although approximately the same number of calories of 
heat has been added to each, the increase in temperature of 
the turpentine mixture is greater than the increase in tem- 
perature of the water. Thus we find that 
more heat is required to raise a certain mass 
of water one degree than to warm the same 
mass of turpentine to the same extent. 

Next, heat equal masses of water, aluminium 
(wire) and mercury to the same temperature by 
placing them in separate test-tubes immersed 
in a bath of boiling water (Fig. 274). Now 
provide three beakers containing equal masses 
of water at the temperature of the room, 
and pour the hot water into the first, the alu- 
minium into the second, and the mercury into 
the third. After stirring, take the temperature in each case. 




-nTTTnimiiiiiiiiiniiiiiinirt 

FiQ.274.— The heating 
of equal masses of 
different substances 
to the same tempera- 
ture in a water bath. 



240 MEASUREMENT OF HEAT 

Tlie temperatures are quite different, the water in the first being 
the liottest, and the contents of the third being the coldest. 

Tliese experiments indicate that the amount of heat 
absorbed or given out by a body for a given change in 
temperature depends on the nature of the body, as well as 
upon its mass and change in temperature. 

The number of heat units required to raise the temperature 
of a body one degree, is called its thermal ccqxicity. The 
thermal capacity per unit-mass is called specific heat. 
Specific heat, accordingly, may be defined as the number of 
heat %inits required to raise the ternperature of a unit-mass 
of the substance, one degree. 

Hence, the quantity of heat required to warm a mass of m 
grams of a substance from a temperature of t-^ to a tempera- 
ture of ^2° = W/ (^2 ~ ^i) *' when s is the specific heat of the 
substance. 

271. The Specific Heat of Water. From the definition of 
heat unit, it follows that the specific heat of water is 1 ; but, 
the heat required to warm a unit-mass one degree differs 
slightly with the temperature of the water. 

Of all known substances except hydrogen, water has the 
greatest thermal capacity, which fact is of great importance 
in the distribution of heat on the surface of the earth. For 
example, land areas surrounded by large bodies of water are 
not so subject to extremes of temperature. In summer the 
water absorbs the heat, and as it warms very slowly, it 
remains cooler than the land. In winter, on the other hand, 
the water gradually gives up its store of heat to the land, thus 
preserving an equable temperature. 

272. Determination of Specific Heat by the Method of 
Mixture. The method depends on the principle that the 
amount of heat lost by a hot body when placed in cold 
water is equal to the amount of heat gained by the water. 
Let us apply the method to find the specific heat of lead. 



DETERMINATION OF SPECIFIC HEAT 



241 




Fig. 275.— Determi- 
nation of specific 
heat of a solid. 



Take a definite mass of sliofc, say 220 grams, and heat it in 

steam from boiling water to a temperature of 

100" C. (Fig. 275). Now place 100 grams of 

water at the temperature of the room, say 

20° C, in a beaker and surround it with wool 

or batting to keep the heat from escaping. 

Pour the shot into the water and, after stirring, 

take the temperature. Let it be 25° C. Then 

the heat gained by the water 

= 100 (25 °- 20°) cal. = 500 cal. 
If now no heat has escaped, 220 grams of 
lead must, in falling from 100° to 25°, have 
lost 500 cal. of heat. Or 1 gram of lead 
in falling 1^ loses 500 -^ (220 x 75) = MO 
calories. 

A general formula may be obtained as follows : — 
Let m = tlie mass of tlie substance, 
and t = its temperature ; 

mj = the mass of the water, 
and ti = its temperature. 
Let ^2 = resulting temperature after mixing. 
Then, heat gained by water = m^ (ig - ^i), 
and heat lost by the substance = m (t - t^) s, where s is its specific heat ; 
Therefore w (t - ij) ^ = '»^i (^2 ~ ^i)> 

111, (to - t-,) 
or s = — ' ^ ■^ 1/. 

m {t - t^) 
The method of mixture applies equally well to other sub- 
stances than water, and to heat lost by water as well as gained 

by it. 

Specific Heats of Some Common Substances 



Aluminium 0.214 

Brass 0.090 

Copper 0.094 

Glass (ci'own). . . 0.16 
Gold 0.032 



Ice (-10° C.)... 0.50 

Iron 0.113 

Lead 0.031 

Marble 0.21G 

Mercury 0.033 



Paraffin 0.694 

Petroleum 0.511 

Platinum 0.032 

Silver 056 

Zinc 0. 093 



242 SPECIFIC HEAT 

PROBLEMS 

(For specific heats see table just above) 

1. What is the thermal capacity of a glass beaker whose mass is 35 grams? 

2. Which has the greater thermal capacity, 68 grams of mercury or 
2 gratiTS of water ? 

3. It requires 360 calories of heat to raise the temperature of a body 
10 degrees. What is its thermal capacity ? 

4. The thermal capacity of 56 grams of copper is 5.204 calories. What 
is the specific heat of copper ? 

5. It requires 902.2 calories of heat to warm 130 grams of paraffin 
from 0° C. to 10° C. What is the specific heat of paraffin ? 

6. How much heat will a body whose thermal capacity is 320 calories 
lose in cooling from 40° to 10° C? 

7. What is the quantity of heat required to raise 120 grams of 
aluminium from 15° to 52° C? 

8. How many calories of heat are given off by an iron radiator whose 
mass is 25 kgnis., in cooling from 100° to 20° C? 

9. A lead bullet whose mass is 12 grams had a temperature of 25° C. 
before it struck an iron target, and a temperature of 100° C. after impact. 
How many calories of heat were added to the bullet ? 

10. Into 120 grams of water at a temperature of 0° C. 150 grams of 
mercury at 80° C. are poured. What is the resulting temperature ? 

11. If 95 grams of a metal are heated to 100° C. and then placed in 114 
grams of water at 7° C the resulting temperature is 15° C. Find the 
specific heat of the metal ? What metal is it ? 

12. A piece of iron, whose mass is 88.5 grams and temperature 90° C, 
is placed in 70 grams of water at 10° C. If the resulting temperature is 
20° C, find the specific heat of iron. 

13. A mass of zinc, weighing 5 kgms. and having a temperature of 80° C, 
was placed in a liquid and the resulting temperature was found to be 
15° C. How much heat did the zinc impart to tlie liquid ? 

14. Find the resulting temperature on placing 75 gi'ams of a substance 
having a sj^ecific heat of 0.8 and heated to 95° C. in 130 grams of a liquid 
at 10° C. whose specific heat is 0.6. 

15. On mixing 1 kgm. of a substance having a specific heat of 0.85, at a 
temperature of 12° C, with 500 grams of a second substance at a tempera- 
ture of 120° C, the resulting temperature is 45° C. What is the specific 
heat of the second substance ? 



CHAPTER XXIX 

Change of State 

273. Fusion. Let us take some pulverized ice at a tempera- 
ture below the freezing point and apply heat to it. It gradually 
rises in temperature until it reaches 0° C, wlien it begins to 
melt. If the ice and the water formed from it are kept well 
stirred, no sensible change in temperature takes place until all 
the ice is melted. On the further application of heat, the 
temperature begins again to rise. 

The change from tlie solid to the liquid state by means of 
heat is caAled fiosioyi or mdfing, and the temperature at which 
fusion takes place is called the melt hig point. 

The behaviour of water is typical of crystalline substances 
in general. Fusion takes place at a temperature which is con- 
stant for the same substance if the pressure remains invariable. 
Amorphous bodies, on the other hand, have no sharply defined 
melting points. When heated, tliey soften and pass through 
various stages of plasticity into more or less viscous liquids, 
the process being accompanied by a continuous rise in temper- 
ature. Paraffin wax, glass and wrought-iron are typical 
examples. By a suitable control of the temperature glass 
can be bent, drawn out, moulded or blown into various 
forms, and iron can be forged, rolled or welded. 

274. Solidification. The temperature at which a substance 
solidifies, the pressure remaining constant, is the same as that 
at which it melts. For example, if water is gradually cooled, 
while it is kept agitated, it begins to take the solid form at 0° 
C, and it continues to give up heat without falling in tempera- 
ture until the process of solidification is complete. 

243 



244 CHANGE OF STATE 

But it is interesting to note that a liquid which under 
ordinary conditions solidifies at a definite point may, if slowly 
and carefully cooled, be lowered several degrees below its 
normal temperature of solidification. The phenomenon is 
illustrated in the following experiment. Pour some pure 
water, boiled to free it from air bubbles, into a test-tube. 
Close the tube with a perforated stopper, through which a 
thermometer is inserted into the water. Place the tube in a 
freezing mixture of ice and salt. If the water is kept quiet 
it may be lowered to a temperature of — 5° C. without freezing- 
it, but the condition is unstable. If the water is agitated or 
crystals of ice are dropped in, it suddenly turns into ice and 
the temperature rises to 0° C. 

275. Change of Volume in Fusion. Most substances suffer 
an increase in volume in passing from the solid to the liquid 
state, but some which are crystalline in structure, such as ice, 
bismuth, and antimony are exceptions to the rule. 

The expansive force of ice in freezing is well known to all 
who live in cold climates. The earth is upheaved and rocks 
are disintegrated, while vessels and pipes which contain water 
are burst by the action of the frost. 

Only from metals which expand on solidification can per- 
fectly shaped castings be obtained. The reasons are obvious. 
Antimony is added to lead and tin to form type-metal because 
the alloy thus formed expands on solidifying and conforms 
completely and sharply with the outlines of the mould. 

276. The Influence of Pressure on Melting Point. If a 

substance expands on melting, its melting point will be raised 
by pressure, while if it contracts its melting point will be 
lowered. We would expect this. Since extra pressure applied 
to a body which takes a larger volume on melting would tend 
to prevent it from expanding, it would be reasonable to suppose 
that a higher temperature would be necessary to bring about 




HEAT OF FUSION 245 

the change ; on the other hand, if the body contracts on melting, 
increased pressure would tend to assist the process of change, 
and a lower temperature should suffice. 

An interesting experiment shows the effect of pressure on 
the melting point of ice. Take a block of ice and rest it on 
two supports, and encircle it with a 
hne wire from which hangs a heavy 
weight (Fig. 276). In a few hours 
the wire will cut its way through the 
ice, but the block will still be intact. 
Under the pressure of the wire the 
ice melts, but the water thus formed 
is below the normal freezing point, ^ig. 276.-Regeiation of ice. 
Hence it flows above the wire and freezes again as the pressure 
there is normal. The process of melting and freezing again 
under these conditions is called regelation. 

277. Heat of Fusion. We have seen (in § 273) tliat during 
the process of melting a crystalline body like ice, no change in 
temperature takes place, although heat is being continuously 
applied to it. In earlier times, when heat was considered to 
be a kind of substance, it appeared that the heat applied 
became hidden in the body and it was called latent heat. 

According to modern ideas, there is simply a transformation 
of energy. When a body in fusing ceases to rise in tempera- 
ture, although heat is still being applied, the heat-energy is 
no longer occupied in increasing the average kinetic energy 
and to some extent the potential energy of its molecules, but 
is doing: work in overcoming; the cohesive forces which bind 
these molecules together in the body as a solid. 

A definite quantity of heat, varying with the substance, is 
required to melt a definite mass of a solid. The amount of 
heat required to melt one gram of a substance without a 
change of temperature is called its heat of fusion. For 



246 CHANGE OF STATE 

example, the heat of fusion of ice is 80 calories, which means 
that 80 calories of heat are required to melt one gram of ice. 

278. Determination of the Heat of Fusion of Ice. The 

method of rtiixtiire (| 272) may be used to determine the heat 
of fusion of ice. For example, if 100 grams of dry snow or 
finely broken ice are dropped into 500 grams of water at 
90° C, and the mixture is rapidly stirred until all the ice is 
melted, it will be found that the resulting temperature is 
about 62° C. 

Then the amount of heat lost by 500 grams of water in 
cooling from 90° C. to 62° C. = 500 (90-62) = 14,000 calories. 

This heat melts the ice and then raises the temperature of 
the resulting water from 0° to 62° C. But to raise the 
resulting 100 grams of water from 0° to 62° C. requires 
100 X 62 = 6200 calories. 

Hence the heat required to melt the 100 grams of ice = 
14,000 - 6200 = 7800 calories, and the heat required to melt 
1 gram of ice = 78 calories. 

A general formula is obtained as follows : — 

Let m = the mass of water (in grams), 
t^ = its initial temperature, 
^2 = its final temperature, 
«j,j = the mass of the ice (in grams), 
X = the heat of fusion. 
Then heat h>st by water in falling from t^ to t^ = m {t^ - t^) cal. 
Heat required to melt -hj-j grams of ice = mi x cal. 
Heat required to raise m^ grams of water from 0° to t^ = "i-i ^2 '''^^• 
But the heat lost by the water is used in melting the ice and raising 
the temperature of the resulting water from 0° to t.,. 
Hence, vi (t^ - t^) = tn^ ^ + "''i ^2» 

and:« = "^(^^ -^-^ -mi ^3. 

279. Heat given out on Solidification. All the heat 
required to melt a certain mass of a substance without change 



HEAT ABSORBED IN SOLUTION 247 

in temperature is given out again in the process of solidification. 
Thus, every gram of water, in freezing, sets free 80 calories 
of heat. The formation of ice tends to prevent extremes of 
temperature in our lake regions. Heat is given out in the 
process of freezing during the winter, and absorbed in melting 
the ice in spring and early summer. 

280. Heat Absorbed in Solution ; Freezing Mixtures. 

Change of state through the action of a solvent is also asso- 
ciated with thermal changes. In cases of ordinary solution, as 
in dissolving sugar or salt in water, heat is absorbed. If a 
handful of salt is dropped into a beaker of water at the 
temperature of the room, and the mixture is stirred with a 
thermometer, the mercury will be seen to drop several degrees. 

The result is much more marked if ice and salt are mixed 
together. Both become li(;[uid and absorb heat in the transi- 
tion. This is the principle applied in preparing freezing 
mixtures. The ordinary freezing mixture of ice and salt can 
be made to give a fall in temperature of about 22"^ C. 

Query. — What is the heat absorbed from ? 

QUESTIONS AND PROBLEMS 

1. Why is it impossible to weld together two pieces of cast-iron ? 

2. Water is sometimes placed in cellars to keep vegetables from 
freezing. Explain the' action. 

3. Why is a quantity of ice at-0° C. more effective as a cooling agent 
than an equal mass of water at the same temperature 'i 

i. If two pieces of ice are pressed together under the surface of warm 
water they will be found to be frozen together on removing them from 
the water. Account for this. 

5. If we pour just enough cold water on a mixture of amnionic chloride 
and ammonic nitrate to dissolve them, and stir the mixture with a small 
test-tube, into the bottom of which has been poured a little cold water, 
the water in the tube will be frozen. Explain. 

[In the following problems take the heat of fusion of ice as 80 calories 
per gram.] 

6. What quantity of heat is required to melt 35 grams of ice at 0° C? 



248 CHANGE OF STATE 

7. How much heat is given off by the freezing of 16 kgms. of water ? 

8. Find the resulting temperature when 40 grams of ice are dropped 
into 180 grams of water at 90° C. 

9. How much ice must be placed in a pail containing 10 kgms. of 
drinking water at 20° C. to reduce the temperature to 10° C? 

10. What mass of water at 80° C. will just melt 80 grams of ice ? 

11. How much heat is required to change 23 grams of ice at — 10° C. to 
water at 10° C? (Specific heat of ice = 0.5.) 

12. What mass of water at 75° C. will convert 120 grams of ice into 
water at 10° C? 

13. What mass of ice must be dissolved in a litre of water at 4° C. to 
reduce the temperature to 3° C? 

14. What is the specific heat of brass if a mass of 80 grams at a 
temperature of 100° C. melts 9 grams of ice ? 

15. Fifty grams of ice are placed in 520 grams of water at 19.8° C. and the 
temperature of the whole becomes 11.1° C. Find the heat of fusion of ice. 

281. Vaporization. Transition from a liquid to a vapour 
is a familiar phenomenon. Water in a shallow dish exposed 
to a dry atmosphere gradually disappears as a vapour into the 
air. If heat is applied and the water is made to boil, the 
change takes place more rapidly. The process of converting a 
liquid into a vapour is called vaporization. The quiet vapori- 
zation taking place at all temperatures at the surface of a 
liquid is known as evaporation. 

In ebullition, or boiling, the production of vapour takes 
place throughout the mass, and the process is accompanied by 
an agitation of the liquid, due to the formation of bubbles of 
vapour within the liquid and their movement upward to the 
surface. 

282. Rate of Evaporation. The rate of evaporation depends 
on the nature of the liquid. A little ether placed on the 
palm of the hand disappears almost at once, while the hand 
remains wet with water for a considerable time. Some dense 
oils can scarcely be said to evaporate at all. Liquids which 
evaporate readily are said to be volatile. 



pressurp: of a vapour 



249 



Temperature also affects the rate of evaporation. Other 
conditions being the same, the rate of evaporation increases 
with the temperature. Clothes and wet roads 
dry more rapidly on a warm day than on a 
cold one, if the atmosphere is equally dry on 
the two days. 

Further, the rate of evaporation is affected 
by the amount of vapour of the liquid in the 
suri'ounding space and also by the presence 
in tliis space of other gases. 

283. Pressure of a Vapour. Let us consider 
the case of evaporation in an inclosed space. 
When a few drops of ether are introduced, by 
means of a medicine dropper with a curved 
stem, into the tube of a cistern barometer and 
allowed to rise to the surface of the mercury, 
evaporation begins at once, and the pressure 
exerted by the vapour formed depresses the 
mercury (Fig. 277). The mercury soon comes 
to rest at a height ah, which remains constant 
so long as the temperature is unchanged. 

If the volume of the vapour is decreased Fior277.-Pre88ure 

,, . nii'ii •: • conditions of evapor- 

by lowernig the tube m the cistern, or m- ation within an in. 

,, .. •,ii T/T» "1 1 closed space. 

creased by raisnig it, the ditierence m level 
ab will not be permanently altered. It is evident, therefore, 
that, under these conditions, the pressure of a vapour is 
iiKlependent of its volume, when the temperature is constant, 
provided some liquid is always present. 

284. Molecular Explanation of Evaporation. According 
to the kinetic theory (§ 151) the molecules of a liquid are in 
rapid motion, and some of these arrive at the surface with 
sufficient velocities to escape from the attraction of the 
neighbouring molecules. These molecules constitute the 
vapour of the liquid. When the ether enters the tube, the 




250 CHANGE OF STATE 

closed space above the mercury at once begins to be filled 
with molecules moving about in straight lines. These bom- 
bard the walls of the tube and the surface of the liquid itself. 
Many of these molecules, as their number increases, come 
again within the range of attraction of the molecules at the 
surface and re-enter the liquid. Evaporation ceases when the 
number of the molecules entering the liquid in a given time 
equals the number which escape. When the tube is lowered 
and the vapour made to take less volume, the density is mo- 
mentarily increased. The number of molecules now entering 
the liquid is greater than that leaving it. In other words, some 
of the vapour is being condensed to a liquid. The process 
ceases when the former pressure and density are restored. 

When the volume of the vapour is increased by lifting the 
tube, the density and pressure are momentarily decreased, and 
the number of molecules escaping per second from the liquid 
becomes greater than the number entering it. Evaporation 
continues until the vapour density and pressure again reach 
tlie maximum. Equilibrium is very quickly restored. 

285. Saturated Vapour. When a vapour has its maximum 

density for any given temperature it is said to be saturated, 
and the corresponding maximum pressure is called the satura- 
tion pressure. Whenever a saturated vapour is either cooled 
or compressed, condensation takes place. For saturation, some 
of the liquid must be present. 

The temperature being constant, the saturation pressure 
varies with the volatility of the liquid. This may be shown 
by introducing other liquids — say alcohol or water — into 
barometer tubes, and noting the pressure as indicated by 
the depression of the mercury. At 20° C. the depression for 
alcohol is about 44 mm. and for water 17.5 mm. 

286. Evaporation into Air. The amount of evaporation 
into a closed space is jDractically the same whether the space 
is filled with air or is a vacuum ; but the presence of the air 



EFFECT OF PRESSURE ON THE BOILING POINT 



251 




Fig. 278.— Determina- 
tion of the boiling 
point of a liquid. 



materially retards the rate of evaporation. When the ether is 
introduced into the barometer tube, the mercury rapidly falls 
as far as it will go, but when ether is enclosed in a tube along 
with air over mercury, it will be several hours before equi- 
librium is restored. The depression in the 
end, however, will represent a vapour pressure 
the same as in the tube void of air. 

It is obvious that there can be no limit to 
the amount *of evaporation when a liquid is 
exposed in an open vessel. Water left in a 
basin in time disappears. But the presence of 
vapour in the layers of air immediately above 
the li(|uid arrests the process, and the action 
of the air currents in carrying away vapour- 
laden air hastens evaporation. Wet articles 
dry very rapidly on a windy day. 

287. Ebullition— Boiling Point. When heat 
is applied to water (Fig. 278) it gradually rises in temperature 
until vapour is disengaged in bubbles from the mass of the 

liquid. No further increase in 
temperature takes place, however 
rapidly the process of boiling is 
maintained. 

The temperature at which a liquid 
boils, or gives off bubbles of its own 
vapour, is called its boilivg ixnnt. 

288. Effect of Pressure on the 
Boiling Point. The boiling point 
varies with the pressure. If the 
pressure of the escaping steam is 
increased by leading the outlet- 
pipe to the bottom of a vessel of 
water as shown in Fig. 279, the temperature of the boiling 
water is increased. On the other hand, a decrease in pressure 




Fig. 279.— Boiling point of a liquid 
raised by means of pressure. 



252 



CHANGE OF STATE 



is accomijanied by a lowering of the temperature. This is 
shown by a familiar but striking experiment. 

Half fill a flask with water and boil for a minute or two in 
order that the escaping steam may carry out the air. While 
the water is boiling remove the flame, and at the same instant 
close the flask with a stopper. Invert the flask and support 

it on a retort stand (Fig. 280), and 
pour cold water over the flask. The 
temperature of the water in the flask 
is below 100° C, but it boils vigor- 
ously. The action is explained as 
follows. The chilling of the flask 
condenses the vapour within and thus 
reduces the pressure on the surface 
of the water. The water, relieved 
of this pressure, boils at a lower tem- 
perature. If we discontinue the 
cooling and allow the vapour to ac- 
cumulate and tlie pressure to increase, 
the boiling ceases. The process may 
In fact, if care is taken in expelling 




Fio. 280. — Boiling point of a 
liquid lowered by decrease of 
pressure. 



be repeated several times, 
the air at the beginning, the water may 
be made to boil even when the temperature 
is reduced to that of the room. 

The reason why the boiling point depends 
upon the pressure is readily found. Bubbles 
of vapour begin to form in the liquid only 
when the pressure exerted by the vapour 
within the bubble balances the pressure on 
the surface of the liquid (Fig. 281). Were 
the pressure in the bubble less, the bubble 
would collapse. But the pressure of a 
vapour in contact with its liquid in an 
enclosed space varies with the temperature 




Fig. 281. — Balance be- 
tween external pres- 
sure of the air and the 
pressure exerted by 
the vapour within a 
bubble. 

Hence, a liquid 



EFFECT OF PRESSURE ON THE BOILING POINT 



253 



will be upon tlic point of boiling when its temperature has risen 
sufficiently lii(i,h for the pressure of the saturated vapour of 
the liquid to Ijo e([ual to the pressure sustained by the surface 
of the li(j[uid. Therefore, when the pressure on the surface is 
high, the boiling point must be high, and vice versa. The 



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Fig. 282. — Curve showing the relation between the pressure and the boiling point of water. 

accompanying diagram (Fig. 282) shows graphically the rela- 
tion between the pressure and the boiling point of water, 
ranging from 1 to 25 atmospheres. 

It is to be noted that the steam bubbles begin in the small 
air or gas bubbles present in the water, and when these are 
removed by prolonged boiling the liquid boils very irregularly 
(bumps). Geyser phenomena occur because of great hydros- 
tatic pressure due to the water. 

Since the boiling point is dependent on atmospheric 
pressure, a liquid in an open vessel will boil at a lower 
temperature as the elevation above the sea-level increases. 
This decrease is roughly 1° C. for an increase in elevation of 
293 metres ( = 961 feet). The boiling point of water at the 
summit of Mont Blanc (15,781 feet) is about 85° C, and at 
Quito (9520 feet), the highest city in the world, it is 90' C. 



254 



CHANGE OF STATE 



In such high altitudes the boihng point of water is below 
the temperature required for cooking many kinds of food, 
and artificial means of raising the temperature have to be 
resorted to, such as cooking in brine instead of pure water, or 
using closed vessels with safety devices to prevent explosions. 
Sometimes longer boiling is all that is required.* 

In the case of liquids liable to burn, evaporation may be 
produced in "vacuum pans" in which boiling takes place 
under reduced pressure (and therefore lowered temperature). 
This arrangement is used, for example, in condensing milk 
and sugar syrups. 

289. Heat of Vaporization. Whenever a given mass of a 
liquid changes into a vapour, a definite amount of heat is 
absorbed. Thus in the process of vaporization a certain amount 
of energy ceases to exist as heat, and (in a manner similar to 
fusion) becomes potential energy in the vapour. In accord- 
ance with the law of Conservation of Energy, all heat which 
thus disappears is recovered when the vapour condenses. 

The amovbnt of heat required to change one gram of 

any liquid into vapour without 
changing the temperature is called 

the HEAT OF VAPORIZATION, Or 

sometimes the latent heat of 
vaporization. For example, the 
heat of vaporization of water is 
536 calories, by which we mean 
that when water is boiling under 

^ -, /^^^^, -^^^ the standard atmospheric pressure 

(76 cm. of mercury) 536 calories 
of heat are required to vaporize 
one gram without change of tem- 
perature. 




Fig. 2S3.— Determination of heat of 
vaporization of water. A, fiask to 
contain water ; B, trap to catch 
water condensed in the tube ; C, 
vessel with known mass of water. 



"Eggs can be boiled hard in an open vessel on Pike's Peak, 11,108 ft. hif?h. 



DETERMINATION OF HEAT OF VAPORIZATION 255 

290. Determination of Heat of Vaporization. The heat of 
vaporization of water may be determined as follows : — By 
means of apparatus arranged as shown in Fig. 283 pass steam 
for a few minutes into a quantity of water in a vessel G. 
Take the weight and the temperature of the water before 
and after the steam is conveyed into it and find the 
increase in mass and temperature due to the condensation 
of the steam. 

Suppose the mass of water in C at first to be 120 grams 
and the increase in mass due to condensation to be 5 grams ; 
and suppose the initial and final temperatures of the water to 
be 10° C. and 35° C. respectively. 

We can make our calculation as follows : — 

Heat gained by the original 120 grams of water = 120 (35 — 10) = 3000 cal. 

This heat comes from two sources, 

(a) The heat received from the condensation of 5 grams of steam at 
100° C. to water at 100° C. 

{h) The heat received from the fall in temperature of 5 grams of water 
from 100° C. to 35° C. = 5 (100 - 35) = 325 cal. 

Hence, the heat set free by the condensation of 5 grams of steam 
= 3000 - 325 = 2G75 cal. 

And the heat set free in the condensation of 1 gram of steam = 2675 
-r 5 = 535 cal. 

QUESTIONS AND PROBLEMS 

1. The singing of a tea kettle just before boiling is said to be due to the 
collapse of the first bubbles formed in their upward motion through the 
water. Explain the cause of the collapse of these bubbles. 

2. When water is boiling in a deep vessel the bubbles of vapour are 
observed to increase in size as they approach the surface of the water. 
Give a reason for this. 

3. Why does not a mass of liquid air in an open vessel immediately 
change into gas when brought into a room at the ordinary temperature ? 

4. Why is it necessary to take into account the pressure of the air in 
fixing the boiling point of a thermometer ? 



256 CHANGE OF STATE 

[In the following problems take the heat <>f vaporization of water as 
536 calories per gram.] 

5. How much heat will be required to vaporize 37 grams of water ? 

6. How many calories of heat are set free in the condensation of 340 
grams of steam at 100° C. into water at 100° C. 1 

7. How much heat is required to raise 45 grams of Avater from 15° C, 
to the boiling point and convert it into, steam ? 

8. How much heat is given up in the change of 365 grams of steam at 
100° to water at 4° C? 

9. What is the resulting temperature when 45 grams of steam at 100° 
C. are passed into 600 grams of ice-cold water ? 

10. How many grams of steam at 100° C. will be required to raise tl.e 
temperature of 300 grams of water from 20° C. to 40° C? 

11. How many grams of steam at 100° C. will just melt 25 grams of ice 
at 0° C. ? 

12. How much heat is necessary to change 30 grams of ice at - 15° C. to 
steam at 100° C? (Specific heat of ice = 0.5.) 

13. An iron radiator whose mass is 55 kgms. and temperature 100° is 
shut off when it contains 100 grams of steam at a temperature of 100° C. 
How much heat is imparted to the room by the condensation of the steam 
and the cooling of the water and the radiator to a temperature of 40° C? 
(Specific heat of iron = 0. 113.) 

14. If 34.7 grams of steam at 100° C. are conveyed into 500 grams of 
water at 20° C, the resulting temperature is 60° C. Find the heat of 
vaporization of water. 

291. Cold by Evaporation. In order to change a liquid 
into vapour, heat is always required. Water placed over a 
flame is turned into vapour, the heat required being supplied 
by tlie flame. If a little ether is j)Oured on the palm of the 
hand it vaporizes at once. Here the heat to produce vapori- 
zation is supplied by the hand, which therefore feels cold. 
For a similar reason wet garments are cold, especially if drying 
rapidly on a windy day. 



APPLICATIONS OP COOLING BY VAPORIZATION 



257 




Fig. 284.— Leslie's experiment; 
freezing water by its own 
evaporation. 



But it is soMictime.s possible to produce vaporization without 
supplying heat from an outside source. In this case the heat 
comes from the liquid itself, which must therefore fall in 
temperature. Indeed, it is possible, by ^ 
producing evaporation, to lower the 
temperature of water so much that 
the water will actually freeze. Tliis 
is well shown in Leslie's experiment. 
A small quantity of cold water in a 
watch glass is enclosed in the receiver 
of an air-pump over a dish of strong 
sulphuric acid (Fig. 284). The air is 
then exhausted from the receiver. 
When the pressure is reduced suffi- 
ciently, the water begins to boil, and 
as the vapour is removed from the receiver, partly by being 
carried off with the air by the pump, and partly by absorption 
into the sulphuric acid, the process continues until the water 
is frozen. 

Similar results are shown in a 
more striking manner by the freez- 
ing of carbon-dioxide by evapora- 
tion from the liquid form. If the 
liquefied gas (contained in a strong- 
steel cylinder) is allowed to escape 
into a bag attached to the outlet 
pipe of the cylinder (Fig, 285), it 
will be frozen into snowy cr3'stals 
by the intense cold produced 
in the rapid evaporation of the 
liquid. 

292. Practical Applications of Cooling by Vaporization. 

Vaporization is our chief source of " artificial cold." The 
applications are numerous and varied. Fever patients are 




Fig. 285. — Freezings of carbon-dioxide 
by evaporation from the liquid 



258 



CHANGE OF STATE 




Fioi 286.— Ice-making machine. G, hig-h-pressure gauge ; 
(?,, low-pressure gauge; A, pump for exhausting low- 
pressure coils and condensing gas ; B, condenser coils 



sponged with volatile liquids to reduce temperature. Ether 
sprays are used for freezing material for microscopic sections. 
Evaporation is also utilized in making artificial ice, in cooling 
cold-storage buildings, and in freezing shifting quicksands for 
engineering purposes. The liquid most commonly used for 

the latter purposes 

V)?ii{ i 'illiiilli!l{;i,!' Ml 'll is ammonia liquefied 

Kijl'jliii'i' '.i!!'.;iii!i!a il ^ . . 

by pressure. This is 
convenient for the 
purpose because the 
gas liquefies at or- 
dinary temperature 
under relatively 

cooled by running water from a pipe placed above them; moderate DrCSSUre 

F, regulating valve ; />, low-pressure coils ; C, tank con- -T 

taining brine; E, can containing water to be frozen. (^about 10 atmOS- 

pheres), and it absorbs a great amount of heat in evaporation. 
Fig. 286 shows the essential parts of an ice-making machine. 
The ammonia gas is forced by the pump into the condenser 
coils and liquefied there by pressure, the heat given out in 
condensation being carried off by the water circulating on 
the outside of the coils. The liquid ammonia escapes slowly 
through the regulating valve into the low-pressure coils, 
where it evaporates, producing intense cold. In consequence 
the brine which surrounds the coils is cooled below the 
freezing point of water, and the water to be frozen, placed in 
cans submerged in it, is converted into ice. 

It will be observed that the process is continuous. The 

pump which forces the ammonia into the condenser coils 

receives its supply of gas from the low-pressure coils. The 
same ammonia is thus used over and over again. 

In some cold-storage plants, the brine cooled as described 
above, is made by a force-pump to circulate in coils distri- 
buted at suitable centres throughout the building. (Fig. 287). 



CONDENSATION-CRITICAL TEMPERATURE 



259 



The temperature of the air in tlie cold-storage rooms is 

thus reduced in hot 
weather by cold coils 
very nmch as it may 
be raised in winter 




Fig. 287.— Cold-storage plant. 

by similar coils containing hot water or steam. 

293. Condensation — Critical Temperature. We have seen 
that a vapour in a condition of saturation is condensed if its 
temperature is lowered or its pressure is increased. At this 
point an interesting question arises. Can an unsaturated 
vapour at any given condition of temperature be reduced to a 
liquid by increase of pressure alone ? The question has been 
answered experimentally. It has been found that for every 
vapour there is a temperature above which pressure alone, 
however great, is ineffectual in producing condensation. This 
temperature is known as the critical temperature, and the 
pressure necessary to produce condensation at this tempera- 
ture is called the critical pressure. For example, Andrews,* to 
whom we owe an exhaustive study of the subject, found that 
to reduce carbon-dioxide to a liquid the temperature must be 
lowered to at least 30.92^ C, and that above that temperature 
no amouijt of pressure would convert it into liquid form. 

The critical temperature of water, alcohol, ammonia, and 
carbon-dioxide are above the average temperature of the air, 
while those of the gases oxygen, hydrogen and air are much 
below it. The critical temperature of water is 865° C. and of 
air -140° C. 

* Thomas Andrews (1813-1885) Professor of Chemistry, Queen's College, Belfast, 1845-1879. 



260 



CHANGE OF STATE 



Below tlie critical temperature a further lowering of the 
temperature lessens the pressure necessary to condensation. 
For example, a pressure of 73 atmospheres is necessary to 
condense carbon-dioxide at the critical temperature, but 60 
atmospheres is sufficient at a temperature of 21.5° and 40 
atmospheres at a temperature of 13.1". Again, a pressure of 
200 atmospheres is necessary to condense steam at the critical 
temperature (365° C.) ; at 100° C. it condenses under a pressure 
of one atmosphere. 

294. Liquefaction of Air. The apparatus generally used to 
condense air into a liquid depends on the fact that when a gas is 
Am B . ^C 




Fig. 288. — Essential parts of a liquid-air machine. 

compressed its temperature rises, and when it expands, thus doing 
work, its temperature falls. In Fig. 288 is shown the essential 
parts of a liquid-air machine. 

To one side of the pump P is joined one end of a coil of pipe A 
which is within J, a jacket through which cold water is always 
running, entering at K and leaving at H. The long coil to the 
right is double. A small pipe" runs within a larger one. In the 
figure the second and third turns (from the top) of the larger pipe 
are shown cut away, exposing the smaller pipe within. The smaller 
pipe enters the larger one at 0, passes on to 1) and down to F. 
Here it emerges and goes over to £J where its end may be closed by 
a valve G. 



CONDENSATION OF WATER- VAPOUR OF THE AIR 261 

The action is as follows : Tlie pump P draws in air from the large 
pipe R, and forces it, at a pressure of about 200 atmospheres, through 
the coil A, where it is cooled to the temperature of the water. The 
air passes on to B and then to C, and going through the inner coil 
it descends to i'^and then to E. Througli the slightly opened valve 
G it expands into the vessel I' being thereby cooled. From here it 
enters the end of the larger pipe of the coil and ascends, it reaches 
D and then C, whence it goes down to enter the pump again. 

Now the air on expanding into T was cooled, and hence as it 
ascends through the outer coil it cools the air in the inner coil. As 
this process is continued the air in the inner coil gets colder and 
colder until at last it becomes liquid and collects in T at a tempera- 
ture of about - 182° C. From this it is drawn off by the tap V. 

To make 1 cu. inch of liquid about one-half a cu. foot of air is 
required, and when the liquefaction has begun fresh air must be 
supplied. It is introduced at A' from an auxiliary compressor at a 
pressure of about 200 atmospheres. 

295. Condensation of Water- Vapour of the Air— Dew- 
point. Evaporation is constantly taking place from water at 
the surface of the earth, and consequently the atmosphere 
always contains more or less water- vapour. This vapour will 
be on the point of condensation when its pressure approaches 
the saturation pressure. Now, since this pressure varies with 
the temperature, the nearness to saturation at any given time 
will depend on the temperature as well as upon the amount of 
vapour present per unit volume. Accordingly, the amount of 
vapour which a given space will contain rises rapidly with the 
temperature. Thus a given space will hold more than three 
times as much vapour at 30° C. as at 10° C. 

If the amount of vapour in a given space remains constant 
and the temperature is lowered gradually, a temperature will 
at length be reached at which condensation will begin to take 
place. This temperature is called the dew-point. 

The dew-point may be determined experimentally by 
Regnault's method as follows. In the apparatus shown in 
Fig. 289 the lower portions of the glass tubes are covered 
with polished metal, and through the corks thermometers and 



262 



CHANGE OF STATE 




Fio. 289. — Determination 
of the dew-point. 



connecting tubes are inserted. Pour ether into the vessel fitted 
with the atomizer bulb and force air through 
it. This agitation of the ether makes it 
evaporate rapidly and thus the temperature 
is lowered. Note the temperature at which 
the polished surface surrounding the ether 
becomes dimmed with dew. Cease forcing 
tlie air and again note the temperature at 
which the moisture disappears. The mean 
of the two temperatures is taken as the 
dew-point. 

The second vessel enables the observer, 
by comparison, to determine more readily 
the exact moment when condensation 
begins. The thermometer in this vessel gives the temperature 
of the air in the room at the time of the experiment. 

296. Relative Humidity. The term humidity, or relative 
HUMIDITY, is used to denote the ratio of the mass of 
water-vapour present in the air, to the mass required for 
saturation at the same temperature. The air is said to be 
very dry when the ratio is low, and damp when it is high. 
These terms, it should be observed, have reference, not to the 
absolute amount, of vapour present, but to the relative degree 
of saturation at the given temperature. At the present 
moment the air outside may be raw and damp, but after 
having been forced by a fan over a series of steam -heated 
coils, it appears in tlie laboratory comparatively Avy. It is 
not to be inferred that the air has lost any of its vapour; 
rather that in being heated it has acquired the capacity of 
taking up more, because the saturation pressure has been 
raised by the increase of temperature. 

The relative humidity is usually expressed as a percentage 
of the maximum amount of vapour possible at the temperature. 



RELATION OF HUMIDITY TO HEALTH 



263 




For example, when a cubic centimetre of air contains but one 
half of the amount of water-vapour necessary for 
saturation, its humidity is said to be 50 per cent. 

This percentage is most accurately determined by 
a calculation from the dew-point. Take a particular 
example. Suppose the dew-point to be 12° C. when 
the temperature of the air in the room is 20° C. 
From a table of constants it is learned that saturated 
water vapour at 12° C. contains 0.0000106 grams per 
cubic centimetre, and at 20 degrees, 0.0000172 grams 
per cubic centimetre. Then since one cubic centi- 
metre actually contains at 20° C. just the amount of 
vapour necessary for saturation at 12° C. the degree 
of saturation is ^-^ or 61.6 per cent. 

The humidity may also be determined by the 
Wet-and-Dry-Bulb Hygrometer. The instrument 
consists of two similar thermometers mounted on 
the same stand (Fig. 290). The bulb of one of the 
thermometers is covered with muslin kept moist by a wick 
immersed in a vessel of water. Evaporation from the wet 
bulb lowers its temperature, and since the ratio of evaporation 
varies with the dryness of the atmosphere, it is evident that 
the differences in the readings of the thermometers may be 
used as an indirect means of estimating the relative humidity 
of the atmosphere. The percentages are given in tables 
prepared by comparison with results determined from dew- 
point calculations. 

297. Relation of Humidity to Health. Humidity has an 
important relation to health and comfort. When the relative 
humidity is high, a hot day becomes oppressive because the 
dampness of the atmosphere interferes with free evaporation 
from the body. On the other hand, when the air becomes too 
dry the amount of this evaporation is too great. This con- 
dition very frequently prevails in winter in houses artificially 



Fio. 290. — Wet- 
and-dry bulb 
hygrometer. 



264 CHANGE OF STATE 

heated. Under normal conditions the relative humidity should 
be from 50 to 60 per cent. 

298. Fog" and Clouds. If the air is chilled below the 
temperature for saturation, vapour condenses about dust 
particles suspended in the air. If this condensation takes 
place in the strata of air immediately above the surface of the 
earth, we have a fog ; if in a higher region, a cloud. The 
cooling necessary for fog formation is due to the chilling 
effects of cold masses at the surface of the earth ; in the upper 
region, a cloud is formed when a stratum of warm moist air 
has its temperature lowered by its own expansion under 
reduced pressure. It would appear from recent investigations 
that under all conditions dust particles are necessary as nuclei 
for the formation of cloud globules. 

299. Dew and Frost. On a warm summer day drops of 
water collect on the surface of a j)itcher containing ice-water, 
because the air in innnediate contact with it is chilled below 
the dew-point. This action is typical of what goes on on a 
large scale in the deposition of dew. After sunset, especially 
when the sky is clear, small bodies at the earth's surface, such 
as stones, blades of grass, leaves, cobwebs, and the like, cool 
more rapidly than the surrounding air. If tlieir temperature 
falls below the temperature of saturation, dew is deposited on 
them from the condensation of the vapour in the films of air 
which envelope them. If the dew-point is below the freezing- 
point the moisture is deposited as frost. 

300. Rain, Snow and Hail. The cloud globules gravitate 
slowly towards the earth. If they meet with conditions 
favourable to vaporization they change to vapour again, but 
if with conditions favourable to condensation they increase in 
size, unite, and fall as rain. 

When the condensation in tlie upper air takes place at a 
temperature below the freezing-point, the moisture crystallizes 



DISTILLATION 



2G5 




in snow-flakes. At low temperatures, also, vapour becomes 
transformed into ice pellets and descends as hail. The hail- 
stones usually contain a core of closely packed snow crystals, 
but the exact conditions under which they are formed are not 
yet fully understood. 

301. Distillation. Distillation is a process of vaporization 
and condensation, maintained usually for the purpose of freeing 
a liquid from dissolved 
solids, or for separating 
the constituents of a 
mixture of liquids. Fig- 
291 shows a simple form 
of distillation apparatus. 
The li({uid to be' distilled 
is evaporated in the flask 
A, and the product of 

the condensation of the ^"*- 291-I>i«tillation apparatus. 

vapour is collected in the receiver B. The pipe connecting A 
and B is kept cold by cold water made to circulate in the 
jacket which surrounds it. 

The separation of liquids by distillation depends on the 
principle that different liquids have different boiling points, 
and consequently are vaporized and can be collected in 
a regular order. For example, when crude petroleum is 
heated in a still the dissolved gaseous hydrocarbons are 
driven off first ; then follow the lighter oils, naphtha, 
gasoline and benzine ; in turn come the kerosene or 
burning oils ; and later the heavier gas and fuel oils, etc. 
To obtain a quantity of any one constituent of a mixture 
in a relatively pure state, it is necessary to resort to 
fractional distillation. The fraction of the distillate which 
is known to contain most of the liquid desired is redistilled, 
and a fraction of the distillate again taken for further 
distillation, and so on. 



266 



CHANGE OF STATE 



QUESTIONS AND PROBLEMS 

1. Why does sprinkling the floor have a cooling effect on the air of the 
rooni ? 

2. As exhaustion of air proceeds, a cloud is frequently seen in the 
receiver of an air-pump. Explain. 

3. Under wliat conditions will " fanning " cool the face ? 

4. Why can one "see his breath " on a cold day ? 

5. In eastern countries and at high elevations water is poured into 
porous earthenware jars and placed in a draught of air to cool. Explain 
the cause of cooling. 

6. Dew does not usually form on a pitcher of ice water standing in a 
room on a cold winter day. Explain. 

7. Why does a morning fog frequently disappear Avith increased 

strength of the sun's rays ? 

8. A tube having a bulb at each end has one 
of its bulbs filled with water, the remaining 
sjjace containing nothing but water vapour. 
The empty bulb is surrounded by a freezing 
mixture (Fig. 292), and after a time it is found 
that the water in the other bulb is fi'ozen. 
Explain. (Such a tube is called a cryophorus, 
which means frost-carrier.) 




Fig. 292. — Cryophorus. 



CHAPTER XXX 







Heat and Mechanical Motion 

302. Mechanical Equivalent of Heat. We have referred 
(§ 241) to fclie fact that during the first half of the nineteenth 

century the kinetic theory of 
heat, advocated by Count Rum- 
ford and Sir Humphry Davy, 
gradually superseded the old 
materialistic conception. The 
modern theory was regarded as 
established when Joule, about 
the middle of the centiny, de- 
monstrated that for every unit 
of mechanical energy which 
disappears in the transformation 
of mechanical motion into heat a 
definite and constant quantity of 
heat is developed. The value of 
the heat unit expressed in units 
of mechanical energy is called 
the "mechanical equivalent of heat. 

303. Determination of the Mechanical Equivalent of Heat. 

The essential features of Joule's apparatus for determining 
the mechanical equivalent of heat 
are illustrated in Fig. 293. A 
paddle-wheel was made to revolve 
in a vessel of water by a falling 
weight connected with it by pulleys 
and cords. Joule measured the 
heat produced by the motion of 
the paddle and the corresponding 
amount of work done by tlie de- 
scending weight. He calculated 
that one B.T.U. of heat was equivalent to 772 foot-pounds of 

267 



James Prescott Joulk (181S-1889). 
Lived near Manchester all his life. Ex- 
perimented on the mechanical equivalent 
of heat for forty jears. 




Fia. 293. — Principle of Joule's ap- 
paratus for determining the me- 
chanical equivalent of heat. 



268 



HEAT AND MECHANICAL MOTION 



mechanical energy. Later investigations by Rowland and 
others placed the constant at 778 foot-pounds for one B.T.U. 
of lieat, which is equivalent to 4.187 joules (41,870,000 ergs) 
or 427 gram-metres of work for one calorie of heat. 

304. Steam-Engine. Mechanical motion arrested by friction or 
percussion becomes transformed into heat energy. On the other 
hand, heat is one of our chief sources of mechanical motion. In 
fact, it is commonly said that modern industrial development, had 
its beginning in the invention of the steam-engine. The develop- 
ment of the engine as a working machine is due to James "Watt, a 
Scottish instrument-maker, who constructed the first engine in 1768. 
The essential working part of the ordinary type of steam-engine 
is a cylinder in which a piston is made to move backwards and for- 
wards by the pressiu-e 
of steam appUed alter- 
nately to its two faces 
(Fig. 294). The steam 
from the boiler is con- 
veyed by a pipe i^into 
a valve-chamber, or 
steam-chest, E. From 
the steam-chest the 
steam is admitted to 
the cylinder by open- 
ings called ports, A 
and B^ at the ends 
of the cylinder. The 
exhaust steam escapes 
from the cylinder by 
the same ports. The 
admission of the steam 
to the cylinder, and 
its escape after it has 
performed its work, is 
controlled by the op- 
eration of a valve D. This valve is so adjusted that when the port 
A is connected with the steam-chest, B is connected with an exhaust 
pipe P, leading to the open air or to a condenser ; and when B is 
connected with the cylinder, A is connected with the exhaust pipe. 
The upper figure shows the steam entering at A and escaping at B. 
The piston, therefore, is being forced to the right, while the valve D 
is being pushed in the opposite direction by the motion of the 




Fio. 294.— Steam engine. A and B, ports ; D, slide valve ; 
E, steam chest; F, pipe to boiler; G, eccentric rod; 
U, eccentric. 



HIGH AND LOW PRESSURE ENGINES 



269 



common 
cylinder 




Fig. 295. — Condenser of 
' ' low pressure " steam- 
engine. 



eccentric rod G. AVIien the piston reaches the end of the stroke, 'the 
valve has moved to the position shown in the middle figure. Steam 
is now entering at B and escaping at yl, and tlie piston is being 
forced to the left. In the meantime the valve is being moved to the 
original position as shown in the upper figure. A to-and-fro motion 
of the piston is thus kept up. This motion is transformed into a 
rotary motion in the shaft by the crank mechanism. The balance- 
wheels serve to give steadiness to the motion and to carry the 
engine over the "dead centres " at the ends of the strokes. 

305. High and Low Pressure Engines. In the 

" high pressure " engine, the steam escapes from the 
directly into the air. In the low pressure or 
condensing engine the exhaust is led into a 
chamber (Fig. 295), where it is condensed by 
jets of cold water. The water is removed by an 
" air-pump." 

Since a more or less perfect vacuum is main- 
tained in the condensing chamber of a low pressure 
engine, it will work under a given load at a lower 
steam pressure than the high pressure engine, 
because its piston does not encounter the opposing 
force of the atmospheric pressure. 

306. The Compound Engine. When the pressure maintained 
in a boiler is high the steam escapes from the cylinder of an engine 
with energy capable of further work. The purpose of the compound 
engine is to utilize this energy latent in exhaust steam. In this 
type, two, three or even four cylinders with pistons connected with 
a common shaft are so arranged that the steam which passes out of 

the first cylinder enters the next, which 
is of wider diameter, and so on until it 
finally escapes into a condensing cham- 
ber connected with the last cylinder. 

The compound engine is used mainly 
in large power plants and for marine 
purjioses, when economy in fuel con- 
sumption is a first consideration, 

307. Turbine Engine. Lately a new 

type of engine known as the steam tur- 
bine has been developed. In it a drum 
attached to the main shaft is made to re- 
volve by the impact of steam directed 
by nozzles against blades attached to its 




Fio. 296. — Action of steam on the 
blades of the drum in a turbine 
engine. 



outer surfaces as shown (Fig. 296). 



270 



HEAT AND MECHANICAL MOTION 



In another type of turbine, nozzles and blades are so adjusted 
that the steam after striking the first series of blades is reflected by 
a similar series of stationary blades against a second set of moving 
blades, and so on until the full working force of the steam is 
exhausted. (Fig. 297.) 

the turbine engines have been used mainly for 
Steam Chest marine purposes and in 

some large electric power 
plants. The Carmania, 
■which came out in Decem- 
ber, 1905, was the first 
Atlantic liner to be pro- 
pelled by steam turbines. 
The first vessel in our 
inland waters to be fitted 
with turbine engines was 
the Turbinia, plying be- 
tween Toronto and Ham- 
ilton. The turbine engine 



So far 



MovingBlades (mriMmmni 
Slationary Blades ^JJJ 
Moving Blades 





Moving Blades [' _' ■ _• "jHj^M 

Fig. 297. — Reflection of steam from moving to 
stationarj' blades in steam turbine. 



takes up less room than the ordinary form of reciprocating engine, 
and runs with much less vibration. 

308. Gas Engines. Gas engines are coming into very general 
use as a convenient power for launches, automobiles, and power 
plants of moderate capacity. 

lu this form of heat engine, the fuel is burnt in the cylinder of 
the engine itself, and the piston is driven forward by the expansion 
of the heated gaseous products of the combustion. The fuel most 
commonly used is fuel-gas, or gasoline vapour, mixed with a suiii- 
cient quantity of air to form an explosive mixture. 

A charge of the combustible mixture is drawn into the cylinder 
through an inlet valve during the forward motion of the piston, and 
compressed into about one-third the space by the return stroke. At 
a properly timed instant, the compressed charge is ignited by an 
electric spark at the points of a spark-plug, connected with an in- 
duction coil and battery, and the piston is forced forward by the 
expansion of the inclosed gas. On the backward motion of the 
piston an exhaust valve is opened, and the burnt gases escape from 
the cylinder. At the end of this stroke the engine is again on the 
point of taking in a new charge of fuel. It will be noted that the 
piston receives an impulse at the end of every fourth single stroke. 
The engine is accordingly described as a four-stroke^ or four-cycle 
engine. 



GAS ENGINES 



271 



The momentum given the balance-wheel at each explosion serves 
to maintain the motion until the piston receives the next impulse. 
To cause the pressure to be more continuous in higli-speed engines, 
two or more cylinders have frequently their pistons connected to 
a common shaft. The action of the four-stroke engine may be 
understood by referring to the accompanying diagrams of a four- 
cylinder, four-stroke engine. 




FiQ. 298. — The working parts of a modern fourcjlinder automobile or launch engine. A, 
main shaft : W, balance-wheel connected to main shaft ; P,, P^, Ptu ^*> pistons ; F,, Fa, 
K5, K,, inlet valves; V^, V ^, V^, K,, exhaust valves; /f,, R„,'eic., valve stems; S,, S.^, 
etc., springs by which vaives are closed; fi, cam-shaft for operating valves, run by gears 
from main shaft; C,, Cj, etc., cams for lifting valves; D, space to contain circulating 
water for cooling cylinder. The small diagram in the upper left-hand corner shows the 
connection between the valve-chamber and cylinder. £,, inlet port; E„, exhaust port; 
F, pipe by which cooling water enters; G, outlet for water. Two spark plugs are shown 
inserted at the top of each cylinder. One is connected with a battery system of ignition, 
the other with a magneto or dynamo. The electrical connections are so made that either 
may be used at will. 

The balance wheel and pistons are moving in the directions of the 
arrows. A charge is being drawn into cylinder No. 4 through the 
inlet valve Fj, raised for the purpose by the pressure of the cam C^ 
on the valve stem Ry The charge which has been drawn in during 
the previous single stroke is being compressed in cylinder No. 2. 
The piston P^ is being forced down by tlie expansion of the gases 
which have just been ignited in cylinder No. 1. The burnt gases 
from the previous explosion are escaping from cylinder No. 3 
through the exhaust valve F^, raised by the action of the cam C^. 



272 



HEAT AND MECHANICAL MOTION 



During the next single stroke, No. 3 will be drawing in a charge, 

No. 4 will be compressing, No. 2 will be exploding, and No. 1 will 

be exhausting ; and so on for succeeding strokes. 

Exercise. — Trace the action in any one cylinder for four successive 

single strokes. 

The two-stroke (or two-cycle) engine differs from the four-stroke, 

in that the piston receives an impulse at the end of every second 

single stroke. This is ac- 
complished as follows : — 
Consider the piston in 
the position shown in 
Fig. 299. During the 
first part of the first 
single, stroke, the burnt 
gases of the previous 
explosion escape by the 
port D, and a charge 
stored in the crank 
chamber enters by the 
port £. In the second 
part of the first single 
stroke, the inlet and ex- 
haust ports are covered 
by the piston and the 
charge is compressed in 
„ . „ the cylinder, while a 

Working parts of a two-stroke gas engine. P, piston ; S, ■', . ■, 

main shaft ; C, crank pin ; A, inlet port to crank chamber ; new Charge IS drawn 

B, inlet port to cylinder ; X>, exhaust port ; W, counterpoise i^to the Crank chamber 
weight. 

from the fuel tank 
through the port A (Fig. 300). The chaige in the cylinder is 
ignited and the piston is forced forward in the second half-stroke 
giving an impulse to the fly-wheel, and compressing the new charge 
in the crank chamber. The action then goes on as before. 

309. Efficiency of Heat Engines. All heat engines are wasteful 
of energy. The best types of compound condensing steam engines 
transform only about 1 6 per cent, of the heat of combustion into useful 
work, while the ordinary high-pressure steam engine in e^'ery-day use 
utilizes not more than 5 per cent, of the energy latent in the fuel. 

The best steam turbines equal in efficiency the most economical 
forms of reciprocating engines. 

The efficiency of the gas engine is much higher than that of the 
steam engine. Under good working conditions it will transform as 
high as 25 per cent, of heat energy into mechanical energy. 




Fig. 299. 



Fio. 300. 



EFFICIENCY OF HEAT ENGINES 273 

PROBLEMS 

1. The average pressure on the piston of a steam engine is 60 lbs. per 
sq. inch. If tlie area of tlie piston is 50 tn[. in. and the length of the 
stroke 10 in., find (a) the work done in one strok-e by the piston ; (6) 
how much heat, measured by B. T. U., was lost by the steam in moving 
the piston. 

2. The coal used in the furnace of a steam pumping-engine furnishes 
on an average 7000 calories of heat per gram. How many litres of water 
can be raised to a height of 20 metres by the consumption of 500 kg. 
of coal, if the efficiency of the engine is 5 per cent. ? 

3. Supposing that all the energy of onward motion possessed by a 
bullet, whose mass is 20 grams and velocity 1000 metres per sec, is 
transformed into heat when it strikes the target, find in calories the 
amount of heat developed. 

4. A train whose mass is 1000 tons is stopped by the friction of brakes. 
If the train was moving at a rate of 30 miles per hour when the brakes 
were applied, how much heat was developed ? 

5. How much coal per hour is used in the furnaces of a steamer when 
the screw exerts a pushing force of 1000 kgms. and drives the vessel at a 
rate of 20 km. jjer hour if the efficiency of the engine is 10 per cent., and 
the coal used gives on tlie average 6000 calories of heat per gram. ? 

6. A locomotive whose efficiency is 7 per cent, is developing on the 
average 400 horse power. Find its fuel consumption per hour if the coal 
furnishes 14,000 B.T.U.'s of heat per pound. 



CHAPTER XXXI 

Transference of Heat 

310. Conduction of Heat. The handle of a silver spoon 
becomes warmed when the bowl is allowed to stand in a cup 
of hot liquid ; the uncovered end of a glass stirrer, under 
similar conditions, remains practically unchanged in tempera- 
ture. Heat creeps along an iron poker when one end is thrust 
into the fire ; while a wooden rod conveys no heat to the hand. 

The transference of heat from hotter to colder parts of the 
same body, or from a hot body to a colder one in contact with 
it, is called conduction, when the transmission takes place, as 
in these instances, without any perceptible motion of the parts 
of the bodies concerned. 

311. Conducting Powers of Solids. The above examples 
show clearly that solids differ widely in their power to conduct 
heat. The tendencies manifest in silver and iron are typical 
of the metals ; as compared with non-metals, they are good 
conductors. Organic fibres, such as wool, silk, wood, and the 
like, are poor conductors. 

The metals, however, differ widely among themselves in 

conductivity. This may be shown roughly as follows : — Twist 

I ■ two or more similar wires of 

n iT' ' 1 different metals — say copper, iron, 

II (^J=^ SZT"^^^ German silver — together at the 

^^^\Jjjiij^iiiiiiE========™' ends and mount them as shown 

Fio. 3oi.-Difference in conductivity of in Fig. 301. By mcans of drops 

of wax attach shot or bicycle 

balls or small nails at equal intervals along the wires. Heat 

the twisted ends. The progress of the heat along the wires 

will be indicated by the melting of the wax and the dropping 

of the balls. When the line of separation between the melted 

and unmelted drops of wax ceases to move along the wire it 

will be found that the copper has melted wax at the greatest 

distance from the source of heat, the iron comes next in 

274 



CONDUCTION IN LIQUIDS 



275 



order, and tlie Geniuui silver last. If the wax wo'e distril)uted 
uniformly, and wires lieated equally at their ends the con- 
ductivities of the wires would be approximately proportional 
to the squares of these distances. 

The following table gives the relative conductivities of 
some of the more commonly used metals referred to copper 

as 100. 

Relative Conductivities of Metals 



Copper 

Aluminium . . 

Brass 

Gold 


. 100 
. 47 
. 32 
. 71 


Iron 


. 23 
. 11 
. 51 
. 2.4 


Platinum . . . 

Silver 

Tin 


.. 12 
.. 133 
.. 21 


Lead 

Magnesiinu . . 
Mercury 


Zinc 


.. 42 






Fig. 302.— Water is a poor 
conductor of heat. 



312. Conduction in Liquids. If we except mercury and 

molten metals, li(|uids are poor conductors 

of heat. Take water for example. We 

may boil the upj)er layers of water held 

in a test-tube over a lamp (Fig. 302) 

without perceptibly heating the water at 

the bottom of the tube. 

The poor conductivity of water is also 

strikingly shown in the following experiment. 

Pass the stem of a Galileo air- 
thermometer (§ 255) through a per- 
forated cork inserted into a funnel as 
shown in Fig. 803. Then cover the 
bulb of the thermometer to a depth 
of about J cm. with water. Now pour 
a spoonful of ether on the surface 
of the water and set fire to it. The 
index of the thermometer shows that 
little, if any, heat is transmitted by 
the water to the bulb from the flame 




Fio. 303.— Illustration of the 
non-conductivity of water. 



at the surface. 



276 TRANSFERENCE OF HEAT 

313. Conduction in Gases. Gases are extremely poor 
conductors of heat. The conductivity of air is estimated 
to be only about 0.000,049 of that of copper. Many 
substances, such as wool, fur, down, etc., owe their poor 
conductivity to the fact that they are porous and con- 
tain in their interstices air in a finely divided state. If 
these substances are compressed they become better con- 
ductors. 

Light, freshly fallen snow encloses within it large 
quantities of air, and consequently forms a warm blanket 
for the earth, protecting the roots of plants from intense 
frost. 

Heat is conducted with the greatest difficulty through a 
vacuum. For holding liquid air Dewar introduced glass flasks 
with hollow walls from which the air has been removed. 
The inner surfaces of the walls are silvered to prevent 
radiation ( § 570). The familiar " Thermos " bottle is con- 
structed in this way. When contained in such a vessel a 
hot substance will remain hot and a cold one cold for a 
long time. 

314. Practical Significance of Conduction in Bodies. The 

usefulness of a suDstance is fre(]uently determined by its 
relation to heat conduction. The materials used to convey 
heat, such as those from which furnaces, steam boilers, 
utensils for cooking, etc., are constructed must, of course, 
be good conductors. 

On the other hand, substances used to insulate heat, to shut 
it in or keep it out, should be non-conductors. A house with 
double walls is warm in winter and cool in summer. Wool 
and fur are utilized for winter clothing because they refuse to 
transmit the heat of the body. 



CONDUCTIVITY AND SENSITIVENESS TO TEMPERATURE 277 




Fio. 304. — Action of metallic gauze 
on a gas-flame. 



Ill this connection the action of metallic gauze in conducting 
heat should be noted. Depress upon the flame of a Bunsen 
Burner a piece of flne wii-e gauze. The flame spreads out 
under the gauze but does not pass through it {B, Fig. 304). 
Again, turn off the gas and hold 
the gauze about half-an-incli above 
the burner and apply a lighted 
match above the gauze {A , Fig. 304). 
The gas burns above the gauze. 
The explanation is that the metal 
of the gauze conducts away the 
heat so rapidly tliat the gas on 
the side of the gauze opposite the 
flame is never raised to a tem- 
perature sufficiently high to light it. This principle is 
applied in the construction of tlie Davy safety lamp for 
miners. A jacket of wire gauze encloses the 
lamp, and prevents the heat of the flame from 
igniting the combustible gas on the outside. 
(Fig. 805.) 

315. Conductivity and Sensitiveness to 
Temperature. We have already referred to 
the fact that our sensations do not give us 
reliable reports of the relative temperatures of 
bodies. 

This is in part due to the disturbing effects 
Fig. 305.— Davy of couductiou. To take an example, iron and 
sa e y amp. ^yQQ(j exposcd to frost in winter or to the 
heat of the sun in summer have, under the same conditions, 
the same temperature; but on touching them the iron 
appears to be colder than tlie wood when the temperature 
is low, and hotter when it is high. These phenomena are 
due to tlie fact that the intensity of the sensation depends 




278 TRANSFERENCE OF HEAT 

on the rate at which heat is transferred to or from the hand. 
When the temperature of the iron is low, heat from the hand 
is distributed rapidly throughout its mass ; when hot, the heat 
current flows in the opposite direction. 

The wood, when cold, takes from the hand only sufficient 
heat to warm the film in immediate contact with it; when 
hot, it parts with heat from this film only. In consequence, 
it never feels markedly cold or hot. 

QUESTIONS 

1. If a cylinder, half brass and half wood, be wrapped with a sheet of 
paper and held in the flame (Fig. 306), the paper in contact with the 
wood will soon be scorched but that in contact with 
the brass will not be injured. Explain. 

2. Why are utensils used for cooking frequently 
supplied with wooden handles ? 

3. Ice stored in ice-houses is usually packed in 
saw-dust. Why use saw -dust ? 

4. Why, in making ice - cream, is the freezing 

mixture placed in a wooden vessel and the cream 
Fig. 306. . ^ , „ 

in a metal one f 

5. Water may be boiled in an ordinary paper oyster-pail over an open 
flame without burning the paper. Explain. 

6. The so-called fireless cooker consists of a wooden box lined with felt 
or other non-conductor. The food is heated to a high temperature and 
shut up in the box. Why is the cooking process continued under these 
conditions ? 

7. Two similar cylindrical rods, one of copper and the other of lead, 
are covered with wax, and an end of each is inserted through a cork in 
the side of a vessel containing boiling water. At first the melting 
advances more rapidly along the lead rod, but after a while the melting 
on the copper overtakes that on the lead, and in the end it is 3 times as 
far from the hot water. Account for tliese phenomena. Compare the 
conductivities of copper and lead. 




CONVECTION CURRENTS 



279 



316. Convection Currents. The water in the test-tube 
(§ 312) remains cold at the bottom when heated at tlie top. If 
the heat is applied at the bottom, the mass of water is quickly 
warmed. The explanation is that in the latter case the heat 
is distributed by currents set up within the fluid. 

The presence of these currents is readily seen if a few 
crystals of potassium permanganate are dropped into a beaker 
of water and the tip of a 
gas-flame allowed to come 
in contact with the bottom 
either at one side as in Fig. 
307 or at the ceiitre as in 
Fig. 308. 

Such currents are called 
convection currents. They 
are formed whenever ine- 





FiG.307.-Convectioncur- qualities of temperature are 

in u'nt.pr npnt.Pn -*- ■*■ 



Fio. 308.— Convection 
currents in water 
heated by gas-flame 
placed at centre of 
bottom. 



rents in water heated 

by gas-flame placed at maintained in the parts of a 

one side of bottom. _ ■•■ 

fluid. To refer to the 
example just cited, the portion of the water in proximity to 
the gas-flame is heated and its density is reduced by 
expansion. The body of hot water is, therefore, buoyed up 
and forced to the top by the colder and heavier portions 
which seek the bottom. 



317. Transference of Heat by Convection. The transference 
of heat by convection currents is to be distinguished from 
conduction. In conduction, the energy is passed from molecule 
to molecule throughout the conductor ; in convection, certain 
portions of a fluid become heated and change position within 
the mass, distributing their acquired heat in their progress. 
The water, heated at the bottom of the beaker, rises to the 
top carrying its heat with it. 



280 



TRANSFERENCE OF HEAT 




Fig. 309. — Convection currents in 
air about a heated flat-iron. 



318. Convection Currents in Gases. Gases are very sensi- 
tive to convection currents. A heated body always causes 
disturbances in the air about it. The 
rising smoke shows the direction of 
the air-currents above a fire. Hold a 
hot iron — say a flat-iron — in a cloud 
of floating dust or smoke particles 
(Fig. 309). The air is seen to rise 
from the top of the iron, and to flow 
in from all sides at the bottom. 

Make a box fitted with a glass front 
and chimneys as shown in Fig. 310. 
Place a lighted candle under one of the 
chimneys, and replace the front. Light 
some touch paper * and hold it over 
the other chimney. The air is observed 
to pass down one chimney and up the 
other. 




Fig. 310. — Convection cur- 
rents in heated air. 



319. Winds. While air-currents are modified by various 
forces and agencies, they are, as we have seen (§ 124), all trace- 
able to the pressure difierences which result from inequalities 
in the temperature and other conditions of the atmosphere. 

The eflfects of temperature difierences are but manifesta- 
tions, on a large scale, of convection currents, like those in 
the air about the heated iron. For various causes the earth's 
surface is unequally heated by the sun. The air over the 
heated areas expands, and becoming relatively lighter, is forced 
upward by the buoyant pressure of the colder and heavier air 
of the surrounding regions. 

Trade winds furnish an example. These permanent air- 
currents are primarily due to the unequal heating of the 
atmosphere in the polar and the equatorial latitudes. 

* Made by dipping blotting paper in a solution of potassium nitrate and drying it. 



APPLICATION OF CONVECTION CURRENTS— COOKING 281 




Fia. 311.— Illustration of land and sea breezes. A, 
direction of movement in sea breeze. B, direction of 
movement in land breeze. 



We have an example also, on a much smaller scale, in land 
and sea breezes. On account of its higher specific heat, water 
warms and cools much more slowly than land. For this reason 
the sea is frequently 
cooler by day and 
warmer by niglit than 
the surrounding land. 
Hence, if there are no 
disturbing forces an ofF- 
sea breeze is likely to 
blow over the land during the day and an ofF-land breeze to 
blow out to sea at niglit (Fig. 311). Since the causes pro- 
ducing the changes in pressure are but local, it is obvious 
that these atmospheric disturbances can extend but a short 
distance from the shore, usually not more than 10 or 15 miles. 

Query. — Why do we, when turning on the di'aught of a stove or a 
furnace, close the top and open tlie bottom ? 

320. Application of Convection Currents— Cooking — Hot 
Water Supply. The distribution of heat B*^ 
for ordinary cooking operations such as 
boiling, steaming, and oven roasting and 
baking obviously involves convection cur- 
rents. 

When running water is 
available, kitchens are now 
usually supplied with equip- 
ment for maintaining; a 
supply of hot water for culi- 
nary purposes. The common 
method of heating the water 
by a coil in the fire-box 
of a stove or furnace is P;o 
r- 010 n, . .• illustrated in the following 

Fig. 312.— Illustration => 

of the principle of experiment. Use a lamp 

heating water by JC^ -t^ 





convection ( 



313. — Connection in a 
kitchen water heater. A 
is the hot- water tank and 
£ia the water-front of the 
stove. The arrows show 
the direction in which the 
water moves. 



1 currents, chimney as a reservoir and 
fit up the connecting tubes as shown in Fig. 312. Drop 



a 



282 



TRANSFERENCE OF HEAT 



crystal or two of potassium permanganate to the bottom of 
the reservoir to show the direction of the water currents. 
Fill the reservoir and tubes tlirough the funnel G and heat 
the tube B with a lamp. A current will be observed to flow 
in the direction of the arrow. The hot water rises to the 
top of the reservoir and the cold water at the bottom moves 
forward to be heated. 

Fig. 313 shows the actual connections in a kitchen outfit. 
The cold water supply pipe G is connected with a tank in 

the attic or with the 

water- works service 

pipes. The hot water 

is drawn off through 

the pipe D. 

321. Hot- Water 

Heating. Hot-water 

systems of heating 

dwelling houses also 

T, o,. T„ depend on convection 

Fig. 314.— Illus- ^ 

tration of the currcuts f Or the dis- 

pnnciple of 

heating build- tributiou of heat. 

ings by hot 

"'^*^'^- The principle may 

be illustrated by a modification 
of the last experiment. Connect 
an open reservoir B with a flask, 
as shown in Fig. 314. Taking 
care not to entrap air-bubbles, 
fill the flask, tubes, and part of 
the reservoir with water. To 
show the direction of the cur- 
rents colour the water in the 
reservoir with potassium perman- 
ganate. Heat the flask. The coloured water in tlie reservoir 
almost immediately begins to move downwards through the 





Fig. 315.— Hot-water heating system. A, 
furnace ; C, C, C, pipes leading to radia- 
tors R, JR. and expansion tank B; D, D, 
pipes returning water to furnace after 
passing through radiators. 



HEATING BY HOT-AIR FURNACES 283 

tube D to the bottom of the flask and the colourless water 
in C appears at the top of the reservoir. 

In a hot-water heating system (Fig. 315) a boiler takes 
the place of the flask. The hot water passes through 
radiators in the various apartments of the house and then 
returns to the furnace. An expansion tank B is also con- 
nected with the system. Observe that, as in the flask, the 
hot water rises from the top of the heater and returns at the 
bottom. 

322. Steam Heating. Steam also is employed for heating 
buildings. It is generated in a boiler and distributed by its 
own pressure through a system of pipes and radiators. The 
water of condensation either returns by gravitation or is 
pumped into the boiler. 

323. Heating by Hot-Air Furnaces. Hot-air systems of 
heating are in very common use. In most cases the circulation 
of air depends on convection currents. The 

development of such currents by hot-air '^IFII/''' 

furnaces depends on the principle that if a C~# - 

jacket is placed around a heated body and ^^ ^^k 

openings.are made in its top and its bottom, ^^=^^^ 

a current of air will enter at the bottom /^^^^N^ 

and escape at a higher temperature at the %..,^F 

top. For example, a lamp shade of the ^^m-^ 

form shown in Fig. 316 forms such a jacket ^,,^ .^^^_^.^ ^^^^^^^^ 
about a hot lamp chimney. When the air T^ackft \^round "I 
around the lamp is charged with smoke a ^^^'^ ° ^' 

current of air is seen to pass in at the base of the shade and 
out at the top. 

A hot-air furnace consists simply of a stove with a 
galvanized-iron or brick jacket A about it. Pipes connected 
with the top of the jacket convey the hot air to the rooms 



284 



TRANSFERENCE OF HEAT 



to be heated. The cold air is led into the base of the 
jacket by pipes connected with the outside air or 
with the floors of the room above (Fig. 317). 

324. Ventilation. Most of the 
methods adopted for securing a 
supply of fresh air for living 
rooms depend on the develop- 
ment of convection currents. 

When a lighted candle is placed 
at the bottom of a wide-mouthed 
jar, fitted with two tubes, as 
shown in B (Fig, 318), it burns 
for a time but goes out as the air 
becomes deprived of oxygen and 
vitiated by the products of com- 
bustion. If one of the tubes is 
pushed to the bottom A (Fig. 
318), the candle will continue to 
burn brightly, because a contin- 
's%'tl'„^"t"/to^tSet?T'sn>e ^ous supply of frcsh air comes 

flue; C, warm-air pipes; D, cold-air • i fnliP nnrl fliP fnnl o-fl"* 

pipe from outside ;£, cold-air pipe from 1" ^J ^"^ lUUe auu tue lOUi g*l8 

room; F, vent flue; F,, valve in pipe p„pj,T^pc, y.,r fl-,p nflipr 

E ; Fj, valve in pipe from outside. eSCapeS Oy tue OLUer. 

The experiment is typical of the means 
usually adopted to secure ventilation in 
dwelling houses. A current is made to 
flow between supply pipes and vents by 
heating the air at one or more points in 
its circuit. 

A warm-air furnace system of heating ^^^ 3i8.-iiiustration of 
provides naturally for ventilation, if the ?^h'e"t'b\s°shouid t^ai 
air to be warmed is drawn from the outside ^^^^' ^ '"'='1 '" diameter, 
and, after being used, is allowed to escape (Fig. 317). To 
support the circulation the vent flue is usually heated. The 





TRANSFERENCE OF HEAT BY RADIATION 285 

iicrurc sliows the vent line pl.iccd aloiio-sido the smoke Hue 
from which it receives heat to create a draught. 

The supply pipes and vent fiues are, as a rule, fitted with 
valves Vi, V.,, to conti'ol the air currents. When the inside 
supply pipe is closed and the others opened a current of fresh 
air passes into and out of the house ; when it is opened and 
the outside supply pipe and vent flue closed, the circulation 
is wholly within the house and the rooms are heated but not 
ventilated. 

With a hot water or steam-heating plant ventilation must 
be effected indirectly. Sometimes a supply pipe is led in 
at the base of each radiator and fresh air drawn in by 
the upward current produced by the heated coils. More 
frequently coils are provided for warming the air before it 
enters the rooms. The coils are jacketed and the method for 
maintaining the current differs from the furnace system only 
in that the air is warmed by steam coils instead of by a stove. 
To secure a continuous circulation in large buildings under 
varying atmospheric conditions, the natural convection cur- 
rents are often re-info reed and controlled by a power-driven 
fan placed in the circuit. 

325. Transference of Heat by Radiation. There is a third 
mode by which heat may be transferred, namely by radiation. 
It is by radiation that the sun warms the earth. By getting 
in the shadow we shield ourselves from this direct effect • 
and the face may be protected from the heat of a fire by 
holding a book or paper between.- A hot body emits 
radiation in all directions and in straight lines. This is 
quite different from convection and conduction. Trans- 
mission by convection always takes place in one direction, 
namely by upward currents ; and conduction is not restricted 
to straight lines, for a bent wire conducts as well as a 
straigiht one. 



286 TRANSFERENCE OF HEAT 

326. Heat from the Sun. It must be carefully observed 
that the heating does not take place until the radiation wliich 
has come from a hot body falls upon a material body. The 
space between the hot source and the receiving body is not 
heated by the passage of the radiation through it. 

The heat required to support life on the earth is received 
by radiation from the sun, but not until it reaches the earth 
is the heating effect produced. Our atmosphere, and especially 
the moisture in it, are of great importance in this connection. 
It acts like a protecting blanket, mitigating the intensity of 
the sun's direct lays, and also preventing the earth from 
quickly radiating into space the heat which it has received. 

On a high mountain or up in a balloon the air is so rare 
and contains so little moisture that its protective action is 
negligible. In such cases the sun's rays produce intense heat 
in what they fall upon, but the air and any object in the 
shade are extremely cold. 

The subject is further discussed in § § 327 to 330 and 547 
to 552. 



PART VII LIGHT 



CHAPTER XXXII 

The Nature of Light; its Motion in Straight Lines 

327. Light Radiation. The ear is the organ for the recep- 
tion of sound, the eye that for light. The investigation of the 
fiensation of vision lies with the physiologist and psychologist; 
in physics light is taken to be the external agency which, if 
allowed to act upon the eye, produces the sensation of 
luminosity. 

For the transmission of sound, the air or some other material 
medium is necessary (§ 192), but such is not the case with 
light. Exhausting the air from a glass vessel does not impede 
the passage of light through it, but rather facilitates it. 
Again, we receive light from the sun, the stars and other 
heavenly bodies, and as there is no matter out in those 
great celestial spaces, the light must come to us through 
a perfect vacuum. Indeed it travels millions of millions of 
miles without giving up any appreciable portion of its energy 
to the space it comes through. 

We do not understand the process by which we obtain the 
sensation, but it is quite certain that to produce it work must 
be done. We see then that the source of light, — the sun, 
a candle, an electric light, — radiates energy, which upon 
reaching the eye is used up in producing the luminous 
sensation, 

328. How is Light Transmitted ? We have been able to 
suggest only two methods by which energy can be transmitted 
from one place to another. A rifle bullet or a cannon ball has 
great energy, which it gives up on striking its aim. Here the 
energy is transferred by the forward bodily motion of a material 
body. But, as explained in §| 176, 177, energy can be handed 
on without transference of matter, namely by wave-motion. 

287 



288 NATURE OF LIGHT ; ITS MOTION IN STRAIGHT LINES 

Now tlie first method, wliich is coininonly called the 
'Emission Theoiy,' was develoj^ed and strongly upheld by 
Sir Isaac Newton* and by others following him, but it has 
been found to be unsatisfactory. There are some experimental 
results contrary to it, and others which it cannot explain. If 
then we must discard it, we necessarily turn to the second 
method, which has been called the ' Wave Theory.' It was 
first propounded by Huygensf, but was really demonstrated 
by Young and Fresnel in the early years of the last century. 
The wave theory of light is now universally accepted by 
scientific men. 

329. The Ether. But we cannot have waves without having 
a medium for them to travel in, and as the light-bearing 
medium is not ordinary matter we are led to assume the 
existence of another medium which we call the ether. Light 
is simply a 'motion in the ether. 

This ether must fill the great interstellar spaces of the 
universe; it must also pervade the space between the mole- 
cules and the atoms of matter, since light passes freely through 
the various forms of matter, — solids, liquids and gases. We 
cannot detect it by any of our ordinary senses, we cannot see, 
feel, hear, taste, smell or weigh it, but as we cannot conceive 
of any other explanation of many phenomena, we are driven 
to believe in its existence. The more one investigates the 
behaviour of light and otlier radiations, the more firmly 
does he become assured of the reality of the ether. 

330. Associated Radiations. It may be well to state here 
that the radiations which afiect the eye never travel alone. 
Indeed those very radiations can also produce a heating efiect 
and can excite chemical action, — in the photographic plate, for 
instance. But associated with the light radiation are others 

* " Are not the Rays of Light very small Bodies emitted from shining Substances?" 
Newton's Opiickx (1704.) 

t Christian Huygens presented his Treatise on Li^ht to the Royal Academy of Sciences, 
Paris, in 1678. It was published in Leyden in 1690. 



WAVES AND RAYS 289 

which do not attccfc the eye ;it .-ill, l)ut wliieh assist healtliy 
growth and destroy obnoxious germs, give us ^^'arlllth necessary 
for Hfe, produce chemical effects as rev'caled in the colours of 
nature, or give us comnuinication by wireless telegraphy. 

These and many other effects are due to undulations of the 
etlier, the chief difference a'mong them being in the lengths of 
the waves. 

We can see the waves moving on the surface of water or 
along a cord ; we can feel the air, and with some effort, per- 
haps, can comprehend its motions ; but to form a notion of 
how the ether is constructed and how it vibrates is a matter 
of excessive difficulty and indeed largely of pure conjecture. 
A very useful picture to have in* one's mind is to think of the 
eye as joined to a source of liglit by cords of ether, and to 
consider the source as setting up in these cords transverse 
vibrations, which travel to the eye and give the luminous 
sensation. 

331. Waves and Rays. Though light is a form of energy, 
and is transferred from place to place by means of waves, we 
usually speak of it as passing in rays. 

Let the light spread out in all direc- 
tions from a source A (Fig. 319). The 
waves will be concentric spheres S^, S.2, 
Ss . . . . , but the light will pass along the 
radii R^, R.^, R^ . . . . , of these spheres. 
The rays thus are the paths along which 
the waves travel, and it is seon that the 
ray is perpendicular to the wave-surface.* „ „,„ ^, 

^ r r Fig. 319.— The waves are 

If we consider a number of rays spheres with ^ as centre ; 

«/ the rays are radii of these 

moving out from A (Fig. 320) we have spheres, 
what is known as a divergent pencil a, and the waves are 
concentric spheres continually growing larger. If the rays 
are coming together to a point we have a convergent pencil b, 

* This discussion refers to homogeneous or isotropic matter. 




290 NATURE OF LIGHT ; ITS MOTION IN STRAIGHT LINES 



and tlie waves are concentric spheres continually growing 
smaller. If now the rays are parallel, as in c, we have a 

_ c 

u _i r -1 1 • I 

A 




Fiat. 320. — A convergent pencil, b ; a divergent pencil, a ; a parallel beam, c. 

parallel beam, and the waves are plane surfaces, perpendicular 
to the rays. Such ra3^s are obtained if the source is at a very 
great distance, so great that a portion of the sphere described 
with the source as centre might be considered a plane. 

QuEUY. — What becomes of the waves of a convergent pencil (b, Fig. 320) 
after they come to a point ? 

332. Light Travels in Straight Lines. In a homogeneous 
medium tlie rays are straight lines. We assume the truth of 
this in many every-day operations. The carpenter could not 
judge that an edge was straight nor could the marksman 
point his rifle properly were he not sure that three objects are 
precisely in a straight line when the light is just prevented 
from passing from the first to the third by the object between. 

When light is admitted into a darkened room — a knot-hole 
in a barn, for instance — we can often trace the straight course 
of the rays by the dust-particles in the air. The rays, them- 
selves, cannot be seen, but when they fall upon the particles of 
matter these are illuminated and send light-waves to the eye. 

333. The Pin-hole Camera. An interesting application of 
the fact that light moves in straight lines is in the pin-hole 
camera. Let 311^ (Fig. 321) be a box 

having no ends. In front of it place y\ / \ 

a candle, or other bright object, AB, g rr2lirr- -[^- " | 

and over the front end stretch tin-foil. rT^^^^- -l^v 
In this prick a hole C with a pin, 
and over the back of the box stretch 
a thin sheet of paper. 



B 



w- 



Fig. 321. — Pin-hole camera. C is a 
small hole in the front and an in- 
verted image of the candle AB\^ 
seen on the back of the box. 



THEORY OF SHADOWS 291 

The light from tlic various poi-fcions ol" AB will pass tlirough 
the hole C and will form on tlio paper an image JJE, of the 
candle. This can be seen best by throwing over the head and 
the box a dark cloth. (Why ?) The image is invei-ted, since 
the light travels in straight lines, and the rays cross at C. 

If now we remove the paper, and for it substitute a sensitive 
photograjjhic plate, a 'negative' may be obtained just as with 
an ordinary camera; indeed the perspective of the scene 
photographed will be truer than with most cameras. The 
chief objection to the use of the pin-hole camera is that with 
it the exposure required, compared to that with the ordinary 
camera, is very long. 

It is evident that to secure a sharp, clear image the hole G 
must be small. Suppose that it is made twice as large. Then 
we may consider each half of this hole as forming an image, 
and as these images wdll not exactly coincide, indistinctness 
will result. On the other hand the hole nnist not be too 
small. As it is reduced in size other phenomena, known as 
diffraction effects, are obtained. These effects show that, in 
all strictness, the light does not travel precisely in straight 
lines after all. The size of the hole required depends on the 
wave-length of light and the length of the camera box. 

334. Theory of Shadows. Since the rays of light are 
straight, the space behind an opaque object will be screened 
from the light and will be in the shadow. If the source of 
the light is small the shadows will be sharply defined, but if 
it is of some size the edges will be indistinct. 

Let A (Fig. 322) be a small 
source, — an arc lamp, for instance, 
— and let B be an opaque ball. It 
will cast on the screen CD a circu- 
lar shadow with sharply defined ^',«,,fo'«rt^if b/Xr,'" 7t \t 
edges. But if the source is a body '°"'''^*'' ^ ^^'^ "''J^*^'- ^^ '^^ «'"'^°"'- 




292 NATURE OF LIGHT ; ITS MOTION IN STRAIGHT LINES 

of considerable size,* such as the sphere S (Fig. 323), tlien it 
is evident that the only portion of space which recei%es no 
light at all is the cone behind the opaque sphere E. This is 

called the umbra, or simjjly 
the shadow, while the por- 
tion beyond it which 
receives a part of the light 
from >S' is the ijenumhra. 
Suppose M is a body 
revolving about E in the 
direction indicated. In the 
position 1 it is just entering 
the penumbra ; in the second position it is entirely within the 
shadow. 

If >S' represents the sun, E the earth, and M the moon, the 
figure will illustrate an eclipse of the moon. For an eclipse 
of the sun, the moon must come between the earth and the 




Fio. 323. — S is a large bright souice, and E an 
opaque object. The dark portion is the shadow, 
thie lighter portion the penumbra. 




Fig. 324.— Showing how an eclipse of the sun is produced. A person at a cannot 
see the sun. 

sun, as shown in Fig. 324. Only a small portion of the earth 
is in the shadow, and in order to see the sun totally eclipsed 
an observer must be at a on the narrow ' track of totality." 

335. Transparent, Opaque and Translucent Bodies. Trans- 
parent bodies, such as glass, mica, water, etc., allow the light 
to pass freely through them. Opaque substances entirely 
obstruct the passage of light; while translucent bodies, such 
as ground-glass, oiled paper, etc., scatter the light which falls 
upon tliem, but a portion is allowed to pass through. 



A lamp with a spherical porcelain shade may be used. 



TRANSPARENT, OPAQUE AND TRANSLUCENT BODIES 293 

QUESTIONS AND PROBLEMS 

1. A photograph is made by means of a pin-hole camera, wliich is 8 
inches long, of a house 100 feet away and 30 feet high. Find the lieight 
of the image ? 

2. Why does the image in a pin-hole camera become fainter as it 
Ijecomes larger {i.e., by using a longer box, or pulling the screen back) ? 

3. Why is the shadow obtained with a naked arc lamp sharp and well- 
defined ? What diffei-ence will there be when a gi'ound-glass globe is 
placed around the arc ? 

4. On holding a hair in sunlight close to a white screen the shadow of 
the hair is seen on the screen, but if the hair is a few inches away, scarcely 
any trace of tlie shadow can be observed. Explain this. 

5. The sun's diameter is 864,000 miles, that of the earth, 8,000 miles. 
If the distance from the earth to the sun is 93,000,000 miles, find the 
length of the earth's shadow (Fig. 323). Calculate the diameter of this 
shadow at the mean distance of the moon from the earth. This distance 
is approximately 240,000 miles. 

6. The earth when nearest the sun (which occurs about January 1) is 
91^ millions of miles away, and the moon when nearest the earth is at a 
distance of 221,600 miles. These distances are from the centre of the 
earth. Supposing an eclipse of the sun to take place under these circum- 
stances, find the width of the shadow (a, Fig. 324) cast on the earth, taking 
the diameter of the moon to be 2,160 miles. 




CHAPTER XXXIII 
Photometry 

336. Decrease of Intensity with Distance from the Source. 

Let a small square of cardboard BG be held at the distance of 
one foot from a small source of light A (Fig. 325), and one foot 
p behind this place a white screen DE. 
The shadow cast by BC on DE is a 
square, each side of which is twice 
that of BC, and hence its area is four 
times that of BG. Next, hold the 

Fig. 325.— Area of DE is 4 times, „ _^ p , p 

and area of FG is 9 times that screen at J^ (r, One loot further away, 
or three feet from A. The shadow of 
BG will now have its linear dimensions three times those of 
BG and its area nine times that of BG ; and so on. The area 
of the shadow varies as the square of the distance from the 
source A. 

Suppose, now, a white screen, (a piece of paper), be held at 
BG. The light A will illuminate it with a certain intensity 
which we shall denote by ly If the screen is held at DE the 
.same light which fell on one square inch when at BG will now 
fall on four square inches, and hence the intensity of illumina- 
tion 1.2 will be \ of /p If placed at FG the same amount of 
light will be spread over 9 square inches, and the illumination 
L^ is equal to \ of ly If the screen be n times as far from A 
as BG is, the illumination In will be ^3 of I^. Thus we obtain 
the law : The intensity of illumination varies inversely as 
the square of the distance from the source of light. 

This is the fundamental law upon which all methods of 
comparing the powers of different sources of light are based. 

It should be carefully observed that for this law to hold, 
the source of light must be small and must radiate freely in 

29A 




RUMFORD'S PHOTOMETER 295 

all directions. The headlight of a locomotive, for instance, 
projects the light mostly in one direction, and the decrease in 
intensity of illumination will not vary according to the above 
law. 

337. Rumford's Photometer. To compare two sources of 
light we require some convenient method of determining 
equality of illumination, and various instruments, known as 
pJiotomefers, have been devised for this purpose. Suppose we 
wish to compare the illuminating powers of the two lamps L^ 
and Zo. The method intro- 
duced by Rumford is to stand 
an opaque rod M (Fig. 326) 
vertically before a screen AB, 
and allow shadows from the 

two lamps to be cast on the fio. 32c.— Rumford'a shadow photometer. 

The liglits //,, in are adjusted until the 
screen. sliadows oast by 'a rod R on the screen 

are equally dark. 

If the screen is of ground- 
glass it should be viewed from the side away from the lamps ; 
if of opaque white paper (white blotting paper is best) the 
observer should be on the same side as the lamps. 

It is evident that the portion ab is illuminated only by the 
lamp Zj, and the portion be only by the lamp L2. 

Now move the lamps until the portions ab, be are equally 
bright (or equally dark), and then measure the distance of 
Zj from ab and of L., from 6c. Let these distances be d^, d.,, 
respectively. We can now calculate the ratio between the 
illuminating powers of the lamps. 

Let the distances d^, <l, be given in feet. Hold a piece of 
paper 1 foot from L^ ; let the intensity of illumination be I^. 
In the same way when held 1 foot from Xg let the intensity of 
illumination be /g. 



296 



PHOTOMETRY 



It is evident then that 

Now the lamp Z^ produces a certain intensity of illumination 
on the portion ah which is distant c?i feet from L^. Let this 
be I. Then 

Similarly, since the intensity of illumination of he is the same 
as of 06, it also is /, and we must have 
I_ 1 

I _I _ _i_ 1 

h^ i\- (fL)2 • {d^r 



Hence 



Or 



^- ^ m 



But 



and so — 



\dJ 



1-2 ^d., 

338. The Bunsen Photometer. The essential part of this 
photometer is a piece of unglazed paper with a grease-spot on 
it. Such a spot is more translucent than the ungreased paper, 
so that if the paper is held before a lamp the grease-spot 
appears brighter than the other portion, while if held behind 
the lamp it appears darker. 

Now move the grease-spot screen between the two light- 
sources Xi, L2 (Fig. 327) 

-di f{ rfj * to be compared until it 

^'v/ \'\ rl ^ is equally bright all 

over its surface. Then 
it is evident that what 
illumination the screen 
loses by the light from 
Xi passing through is 
precisely compensated by the light from Xg transmitted 
through it. Thus the intensity of illumination due to each 




Fio. 327. —The Bunsen grease-spot photometer. 



VERIK1(;ATF0N of the law of inverse S(MJAKES 



297 



f/,, (/., are the distances from the 



GO'. 



lamp is the same. Hence, it' 
screen of Zj, Z,,, respectively, 

as before. 

339. Joly's Diffusion Photometer. Two pieces of paraffin 
wax, each about 1 inch square and \ inch thick are cut from 
tlie same block of paraffin, carefully made of the same thick- 
ness and then put together with tin-foil between them (Fig. 
328). This is adjusted between the two lamps to be compared, 
until the two pieces are equally illuminated, at which time 
the line of separation disappears. 

This is a simple and very useful photometer. The block of 
paraffin should be viewed through a 
tube, using a single eye. 

For the block of paraffin one may 
substitute a wooden prism having two 
faces covered with unglazed paper, and 
the edge being turned towards the 
experimenter. 

All photometric work should be done in a darkened room, 
and the eyes should be shielded from the direct light from the 
lamps which are being compared. There will usually be diffi- 
culty in adjusting the photometer due to a difference in the 
colour of the lights. This cannot be avoided, however. 

340. Verification of the Law of Inverse Squares. To do 

this let us use the Joly photometer (Fig. 329). Place 1 candle 

at one end of a board and 4 
candles at the other. Now 
move the photometer until the 
line between the paraffin blocks 
disappears, and measure its 
distance from the 1 candle and 
the 4 candles. The latter will 



I, 



Fig. 328. -Joly Diffusion Photo- 
meter, consistiiiK of two similar 
blocks of paraffin, set close to- 
gether. 




Fio. 3-2!).— If the blocks are equally illumi- 
nated the 4 candles are twice asfarfiom 
the photometer as the single candle. 



298 



PHOTOMETRY 



be twice the former. Next, replace the 4 candles by 9 and 
adjust as before. The distance from the 9 candles will be 3 
times that from 1. 

Thus if tlie distance is doubled the illumination is reduced 
to 5, since it requires 4 times as many candles to produce 
equality. In the same way if the distance w^ere n times as 
great we should require n'^ candles to produce an illumination 
equal to that given by the single candle. 

341. Standards of Light. By the photometer we can 
accurately compare the strengths of two sources of light, but 
to state definitely the illuminating power of any lamp we 
should express it in terms of some fixed standard unit. We 
have definite standard units for measuring length, mass, time, 
heat, and most other quantities met with in physics ; but no 
perfectly satisfactory standard of light has yet been devised. 

The one most commonly used is the candle. The British 
standard candle is made of spermaceti, weighs 6 to the pound 
avoirdupois, and burns 120 grains per hour. The strength 
varies however with the state of the atmosphere and with the 
details of the manufacture of the wick. Yet, notwithstanding 
this inconstancy, it is usual to express the illuminating powder 
of a source in terms of the standard candle. 

A standard much used in scientific work is the Hefner lanq) 
(Fig. 830). This is a small metal spirit- 
lamp with a cylindrical bowl 7 cm. in 
diameter and 4 cm. high. The wick-holder 
is a German-silver tube 8 mm. in interior 
diameter, 0.15 mm. thick, and 25 mm. high. 
The wick is carefully made to just fit the 
tube, and the height of the flame is adjusted 
to be 4 cm. The liquid burned is pure 
F.o. 330. -The Hefner amyl acetate. The lamp is very constant, 
l«a"ch,?,L^T is ?or and its power is given as 98 per cent, of the 

accurately adjusting -q -i • i "ii 

the height of the flame. rJritlSU CaUQie. 




STANDARDS OF LIGHT 299 

QUESTIONS AND PROBLEMS 

1. Distinguish between illn,minati7ig ^wwer and intensitij of illnmiiMtion. 

2. When using a Rumford photometer (Fig. 326) the distance -L^t was 
found to be 20 inches and L._,b was 50 inches. Compare the illuminating 
powers of L^ and Lg- 

3. Two equal sources of light are placed on opposite sides of a sheet of 
paj^er, one 12 inches and the otlier 20 inches from it. Compare the 
intensity of ilhunination of the two sides of the paper. 

4. A lamp and a candle are placed 2 m. apart, and a paraffin-bh)ck is 
in adjustment between them when 42 cm. from the candle. Find the 
candle-poMjer of the lamp. 

5. For comfort in reading the illumination of the printed page should 
be not less than 1 candle-foot (/.e., 1 candle at a distance of 1 foot). How 
far might one read ironi a IG candle-power lamp and still have sufficient 
illumination? 

6. A candle and a gas-flame which is four times as strong are placed 6 
feet apart. There are two positions on the line joining these two sources 
whore a screen may be placed so that it may be equally illuminated by 
each source. Find these positions. 



CHAPTER XXXIV 
The Velocity of Light 
342. Roemer's Great Discovery. Galileo constructed the 

telescope in 1609 and the first fruit of its use was the discovery that 
Jupiter was attended by four moons. At present we know that the 
planet has eight moons, but while the four first discovered can be 
seen with a small telescope, the last four are very small bodies and 
very difficult to see. 

Roemer, a young Danish astronomer, while at the Paris Observa- 
tory, made an extended series of observations on Jupiter's First 
Satellite; and inequalities in these observations led him to announce 

in 1675 the discovery 

tthat light travelled with 
a finite velocity. 
In the figure (Fig. 
331) let ^S* be the sun, 
E^, E\ E", E, the earth 
in various positions in its 
orbit, J^, Jy the planet 
Jupiter in two positions, 
and M the moon under 

Fig. 331. -Illustrating the eclipse of Jupiter's satellite, ob^prvafinn Tn \\\(^ r.n«i 

S is the sun, H the earth, J Jupiter, and M its satel- OO^^ei vation. Ill tne pOSl- 

lite. When the satellite passes into the shadow cast tioil S E^ J,, in which 

by J it cannot be seen from E. xi i j. i ^i 

•' the planet and the sun 

are on opposite sides of the earth, Jupiter is said to be in opposition, 
while in the position E^ S J.^ in which the planet and the sun appear 
to be a straight line, as seen from the earth, Jupiter is said to be in 
conjunction. 

Every time the moon revolves about Jupiter it plunges into its 
shadow and is eclipsed. Now the First Moon is neither the largest 
nor the brightest, but as it makes a revolution in 42| hours its 
motion is rapid, and the time of an eclipse can be determined with 
considerable accuracy. 

Suppose we observe successive eclipses near the time of opposition. 
We thus obtain the interval between them, and by taking multiples 
of this we can tabulate the times for future eclipses. Now Roemer 
found that the observed and tabulated times did not agree, — that as 
the earth moved to E', E" and E^, continually getting farther from 
the planet, the observed time lagged more and more behind the 
tabulated time, until when at E,,, and Jupiter at J^, the difference 

.300 . 



ILLUSTRATIONS OF VELOCITY OF LIGHT 301 

between the tiiiu>.s liad grown to 16 m. 40 fs. or 1000 K(!conds.* As 

the earth moved round to opposition again the inecpiaUty disappeared 

and the times observed and tabulated coincided. 

Roepaer explained the peculiar observations by saying that at 

conjunction the light travels the distance E^ J^, which is greater 

than the distance E^ J^ travelled at opposition by the diameter of 

the earth's orbit, and hence the observed time at E^. should be later 

than the tabulated time by the time required to travel this extra 

distance. Taking the diameter of the orbit to be 186,000,000 miles, 

the velocity is 

186,000,000 TO. ^^^ ., , 

^ = 186,000 mues per second. 

1000 ' ^ 

343. Other Determinations. Roemer's explanation was not 
generally accepted until long after his death (1710). In 1727 
Bradley, the Astronomer Royal of England, discovered the "aber- 
ration of light," and fully confirmed Roemer's results. In more 
recent times the velocity of light has been directly measured on the 
earth's surface. In 1862 Foucault, a French physicist, actually 
measured the time taken by light to travel 40 m., the entire experi- 
ment being performed in a single darkened room. Very accurate 
measurements have been made by others, especially by Michelson and 
Newcomb in the United States and Cornu and Perrotin in France, 
and the result is 299,860 kilometres or 186,330 miles per second. 

344. Illustrations of Velocity of Light. The speed of light 

is so enormous that one can hardly appreciate it. It would travel 
about the earth 1^ times in a single second. The distance from the 
earth to the sun is 93,000,000 miles. A celestial railway going 60 
miles an hour without stop would require 175 years to traverse this 
distance, but light comes from the sun to us in 8J minutes ! And 
yet the time taken for the light to reach us from the nearest of the 
fixed stars (named Alpha Centauri) is 4.3 years. From Sirius, our 
brightest fixed star, the time is 8.6 years, while from the Pole Star 
it is 44 years. That star could be blotted out and we would not 
know of it until 44 years afterwards. 

345. Velocity in Liquids and Solids. Michelson measured 

the velocity of light in water and in carbon bisulphide, and found it 
less than in air in both cases. Indeed the velocity in air is 1 J times 
that in water and If times that in carbon bisulphide. These results 
will be referred to again, when dealing with refraction. We shall 
find that the velocity in all transparent solids and liquids is less 
than in air. 

♦This is the modern value ; Roemer's result was 22 m. 



CHAPTER XXXV 



Reflection of Light : Plane Mirrors 

346. The Laws of Reflection. Let a lighted candle, placed 
in front of a sheet of thin plate glass, stand on a paper 

(or other) scale arranged 
perpendicular to the sur- 
face of the glass (Fig. 
332). We see an image 
of the candle on the 
other side. Now move 
a second candle behind 
the glass until it co- 
incides in position with 
the imaofe. 




Fig. 332. — A lighted candle stands in front of a she et of 
plate glass (not a mirror). Its image is seen bv the 
e.xperinienter, who, with a second lighted caiuUe in 
his hand, is reaching round behind and trying to 
place it so as to coincide in position with the image 
of the first candle. 



On examining the scale 
it will be found that the 
two candles are both on 

the paper scale and at equal distances from the glass plate. 

We can state the LAW of reflection, then, in this way : — 

If an object be placed before a plane onirror its image 
is as far behind the mirror as the object is in front of it, 
and tJte line joining object and image is perpendicular to 
the mirror. 

Thus light goes from the candle, strikes the mirror, from 

which it is reflected, and reaches the eye as though it came 

from a point as far behind the mirror as the candle is in front 

of it. Of course the image is not real, that is, the light does 

not actually go to it and come from it — it only appears to do 

so. But the deception is sometimes perfect and we take the 

302 



THIO LAWS OF REFLECTION 



303 




image for a real object. This illusion is easily producv'd it" the 
mirror is a good one and its edges are liiddeii hy drapes or in 
some other \v;i,y.* 

This law of reflection can be stated in another way. Let 
MN (Fig. 838) be a section of a plane 
m i rror. Li gh t proceeds f njm A , sti'i k es 
the nn'rror and is reflected, a portion 
being received by the eye E. To this 
eye the light appears to come from 
B, where AM = ]\IB and AB is per- 
pendicular to MN. 

Consider the ray AC, which, on '"'^v^^.^.-^c is an incident raj-^ 

■/ ' ' CF the reflected ray, and CP 

ivflppfinn o-nps5 in flip dirppt-inn ffF ^'^^ noniial to the surface MN. 

lenection, goes ni une uuection ui*. ^^^^^ ,^,^„.,g ^^ incidence ^cp is 

_ equal to anirle of reflection FCP. 

In the triangles AMG, BMC we 
liave AM = MB, MC is common to the two triangles, and 
angle AMC = angle BMC, each being a right-angle. 

Hence the triangles are equal in every respect, and so the 
angle ACM = angle BCM. 

But angle BCM = angle FCM', and hence the angles AC3I 
and FCIi are equal to each other. 

From C let now CP be drawn perpendicular to MN. It is 
called the normal to the surface at C. At once we see angle 
ACP = angle FCP. 

Now ^Cis defined to be the incident ray, CF the reflected 
ray, ACP the angle of incidence and FCP the angle of reflec- 
tion. Hence we can state our law of reflection thus : 

The angle of incidence is equal to the angle of rejiection. 

This statement of the law, which is precisely equivalent to 
the other, is sometimes more convenient to use. 

•Wordsworth in "Yarrow Unvisited" refers to a case of perfect reflection: 

" The swan on still St. Mary's Lake 
Floats double, swan and shadow." 



304 



REFLECTION OF LIGHT: PLANE MIRRORS 




B 

Fig. 334.— Waves on still water 
reflected from a plank Ij'ing on 
its surface. 



Another law wliould be added, namely, — 

The incident ray, the reelected ray and the nornud to the 

surface are all in one ■pktyne. 

347. Law of Reflection in Accordance with the Wave 
Theory. The law of reflection, which we obtained experi- 
mentally, is just what we should expect if liglit is a 
wave-motion. Let a stone be thrown 
into still water. Waves, in tlie form 
of concentric circles, spread out from 
the place A (Fig. 334) where it entered 
the water. If a plank lies ori the sur- 
face near by, the waves will strike it 
and be reflected from it, moving off" as 
circular waves whose centres B are as 
far behind the reflecting edge as A is 
in front of it. In the figure the dotted circles are the reflected 
waves. AM is an incident 
and MR the reflected "ray." 
The reflection of circular 
waves is well illustrated in 
Fig. 335, which is made 
from an instantaneous pho- 
tograph* of waves on the 
surface of mercury. The 
waves were produced by 
attaching a light " style " 
to one prong of a tuning- 
fork and making it vibrate 
with the end just touching 
the surface. A triangular 
piece of glass lies on the 

surface and from it the F'^- 335.— The circular ^\aves on the svirface of 

mercury spread out and are reflected from a glass 

waves are reflected, their plate. '(From a photograph.) 




"Taken, with the aid of an electric spark, by J. H. Vincent, of London, England. 




REGULAR AND IRREGULAR KEFLECTION 305 

centres l)einj( as far lieliind tl>e reflecting edge as the source 
is in front of it. 

348. Regular and Irregular Reflection. Mirrors are usually 
made of polished metal or of sheet glass with a coating of 
silver on tlie back surface. When light falls on a mirror it is 
reflected in a definite direction and the reflection is said to be 
regular. Reflection is also regular from the still surfaces of 
water, mercury and other liquids. 

Now an unpolished surface, such as paper, altliough it may 
appea,r to the eye or the hand as quite smooth, will exhibit 
decided inequalities when examined 
under a microscope. The surface will 
appear somewliat as in Fig. 336, and 
hence the normals at the vai'ious parts 
of the surface will not be parallel to fw. 336. -soattering of lis^ht 

from a rouffh surface. 

each other, as they are in a well- 
polished surface. Hence the rays when reflected will take 
various directions and will be scattered. 

It is by means of this scattered light that objects are made 
visible to us. When sunlight is reflected by a mirror into 
your eyes you do not see the mirror but the image of the sun 
formed by the mirror. Again, if a beam of sunlight in a dark 
room falls on a plate of polished silver, practically the entire 
beam is diverted in one definite direction, and no light is given 
to surrounding bodies. But if it falls on a piece of chalk the 
light is diffused in all directions, and the chalk can be seen. 
It is sometimes difficult to see the smooth surface of a pond 
surrounded by trees and overhung with clouds, as the eye 
considers only the reflected images of these objects; but a 
faint breath of wind, slightly rippling the surface, reveals 
the water. 



306 



REFLECTION OF LIGHT : PLANE MIRRORS 



«!^««j^ 




Fig. 337.— How an eye sees the 
imau^e of an object before a plane 
mirror. 



349. How the Eye receives the Light. An oljjcct AB 
(Fig. 337) is placed before a plane 
mirror MM, and the eye of the ob- 
server is at E. Then the image 
A'B' is easily drawn. The light 
which reaches the eye from A will 
appear to come from A', which is the 
image of A and which is as far be- 
hind MM as A is before it. 

It is therefore by the pencil AaE 
that the point A is seen. In the same 
way the point B is seen by the small pencil BbE, and similarly 
for all ofclier points of the object. 

It will be observed that when the eye is placed where it is 
in the ligure, the only portion of the mirror which is used is 
the small space between a and b. 

An interesting exercise for the student is to draw a figure 
showing that, for a person standing before a vertical mirror to see 
himself from liead to foot, the mirror need be only half his height. 

350. Lateral Inversion. The image in a plane mirror 
is not the exact counterpart of the object producing 
it. The right hand of the object becomes the left 
hand of the image. If a 
printed page is held before 
the mirror the letters are 
erect but the sides are inter- 
changed. This effect is 
known as lateral in version. 
By writing a word on a 
sheet of paper and at once 
pressing on it a sheet of 
clean blotting-paper the 
writing on the blotting- 
paper is inverted ; but if it is held before a mirror it is 




Illustrating "lateral inversion" bj' a 
plane mirror. 



REFLECTIONS FROM PARALLEL MIRRORS 



307 



reinverted and l^ecomes leufil:)le. Tbo effect is illusiraled in 
Fig. 338, sliovving the iuia<;e in a plane mirror of tiie word 
STAR. It may be remaik(Ml, tlierefore, that on looking in a 
mirror we do not ' S(;e ourselves as others see us.' 

351. Reflections from Parallel Mirrors. Let us stand two 
mirrors on a table, parallel to each other, and set a lighted candle 
between them. An eye looking over the top of one mirror at the 
other will see a long vista of images stretching away behind 
the mirror. These are produced by successive reflections. 

In Fio;. 339, 1 and // are the mirrors and the candle. A^ is 




B, 



Fio. 339.— Showing: many images produced l>y two minoi-s /, //, parallel to each other. 

the image of in I,A.^ the image of A^ in //, Ao, that of J. 2 in 
/, and so on. Also B^ is the image of in //, B.^ that of B^^ in 
/, £3 that of B.^ in //, and so on. The path of the light which 
produces in the eye the third image Ao, is also shown. It is 
reflected three times, namely, at 7)1, n and 'p, and from the figure 
it will be seen that the actual path OmnpE, which the light 
travels, is equal to the distance A.^ E, from the image to the eye. 

352. Images in Inclined Mirrors. Let the mirrors ilfj, 
M., (Fig. 340) stand at right angles 

to each other and be a candle B ^i\....y^.^-...y,(} 

between. There will be three 
images, A being the first image in 
ilfi, B the first image in J/„, while 
G is the image of A in il/^ or of 
B in i/p these two coinciding. 

353. The Kaleidoscope. If the 
mirrors are inclined at 60° the imao^es will be formed at the 




Fig. 340.— Images produced by two 
mirrors placed at right angles. 



308 



REFLECTION OF Lir4HT : PLANE MIRRORS 




Ima>;es produced 



places sliown in Fig. 341. They are all located on the circum- 
ference of a circle having the intersec- 
tion of the mirrors as its centre, and an 
inspection of the figure will show how 
to draw them. 

The kaleidoscope is a toy consisting of 
a tube having in it three mirrors form- 
ing an equilateral triangle, with bits of 
by mirrors iiicrmtd'Ti"^an coloured gUiss between. The multiple 

angle of 00°. . . , . 

nnages produce some very pleasing 
hexagonal figures. It was invented in 1816 by Sir David 
Brewster and created a great sensation. 

QUESTIONS AND PROBLEMS 

1. Why is a room lighter when its walls are white than when covered 
with dark paper ? 

2. The sun is 30" above the horizon and you see its image in still water. 
Find the size of the angles of incidence and reflection in this case. 

3. Two mirrors are inclined at 45° and a candle is placed between 
them. By means of a figure show the position of the images. Do the 
same for mirrors inclined at 72°. 

4. Two mirrors are inclined at an angle of 60°. A ray of light travelling 
parallel to the first mirror strikes the second, from which it is reflected, 
and, falling on the first, is reflected from it. Show that it is now moving 
jjarallel to the second mirror. 

5. The object between two mirrors standing parallel to each other 
(Fig. 339) is 8 inches from A and 12 inches from B. Find the distances 
A^B^, A^B.^, A^B^. 




Fio. 342.— A section of a spherical 
mirror. 



CHAPTER XXXVI 
Reflection from Curved Mirrors 

354. The Curved Mirrors used in Optics; Definitions. 

The curved mirrors used in optics 
are generally segments of spheres. If 
the reflection is from the outer surface 
of the sphere the mirror is said to be 
convex; if from the inner surface, 
concave. 

In Fig. 342 il/yliV represents a sec- 
tion of a spherical mirror. C, the centre of the sphere from 
which the mirror is cut, is the centre of curvature, and CM, 

CA or CN is a radius of curvature ; 
MN is the linear, and MCN the 
angular, aperture; A, the middle 
point of the face of the mirror is 
the vertex; CA is the lyrincipal 
axis, and CD, any other straight 
line through C, is a, secondary axis. 

355. How to Draw the Reflected Ray. The laws of reflec- 
tion hold for curved as well as for plane -mirrors. Let QR 
(Fig. 348) be a ray incident on the 
concave mirror at R. By joining R 
to C we obtain the normal at R, and 
by making CRS (the angle of reflec- 
tion) equal to CRQ (the angle of 
incidence), we have RS, the reflected fiq. 344.-Reflection from a 

mirror. 

ray. 

In Fig. 344 is sliown the construction for a convex mirror, 

QR being the incident and RS the reflected ray. 

309 




Fig. 343. — Reflection from a concave 
mirror. 




310 



REFLECTION FROM CURVED MIRRORS 




356. Principal Focus. In Fig. 345 let QR be a ray- 
parallel to the j)rincipal axis; then, 
making the angle CRS = angle CRQ, 
we have the reflected ray RS. But 
since QR is parallel to AC, angle CRQ 
= ano-le RCF. Hence angle FRC = 
angle FCR, and the sides FR, FC are 
equal. 

Now if R is not far from A, the vertex, FR and FA are 
nearly equal, and hence AF is approximately equal to FC, i.e., 
the reflected ray cuts the principal axis 
at a point approximately midway be- 
tween A and C. 



Fig. 345.— The ray QR, parallel 
to the principal axis AC, on 
rt flection passes through the 
principal focus F. 




It is evident, then, that a beam of raj's A 
parallel to the principal axis, striking the 
mirror near the vertex, will be converged „„,„., 

" Fig. 346. — A beam of ravs 

by the concave mirror to a point F, mid- parallel to the principal axis 

•z ^ ' passes, on reflection, through 

way between A and C. This point is -f, the principal focus. 
called the principal foe as, and AF is the focal length of the 
mirror. Denoting AF by / and AC hy r, we have / = r/2. 

In the case shown in Fig. 346 the rays actually pass 
through F which is therefore called a real focus. 

Rays which strike the mirror at some distance from A do 
not pass precisely' through F. For instance, the ray Qif cuts 
the axis at G ; this ivandering from F is called aberration, 
which amounts to FG for this ray. 

For a convex mirror the same method is followed. In Fig. 

347 a beam parallel to the principal 
axis is incident near tlie vertex. 
The reflected rays diverge in such 
a way that if produced backwards 
, . tlu'Y pass throuoh F, the principal 

Fio. 347. — Showing reflection of a. ^ i- o ' i i. 

parallel beam from a convex minor. focus. Ill this CaSC tllC rayS do 

not actually pass through F, but only appear to come from it. 




EXPERIMENTAL DETERMINATION OF FOCAL LENGTH 311 

For this reason F is called a virtual focus. lu the figure is 

also shown a ray QM, which strikes the mirror at some 

distance from the vertex. Upon reflection this appears to 
come from G, and FG is the aberration. 

357. Experimental Determination of the Focal Length. 

Hold a concave mirror in the sun's rays or in a parallel beam 
from a projecting lamp, and shake chalk-dust in the air. In 
this way one can see how the liglit passes through the air, 
strikes the mirror, converges to a point and then spreads out 
again. This point is the principal focus, and by placing a 
piece of paper there its position can be well determined. Its 
distance from the vertex is the focal length required. 

If a sheet of paper with a hole cut in it is placed over the 
mirror so as to use only those rays which strike the mirror 
near its vertex, the light will converge more accurately to a 
point but the image will not be so bright. 

For a convex mirror the method is not quite so direct. 
Make a round paper disc to cover the face of the mirroi-, and 
in it cut two slits at a measured distance 
apart {a, Fig. 348). Use a screen like 
that shown (6, Fig. 348). Now let the 
sun's rays pass through the hole in the 
screen and strike the small uncovered 
spots m, J), of the mirror. Then nm 
is the incident ray, which is reflected 
along mL, and qp, that which is re- 
flected along pM. There will be two FiG.348.-IllustratinK a method 
b. ,. . : T -nT 1111 r- of findinir the focal length of 

right spots at L, 31, on the back surtace a convex mirror. 

of the screen. Move the mirror until the distance LM = 2 mp. 

Now, from the figure we see that LFN^ and Lmn are similar 
triangles, and if LJSF = 2Ln, then FN = '2mn = 2 AN, or 
FA = AN, and lience the focal length is equal to the distance 
of the screen from the mirror. 










L 




\m^ 






F...-- 


Y 


n 


JV 




••■ 








/p^ 


^ 


M 



312 



llEFLECTION FROM CURVED MIRRORS 















t 


t^ a, a. 




h 


^ . 








\ 














hf 






' 












J^ 


^^ 






-L 








V 


/ ' 








/ 








\ 










b. 


\ 


b 



358. Explanation by the Wave Theory. The behaviour of 
curved mirrors can be easily accounted for by means of the 

wave theory. In Fig. 349 a h, 
Ui h^, ctg fto' • • • • represent plane 
waves moving- forward to the 
concave mirror. The waves 
reach the outer portions of the 
mirror first and are turned back, 

Fio. 349.-Showing: how plane waves by [^^ Q^[^ y^.^y Reiner chancred iuto 
reflection at a concave mirror are changed j » » 

to spherical waves. sphcHcal waves which contract, 

pass through F and then expand again. 

This action of a concave mirror is well illustrated in Fig. 

350 from an in- 

stantaneous pho- 
tograph of ripples 
on the surface of 
mercury. The 
plane waves were 
produced by a 
piece of glass 
fastened to one 
pron^ of a tun- 
ing - fork. They 
move forward and 
meet a concave 
reflector, by which 
they are changed 
into circular 
waves convercrinof 






to the prniCipal piQ 350. — instantaneous photograph of waves on the surface of 
C mi mercurv. (Bj' J. H. Vincent.) 

locus. Ihey pass 

througli this and then expand again. 

Exercise. — Draw for a convex mirror the figure corresponding to 
Fig. 349. 



CONJUGATE FOCI— ILLUSTRATIVE EXPERIMENTS 



813 




Fio. 351.— Conjugate foci in a concave mirror, 
and P' are conjugate. 



359. Conjugate Foci. We liavo seen tlmt light ra^-s moving 
parallel to the principal axis are brought to a focus, real or 
virtual, by a spherical mir- 
ror, but a focus can be 
obtained as well with light 
not in parallel rays. For 
instance, let the light di- 
verge from P (Fig. 851); 
after reflection from the concave mirror it converges to P'. 

Now it is evident that if the light originated at P', it would 
be converged by the mirror to P. Each point is the image of 
the other and they are called conjugate foci. 

In the case shown in Fig. 851 both foci are real, since the 
rays which come from one actually pass through the other. 

It is possible, however, for 
one of them to be virtual. 
Such a case is shown in 
Fig. 352. Here P' is con- 
jugate to P, but is virtual. 
It will be noticed that P is 
between the mirror and F. 
Under these circumstances the conjugate focus is virtual, under 
all others it is real. 

Exercise.— Draw the v:aves in these and in other cases of conjugate 
foci, taking P at various positions on the axis. 

360. Illustrative Experiments. Into a darkened room take 
a concave mirror, and at the other end of the room place a 
lighted candle facing the mirror. The position of the image 
can be found by catching it on a small screen. It will be very 
near the principal focus, and will be real, inverted and very 
small. Now carry the candle towards the mirror. The image 
moves out from the mirror and increases in size, but it remains 
real, invex'ted and smaller than the candle, until when the 




Fig. 352. — Conjugate foci in a concave reflector, 
one being virtual. 



314 REFLECTION FROM CURVED MIRRORS 

candle reaches the centre of curvature, the image is there also 
and is of the same size. 

Next, bring the candle nearer the mirror ; the image moves 
farther and farther avv^a'y, and is real, inverted and enlarged. 
When the candle reaches a certain place near the principal 
focus, the image will be seen on the opposite wall, inverted, 
and much enlarged ; but when the candle is at the focus, the 
light is reflected from the mirror in parallel rays, — the image 
is at infinity. 

When the candle is still nearer the mirror, i.e., between the 
principal focus and the vertex, the reflected rays diverge from 
virtual foci behind the mirror (see Fig. 352). No real image 
is formed, one cannot receive it on a screen, but on looking 
into the mirror one sees a virtual, erect and magnified image. 

If the candle is held before a convex mirror the imasre is 
always virtual, erect and smaller than the candle. A simple 
example of such a mirror is the outer surface of the bowl of 
a silver spoon. 

361. To Draw the Image of an Object. Suppose PQ to be 
a small bright object placed before a concave mirror (Fig. 353). 

The light which starts out 
from P will, after reflection, 
converge to the focus con- 
jugate to P. Again QCT 
r. o.o XT . , . .V • ... is a secondary axis, and 

Fig. 353.— How to locate the image prodiiced by a •' 

concave mirror. raj^s starting out from Q 

will converge to a point on QCT which is the conjugate focus 
of Q. P and Q are only two points of the object, but by 
similar reasoning we see that every point in FQ has a 
conjugate real image. We wish to draw the real image of PQ. 
Now all the rays fi'om Q after reflection pass through its 
image, and it is clear that we can locate the position of this 
image if we can draw any two rays which pass through it. 



M,R 




q 


r- 


-^z- i?'- - - 





RELATIVE SIZES OF IMAGE AND OBJECT 



315 



Draw a ray QR, parallel to PA ; this will, upon reflection, 
pass through F. Also, the ray QC will strike the mirror at 
right angles, and when reflected will return upon itself. The 
two reflected rays intersect at Q' which is therefore the image 
of Q. Drawing Q'P' perpendicular to AC we obtain P', the 
image of P, and P'Q' is the image of PQ. 

It is evident that the ray QF will, after reflection, return 
parallel to the axis AC, and will, of course, also pass through Q'. 

By drawing any two of the three rays QR, QC, QF we can 
alwaj^s find Q', the image of Q. It should be observed, 
however, that all the other rays from Q as well as those 
drawn will after reflection pass through Q'. 

It will be very useful to draw the image of an object in 
several positions. In Fig. 
354 the object PQ is be- 
tween A and F. By draw- 
ing QR, parallel to the 
axis, and QT, which passes 

through the centre of cur- ^la. 354.— How to draw the image when the object 
, 1 I • J 1 • is between the principal focus and the vertex. 

vature, we obtain the image 

It is virtual and behind the mirror. 




P'Q'. 




Fia. 355.— How to draw the image produced by 
a convex mirror. 



362. Relative Sizes of Image 
and Object, Let PQ be an object 
and P'Qf its image in a concave 
mirror (Fig. 356). 



In Fig. 355 the mirror is 
^ convex, and the image P'Q' is 
virtual, erect, behind the 
mirror and smaller than PQ. 
It is always so in a convex 
mirror. 




The ray QA , Fiq. SoG.— The size of the object PQ ia 

, . ■. . ., , 1 ii *° "^'^'' o^ ^^^ image P'Q' aa their 

which strikes the mirror at the distances from the mirror. 

vertex, is reflected along AQ', and the angle QAP = Q'AP'. 



316 



REFLECTION FROM CURVED MIRRORS 



Also, the angle APQ = angle AP'Q', each being a right angle, 
and hence the two triangles APQ, AP'Q' are similar to each 
other. 

The ratio of the length of tlie image to tliat of the object is 
called the magniJiGation. Hence we have. 



Magnification 



P'Q' _ AP' _ distance of image from mirror 
PQ AP distance of object from mirror 



In the case illustrated in the figure the mao-nification is less 
than one. 

363. The Rays by which an Eye sees the Image. In § 361 

a graphical method is given for locating the image of an 
object, but the actual rays by which an eye sees the image are 
usually not at all those shown in the figures. 

In Figs. 857, 358, 359 
are shown actual rays from 
jDoints P and Q which reach 
tlie eye. In each figure the 
image is supposed to have 
been obtained by the graphical method. The image is real and 
inverted in Fig. 357, virtual and erect in the other two cases. 




Fia. 357.— How the rays pass from the object to 
the ej'e. (Real image in concave mirror.) 





Fig. 358.— How the rays go from the object Fio. 359.— How the eye sees an object in a 
to the eye. (Virtual image in concave a convex mirror. (Image always virtual.) 

mirror.) 

Now in each instance the light enters the eye as though it 
came from P'Q'. Join Q' to the outer edge of the pupil of the 
eye, forming thus a small cone with vertex at Q'. This cone 
meets the mirror at S, and it is clear that the light starts from 
Q, meets the mirror at S, is reflected there and then passes 



PARABOLIC MIRRORS 



317 



through Q' (really or virtually), and reaches the eye. In the 
figures are sliown also rays starting out from P, the other end 
of the object. They meet the mirror at R, where they are 
reflected and then received by the eye. In the same M^ay 
we can draw tlie rays which emanate from any point in the 
object. 

It will be seen that for the eye in the position E, shown in 
the figures, the only part of the mirror which is used is that 
space from R to >S^. The rays which fall on other parts of the 
mirror pass above or below or to one side of the eye. 

364. Parabolic Mirrors. In the case of a spherical mirror 
only those rays parallel to the axis which are incident near 
the vertex pass accurately through the principal focus ; if the 
angular aperture is large the outer rays after reflection pass 
through points some distance from the 
focus (see Fig. 346). Conversely, if a source 
of light is placed at the principal focus, 
the rays after reflection will not all be 
accurately parallel to the axis, but the 
outer ones (Fig. SCO) will converge in- 
ward, and later on after meeting will of 
course spread out. Hence at a great 
distance the light will be scattered and 
weakened. 




FiQ. 360.— If a source of light 
is placed at the principal 
focus of a hemispherical 
mirror the outer rays 
converge and afterwards 
diverge again. 



Now a parabolic mirror overcomes this spread- 
ing of the rays. In Fig. 361 is shown a parabola. 
All rays wdiich emanate from the focus, after 
reflection are parallel to the axis, no matter 
how great the aperture is. Parabolic mirrors 
are used in searchlights and in locomotive 
parabolic reflector headlights. If a powcrful sourcc is used a 

sends out parallel . i. - i. i. v i. • l\, 

rays. beam can be sent out to great distances with 

little loss of intensity. 




318 REFLECTION FROM CURVED MIRRORS 

QUESTIONS AND PROBLEMS 

1. Distinguish between a real and a virtual image. 

2. Prove that the focal lengtli of a convex spherical mirror is equal to 
half its radius of curvature. 

3. Show by diagrams that the image of a candle placed before a convex 
mirror can never be inverted. 

4. Find tlie focus conjugate to each of the following points : 

(a) the centre of curvature ; 

(J)) a point on the axis at an infinite distance ; 

(c) the vertex ; 

(d) the principal focus. 

[By means of diagrams carefully drawn to scale solve the following 
three problems.] 

5. An object 5 cm. high is placed 30 cm. from a concave mirror of 
radius 20 cm. Find the position and size of the image. 

6. If the object is 8 cm. from the mirror, find the position and size of 
the image. 

7. An object 6 cm. high is held 15 cm. in front of a convex mirror of 
radius 60 cm. Find the position, nature and size of the image. 




CHAPTER XXXVII 

Refraction 

365. Meaning of Refraction. Suppose a ray of light PA, 
(Fig. 362), travelling through air, to arrive at tlie surface of 
another medium, water for instance. Some of tlie light will 
be reflected, and the remainder will enter the medium, but in 
doing so it will abruptly change its direction. Tliis bending 
or breaking of its patli is called refraction. 

The angle i, between tlie incident ray and the normal, is 
the angle of incidence; and the angle r, 
between the refracted ray and tlie normal, 
is the angle of refraction. 

In the figure, the angle r is smaller than 
i. This always happens when the second 
medium is denser than tlie first. The term 
dense, however, as used in optics is not 
synonymous with that used in mechanics 
(§ 17). Thus oil of terpentine (sp. gr., 0.87), or olive oil 
(sp. gr., 0.92), is less dense than water as defined in mechanics; 
and yet a ray of light when passing from air into oil of 
turpentine or olive oil is refracted more than it is when 
passing into water. We say that these substances are 
optically denser than water. 

366. Experiments Illustrating Refraction, Place a coin 
PQ on the bottom of an opaque vessel (Fig. 363), and then 

move back until the coin is just hid- 
den from the eye E by the side of 
the vessel. Let water be now poured 
into the vessel. The coin becomes 
visible again, appearing to be in the 

F.o.363.-The bottom of the vessel POsitioU FQ'. The bottom of the 
appears raised up by refraction. vCSScl SCemS tO have risCU and the 

water looks shallower than it really is. 

319 



Fio. 362.— Illustrating 
refraction from air 
to water. 




320 



REFRACTION 




Fig. 364. — The stick appears broken at the 
surface of the water. 



The rea.son for this is readily understood from the figure. 
Rays proceed from Q to 7^, and on leaving the water are bent 
away from the normal, ultimately entering the eye as though 
they came from Q'. Similarly rays from P will be refracted 
at the surface, and will enter the eye as though they came 
from P'. 

Another familiar illustration of refraction is the appearance 

of a stick — an oar, for ex- 
ample — when held obliquely 
in the water (Fig. 864). A 
pencil of light coming from 
any point on the stick, upon 
emergence from the water, 
is refracted downwards and 
enters the eye as though it 
came from a point nearer the surface of the water. Thus the 
part of the stick immersed in the water appears lifted up. 

367. Explanation of Refraction by Means of Waves. First, 

lei us consider what might naturally happen wlien a regiment 

of soldiers passes from smooth ground to rough ploughed 

land. It is evident that the 

rate of marching over the rouo-h 

land should be less than over 

the smooth. Let the rates be 3 

and 4 miles an hour, respectively. 

In the figure (Fig. 865) are 
shown the ranks of soldiers 
moving forward in the direc- 
tion indicated by the arrows. 
The rank AB is just reaching the 
boundary between the smooth 
and the rough land, and the 
pace of the men at the end A is at once reduced. A short 



B Smooth 
.Ground 

d 




Bough 
Land 



Fig. 365. — Illustrating how a change in 
direction of motion may be due to 
change in speed. 



EXPLANATION OF REFRACTION BY MEANS OF WAVES 321 



time later tliis rank reaches the position a b, part being on 
the rougli and the rest still on the smooth ground. Next, it 
readies the position c d, and tlicn the whole rank readies the 
position CD, entirely on the rough land. If now it proceeds 
in a direction at right angles to the rank, as shown by the 
arrows, it will move off in a direction quite different from 
the original one. The succeeding ranks, of course, follow 
in the same manner, and tlie new direction of motion is DE. 

Now it is clear that tlie space ED of smooth ground is 
marched over in the same time as the space AG of rough land, 
and as the rates are 4 miles and 3 miles an hour, respectively, 
we have BD 4 

AC^ 3' 

We have used ranks of soldiers in the illustration but 
waves behave very similarly. In Fig. 366 is reproduced a 
photograph of waves on the surface of water. These waves 
were produced by 
attaching a piece 
of thin glass to one 
prong of a tuning- 
fork and then 
vibrating it, just 
touching the sur- 
face. The waves 
move forward in 
the direction shown 
by the arrow, but 
on reaching the 
shallower water 
over a piece of glass 
lying on the bottom 
of the vessel, their speed is diminislied (§§ 181, 183) and 
the wave-fronts swerve around, thus abruptly clianging the 
direction of propagation. 






Fia. 366.— Plane waves on passing into shallower water are 
refracted as shown by the arrow. (Photograph by J. H. 
Vincent. ) 



322 



REFRACTION 




368. The Laws of Refraction. In Fig. 367 GD is a ray 

incident on the surface of 
glass, DE is the corresponding 
refracted ray, and i and r are 
the angles of incidence and 
refraction, respectively. With 
centre D describe a circle, cut- 
ting the incident ray at G and 
the refracted ray at E. GH 
and EF are perpendiculars 
upon HF, the normal to the 
surface at the point D. 

Then the angles i and r bear a definite relation to each 
other. Another ray, with a different i, will give rise to a 
refracted ray with a different r, but the relation between the 
two angles will be the same as before. We wish to discover 
what this relation is. 

Let us consider the passage of the waves from the air to the 
glass. J. 5 is a wave in the air just entering the glass, while 
CD is the position of the same wave when it has just got 
within the glass. Remember that the rays are perpendicular 
to the waves. Then from S 367 we have 



Pig. 367. — Diatrram to explain the law of refrac- 
tion. The lenjfth of QH is to that of FE .as 
the velocity in air is to that in water. 



BD 

AG 



Velocity in air 



Velocity in glass 

Now compare the two triangles GHD and ABD. The 
angles GHD and ABD are equal, each being a riglit angle. 
Also, since GH is parallel to AD and GD meets them, tlie 
angle HGD = angle ADB. Hence also the angle GDH = 
angle DAB. 

Also, the side GD = side AD. Tlius tlie two triangles 
GHD, ABD are equal in every respect, the side GH being 
equal to side BD. 



TABLE OF INDICES OF REFRACTION 323 

Again A DF and GDE are right angles, and if we take from 
each the angle CDF, which is common to both, we liave angle 
ADG = angle EDF. In the same way as before we can 
show that the two triangles ADG and EDF are equal in every 
respect, and that the side AG = side EF. 

TT GH BD Velocity in air 

-tXGllCG ~ —-^ 

EF ~ AC ~ Velocity in glass' 

Now the ratio between the velocities is a numerical constant. 
It is usually denoted by tlie Greek letter /j. (pronounced mfi) 
and is called the index of refraction from the first medium 
into the second. 

We find, then, that the angles of incidence and refraction 
are related to each other in the following way. Describe a 
circle having as its centre the point where the incident ray 
strikes the surface of the second medium, and let this cut the 
incident and refracted rays. If now from these points of 
intersection 2:)erpendiculars he dropped upon tlte normal to 
the surface, then the ratio hetiveen the lengths of these per- 
pendiculars is a numerical constant and is knoivn as the 
index of refraction from tlte first medium into tlie second. 

This is the first Law of Refraction. It can be expressed 
much more simply by using the trigonometrical term called 
the sine, and is sometimes referred to as the sine laiv.* 

The second Law of Refraction is : — TJte incident ray, the 
refracted ray and, the normcd to the surface are in the same 
plane. 

369. Table of Indices of Refraction. The following table 
gives the values of the indices of refraction from air into 
various substances. If the first medium were a vacuum we 
would have the absolute index, but as the velocity of light in 
air differs very little from that in a vacuum the absolute 
indices diflfer very slightly from the values given here. 

* Since sm i = — — , and sm r = -— , then -: — = -—=, = /n, the index of refraction. 
GD ED sirir EF 



324 



REFRACTION 



It mu.st be noted, however, that tlie indices are not the same 
for li(;hts of all colours, those for blue light being somewhat 
greater than for red. The values given here are for yellow 
light, such as is obtained on burning sodium in a Bunsen or 
spirit flame. 





Indices of 


Refraction 


Crown-glass 


.1.514 to 1.560 


Hydrochloric acid (at 20° C.).1.411 


Flint-glass 


.1.608 to 1.792 


Nitric acid (at 20° C.) 1.402 


Rock salt 


1.544 


Sulphuric acid (at 20" C). . .1.437 


Sylvine (potassium 


chloride).1.490 


Oil of turpentine (at 20° C). 1.472 


Fluor spar 


1.434 


Ethyl alcohol (at 20° C). . . . 1.358 


Diamond 


...2.42 to 2. 47 


Carbon bisulphide (at 20° C.).1.628 


Canada balsam . . . 


1.528 


Water (at 20° C.) 1.334 




370. Refraction Through a Plate. A plate is a portion of a 
medium bounded by two parallel planes. In Fig. 368, PQRS 

shows the course of a ray of light 
through a plate of glass. It is re- 
fracted on entering the plate and 
again on emerging from it. Since the 
normals at Q and R are parallel, the 
angles made with these by QR are 
equal. Each of them is marked r. 
Then since the angles of incidence and 
refraction depend on the velocities of 
light in the two media, and if we send 
the light along SR it will pass through by the course RQP 
it is evident that the angle between SR and the normal at R 
is equal to that between FQ and the normal at Q. Each of 
these is marked i. 

It is clear, then, that the incident ray PQ is parallel to the 
emergent ray RS, and therefore that the direction of the ray 
is not changed by passing through the plate, though it is 
laterally displaced by an amount depending on the thickness 
of the plate. 



Fig. 368. — Showing the course of 
a ray of light through a glass 
plate. 



TOTAL REFLECTION 



325 




Fio. 369.— Showing why, 
when viewed throujfh a 
glass plate, an object 
appears nearer. 



371. Vision Through a Plate. Let P be an object placed 
behind a glass plate and seen by an eye E 
(Fig. 3G9). The pencil of light will be 
refracted as shown in the figure, RE, TF 
being parallel to PQ, PS, respectively. 
The object appears to be at P', nearer to 
the eye than P is. 

This effect is well illustrated by laying 

a thick plate of glass over a printed page. 

It makes the print seem nearer the eye, and 

the plate appears thinner than it really is. 

Exercise. — Draw the waves as they pass from 
P to the eye. 

372. Total Reflection. Up to the present 

we have dealt mainly with the refraction 

of light from a medium such as air 

into one which is optically denser, such as water or glass. 

When we consider the light passing in the reverse direction 

we come upon a peculiar phenomenon. 

Let light spread out from the point P, under water 

(Fig. 370). The ray Pm, 
which falls perpendicularly 
upon the surface, emerges 
as mA, in the same line. 
The rays on each side are 
refracted as shown in the 
figure, but the ray PB upon 
refraction just skims along 

the surface. What becomes of a ray such as PC ? It cannot 

emerge into the air, and so it is refiiected back into the water. 

Moreover, since none of the light escapes into the air, it is 

totally reflected. 

It is evident that all rays beyond PB are totally reflected. 

Now the angle of incidence of the ray PB is PBii, which 




Fio. 370.— PB is the critical ray, and PBn (which 
is equal to BPm) is the critical angle for water 
and air. 



326 



REFRACTION 



is equal to BPm. Hence if the angle of incidence of any 
ray is greater than PBn it will suffer total reflection. This 
angle is called the critical angle which may be defined 
thus : — 

If a ray is travelling in any medium in such a direction 
that tJte emergent ray just grazes the surface of the onedium, 
the angle ivhich it makes with the normal is called the critical 
angle. 

373. Values of Critical Angles. It is evident that the 
denser or more refractiv^e a medium is, the smaller is its critical 
angle, and consequently the greater will be the amount of 
light totally reflected. The diamond is very refractive, and 
its brilliant sparkling is largely due to the great amount of 
total reflection within it. 

The values of the critical angles for some substances are 
approximately as follows : — 

Water 48^° Crown-glass . . .40i° Carbon Bisulphide . . 38° 

Alcohol . . . A7h Flint-glass 36| Diamond 2U 

374. Total Reflection Prisms. Let ABG (Fig. 371) be a 
A glass prism with well-polished faces, the 

angles A and B each being 45°, and C 
therefore 90°. If light enters as shown in 
the figure, the angle of incidence on the 
face AB is 45°, which is greater than the 
Fig. 371.— a total- Critical angle. It will therefore be totally 

"reflection prism. n , -i i • . 

reflected and pass out as 
indicated. Another form of total-reflecting 
prism is shown in Fig. 372 in which 
the angle B is 135°, A and G each 67|°. 
The course of the light is shown. Such 
arrangements are the most perfect reflectors 
known, and are frequently used in optical 
instruments. 





Fig. 372.— Another 
form of total-re- 
flection prism. 



COLLADON'S FOUNTAIN OF FIRE 



327 



This principle is also used in one form of the so-called 
' Lnxfer ' prisms, two patterns of 
which are shown in Fig. 373. 
They are firmly fastened in iron 
frames which are lot into the pave- 
ment. The sky-light enters from 
above, is reflected at the hypothenusal 
faces, and effectively illuminates the 
dark basement rooms. 




Fia. 373. — 'Luxfer' prisms, use- 
ful in lighting basements. 




375. Colladon's Fountain of Fire. Another beautiful illus- 

tration of total reflection is seen in the 
experiment known as Colladon's fountain. 
A reservoir A (Fig. 374), about one foot in 
diameter and three feet high, is filled with 
water. Near the bottom is an opening B, 
about I inch in diameter, from which the 
water spurts. A parallel beam of light from 
a lantern enters from behind, and by a lens 
C is converged to the opening 
from which the water escapes. 
Tlie li("-lit enters the falling 
water, and being incident at 
angles greater than the critical 
angle it is totally reflected from side to side. The light 
imprisoned within the jet 
gives the water the appear- 
ance of liquid fire. Coloured 
glasses may be inserted at D, 
and beautify the effect. 

376. Atmospheric Refrac- 
tion. As we ascend in the 
atmosphere its density gradually 
diminishes, and hence a ray of 

Ught on passing from one layer to another must gradually change 
its direction. Let the observer be at A (Fig. 375), and let AZ be the 



Fio. 374.— The 'fountain of fire.' The 
falling water seems to be on (ire. 




Fig. 375. — Showing how the atmosphere 
changes the apparent position of a heavenly 
body. 



328 



REFRACTION 



direction of the plumb-line. Z is then the observer's zenith, 
Tlie plane through A, at right angles to A^Z, is the horizon. A 
star at Z will appear in its proper direction since the light 
from it strikes the atmospheric strata perpendicularly and its 
direction is not altered. But the light from any other star, 
such as B, passes obliquely through the strata, and as it passes from 
the rarer to the denser, it will be curved downwards until, on arrival 
at .4, it will appear to come from B' . Thus this star will seem to be 
nearer the zenith than it really is. For a similar reason the body 
S — the sun, say — though actually below the horizon, appears to be 
at »S', above it. In this way the period of daylight is made, in our 
latitude, from four to eight minutes longer than it would be if there 
were no atmosphere. 

In all astronomical observations of the positions of the heavenly 
bodies allowance must be made for this change of direction due to 
refraction, but it may be remarked that the change is not nearly so 
great as is shown in the figure. 

377. Refraction Through Prisms. A prism, as used in 
optics, is a wedge-shaped portion of a refracting substance, 

contained between two plane faces. 
The angle between the faces is 
called the refracting angle, and 
the line in which the faces meet is 
the edge of the ijrism. 

In figure 376 is shown a section 
of a prism the refracting angle A 
of which is 60°, and PQRS is a ray of light passing through it. 
The ang-le D between the original direc- 
tion PQ and the final direction RS is the 
angle of deviation. The deviation is 
always atuay from the edge of the 
prism. 

By holding a prism in the path of a 
beam of light from the sun or from a 
projecting lantern one can easily exhibit 
the original and final directions of the 
light, and also the angle of deviation ; and by rotating the 




Fig. 376. 



-The path of light through a 
prism. 




Fio. 377.— The ray is deviated 
more when it passes unsym- 
inetrically through the prism. 



REFRACTION THROUGH PRISMS 329 

prism it will be found that there is one position in which this 
angle has a mininium value. This is the case when the 
angles of incidence and emergence of the ray are equal, or 
the ray passes symmetrically through the prism (see Fig. 376). 
In any other position of the prism, such as that shown in 
Fig. 377, the angle of deviation is greater. When a prism 
is used in an optical instrument it is almost invariably 
placed in the position of minimum deviation. 

QUESTIONS AND PROBLEMS 

1. If the index of refraction from air to diamond- is 2.47, what is the 
index from diamond to' air ? 

2. The index of refraction from air to water is f , and from air to crown- 
glass is f . If the velocity of light in air is 186,000 miles per second find 
the velocity in water and in crown-glass ; also the index of refraction from 
water to crown-glass. 

3. Explain the wavy appearance seen above hot bricks or rocks. 

4. A lighted candle is held in the beam of a projecting 
lantern. Explain the smoky appearance seen on the 
screen above the shadow of the candle. 




5. In spearing fish one must strike lower than the 
apparent place of the fish. Draw a figure to explain why. 

6. A strip of glass is laid over a line on a paper, (Fig. Fiq. 378.— Why does 
378). When observed obliquely the line appears broken. bJoken"f ^^^^^' 
Explain why this is so. 

7. The illumination of a room by daylight depends to a great extent 
on the amount of sky-light which can enter. Show why 
a plate of prism glass, having a section as shown in 
Fig. 379 placed in the upper portion of a window in a 
store on a narrow street is more effective in illuminating 
the store than ordinary plate-glass. 

8. Light passes from air into water, with an angle of 

incidence of 60°. By means of a carefully drawn figure 

Fig. 379. —The ^^^^^ ^ protractor find the angle of refraction (,« = 4)- 
plane face IS on '■ ° v< j/ 

9. The critical angle of a substance is 41°. By means 
of a drawing determine the index of refraction. 




CONVERGING. 



DIVEKGING. 



Double- 
convex. 



Plauo- Concavo- 
convex, convex. 



Double- 
concave. 



Piano- Convexo- 
concave, concave. 



CHAPTER XXXVIII 

Lenses 

378. Lenses. A lens is a portion of a transparent refracting 
medium bounded either by two curved surfaces or by one plane 
and one curved surface. 

Almost Mdthout exception the medium used is glass and the 
curved surfaces are portions of spheres. 

379. Kinds of Lenses. Lenses may be divided into two 
classes : 

(a) Convex or converging lenses, which are thicker at the 

centre than at the edge. 
(5) Concave or diverg- 
ing lenses, which are 
thinner at the centre 
than at the edge. 

In Fig. 380 are shown 
sections of different types 
of lenses. The concavo-convex lens is sometimes called a 
converging meniscus, and the convexo-concave a diverging 
meniscus. A meniscus is a crescent-shaped body. 

380. Principal Axis. The principal axis is the straight line 
joining the centres of the spherical surfaces bounding the lens, 
or if one surface is plane, it is the straight line drawn through 
the centre of the sphere and perpendicular to tlie plane surface. 

381. Action of a Lens. Let a pencil of rays parallel to the 

principal axis fall upon a convex lens (Fig. 381). That ray 

which passes along the principal 

axis meets the surfaces at right 

angles, and hence passes through 

without suffering any deviation. 

But all other ra^ys are bent from 

their original paths, the deviation 

being greater as we approach the edge 

330 



Fia. 380. — Lenses of different tj'pes. 




Fm. 381. 



Parallel rays converged to the 
principal focus F. 

The result is, the 



7v..-./::y-'-^f -^^ 



FOCAL LENGTH AND POWER OF A LENS 331 

rays are converged approximately to a point F on the principal 
axis. This point is called the 'principal focus, and in the 
case shown in the figure, since the 
rays actually pass through the point, 
it is a Teal focus. 

A parallel beam, after passing- 
through a concave lens (Fig. 382) is fio. 382.-In a diverRins the 
1 , . 1 ±1 J. i_i principal focus /•' is virtual. 

spread out in such a way tliat the rays 

appear to come from F, which is i\\Q principal focus and which, 

in this case, is evidently virtual. 

382. Focal Length and Power of a Lens. The focal length 
of a lens is the distance from the principal focus to the lens, 
or more accurately, to the centre of the lens. 

The more strongly converging or diverging a lens is, the 
shorter is its focal length and the greater is its power. Hence 
if / is the focal length and P the power of a lens, we have 

/ 
If a lens has a focal length of 1 metre its power is said to 
be 1 dioptre; if the focal length is | metre the power is 2 
dioptres ; and so on. Conversely, let us suppose a lens to 
have a power of 2.5 dioptres, we must have 

Focal length, / = - m. = 40 cm. 
" ■' 2.5 

In prescribing spectacles the oculist usually states ia 

dioptres the powers of the lenses required. 

383. Experimental Determination of Focal Length. By 

holding various lenses in sunlight or in a parallel beam from a 
projecting lantern, and shaking chalk-dust in the air, the 
nature of a lens can easily be observed. 

If it is convex the principal focus is easily found by moving 
a paper, or a ground-glass screen, back and forth in the light 
until the brightest and smallest image is found. Then simply 
measure the distance from it to the lens. 



332 



LENSES 



\m p Ja 




Fig. 383.— Finding the focal 
length of a concave lens. 



As -the focus of a concave lens is virtual the determination 
of its focal length is not so simple, but it may be found in the 
following way, which is similar to that used for a convex 
mirror (§ 357). 

Make two slits m, p in a circular disc {a, Fig. 383) of paper 
just large enough to cover the lens. 
Moisten the paper, stick it on the lens, 
and allow parallel rays to fall on the 
lens. Now move a screen back and 
forth until the two bright spots L, M, 
made by the light passing through 
the slits, are just twice as far apart 
as the slits in the paper disc ; that is, 
LM = 2 mp, and LN = 2 mA. 
Then the distance of the screen from the lens is equal to 
the focal length. 

From the figure it is evident that LFN and mFA are similar 

triangles, the former having just twice the linear dimensions of 

the latter. Hence F^^ = 2 FA, and therefore FA or f = AN. 

This is not a very good method ; a better one is described in 

the next section.* 

384. Combinations of Lenses. Since the action of a convex 
lens is opposite to that of a concave lens, one converging while 
the other diverges the light, if we call one positive we should 
call the other negative. Let us take the convex lens to be 
positive. 

Consider two converging 
lenses of focal lengths f\, fo and 
powers Pi, Po. Then P^ = 

. P., = — Let us put them 

close together (Fig. 384). Then 

the convergency produced by the tirst is increased by the 

* A third method is given in the Lahoratot); Manual designed to accompany this work. 




/} P, 



-Combination of two con- 
\ergin<' lenses. 



CONJUGATE FOCI 



333 



second, and the power of tlie combination is P^ + P.,- The 
focal length of the combination will be — — • 

Next, consider the combined action of a convex and a 
concave lens (Fig. 385). Let 
the numerical values of the 
powers be P^ Po. Then, since 
the concave lens divei'ges, while 
the convex converges, the power 
of the combination is P^ — P.,, 






Fio. 385.— Combination of a converging: 
and a diverging lens. 



and the focal length of the combination is 



P — P 



From this result we can deduce a method for finding the 

focal length of a concave lens. 

First, find the focal length of a convex lens ; let it be f^. 

Then place the concave lens beside the convex one and find 

the focal length of the combination ; let it be /. Then if f^ is 

the focal length of the concave lens, we have 

y- = Pj, the power of the convex lens, 

-J- = P.,, the power of the concave lens (numerically), 

-y = P, the power of the combination. 

Now P = P^ - P2, 

that is, -^ =~r —-r and therefore -r = 7~ - ~r' 
7/1/2 J 2 J I J 

In order to use this method the convex lens should be con- 
siderably more powerful than the concave one. 

For example, let the focal length of the convex lens be 20 cm., and that 
of the combination be 60 cm. 

Then y = -}o ~ tio = sV ^^^ f-2 = 30 cm. 

385. Conjugate Foci. («) Converging Lens. If the light 

is moving parallel to 
the principal axis 
and falls upon a 

Pig. 386.— P and P' are conjugate foci. „„ ^ 1 'i. • 

convex lens it is con- 
verged to the principal focus (Fig. 381). Next, let it emanate 



334 LENSES 

from a point P, on the j)rincipal axis (Fig. 386). The lens 
now converges it to the point P', also on the principal axis and 
farther from the lens than F. 

Again, let us consider the direction ^of the light as reversed, 
that is, let it start from P' and pass through the lens. It is 
evident that it will now converge to P. Hence P and P' are 
two points such that light coming from one is converged by 
the lens to the other. Such pairs of points are called con- 
jugate foci, as in the case of curved mirrors. 

As P is taken nearer the lens its conjugate focus P' moves 
farther from it. If P is at F, the principal focus, the rays 
leave the lens parallel to the principal axis (Fig. 387), and 
when P is closer to the lens than F (Fig. 388) the lens 






Fig. 387. — Light emanating from Fig. 388.— Here P' , the focus conjugate 

the principal focus comes from to P is virtual, 

the lens in parallel rays. 

converges the rays somewhat and they move off apparently 
from P' which in this case is a virtual focus. 

(6) Diverging Lens. In the case of a diverging lens, if the 
incident light is parallel to the principal axis it leaves the lens 
diverging from the principal focus F (Fig. 382). Let the light 





Fig. 389.— P' is conjugate to P. Fig. 390.— Conjugate foci in a diverging lens. 

start from the point P (Figs. 389, 390). The light is made 
still more divergent by the lens, and on emergence from it 



EXPLANATION BY MEANS OF WAVES 



335 



appears to move off from P' which is conjugate to P and is 
virtual. 



386. Explanation by Means of Waves. The theory 

light consists of waves easily accounts for the action of lenses. 
us suppose that waves of light 
travelling through the air pass 
through a glass lens. 



that 
Let 




Fig. 391.— Plane waves made spherical by 
a converging lens. 



In Fig. 391 plane waves (parallel 
rays) fall on the lens. Now their 
velocity in. glass is only | that in 
air, and that part of the waves 
which passes through the central 

part of the convex lens will be delayed behind that which traverses 
the lens near its edge, and the result is, tlie waves are concave on 
emerging from the lens. They continue moving onward, continually 
contracting, until they pass through F, the principal focus, and 
then they enlarge. 

In Fig. 392 spherical waves spread out from P. On traversing 
the central portions they are held back by the thicker part of the 




ii3i*-«i«ii 



Fig. 392. — Waves expanding- from P are changed by the lens into 
contracting spherical waves. 

lens, and on emerging they ai-e concave, but they do not converge 
as rapidly as in the first case. 

In Fig. 393 is shown the effect of 
a concave lens. The outer portions 
of the lens being thicker than the 
central, retard the waves most, with 
the result that the convexity of the 
waves is increased, so that they 
move off having P' as their centre. 

Fig. 393. -Waves going out from p are These results are further illus- 

niade more curved by the lens, and ..i- i-i- i ^ ,.ci 

appear to have P' as their centre. trated m a Stllkmg and beautltul 

manner by using an air lens in 
an ' atmosphere ' of water. Such a lens can be constructed without 
difficulty by cementing two ' watch-glasses ' into a turned wooden 




336 



LENSES. 




Fig. 394. — A concave air lens in an 
atmosphere of water converges 
the light. 



or ebonite rim. In Fig. 394 is shown a double-concave lens immersed 

in water contained in a tank with 
plate-glass sides. 

Plane waves from a lantern pass 
into the water, and on entering the 
lens the outer portions, since they 
travel in the air, rush forward ahead 
of the central part, thus rendering 
the waves concave and converging to 
a focus F. Thus a concave air lens in 
water is converging ; in a similar way 
it can be shown that a convex air lens 
in a water atmosphere is diverging. 

387. Experimental Illustrations. The relative positions of 
object and image can be easily exhibited experimentally, in a 
way similar to that used in the case of curved mirrors (§ 860). 

First place a convex lens on the table, and as far from it as 
possible set a candle. Then by moving a sheet of paper back 
and forth behind the lens the small bright image is found. 
Examine it closely and you will see that it is inverted. 

Now bring the candle slowly up towards the lens, at the 
same time moving the screen so as to keep the image on it. 
We find that the image gradually moves away from the lens, 
continually increasing in size as it does so. 

At a certain place the image is of the same size as the object, 
but inverted. By measurement we find that each is twice the 
focal length from the lens. 

Bring the candle still nearer to the lens. • The image retreats, 
and when the candle is at 
the principal focus the image 
is at an infinite distance, — 
the rays leave the lens par- 
allel to the principal axis. 

Finally, hold the candle 
between tlie principal focus 
and the lens ; no real image is formed (Fig. 388). 




FiQ. 395.— An optical bench, foi studying object 
and image. 



HOW TO LOCATE THE IMAGE 



337 




Fio. 39G.— Showing how to locate the iniajje of PQ. 



For making ineasurcnients of tlie distances of object and 
image from the lens the most convenient arrangtMiuMit is an 
optical bench, one form of wliieh is shown in Fig. 395. 

On using a concave lens we cannot obtain a real image of 
the object. If we view the candle through a concave lens we 
always see an erect image smaller than the candle, apparently 
between the lens and the candle. It is always virtual (see 
Figs. 389, 390). 

388. How to Locate the Image. Let PQ (Fig. 396) be an 
object placed before a 
convex lens A. The 
position of the image 
can be very easily 
located in the follow- 
ing way. 

From Q draw a ray parallel to the principal axis; on 
emerging from the lens it will pass through F, the principal 
focus. Again, the ray QA which passes through the centre of 
the lens is not changed in direction. Let it meet the former 
ray in Q. Then Q' will be the point on the image corres- 
ponding to Q on the object. Draw Q'P', perpendicular to the 
principal axis. This is the image of QP. Also, the ray QF\ 
which passes through tlie principal focus on the nearer side, 
will, after passing through the lens, proceed parallel to the 
principal axis and will pass through Q'. 

Q' The position of Q can al- 
wax's be located by drav^jing 
two of these three rays. 

In Fig. 397 is sliown the 

FiQ. 397.— How to draw the image when the . i • i j i i • . • 

object is between the lens and the principal CaSC lU WhlCh the ODjeCt IS 

between the lens and the 
principal focus. The rays drawn parallel to the axis and 
through the centre of the lens do not meet after passing 




338 



LENSES 




Fig. 398. 



-How to draw the image in a con- 
cave lens. 



througli the lens, but on producing them backwards they inter- 
sect at Q'. Q'P' is the image 
of QP. It is virtual, erect 
and larger than the object. 

For a concave lens we have 
the construction shown in Fig. 
398. The image is virtual, 

erect and smaller than the object. 

389. Magnification. On examining Figs. 396-8, it will be 
seen that the triangles QAP, Q'AP' are similar, and as before 
(I 862) calling the ratio of the length of the image to that of 
the object tlie magnification, we have 

-fi f _ ^ Q' ■^^' _ <listance of image from lens 
° FQ AF distance of object from lens 

390. Vision Through a Lens. In § 388 is explained a 
method of finding the position of an image produced by a lens 
but it should be remembered that this is simply a geometrical 
construction and that the rays shoAvn there are usually not 
those by which the eye sees the image. Let us draw the rays 
which actually enter the eye. 

In Fig. 399 P'Q' is the (real) image of PQ, and E is the eye. 

From Q' draw 

rays to fill the 

pupil of the eye. 

Then produce 

these backwards 

to meet the lens and finally join them to Q. Thus we obtain 

the pencil by which Q is seen. In tlie same way we trace the 

light from P to the eye. 

In Fig. 400 P'Q: is virtual, 
but the construction is the 
same as before. The student 
should draw other cases. The 

FiQ. 400. -The rays reach the eye by the .i,„J • oi,Tr.ilQi. +r. tlnf 

paths shown. mcthod IS suBilai to tnat 

explained for curved mirrors (§ 863\ 




^^^^ 



Fig. 399.— Showing the rays by which the eye sees the image of an 
object. 




CHAPTER XXXIX 

Dispersion, Colouii, the Spectrum, Spectp.um Analysis 



391. Another Refraction Phenomenon. In Cliap. XXXVII 
we liave explained various phenomena of refraction, but there 
is one, — a very important one, too, — which we have not 
discussed at all. When white light passes obliquely from one 
medium into another of different refractive power, the Hght is 
found, in the second medium, to be split up into parts which 
are of different colours. This separation or spreading out of 
the constituents of a beam of light is called dispersion. 

392. Newton's Experiment. Newton was the first to ex- 
amine in a really scientific way the dispersion produced by a 
prism, and Fig. 401 illustrates 
his method of experimenting. 
Ho admitted sunlight through a 
hole in a window-shutter, and 
placed a s^lass prism in the path 
of the beam. On the opposite 
wall, 18 1 feet from the prism, 
lie observed an oblong image, 
which had parallel sides and 
semi-circular ends, 2^ inches 
wide and 10| inches long. That end of the image farthest 
from the original direction of the light was violet, the other 
end red. 




G. 401.— Light enters through a hole in 
the window -shutter, passes through a 
prism and is received on the opposite 
wall. 



This image Newton called the spectrum. On careful 

inspection he thought he could recognize seven distinct 

colours, whicli he named in order : — red, orange, yellow, green, 

blue, indigo, violet. 

339 



840 



DISPERSION, COLOUR, SPECTRUM ANALYSIS 



It should be noted, however, that there are not seven 
separate coloured bands with definitely marked dividing lines 
between them. The adjoining colours blend into each other, 
and it is impossible to say where one ends and the next 
begins. Very often indigo is omitted from the list of colours, 
as not being distinct from blue and violet. 

From Newton's experiment we conclude : — 

(1) That white light is not simple but composite, that it 
includes constituents of many colours. 

(2) That these colours may be separated by passing the 
light through a prism. 

(3) That lights which differ in colour differ also in degrees 
of refrangibility, violet being refracted most and red least. 

It will now be understood why, in § 369, when giving the 
indices of refraction for various substances, it was necessajy 
to specify to what colour the values referred. 

393. A Pure Spectrum. It is often inconvenient to use 

sunlight for this experiment, 
and we may substitute for it 
the light from a projecting 
lantern. 

A suitable arrangement is 
illustrated in Fig. 402. The 
lioht emerges from a narrow 
vertical slit in the nozzle of 
the lantern, and then pas.ses 
through a converging lens, so 
placed that an image of the 
slit is produced as far away 

as is the screen on which we wish to have the spectrum. 

Then a prism is placed in the path, and the spectrum appears 

on the screen. 




Fig. 402.— Showing how to produce a pure 
spectrum. 



COLOURS OF NATURAL OBJECTS 341 

The spectrum thus produced in purer than that obtained by 
Newton's simple method. Imagine the round hole used by 
Newton to be divided up into narrow strips parallel to the 
edge of the prism. Each strip will produce a spectrum of its 
own, but the successive spectra overlap, and hence the colour 
produced at any place is a mixture of adjacent spectral colours. 
Thus to obtain a pure spectrum, that is, one in which the 
colours are not mixtures of several colours, we require a 
narrow slit as our source. In addition, the lens must be used 
to focus the image of the slit on the screen, and the prism 
should be placed in the position of minimum deviation (§ 377,). 

394. Colours of Natural Objects. Let us produce the 
spectrum on the screen by means of the projecting lamp ; we 
obtain all the colours as in a, iBi^^^B^^^B^^iH^^™— ■ 
Fig. 403. Next place over the " I i? j ,^^ ^^^^^! 
slit a red glass; the beam now ^|MM||^^^^^H^H^H 
transmitted consists mainly of 

, ,. , . T, .1 1 Fig. 403.— a red glass transmits only red 

red liglit, a little orange perhaps and some orange. 

being present (h, Fig. 403). The glass does not owe its colour 
to the introduction of anything into the spectrum which did 
not previously exist there, but simply because it absorbs or 
suppresses all but the red and a little orange. We obtain 
similar results with green, yellow, or other colours. It is to 
be noted, however, that scarcely any of the transmitted colours 
are pure. Several colours will usually be found present, the 
predominating one giving its colour to the glass. 

Next hold a bit of red paper or ribbon in different portions 
of the spectrum. In the red it appears of its natural colour, 
but in every other portion it looks black. This tells us that a 
red object appears red because it absorbs the light of all other 
colours, reflecting or scattering only the red. In order to 
produce this absorption and scattering, however, the light 
must penetrate some distance into the object ; it is not a 
simple surface effect. Similarly with green, or blue, or violet 



342 DISPERSION, COLOUR, SPECTRUM ANALYSIS 

ribbons, but, as in the case of the coloured glass, the colours 
will usually be far from pure. Thus a blue ribbon will 
ordinarily reflect some of the violet and the green, though it 
will probably appear quite black in the red light. 

Let us think for a moment what happens when sunlight 
falls on various natural objects. The rose and the poppy 
appear red because they reflect mainly red light, absorbing the 
more refrangible colours of the spectrum. Leaves and grass 
appear green because they contain a green colouring matter 
(chlorophyll) which is able largely to absorb the red, blue and 
violet, the sum of the remainder being a somewhat yellowish 
green. A lily appears white because it reflects all the com- 
ponent colours of white light. When illuminated by red light 
it appears red ; by blue, blue. 

A striking way to exhibit this absorption eflfect is by using 
a strong sodium flame in a well-darkened room. This light is 
of a pure yellow, and bodies of all other colours appear black. 
The flesh tints are entirely absent from the face and hands, 
which, on this account, present a ghastly appearance. 

We see, then, that the colour which a body exhibits depends 
not only on the nature of the body itself, but also upon the 
nature of the light by which it is seen. 

At sunrise and sunset the sun and the bright clouds near it 
take on gorgeous red and golden tints. These are due chiefly 
to absorption. At such times the sun's rays, in order to reach 
us, have to traverse a greater thickness of the earth's atmos- 
phere than they do when the sun is overhead (compare Fig. 
375), and the shorter light-waves, which form the blue end of 
the spectrum, are more absorbed than the red and yellow, 
which tints therefore predominate. 

In § 195 reference was made to the stupendous volcanic 
eruption at Krakatoa in 1883. For many weeks after this 
the atmosphere was filled with dust, and sunsets of extra- 
ordinary magnificence were observed all over the world. 



RECO IMPOSITION OF WHITE LIGHT 



343 




Fig. 404.— The second prism 
counteracts the first. 



Somewhat similar absorption effects are produced in the 
neighbourhood of great forest fires, the ashes from which are 
conveyed by winds over considerable areas. 

395. Recomposition of White Light. We have considered 
the decomposition of white hght into its constituents ; let us 
now explain several ways of performing the reverse operation 
of recoinbining the various spectrum colours in order to obtain 
white light. 

(1) If two similar prisms be placed as shown in Fig. 404, 
the second prism simply reverses the 
action of the first and restores white 
light. The two prisms, indeed, act 
like a thick plate (§ 370). 

(2) By means of a large convex 
lens, preferably a cylindrical one (a tall beaker filled with 
water answers well), the light dispersed by the prism may be 
converged and united again. The image, when properly 
focussed, will be white. 

(3) Next, we may allow the dispersed light to fall upon 

several small plane mir- 
rors, and then by adjusting 
these properly the various 
colours may be reflected to 
one place on the screen, 
which then appears white 
(Fig. 405). 

In place of the several 
small mirrors we may ad- 
vantageously use a single 
strip of thin plate glass 
(German mirror), say 2 feet long by 4 inches wide. First, 
hold this in the path of the dispersed light so as to reflect it 




Fig. 405.— The light after passing through the 
prism falls on several small mirrors which 
reflect it to one place on the screen. 



344 



DISPERSION, COLOUE, SPECTRUM ANALYSIS 



upon the opposite wall of the room. Then, by taking hold of 
the two ends of the strip, gently bend it until it becomes 
concave enough to converge the various coloured rays to a 
spot on the screen. 

(4) In all the above cases the coloured lights are mixed 
together outside the eye. Each colour gives rise to a colour- 
sensation, and a method will now be explained whereby the 
various colour-sensations are combined within the eye. The 
most convenient method is by means of Newton's disc, which 
consists of a circular disc of cardboard on which are pasted 
sectors of coloured paper, the tints and sizes of the sectors 
being chosen so as to correspond as nearly as possible to the 
coloured bands of the spectrum. 

Now put the disc on a whirling machine (Fig. 406) and set 
it in rapid rotation. It appears white, or 
whitish-gray. This is explained as follows :— 
Luminous impressions on the retina do not 
vanish instantly when the source which ex- 
cites the sensation is removed. The average 
duration of the impression is ^-^ second, but it 
varies with different people and with the 
intensity of the impression. If one looks 
closely at an incandescent electric lamp for 
some time, and then closes his eyes, the 
impression will stay for some time, per- 
With an intense light it will last longer 




Fio. 406.— Newton's 
disc on a rotating 
machine. 



haps 
still. 



a minute. 



If a live coal on the end of a stick is whirled about, it 
appears as a luminous circle ; and the bright streak in the sky 
produced by a " shooting star " or by a rising rocket is due to 
this persistence of luminous impressions. In the same way, 
we cannot detect the individual spokes of a rapidly rotating 
wheel, but if illuminated by an electric spark we see them 



COMPLEMENTARY COLOURS 345 

distinctly. Tlie duration of the spark is so short that the 
wheel does not move appreciably while it is illuminated. 

In the familiar " moving pictures " the intervals between 
the successive pictures are about -^-5- second, and the continuity 
of the motion is perfect. 

If then the disc is rotated with sufficient rapidity the 
impression produced by one colour does not vanish before 
those produced by other colours are received on the same 
portion of the retina. In this way the impressions from all 
colours are present on the retina at the same time, and they 
make the disc appear of a uniform whitish-gray. This gray 
is a mixture of white and black, no colour being present, and 
the stroncjer the liirht fallincr on the disc the more nearly does 
it approach pure white, 

396. Complementary Colours. Let us cut out of black 
cardboard a disc of the shape shown in Fig. 407, and fasten it 
on the axis of the whirling machine over the 
Newton's disc so that it just hides the red 
sectors. On rotating, the colours which are 
exposed produce a bluish-green. It is evident, 
then, that this colour and red when added 
too;ether will o-ive white. Any two colours Fia 407.-Disc to 

» o ^ 1/ put over Newton 3 

which by their union produce %vJdte light ai'c deslreVco^our'^"^ 
called coinplevrientary. From the way it was 
produced we know that this blue-green is not a pure colour, 
but the eye cannot distinguish it from a blue-green of the 
same tint chosen from a pure spectrum. By covering over 
other colours of the Newton's disc we can obtain other com- 
plementary pairs. A few of these pairs are given in the 
following table : — 

COMPLEMETARY COLOURS 



and fasten it 

(D 



Red 

Green-blue 



Orange 
Bluish-wreen 



Yellow 
Blue 



Green-yellow 

Violet 



Green 
Purple 



346 



DISPERSION, COLOUR, SPECTRUM ANALYSIS 




Fig. 40S.— The radially 
opposite colours are 
complementary. 




Fig. 409.— a com- 
plementary colour 
disc. 



In Fig. 408 these are arranged about a circle. Note that 
the complement of green is purple, which 
is not a simple spectral colour but a 
compound of red and violet. 

397. Mixture of Pigments. On rotating 
a disc with yellow and blue sectors,* as 
indicated in Fig. 409, we obtain white. 
On the other hand, if we mix together 
yellow and blue pigments we get a green 
pigment. Wherein is the difference ? It arises 
from the fact that the mixing of coloured 
liglits is a true addition of the separate effects, 
while in mixing pigments there is a subtraction 
or absorption of the constituents of the light 
which falls on them. 

Ordinarily blue paint absorbs the red and the 
yellow from the incident light, reflecting the blue and some of 
the adjacent colours, namely green and violet. Yellow paint 
absorbs all but the yellow and some red and green. Hence 
when yellow and blue paints are mixed the only coloured 
constituent of the incident light which is not absorbed is 
green, and so the resulting effect is green. 

Thus mixing pigments and mixing colours are processes 
entirely unlike in nature, and we should not be surprised if the 
results produced are quite dissimilar. Indeed the result obtained 
on mixing two j)iginents does not even suggest what will happen 
when two coloured lights of the same name are' added together. 

398. Achromatic Lenses. The focal length of a lens depends 
on the index of refraction of tlie material from which the lens is 
made, and as the index varies with the wave-length, or the colour, 
the focal length is not the same for all colours. 

As the violet rays are refracted more than tlie red, the focal 
length for violet is shorter than for red. Thus, in Fig. 410, the 

* We might use a single sector of blue and one of yellow but the speed of rotation would 
then have to be doubled. 



ACHROMATIC LENSES 



347 




Fio. 410.— The foci for violet and red 
rays are quite separated. 



violet rays come to a focus at V while the red converge to Ji, the 
foci for the other colours lying between 
V and /('. A screen held at A will 
show a- circular patch of light edged 
with red, while if at B it will show a 
patch edged with violet. This inability 
to converge all the constituents of a 
beam of white light to a single point 
is a serious defect in single lenses, 
and is known as chromatic aberration. 

Thus there is no single point to which all the light converges, and 
in determining the principal focus it is usual to find the focus for 
the yellow rays, which are brightest. 

Newton endeavoured to devise a combination of lenses which 
would be free from chromatic aberration, but he failed. He con- 
cluded that if a second lens counteracted the dispersion of the first 

it would also counteract its re- 
fraction or bending of the rays, 
in which case the two lenses 
would not act as a lens any 
longer. In this he was mistaken, 
however. In 1757 Dollond, a 
London optician, discovered a 
combination of lenses which was 
free from chromatic aberration. The arrangement is shown in Fig. 
411. Flint-glass is more dispersive than crown-glass, and a crown- 
glass converging lens is combined 
with a flint-glass diverging lens 
of less power. The crown-glass 
lens would converge the red rays 
to R and the violet to F, wliile 
the flint-glass then diverges both 
of these so that they come to- 
gether at F. 

Such compound lenses are said 
to be achromatic. They are used 
in the construction of all tele- 
scopes and microscopes. In the 
modern microscope objective, 
however, the simple combination of two lenses does not suffice to 
give an image perfectly free from all defects, and many other 
combinations are used. In some high-power objectives there are 
as many as ten single lenses, made of various kinds of glass and 
having surfaces of various curvatures. (Fig. 412.) 




-An achromatic combination of 

lenses. 




Fio. 412. — A section of an apochromatic 
microscope objective made by Zeiss. 



348 



DISPERSION, COLOUR, SPECTRUM ANALYSIS 




399. The Rainbow. In the rainbow we have a solar spectrum 
on a grand scale. It is produced through the refraction and disper- 
sion of sunlight by 
rain-drops. In order 
to see it the observer 
must look towards 
falling rain, with the 
sun behind him and 
not more than 42° 
above the horizon. 
Frequently two liows 
are visible, the^;rim- 
ary bow and the 
secondary bow. The 
former is violet on 

Fig. 413.— Illustrating how the rainbow 18 produced. ^\^q inside and red 

on the outside ; while in the secondary bow which is larger and fainter, 
the order of the colours is reversed. Both bows are arcs of circles 
having a common centre (C, Fig. 413), which is on the line which 
passes through the sun and the eye of the observer. 

A line drawn from the eye to the primary bow makes an angle 
of about 41° with this line, while a line to the secondary bow makes 
an angle of about 52° with it. 

In Fig. 413 is shown. the relative positions of the sun, the rain- 
drops and the ob- 
server, while in Figs. 
414, 41.5 is shown 
the manner in which 
the sun's rays pass 
through the drops. 
For the primary bow 
the rays are refracted 

into the drop at A (Fig. 414), reflected at B, 
and refracted out at G. For the secondary, 
the light enters at A (Fig. 415), is reflected first at B and then at 
C and is refracted out at i).* 

400. The Spectroscope. In § 393 a method was explained 
for projecting a pure spectrum upon the screen. This can be 
done when the source is very bright (sucli as the sun, the arc- 
lamp or the lime-light), but for a faint light the method is not 
practicable. It is necessary to receive the light, after disper- 

*For further information more advanced works must be consulted. 





Fig. 4U.— Showing how the 
light passes to form the 
primary bow. 



Fig. 415.— Showing how the light 
passes to form the secondary 
(outer) bow. 



THE SPECTPvOSCOPE 



349 



R 



sioii, directly into the eye, wliicli is marv^ellously sonsitix'e, or 
ou a pliotourapliic plate. 

The simplest method of all is ilhisti'alefl in Fio-. 4I(>, in 
wliicli >S' is a slit y\j- or -}j^ inch wide in a- sheet of metal, and 
beliind it is placed L the source of ■ .y 

light to be examined. This may 
be a Buusen or alcohol flame (which 
are themselves colourless), in which 
substances are burnt, or any other 
convenient source. The experi- 
menter then stands at a distance 
of 10 feet or more from the slit 
and observes it through a prism 
which is held near the eye. The spectrum will appear directly 
ahead, as at VR. In tliis arrangement the liglit comes from 
the slit to the prism in a narrow parallel beam, and tlie lens 
of the eye focusses it upon the retina. 




Fio. 41C. — A simple method of pro- 
fluoirif^ a pure spectrum. L ia the 
light source behind a slit S, and SP 
ia about 10 feet. 




Fia. 417. — A sing^leprism spectroscope. 



Fig. 418 —A horizontal section of a 
sing-le-prism spectroscope. 



If a small telescope is placed between tlio prism and the 
eye, and focussed on the slit, the spectrum will be seen to 
better advantage. 

But the most satisfactory method is to use a spectroscope, 
which is an instrument especially designed to examine the 
spectra of various sources. A simple form is illustrated in 
Fig. 417 and a sectional plan is given in Fig. 418. The tube 



350 DISPERSION, COLOUR, SPECTRUM ANALYSIS 

C, known as the collimator, has a slit S at one end and a lens 
L at the other. The slit is at the focus of the lens, so that the 
light emerging from the tube is a parallel beam. It then 
passes through the prism P, and is received in a telescope T, 
the lens of which focusses the spectrum in the plane ah. It 
is then viewed by the eye-piece E. 

The light to be examined is jDlaced before 8. Usually a 
third tube R, is added. This has a small transparent scale vi 
at one end and a lens at the other. A lamp is placed before 
the scale, and the light passes through the tube, is reflected 
from a face of the prism and then enters the telescope, an 
image of the scale being produced at ah, above the spectrum. 
By referring to this scale any j)eculiarities of the spectrum of the 
light which is under examination can be localized or identified. 

401. Direct-vision Spectroscope. By using three prisms, 
one of flint and two of crown-glass (Fig. 419), it is possible to 

get rid of the deviation of 

^ ^-_z-:-^ ^^JL/XL j ^^^ ^^^® middle rays of the spec- 

■^i V \ ^ ^ J l ^ trum while still dispersing 

the colours. Such a com- 
bination is used in pocket 
spectroscopes. The slit S admits the light and a convex lens 
converts the light into a parallel beam, which, after traver- 
sing the prisms, is seen by the eye at JE. One tube can be 
slid over the other in order to focus the slit for the eye. 

402. Kinds of Spectra. By means of our spectroscope let us 
investigate the nature of the spectra given by various sources of light. 

First, take an electric light. It gives a continuous coloured 
band, extending from red to violet without a break. A gas-flame, 
an oil lamp or the lime-light gives a precisely similar spectrum. 

Next, place a colourless Bunsen or alcohol flame before the slit, 
and in it burn some salt of sodium, (chloride or carbonate of sodium, 
for instance). The flame is now bright yellow, and the spectrum 
shown in the spectroscope is a single bright yellow line.* Using 

* There are really two narrow lines very close together, which can be seen even with some 
pocket spectroscopes. 



Fig. 419. — A direct-vision spectroscope. 



SPECTRUM ANALYSIS 



351 



sbroiitiuiii nitrate tlio flaino is ei-iinsoii, and the spectrum consists of 
several red and orange lines and a blue one. The salts of barium, 
potassium and other metals give similar results, each however with 
its own particular arrangement of lines. 

Again, place an electric lamp before the slit of tlie instrument, 
and then between it and the slit place a vessel with plate-glass sides 
containing a dilute solution of permanganate of potash. The 
spectrum is now continuous except that it is crossed by fine dark 
bands in the green. Using a dilute solution of human blood we 
get a continuous spectrum except for well-marked dark bands in the 
yellow and tlie green. 

After long experimenting on light sources of various kinds we 
have been led to divide spectra into three classes : — 

(1) Continuous Spectra. In these there is present light of every 
shade of colour from the red to the violet, with no gaps whatever in the 
band. Such spectra are obtained from all white-hot solids or liquids 
(molten metals for instance), and from gases under great pressure. 
The flame of gas or of a candle gives a continuous spectrum. This 
is due to the white-hot particles of carbon present. These may be 
collected by holding a piece of cold glass or porcelain over the flame. 

(2) Discontinuous or Bright-line Spectra. These consist of 

bright lines on a dark background, and are given by glowing vapours 

and by gases under smaller pressure. The gas is 

generally enclosed in a glass tube such as is shown in 

Fig. 4"20, the pressure being a few millimetres of 

mercury, and the tube being rendered luminous by 

an induction coil (§ 535). 

(3) Absorption or Dark-line Spectra. These 

are just the reverse of those in class 2. Usually all 
the colours are present but the continuity is broken 
by dark bands, sometimes narrow and well-defined, 
at other times wide and diffuse. The background is 
bright and the distinctive lines or bands across it are 
dark. Such spectra are given by the sun, the moon, 
the planets and by the stars. 

403, Spectrum Analysis. Now each element, 
when in the form of a vapour, has its own peculiar 
spectrum, the arrangement of the bright lines in no 
two spectra being exactly alike. Hence by means of 
its spectrum the presence of a substance can be recog- 
nized. If several elements are present their spectra will all be shown 
and the elements can be thus recoarnized. This method of detecting 



Fro. 420.— A tube 
for holding a gas 
to be examined 
by the spectro- 
scope. 



352 DISPERSION, COLOUR, SPECTRUM ANALYSIS 

the presence of aii elenieiib is known as spectrum analysis. It is an 
extremely sensitive method of analysis. Thus the presence of ^^^^j 
nig. of barium, of eooWiJ ™o- ^^ Hthiiun, or of ttothjooo ™g- ^^ sodium 
is sufficient to show the lines characteristic of these elements. This 
method enables the chemist to apply a delicate test for the presence 
of a substance, and by it the astronomer has wonderfully extended 
our knowledge of the nature and the motions of the heavenly bodies. 

404. The Solar Spectrum. In 1802, Wollaston, a London 
physician, while examining the sunlight by means of a pri.sm, 
observed /our dark lines across its spectrum. Some years later, 
Fraunhofer, a scientific optician of Munich, using a prism and 
telescope* (the second method described in §400), discovered not 

just four but a multitude 
AaBC D Eb F G H ^ of dark lines. With great 

care and skill he mapped 
over 500 of these dark 



JL=. 



1 



Red Orange Yellow Green Blue Indigo miel lines, naming the chief 

ones after the first letters 

Fia. 421.— Showing some of the 'dark lines' in the of the alpliabet. A, a, 
spectrum of sunlight. ^^ ^,^ ^^ ^^ ^^ ^^ g^ jj 

(Fig. 421); but they are often called Fraunhofer' s lines. They 
always have the same position in the spectrum, and are convenient 
'landmarks' from which to make measurements. 

Thus we see that the solar spectrum is ni\ absorption spectrum, 
the dark lines being numerous and fine. Photographs have revealed 
the existence of at least 20,000 of these lines. 

405. The Meaning- of the Dark Lines. It was long felt that 

the interpretation of these dark lines was a matter of great import- 
ance, and the mystery was at last solved in 1859 by Kirchhoff". 

In the orange-yellow of the solar spectrum is a prominent dark 
line, — or rather a pair of lines very close together, — named D by 
Fraunhofer. Now sodium vapour shows two fine bright yellow 
lines, which, by reference to the scale of our spectroscope, we see 
coincide in position with the solar D dark lines. Indeed, by means 
of a srpall total-reflection prism with which the slit-end of the 
spectroscope is usually supplied, it is possible to observe the spectrum 
of the sun and of sodium vapour at the same time, one spectrum 
being above the other, and by this arrangement the coincidence in 
position is seen to be exact. From this result we would at once 
suspect that the D lines in the sun must have some connection with 
.sodium. 

♦Fraunhofer (1787-1820) constructed hia own prism and telescope, and engraved his own 
spectrum maps when he published his investigations in 1815. 



THE MEANING OF THE DARK LINES 353 

Just what this connection is may he shown in the following way. 
First place before tlie slit of the spectroscope an intense source of 
light, such as the arc or the lime-light. This gives a continuous 
spectrum with no dark lines at all. Now, while observing this, 
introduce between the intense source and the slit a Bunsen flame 
full of sodium vapour. This addition of yellow light we would 
naturally expect to make the yellow portion of our spectrum more 
intense, but that is not what happens at all ! On the contrary, we 
see two dark absorption lines in precisely the position where the 
bright sodium lines are produced. By screening off the intense 
source the bright sodium lines are seen. 

A simple method of performing this experiment is shown in 
Fig. 422. Here the origin of the light is an arc lamp. In order 
to obtain sodium vapour one end of a wire is made into a ring, 
about which asbestos wick is wrapped, while the other end is coiled 
so as to fit over a Bunsen burner. The asbestos is dipped in a 
strong solution of common salt and allowed to dry. When placed 
in position on the burner it gives a strong yellow flame. Metallic 
sodium burned on a platinum spoon in the flame gives an even 
intenser yellow flame. The eye is placed behind a simple direct- 
vision spectroscope (§ 401). 

We thus see that when light from an intense source passes 
through the (cooler) sodium vapour those rays are absorbed by the 
vapour which it, itself, » 

emits. The rest of the \\ /<- A J L „ t~^. 

continuous spectrum is -^<^^ "'"' ' L — .^^....^ iii' 

unaffected by the sodium ^ 
vapour. 

We conclude that the 
dark D lines in the sun's 

spectrum are due to the Fio. 422. -Light from the arc lamp passes through sodium 

fact that the li^ht which vapour in the Bunsen flame and is then examined by the 

, , , ,f spectroscope. A dark band in the yellow is seen. 

would naturally appear 

where they are has been absorbed by sodium vapour, and at once 

we obtain evidence of the constitution of the sun. 

The inner portion of the sun is inten.sely hot and undoubtedly 
emits light of all colours or wave-lengths, which would produce a 
perfectly continuous spectrum. On coming through the vapours of 
elements which are in the solar atmosphere the light is robbed of 
some of its constituents, and the absence of these is shown by the 
dark lines. Thus we believe sodium to exist in the sun's atmosphere. 

By comparing the positions of the dark solar lines with the 
positions of bright lines obtained by vaporizing various substances 




854 DISPERSION, COLOUR, SPECTRUM ANALYSIS 

in our laboratories, it lias been sliown that sodium, iron, calcium, 
hydrogen, silver, titanium and about 30 more elements with which 
we are acquainted certainly exist in the sun. Others will probably 
be recognized. In the. case of the gas helium the order of its 
discovery was reversed. For many years a remarkably intense line 
in the spectrum of the outf-r portion (the chromosphere) of the sun 
had been observed, and as it did not correspond to any known 
substance on the earth it was provisionally said to be dne to helium^ 
which means "solar substance."* In 1895, however, the chemist 
Ramsay discovered the long-sought substance in a rare mineral 
called cleveite. 

The dark lines in the spectra of the moon and the planets are the 
same as those in the sun, showing that these bodies shine by 
reflected sunlight. In recent times the spectroscope has been 
applied to the stars. These are self-luminous bodies like our sun, 
and many terrestrial substances have been recognized in them. 
Thus the spectroscope reveals a wonderful unity in the entire 
universe. It is believed, also, that we can trace in the spectra of 
the stars the course of their formation, development and decay, — in 
other words, their life-history. 

406. Effect of Motion of the Radiating Body. As explained 

in § 235, if a body which is emitting waves of any kind is in motion 
towards or away from the observer the wave-length of the radiation 
is thereby shortened or lengthened. 

Now light is a wave-motion. Hence if a star is approaching us 
the lines in its spectrum will appear to be displaced towards the 
blue end ; if it is receding from us the lines are displaced towards 
the red end. The actual displacements of the lines measured on the 
photographs of the star's spectrum, are extremely small, but by 
utilizing especially adapted instruments, and exercising great care 
the motions of many -of the stars relative to our solar system have 
been determined with considerable accuracy. For' instance it has 
been found that the pole star is approaching us at the rate of 1 6 miles 
per second, while Capella'is receding from us at 15 miles per second. 

Many other wonderful results have been deduced through the 
same principle. Campbell, of the Lick Observatory (on Mt. 
Hamilton, California), has shown that our entire solar system is 
moving through space, almost towards the bright star Vega, at the 
rate of about 12 miles per second. It may be remarked, however, 
that though we move at this great rate continually towards this star 
we shall require 310,000 years to make the journey thither.f 

•Greek ffeZtos = sun. 

t Light requires 20 years to come from Vega to us. 



EFFECT OF MOTIOX OF THE RADIATING BODY 355 

QUESTIONS AND PROBLEMS 

1. A ribl)oii purchased in daylight appeared 1)hie, l)ut wlien .seen by 
gas-light it looked greenish. Explain this. 

2. One piece of ghiss api)ears dark red and ancither dark green. On 
holding them together you cannot see through them at all. Why ia this? 

3. Where would you hjok for a rainbow in the evening ? At Avhat time 
can one see the longest bow ? Under what circumstances covdd one see 
tlie bow as a complete circle ? 

4. An achromatic lens is composed of a converging lens of focal length 
10 cm. and a diverging lens of focal length 15 cm. What is the focal 
lengtli of the combination ? (§ 384.) 

5. On observing the spectrum of sodium vapour in a spectroscope two 
fine lines are seen close together. What will be the effect of widening 
the slit? 



CHAPTER XL 
Optical Instruments 




Choroi 
OpticNerve'M 



Sclerotic 



Fio. 423. — Horizontal section of a right 
eye. ^./i., aciueous humour ; 1'.,?., 
yellow spot ; B.S., blind spot. 



407. The Eye. The mo.st important as well as the most 
wonderful of optical instruments is the human eye. In form it is 
Cornea almost spherical (Fig. 423). The 

horny outer covering, the " white of 
the eye," is called the sclerotic coat. 
The front portion of this protrudes 
like a watch face and is called the 
cornea. Within the sclerotic is the 
choroid coat, and within this, again, 
is the retina. 

The portion of the choroid coat 
visible through the cornea is called 
the iris. This forms an opaque cir- 
cular diaphragm, which is variously 
coloured in different eyes. The apei*- 
ture in it is called the 2^^^pii, and the 
size of the pupil alters involuntarily 
to suit the amount of light which enters the eye. When the light 
is feeble the pupil is large. On passing from darkness into a 
brilliantly-lighted room the eye is at first dazzled, but the pupil 
soon contracts and keeps out the excessive supply of light. 

Behind the pupil is the double-convex crystalline lens. The radii 
of curvature of its front and back surfaces are about 1 1 and 8 mm., 
respectively ; but by means of the muscles attached to the edge of 
the lens, the curvature of its faces, and hence its converging power, 
can be changed at will. 

The portion of the eye between the lens and the cornea is filled 
with a watery fluid called the aqueous humour, while between the 
lens and the retina is a transparent jelly-like substance called the 
vitreous humour. 

The retina is a semi-transparent network of nerve-fibres formed 
by the spreading out of the termination of the optic nerve. Near 
the centre of the retina is a small round depression known as the 
yellow spot, and vision is most distinct if the image of the object 

356 



THE IMAGE ON THE RETINA— ACCOMMODATION 



357 



looked at is formed at this place. When one desires to see an 
object he turns his head until the image comes on the yellow spot. 
About 2|- mm. from the yellow spot, towards the nose, is the blind 
spot, which is the place where the optic nerve enters the eye. This 
spot is insensitive to light. 

The existence of this blind spot can easily be shown experi- 
mentally. On a piece of paper make a cross X and about 4 inches 
to the right of it make a circle O. Now cover the left eye, and 
while looking intently on the X, vary the distance of the paper from 
the eye. At a certain distance (7 or 8 inches) from the eye the O 
will be invisible, while at a gi-eater or less distance it will be seen. 
It becomes invisible when its image falls on the blind spot, the 
image of the X being kept on the yellow spot all the time. 

408. The Image on the Retina. The eye as a whole acts like 
a converging lens. It forms on the 
retina an inverted real image of the 
object before it. The fact that it is 
inverted can be shown in the following 
way. 

Look at the sky through a pin-hole 
in a visiting card held about an inch 
from the eye, and then hold a pin-head 
between the eye and the small illumi- 
nated aperture and as near to the eye 
as possible (Fig. 424). It is clear that 
in this case the image* on the retina is 
erect, and yet it seems to be inverted. 
This shows that the brain recognizes 
as the highest part of an object that 
which gives rise to the lowest part of 
the image on the retina. 

409. Accommodation. The eye when at rrst is adjusted so 
that parallel rays entering it are focussed on the retina, that is, it is 
adjusted for viewing distant objects. Under these circumstances 
light from an object near at hand would be brought to a focus 
behind the retina (§§387, 388). But when we wish to see an object 
close at hand we involuntarily alter the curvature of the surfaces — 
chiefly the forward surface — of the crystalline lens, making it more 
convex, so that the image is brought upon the retina and we see it 
distinctly. This alteration of the converging power of the eye to 
adapt itself for near or distant objects is known as accommodation. 

* It is not a true image, but a shadow cast upon the retina. 




Fig. 424.- How to show that the 
image on the retina is inverted. 



358 OPTICAL INSTRUMENTS 

In order to see an object distinctly we naturally bring it near to 
the eye. As it approaches, our vision of it improves until it gets 
within a certain distance, and then we have to strain tlie eye to see 
it clearly, and when it gets too close the image is blurred. The 
shortest distance from the e\'e at which distinct vision can be 
oVjtained without straining the eye is known as the least distance of 
distinct vision. This distance for persons of normal vision is from 
25 to 30 cm. (10 to 12 inches). 

The magnifying power of an optical instrument depends on this 
quantity, and in calculating the magnification it is taken as 25 cm. 
or 10 inches, although as a matter of fact it is quite variable with 
different eyes. 

410. Why we have Two Eyes. The images of a solid object, 

formed on the retinas of the two eyes, are not identical. On account 
of the distance between the eyes the right eye can see somewhat 
more of the right side of an oljject than is visible to the left 
eye. Thus we obtain an idea of the depth of the object. 

The effect of depth or solidity to a picture is given by the stereoscope. 
Two photographs, taken from slightly different points of view, are 

mounted side by side, and are then viewed in the 

^..„_ stereoscope. In this instrument there are two por- 

!', tions of a convex lens, or a kind of prismatic lens, 

fSi placed with the edges toward each other (Fig. 425). 
Each lens gives an enlarged view of the picture, as 
in the simple microscope C§ 414), and the instru- 
ment is adjusted until these are produced on 
corresponding portions of the retinas of the two 
^ eyes. Under these circumstances they are seen as 
k one, with the same effect as is obtained with the 
'^ two eyes. The picture is no longer a flat lifeless 
^Btereosco^^'^^ ^bing, but the various objects in it stand out in 
relief. 

411. Defects of the Eyes. A person possessing normal vision 
can see distinctly objects at all distances varying from 8 or 10 inches 
up to infinity. But, as we well know, there are many eyes with 
defects, the chief of which are short-sightedness, long-sightedness, and 
astigmatism. 

A short-sighted eye cannot see objects at any considerable distance 
from the eye. The image of an object near at hand is produced on 
the_ retina, but the eye cannot accommodate itself for one farther off. 
In such a case the imajre is formed in front of the retina, and to the 



THE PHOTOGRAPHIC CAMERA 



359 




Fig. 426. — In a short-sighted eye parallel rays converge 
to a poitit before the retina; in a long-sighted eye, 
behind the retina. 



observer it appears blurred. In a short-sigbted eye tlie lens is too 
strongly convergent, and in order to remedy this we must use spec- 
tacles producing the opposite effect, that is having diverging lenses. 
A long-sighted eye, in its passive condition, brings parallel rays of 
light to a focus behind the rethia. Such an eye can accommodate 
itself for distant objects, 
bringing the image for- 
ward to the retina ; but 
for near oljjects its power 
of accommodation is not 
sufficient. In this case the 
crystalline lens is not con- 
verging enough, and in 
order to assist it spectacles 
with converging lenses 
should be used. As a person grows older there is usually a loss of 
the power of accommodation, and the eye becomes long-sighted, 
requiring the use of converging spectacles. In Fig. 426, F is the 
position of the focus for parallel rays in a normal eye, F-^ for a short- 
sighted and F^ for a long-sighted eye. These distances from the retina 
are greatly exaggerated in the diagram for the sake of clearness. 

The defect known as astigmatism is due to a lack of symmetry in 
the surfaces of the cornea and the lens, but principally iu the former. 
Ordinarily these are spherical, but sometimes 
the curvature is greater in one plane than in 
others. If a diagram, as shown in Fig. 418, be 
drawn about one foot in diameter and viewed 
from a distance of about 15 feet an astigmatic 
eye will see some of the radii distinctly, while 
those in a perpendicular direction will be 
blurred. In most cases the vertical section of 
the cornea of an astigmatic eye is more curved 
than a horizontal section. The proper spectacles 
to use are those in which one surface of the lens 
is a part of a cylinder instead of a sphere. 

412. The Photographic Camera. The pin-hole camera was 
described in ^ o3.3. This would be quite satisfactory for taking 
photographs, except for the fact that as the pin-hole is very small, 
little light can get through it and so the time of exposure is long. 
This .serious defect is overcome by making the hole larger and 
putting in it a converging lens. The greater the aperture of this 
lens is, provided the focal length is not increased, the shorter the 
exposure required. 




Fio. 427.— Diagram for 
testing for astigma- 
tism. 



360 



OPTICAL INSTRUMENTS 




Fig. 428.— a photographic 
camera. 



plate 



In Fig. 428 is illustrated an ordinary camera. In the tube A is 
the lens, and at the other end of the apparatus is a frame C con- 
taining a piece of ground glass. By means 
of the bellows B this is moved back and 
forth until the scene to be photographed is 
sharply focussed on the ground glass. Then 
a holder containing a sensitive plate or film 
is inserted in front of the frame C, the sensi- 
tized surface taking exactly the position 
previously occupied by the ground surface 
of the glass. 

The exposure is then made, that is, light 
is admitted through the lens to the sensitive 
plate, after -which, in a dark room, the 
IS removed from its holder, developed and fixed. 

Only in the cheapest cameras is a single convex lens used, a 
combination of two lenses being ordinarily 
found. If we wish to secure a picture which 
is perfectly focussed all over the plate, and to 
have a very short exposure, we must u.se one of 
the modern objectives, which have been brought 
to a high degree of efficiency. A section of 
one of these is shown in Fig. 429, in which it 
will be seen there are four separate lenses Fio. 429. 
combined. Others contain even more lenses, 
and as these are made from special kinds of 
glass and have surfaces with specially com- 
puted curvatures, they are expensive. Great eflfort and marvellous 
ingenuity have been expended in producing the extremely compact 
and efficient cameras now so familiar to us. 

413. The Projection Lantern. In Fig. 430 is shown h 
vertical section of a projecting lantern. Its two essential 
parts are the 

source of light A \\ JS_ ^C 

and the pioject- 
ing lens, or set 
of lenses, D. 

The source 
should be as intense as possible. [Why ?] In the figure it 




-Section of a 
Zeiss "Tessar" photo- 
graphic objective. The 
light enters in the direc- 
tion shown by the arrow. 




FiQ. 430.— Diagram ilhistrating the action of a projection lantern. 



THE SIMPLE MICROSCOPE OR MAGNIFYING GLASS 361 



iy an electric arc lamp, but the lime-liglit (a cylinder of lime" 
made white-hot by the oxy-hydrogen flame), an acetylene jet 
or a strong oil lamp may be used. The light diverging from 
the source is directed by means of the so-called condensing 
lenses B upon the object G which we wish to exhibit on the 
screen E. This object is usually a pliotograph on glass, and 
is known as a lantern slide. 

In a tube is D the projecting lens. By moving this nearer 
the slide or farther from it a real and much enlarcred imacfe of 
the picture on tlie slide is produced on the screen. The slide 
and the screen are conjugate foci (§§ 385, 388). As the image 
on the screen is erect, and since the projecting lens inverts 
the image, it is evident that the slide G must be j)laced in 
its carrier with the picture on it upside down. 

414. The Simple Microscope or Magnifying Glass. In 

order to see an object well, tliat is, to recognize details of it, 
we bring it near to the eye, but we have learned (§ 409) that 
when it gets within a certain distance the image is blurred. 
By placing a single convex lens before the eye (which is 
equivalent to making the eye short-sighted) we are enabled to 
bring the object quite close to the eye and still have the image 
of it on the retina distinct. 

How this is done is shown in Fig. 431. (See also Figs. 396- 
400.) The object PQ is 
placed within the principal 
focus F. The image i^q is 
virtual, erect and enlarged 
(see Fig. 397). The lens is 
moved back and forth until 
the image is focussed, in 
which case the image is at 
tlie least distance of dis- 
tinct vision from the eye. l^ic magnification is greatest when 
the eye is close to the lens. 




Fig. 431.— Illustrating the action of the simple 
mioiosL'ope. 



362 



OPTICAL INSTRUMENTS 




Fig. 432. — The magnification is the ratio of pq to 
PQ- 



415. Magnifying- Power of Simple Microscope. Let us find 

the magnification. The apparent size of an object is determined by 
_ the .size of the angle subtended 

't ---. at the eye by the object. Con- 

sider tlie eye to coincide in 
position with the lens. Then 
in Fig. 432 the angle sub- 
tended at the eye by the object 
PQ is POQ, tliat" subtended 
])y the \n\a.^e pq\^pOq. These 
angles are identical and at 
first sight we might think 
there was no magnification. It must be noted, however, that if we 
were looking at PQ directly, without using the lens, we would place 
it at PQ', at the same distance from as jjq, and the angle then 
subtended at the eye is P'OQ'. 

Hence niacrnification = — S — P 1 _ I'l (ai)prox.) = ^. 
angle P'OQ' P'Q' ^ ^ ^ ' PQ 

Now OPQ and Opq are similar triangles, and OC, OF are perpen- 
diculars from upon corresponding sides PQ, j^q- 

Hence ^ = ^^. 
PQ 00 

Again PQ is always placed near the principal focus of the lens, 
and if y is its focal length, OC = y approximately. Also putting 
OB = A, the least distance of distinct vision, we have 

A 
Magnification = — r* 

For example, if focal length = 1 cm. and A = 26 cm., then 
magnification = 25 -r 1 = 25. 

It might be noted that since P, the poiver of a lens, is inversely 
proportional to its focal length (§ 382) 

Magnification = A x P. 

The smaller the focal length the greater is the power and also the 
magnification. The greatest magnification, however, which can be 
obtained is about 100. 

416. The Compound Microscope. For higher magnifications 
we must use a combination of convex lenses known as a compound 
microscope. In its simplest form it consists of two lenses, the 
objective and the eyepiece, the action of which is illustrated in 
Fig. 433. 



THE ASTRONOMICAL TELESCOPE 



3G3 



The object PQ is placed 'at A, before the objective and just 
beyond its principal focus. Thus a real enlarged inverted image 
P'Q' is produced at B, and the eyepiece E is so placed that F'Q' is 



<Zi^ 




Fig. 433. — Diagram illustrating the compound microscope. 

just within its focal length. The eyepiece E then acts as a simple 
microscope magnifying !'(/. It forms an enlarged virtual image 
pq at the distance of distinct vision from the eye. This distance 
is approximately the length L of the microscope tube. 

We see, then, that the objective and the eyepiece both magnify 
the object, and the total magnification is obtained by compowiding 
(i.e., nmltiplying) these two magnifications. 

The magnification produced by the objective 

= ?19^ , which = — (see 3 389). 

Now AO = F, the focal length of objective, approximately, 
and BO = L, the length of the nucroscope tube, approximately. 

Mence — i- = - , approxmiately. 

Also, if / = focal length of eyepiece (in cm.), 

25 
Magnification by eyepiece = -_ (§ 415) 

and total magnification = — x "- = 

F f Ff 

417. The Astronomical Telescope. The arrangement of the 
lenses in the astronomical telescope is the same in principle as in 
the compound microscope. In the case of the latter, however, the 
object to be observed is near at hand and we can place it near the 



364 



OPTICAL INSTRUMENTS 




Fio. 434. — Showing why the objective of an astronomical 
telescope should have a long focus. 



objective. Under these circumstances a lens of short focal length 

is best to use. 

But the objects viewed by the telescope are far away, and we 

must use an objec- 
0, Qt tive with as great a 

focal length as pos- 
sible. The reason for 
this will be evident 
from Fig. 434. Let 
AC he a, ray from 
the upper part of the 

object looked at, passing through the centre C of the objective 0. 

Now the image of an object at a great distance is formed at the 
principal focus. If then F^ is the principal focus P^Q^ is the image, 
and if F^ is the principal focus P^Qo ^^ ^^^ image. It is clear that 
P^Q^ is greater than P-^Q-^, and indeed that the size varies directly 
as the focal length. Hence the greater the focal length of the 
objective the lai-ger will be the image produced by it. 

Further, since the celestial bodies (except the sun) are very faint, 
the diameter of the objective should be large, in order to collect as 
much light from the body as possible. 

A diagram illustrating the action of the telescope is given in Fig. 
435. The ob- <7| 

jective forms 
the image at its 
principal focus 
B, that \& OB 
= F, its focal 
length. This is 
further raagni- 




FiG. 435.— The astronomical telescope. 



fied by the eyepiece E, which forms the image at -pq. B is just 
within the principal focus of the eyepiece, and so OE, the distance 
between objective and eyepiece, is approximately equal to F + f 
the sura of their focal lengths. 

The magnification produced by the telescope is equal to Fjf, 
though we cannot here deduce this formula.* 

In the great telescope of the Lick Observatory the diameter of the 
objective is 36 inches and its focal length is 57 feet. On using an 
eyepiece of focal length ti inch the magnification is 1368. The 
diameter of the Yerkes telescope (belonging to the University of 
Chicago) is 40 inches and its focal length is 62 feet. 

* See Ganot's Physics ; or Watson's Physics, p. 492. 



OBJECTIVES AND EYEPIECES 



365 



418. Objectives and Eyepieces. In telescopes the objective 

usually consists of an aciirouiatic pair of lenses as shown in Fig. 411, 
the lenses being sometimes cemented together, at others times 
separated a small distance. Some objectives are now made up of 
three lenses. The objective of the micr'oscope is frequently a 
complicated system of lenses (Fig. 412). 

There are two chief types of eyepieces, known as positive and 
negative. The simplest example of the former is that devised by 
Ramsden. It consists of two plano-convex lenses of equal focal 





Ramsden Kellner Monocentric 

Fig. 436.— Some modern eyepieces. 



Orthoscopic 



Fio. 437.— The Huygens 
eyepiece. 



length and § of that length apart. Other more modern eyepieces 
are shown in Fig. 436. These are used in telescopes when we wish 
to make measurements, such as the space 
between two stars or the diameter of a planet. 
They can be used as simple microscopes, as the 
principal focus is outside the lenses. 

The Huygens eyepiece has two plano-convex 
lenses (Fig. 437), the one next the eye having a 
focal length J that of the other, and tlie distance between being 
twice the focal length of the shorter. This eyepiece is ordinarily 
found in microscopes, and it cannot be used as a simple microscope. 

419. The Opera Glass. The opera glass has a convex lens for 
objective and a concave lens for eyepiece (Fig. 438). Light from 

the object passes through the 
objective 0, and would, if 
allowed to do so, form a real 
image J^-^Qy I^^t a concave 
lens -£", placed in its way, 
diverges the rays so that on 
entering the eye they seem 
to come from /;</. This image 
is erect and virtual. 

This instrument is also 
known as Galileo's telescope. 
It was devised by this great man, and with it he discovered the 
first four satellites of Jupiter (1610), and also Saturn's Ring. 

Ordinary opera or field-glasses consist of two Galilean telescopes, 
one for each eye. Such telescopes are simple in construction, of 




FiQ. 438.— A section of the ordinary opera glass. 



366 



OPTICAL INSTRUMENTS 



convenient length and give an image right-side-up, hut their field of 
view is not very great and they are not very serviceable for high 
magnification. 

420. Terrestrial Telescope. Wlien an ordinary telescope is to 
be used for terrestrial purposes it is inconvenient to have the image 
inverted, and to overcome this an "erecting eyepiece" is employed. 
This contains, in addition to the ordinary eyepioce, two lenses of equal 
focal length placed so that they simply erect the image without other- 
wise altering it. Such an eyepiece also increases the field of view. 

421. The Prism Binocular. In recent years there has come 
into use the prism binocular, which combines the compact form of 
the Galilean telescope with the wide field of view of the terrestrial 
telescope. 

Its construction is illustrated in Figs. 439 and 440. The former 
shows the appearance of the instrument, while the latter shows the 
optical arrangement. The lenses are precisely the same as in an 
astronomical telescope, but the compactness is obtained by using 
two reflection prisms. The light traverses the length of the instru- 
ment three times, which reduces the necessary length, while the 
reflections from the faces of the prisms erect the image. The field 
of view is from 7 to 10 times as great as with ordinary field-glasses 
of the same power. 





ilQ. 439.— The prism binocular. Fig. 440.— Showing the path of the light. 

The use of prisms was devised by Porro about CO years ago, but 
on account of difficulties in their manufacture they did not come 
into use until quite recently. 

In the form shown in Fig. 439, that made by Zeiss, a further 
advantage is in the enhanced stereoscopic power. It will be seen 
that the distance between the objectives is about If times as 
great as between the eyepieces, and hence the stereoscopic power is 
multiplied that many times. 



PART VIII-ELECTRICITY AND MAGNETISM 



CHAPTER XLI 
Magnetism 

422. Natural Magnets. In various countries there is found 
an ore of iron which possesses the remarkable poMer of 
attracting small bits of iron. Specimens of I 

this ore are known as natural 'magnets. 

Tliis name is derived from Magnesia, a town V *^ 

of Lydia, Asia Minor, in the vicinity of ' ^^ 

which the ore is supposed to have been ;i5 

abundant. Its modern name is magnetite. 

It is composed of iron and ox^'gen, the i' ' 

chemical formula for it being Fe30^. i 

If dipped in iron filings many will cling ^'ciinging~toTnam'rli 
to it, and if it is suspended by an untwisted "^^^^'"st. 
fibre it will come to rest in a definite position, thus indicating 
a certain direction. On account of this it is known also as a 
lodestone, {i.e., leading-stone) Fig. 441. 

423. Artificial Magnets. If a piece of steel is stroked over 
a natural magnet it becomes itself a magnet. There are, 
however, other and more convenient methods of magnetizing 
pieces of steel (§ 502), and as steel magnets are much more 
powerful and more convenient to handle than natural ones, 
they are always used in experimental work. 

Permanent steel magnets are usually of the bar, the horse- 



Fi0. 442. — Bar-ma>jiiets. Fio. 443. — A horse shoe niajfnet. 

shoe or the compass needle shape, as illustrcited in Figs. 442, 

443, 444. 

424. Poles of a Magnet. Iron filings when scattered over a 

bar-magnet are seen to adhere to it in tufts near the ends, 

367 



368 



MAGNETISM 



none, or scarcely any, being found at the middle (Fig. 445). 

c ca A^ The strength of the niamiet seems 

to be concentrated in certain places 
near the ends; these places are 
called the 2^oles of the magnet, and 




Fig. 445.— The filings cling 
mostly at the poles. 



FiQ. 444.— A compass- needle magnet. 

a straight line joining them is called the axis of the magnet. 
If the magnet is suspended so that it can turn freely in a 
horizontal plane (Fig. 444) this axis will assume a definite 
north-and-south direction, in what is known as the magnetic 
meridian^ wdiich is usually not far from the geographical 
meridian. That end of the magnet which points north is called 
the north-seeking, or simply the iV^-pole, the other the south- 
seeking or /S-23ole. 

425. Magnetic Attraction and Repulsion. Let us bring 
the /S-pole of a bar-magnet near to 
the iV"-pole of a compass needle 
(Fig. 446). There is an attraction 
between them. If we present the 
same pole to the <S-pole of the 
needle, it is repelled. Reversing 
the ends of the magnet, we find 
that its iV-pole now attracts the 
<S-pole of the needle but repels the iV-pole. 

We thus obtain the law : — Like magnetic poles repel, unlike 
attract each other. 

This experiment can be repeated with very simple means. 
Magnetize two sewing-needles by rubbing them, always in the 
same direction, against one pole of a magnet. Then thrust 
them into corks floating on the surface of water. On pushing 
one over near the other, the attractions and repulsions will be 
beautifully shown. 




Fig. 446.— The S-pole of one magnet 
attracts the .W-pole of another. 



MAGNETIC SUBSTANCES 369 

It is to be observed tliat uninagnetized iron or steel Avill bo 
attracted by both end; of a magnet. It is only wlien botii 
bodies are magnetized that we can obtain repulsion. 

426. Magnetic Substances. A magnetic substance is one 
which is attracted by a magnet. Iron and steel are the only 
substances which exhibit magnetic effects in a marked manner. 
Nickel and cobalt are also magnetic, but in a much smaller 
degree. In recent years Heusler, a German physicist, has 
discovered a remarkable series of alloys possessing magnetic 
properties. They are composed of manganese (about 25 per 
cent.), aluminium (from 3 to 15 per cent.) and copper. These 
substances taken singly are non-magnetic, but when melted 
together are able easily to affect the magnetic needle. 

On the other hand, bismuth, r.ntimony and some other sub- 
stances are actually repelled by a magnet. These are said to 
be diamagnetic substances, bu^, "-heir action on j^ 

a magnet is very weak. For all practical pur- ——(? 

poses iron and steel may be considered to be the T5 

only magnetic substances. ^ 

427. Induced Magnetism. If a piece of iron ® 

1 •! *T- I- u 1 i? i f"'"- 447.— A nail if 

rod, or a nail,* be held near one pole oi a strong held nearamagnet 
magnet, it becomes itself a magnet, as is seen inaguet by indue- 
by its power to attract iron filings or small 
tacks placed near its lower end (Fig. 447). If the nail be 
allowed to touch the pole of the magnet, it will be held there. 
A second nail may be suspended from the 
lower end of this one, a third from the second, 
and so on. (Fig. 448.) On removing the magnet, 
however, the chain of nails falls to pieces, 
Fio. 448.-A chain ^q \X\\\s, scc that a piecc of iron becomes a 

of magnets by in- -T 

duction. temporary magnet when it is brought near one 

pole of a permanent steel magnet. Its polarity can be tested 
in the following way : — 

* Ordinary steel nails are not very satisfactory. Use clout nails or short pieces of stcve-pipe 
wire. 



370 MAGNETISM 

Suspend a bit of soft-iron (a narrow strip of tinned-iron is 

xery suitable), and place the iV^-pole of a bar-magnet near it 

(Fig. 449). Then bring the iN'^-pole of a second bar-magnet near 

/ the end n of the strij), farthest from the 

J^ s / n ^^'^^ niagnet. It is repelled, showing that 

'^ . ' it is a i\^-pole. Next bring the >S-pole of 



Fig. 449.— Polaritv of induced i i i i i 1 1 

magnetism. the scconQ magnet slowly towards tlie 

end s of the strip. Repulsion is again observed. This shows, 
as we slionld expect from the law of magnetic attraction and 
repulsion (| 425), that the induced pole is opposite in kind 
to that of the permanent magnet adjacent to it. 

428. Retentive Power. The bits of iron in Figs. 447, 448, 
449, retain their magnetism only when they are near the 
magnet; when it is removed, their polarity disappears. 

If hard-steel is used instead of soft-iron, the steel also 
becomes magnetized, but not as strongly as the iron. However, 
if the magnet is removed the steel will still retain some of its 
magnetism. It has become a perinaiient magnet. 

Thus steel offers great resistance both to being tnade a 
magnet and to losing its magnetism. It is said to have great 
retentive "power. 

On the other hand, soft-iron has small retentive power. 
When placed near a magnet, it becomes a stronger magnet 
than a piece of steel would, but it parts with its magnetism 
quite as easily as it gets it. 

429. Field of Force about a Magnet. The space about a 
magnet, in any part of which the force from the magnet can 
be detected, is called its riiagnetic field. 

One way to explore the field is by means of a small compass 
needle. Place a bar-magnet on a sheet of paper and slowly 

move a small compass needle about it. ...--«> 

The action of the two poles of the 

magnet on the poles of the needle ^ f , „ ,,„ ,,,2 ^ 

will cause the latter to set itself at Fig. 450.— Position assumed by 
. , 1 1 . 1 • 1 • a needle near a bar-magnet. 

various pomts along lines winch ni- 

dicate the direction of the force from the magnet. These 



FIELD OF FORCE ABOUT A MAGNET 



371 



curves run ffoni oiio 2)<)lo to the otlicr. In Fig. 450 is sliown 
the direction of the needle at several points, as well as a line 
of force extending from one pole to the other. 

Another way to map the field is by means of iron tilings. 
This is very simple and very effective. Place a sheet of paper 
over the magnet, and 

I' 



sift from a muslin bag 
iron filings evenly and 
th i nly o ver it. Tap the 
paper gently. Each 
little bit of iron be- 
comes a magnet by 
induction, and tapping 
the paper assists them 
to arrange themselves 
along the magnetic 
lines of force. Fig. 
451 exhibits the field 
about a bar-masfnet, 




FiQ. 451.— Field of force of a bar-majjnet. 



while Fig. 452 shows it about similar poles of two bar-magnets 

standing on end. 

The magnetic force, 
as we have seen, is 
greatest in the neigh- 
bourhood of the poles, 
and here the curves 
shown by the filings 
are closest together. 
Thus the direction of 
the curves indicates 
the direction of the 
lines of force, and 
their closeness to- 
gether at any point 

indicates the strength of the magnetic force there. 







Fio. 452.— Field of force of two like poles. 



372 



MAGNETISM 



1^ ^^gjjSSSm 



>■■ 

"■-->•- 



There are several ways of making these filings figures per- 
manent. Some photographic process gives the best results, but a 
convenient way is to produce the figures on paper which has been 
dipped in melted paraffin, and then to heat the paper. The filings 
sink into the wax and are held firmly in it when it cools down. 

430. Properties of Lines of Force. The lines of force 

belonging to a magnet are con- 
.'.■.'->"'. ^ '' , sidered to begin at the iV-pole, pass 
, tlirough the surrounding space, 
' enter at the >S-pole and then con- 
tinue through the macjnet to the 
>- i\^-pole again (Fig. 453). Thus each 
' line of force is a closed curve. It 
is evident, also, that if we could 

Fig. 453. — The lines of force run from i , i -jir i ^ j i 

the iv-poip through the surrounding cietach a iV-pole irom a magnet and 

medium to the 5-pole, and then i •■ ■%• on i a 

through the magnet back to the place it on any luie oi lorce, at A 

starting point. p • i •• i i i 

tor instance, it would move along 
that line of foi"ce until it would 
come to the >Sf-pole. 

Great use is made of the 
conception of lines of force in 
computations in magnetism and 
electricity, for example, in design- 
ing dynamos. This method of 
dealing with the subject was in- 
troduced by Faraday about 1880. 

431. Magnetic Shielding. Most 
substances when placed in a 
magnetic field make no appre- 
ciable change in the force, but 
there is one pronounced exception 
to this, namely iron. 

Place a bar-magnet with one 
pole about 10 cm. from a large compass needle (Fig. 454), 




Michael Faraday (1791-1867). Born 
and lived in London. The greatest ot 
experimental scientists. His discoveries 
form the basis of all our applications 
of electricity. 




MAGNETIC PERMEABILITY 373 

Pull aside the needle and let it go. It will continue vibrating 
for some time. Count the 
number of vibrations per 
minute. Then push the mag- 
net up until it is 6 cm. 
from the needle, and again 

time the vibrations. They Fio. 454.-Arrangement for testin- magnetic 

" shielding'. 

will be found to be much 

faster. Next, put the magnet 3 cm. from the needle ; the 
vibrations will be still more rapid. Thus, the stronger the force 
of the magnet on the needle, the faster are the vibrations. 

Now while the magnet is 3 cm. from the needle place 
between them a board, a sheet of glass or of brass, and 
determine the period of the needle. No change will be 
observed. Next, insert a plate of iron. The vibrations will 
be much slower, thus showing that the iron has shielded the 
needle from the force of the magnet. 

The lines of force upon entering the iron simply spread 
throughout it, meeting less resistance in doing so than in 
moving out into the air again. A space surrounded by a 
thick shell of iron is effectually protected from external 
magnetic force. 

432. Magnetic Permeability. The lines of force pass more 
easily through iron than through air. Thus iron has greater 
pervieability than air, and the softer the iron is the greater is 
its permeability. Hence when a piece of iron is placed in a 
mao-netic field, many of the lines of force are drawn together 
and pass through the iron. This explains why soft-iron 
becomes a stronger magnet by induction than does hard-steel. 

433. Each Molecule a Magnet. On magnetizing a knitting 
needle or a piece of clock-spring (Fig. 455) it exhibits a 
pole at each end, but no magnetic effects at the centre. 
Now break it at the middle. Each part is a magnet. If 



374 , MAGNETISM 

we break these portions in two, each fragment is again a 
magnet. Continuing this, we find that each free end always 

gives us a magnetic pole. If 
jS all the parts are closely joined 



M. ^ ,, 1 5 



Nc 



S N 



^ ^ jy ^ Jy ^' jy ^ ' again the adjacent poles neu- 

Fia. 455.— Each portion of a magnet is a trahze cach other and vvc liave 

"'^^"^'- only the poles at the ends, as 

before. If a magnet is ground to powder each fragment still 

acts as a little magnet and shows polarity. 

Again, if a small tube filled with iron filings is stroked 
from end to end with a magnet it will be found to possess 
polarity, which, however, will disappear if the filings are 
shaken up. 

All these facts lead us to believe that each molecule is a 
little magnet. In an unmagnetized iron bar they are arranged 
in an irregular, haphazard, fashion (Fig. 456), and so there is 



mgm^mmm. 



FiQ. 456.— Haphazard arrangement of Fig. 457. — Arrangement of molecules of 

molecules of iron ordinarily. iron when magnetized to saturation. 

no combined action. When the iron is magnetized the mole- 
cules turn in a definite direction. Striking the rod while it is 
being magnetized assists the molecules to take up their new 
positions. On the other hand rough usage destroys a magnet. 
When the magnet is made as strong as it can be the mole- 
cules are all arranged in regular order, as illustrated in 
Fig. 457. 

The molecules of soft-iron can be brought into alignment 
more easily than can those of steel, but the latter retain their 
positions nmch more tenaciously. 



EFFECT OF HEAT ON MAGNETIZATION 375 

434. ElBfect of Heat on Magnetization. A magnet loses its 
niacfnetisra when I'aised to a bright red heat, and when iron is 
heated sufficiently it ceases to be attracted by a magnet. This 
can be nicely illustrated in the following way. Heat a cast- 
iron ball, to a white heat if possible, and suspend it at a little 
distance from a magnet. At first it is not attracted at all, but 
on cooling to a bright red it will be suddenly drawn in to 
the magnet. 

The Heusler alloys, mentioned in §426, behave peculiarly in 
respect to temperature. Above a certain temperature they are 
entirely non-magnetic. The temperature depends upon the 
proportions of aluminium and manganese present. 

435. Mariner's Compass. In the modern ship's compass 
several magnetized needles are placed side by side, such a 
compound needle being found more reliable than a single one. 
The card, divided into the 32 " points of the compass," is itself 
attached to the needle, the whole being delicately poised on a 
sharp iridium point. 

436. The Earth a Magnet. The fact that the compass 
needle assumes a definite position suggests that the earth or 
some other celestial body exerts a magnetic action. William 
Gilbert,* in his great work entitled De Magnete (i.e., " On the 
Magnet "), which was published in 1600, demonstrated that 
our earth itself is a great magnet. 

In order to illustrate his views Gilbert had some lodestones 
cut to the shape of spheres ; and he found that small magnets 
turned towards the poles of these models just as compass 
needles behave on the earth. 

The magnetic poles of the earth, however, do not coincide 
with the geographical poles. The north magnetic pole was 



expe 



Gilbert (1540-1603) was physician to Queen Elizabeth, and was England's first great 
jeriniental scientist. 



376 MAGNETISM 

found by Sir James Ross* on June 1, 1831, on the west side of 
Boothia Felix, in N. Lat. 70' 5', W. Long. 96° 46'. In 1904-5 
Roald Amundsen, a Norwegian, explored all about the pole. 
Its present position is about X. Lat. 70", W. Long. 97°, not far 
from its earlier position. 

The south magnetic pole was only recently attained. On 
January 16, 1909, three members of the expedition led by Sir 
Ernest Shackleton discovered it in S. Lat. 72° 25', E. Long. 
155° 16'. In both cases the magnetic pole is over 1100 miles 
from the geographical pole, and a straight line joining the 
two magnetic poles passes about 750 miles from the centre of 
the earth. 

437. Magnetic Declination. We are in the habit of saying 
that the needle points north and south, but it has long been 
known that this is only approximately so. Indeed, knowing 
that the magnetic poles are far from the geographical 
poles, we would not expect the needle (except in particular 
places) to point to the true north. In addition, deposits of 
iron ore and other causes produce local variations in the 
needle. The angle which the axis of the needle makes 
with the true north-and-south line is called the Tnagnetic 
declination. 

438. Lines of Equal Declination or Isogonic Lines. Lines 
upon the earth's surface through places having the same 
declination are called isogonic lines ; that one along which the 
declination is zero is called the agonicf line. Along this line 
the needle points exactly north and south. 

On January 1, 1910, the declination at Toi'onto was 5° 55' 
W. of true north, at Montreal, 15° 4' W., at Winnipeg, 14° 4' E., 
at Victoria, B.C., 24° 25' E., at Halifax, 21° 14' W. These values 

* The cost of the arctic expedition, which was made by John Ross and his nephew James, 
was defrayed by a wealthy Englishman named Felix Booth, 
t Greek, igos = equal, gonia = angle; a = not, gonia = angle. 



LINES OF EQUAL DECLINATION OR ISOGONIC LINES 877 

are subject to slow changes. At London, in 1580, the decHna- 
tion was 11° 17' E. This slowly decreased, until in 1G57 it 
was 0° 0'. After tliis it became west and increased until in 
1816 it was 24° 30'; since then it has steadily decreased and is 
now 15° 8' W. 

In Fig. 458 is a map showing the isogonic lines for the 
United States and Caiiada for January 1, 1910. 




Fig. 458. -Isogonic Lines for Canada and the United States (Janviary 1, 1910). 
The data for regions north of latitude 5.5° are very meagre and discordant ; the regions west of 
Hudson Bay where recent determinations have been made show considerable local disturbance ; 
the lines north of latitude 70° are drawn largely from positions calculated theoretically, but 
modified where recent obser^ ations have been made. The above map was kindly drawn for this 
work by the Department of Research in Terrestial Magnetism of the Carnejrie Institution of 
yVashington. 



378 



MAGNETISM 




Fig. 459.— a simple dip- 
ping needle. 



439. Magnetic Inclination or Dip. Fig. 459 shows an 
instruineut in which the magnetized needle can move in a 
vertical plane. The needle before being 
magnetized is so adjusted that it will rest 
in any position in which it is placed, but 
when magnetized the iV^-pole (in the 
northern hemisphere) dijos down, making 
a considerable angle witli the horizon. If 
the magnetization of the needle is reversed, 
the other end dips down. Such an instru- 
ment is called a dipping needle. When 
using it the axis of rotation should point 
east and west {i.e., at right angles to the 
magnetic meridian), and the needle should move with the least 
possible friction. 

The angle which the needle makes with the horizon is called 
the inclination or dip. At the magnetic equator the dip is 
zero (or the needle is horizontal), but north or south of that 
line the dip increases, until at the magnetic poles it is 90°. 
Indeed the location of the poles was determined by the dipping 
needle. 

At Toronto the dip is 74° 87'; at Washington, 71° 5'. 

440. The Earth's Magnetic Field. As the earth is a great 
magnet it mu.st have a magnetic field about it, and a piece of 
iron in that field should become a magnet by induction. If an 
iron rod {e.g., a poker, or the rod of a retort stand) is held 
nearly vertically, with the lower end inclined towards tlie 
north, it will be approximately parallel to the lines of force 
and it will become magnetized. If struck smartly when in 
this position its magnetism will be strengthened. (Why?) 
Its magnetism can be tested with a compass needle. Carefully 
move the lower end towards the /S-pole; it is attracted. 



THE EARTH'S MAGNETIC FIELD 379 

Move it near the iV-pole ; it is repelled. This shows the 
rod to be a magnet. 

Now when a magnet is produced by induction its polarity 
is opposite to that of the inducing magnet. Hence we see 
that what we call the north magnetic pole of the earth is 
opposite in kind to the i\^-pole of a compass needle. 

Iron posts in buildings and the iron in a ship when it is 
being built become magnetized by the earth's field. 



CHAPTER XLII 

Electricity at Rest 

441. Electrical Attraction. If a stick of sealing-wax or a 
rod of ebonite (hard rubber) be rubbed with flannel or with 
cat's fur and then held near small bits of pa,per, pith or other 
light bodies, the latter will sjDring towards the wax or the 
ebonite. A glass rod when rubbed with silk acts in the same 
way.* 

As early as 600 B.C. it was known that amber possessed this 
wonderful attractive power on being rubbed. The Greek name 
for amber is electron, and when Gilbert (see § 436) found that 
many other substances behaved in the same way he called them 
all electrics. The bodies which have acquired this attractive 
power are said to be electrified or to be charged with electricity. 
In later times it has been shown that any two diflferent bodies 
when rubbed together become electrified. 

A good way to observe the force of attraction is to use a 
small ball of elder 
pith or of cork, 
hung by a silk 
thread (Fig. 460). 
<^ On holding the 
f^ rubbed glass near 
^^# it the ball is drawn 

towards it. 
It can also be 
shown that the electrified body is itself attracted by one that 
has not been electrified. Let us rub a glass rod and hang it in 
a wire stirrup supported by a silk thread (Fig. 461). If the 




^, 



Fio. 460. — A pith ball on the 
end of a silk thread drawn 
towards the electrified rod. 



Fig. 461.— The electrified rod 
moves towards the hand. 



*In these experiments the substances should be thoroughly dry. 
winter since there is much less moisture in the air then. 

380 



They succeed better in 



ELECTRICAL REPULSION 381 

liand (or other body) be lield out towards the suspended body 
the latter will turn about and approach the hand. A rod of 
sealing-wax or of ebonite when rubbed acts similarly. 

442. Electrical Repulsion. Suppose, however, we allow 
the pith ball (Fig. 4G0) to touch the electrified glass roil. It 
clings to it for a moment and then flies off. If the end of the 
rod is brought near to it, the ball continually moves away 
from it. There is repulsion between the two. Next, rub an 
ebonite rod with flannel and hold it to the pith ball. It is 
attracted. Thus the glass now repels the pith ball, but the 
ebonite attracts it. 

Again, hold a rubbed glass rod near the suspended glass rod 
(Fig. 461); they repel each other. Two ebonite rods behave 
similarly. If, however, we hold a rubbed ebonite rod near the 
glass rod there is attraction between them. 

443. Two Kinds of Electrification. It is evident from 
these experiments that there are two kinds of electrifica- 
tion or of electrical charge, and it is customary to call 
that produced on rubbing glass with silk positive; that 
produced on rubbing ebonite or sealing-wax with flannel, 
negative. The pith ball on touching the glass became charged 
positively. 

The above and numberless other experiments allow us to 
formulate the following : — 

Law of Electrical Attraction and Repulsion. — Elec- 
trical charges of like kind repel each other, those of unlike 
kind attract each other. 

444. Conductors and Non-conductors. We may rest a 
piece of electrified ebonite on another piece of ebonite or on 
dry glass, or sulphur or paraffin, and it will retain its electrifi- 
cation for some time ; but if it is passed through a flame, or 
is gently rubbed over with a damp cloth, or simply with the 



382 ELECTRICITY AT REST 

hand, it loses its electrification at once. The ebonite, the glass, 
the sulphur and the paraffin are said to be non-cmidicctors of 
electricity ; while the damp cloth and the hand are said to be 
conductors of electricity, the electric charge escaping freely 
by way of them. 

If we hold a piece of brass tube in the hand and rub it vrith 
fur or flannel or silk it will show no signs of electrification ; 
but fasten it to an ebonite handle and flick it with dry cat's 
fur and it will be negatively electrified. Approach it to a 
suspended rubbed ebonite rod (Fig. 461) and it will repel it. 
In the first case the brass was electrified, but the electrical 
charge immediately escaped to earth by way of the experi- 
menter's body. In the second case the escape was prevented 
by the ebonite handle, and the metal remained electrified. It 
is to be noted, too, that a non-conductor exhibits electrification 
only where it is rubbed, while in a metal the charge is spread 
all over its surface. 

Those substances which lead off an electrical charge quickly 
are called conductors, while those which prevent the charge 
from escaping are called iioa-conductors or insulators. If a 
conductor is held on a non-conducting support it is said to be 
insulated. Thus, telegi'aph and telephone wires are held on 
glass insulators; and a man who is attending electric street 
lamps often stands on a stool with glass feet, and handles the 
lamps with rubber gloves. 

Good Conductors : metals. 

Fair Conductors : the human body, solutions of acids and salts in 

water, carbon. 
Poor Conductors : dry paper, cotton, wood. 
Bad Conductors, or Good Insulators: glass, porcelain, sealing-wax, 

mica, dry silk, shellac, rubber, resin, and oils generally. 

445. The Gold-leaf Electroscope. The object of the elec- 
troscope is to detect an electric charge and to determine 



ELECT KIPICATION BY INDUCTION 



383 




Fio. 4G2.— The Gold-leaf 
Electroscope. 



whether it is positive or negative. A metal rod with a knob 

or disc at the top (Fig. 462) extends 

through a well-insulated cork into a flask. 

From its lower end two leaves of gold or 

of aluminium leaf hang by their own 

weight. The rod may pass through a 

glass tube, well coated with shellac, which 

is inserted through the cork. The flask 

should be also varnished with shellac, as 

this improves the insulation greatly. If a 

charge, either positive or negative, is given to the electroscope, 

the two leaves, being charged with electricity of the same kind, 

repel each other and separate. 

Another form of electroscope is shown in Fig. 463. The 
protecting case is of wood with front 
and back of glass. The sides of the 
case are hned with tin-foil, to which a 
binding post is connected. By this the 
case may be joined to earth and thus 
be kept con ;tantly at zero potential (see 
§ 455). The rod supporting the leaves 
passes through a block of unpolished 
ebonite or other good insulator, and 
the small disc on top may 
be removed if desired. 
The electroscope may be charged by touching a 

charged body to the knob, or by connecting it to 

the knob by a conducting wire. But sometimes 

it is more convenient to use a j'^^'^oof-plane (Fig. 

464) which is simply a small metal disc on an 

insulating handle. This is touched to the charged 

body and then to the knob of the electroscope. 
446. Electrification by Induction. Let us slowly bring a 

rubbed ebonite rod towards the knob of the electroscope. The 




Fio. 463.— Another form of 
electroscope. 



Fio. 464. — A 
proof-plane. 



384 ELECTRICITY AT REST 

leaves are seen to separate even though the rod be a foot or 
more away. This experiment shows that the mere presence of 
an electrified body is sufficient to produce electrification in 
neighbouring conductors. The charge is said to be produced 
by electrostatic influence or induction. As soon as the 
charged body is removed tlie leaves collapse again. 

This experiment also impresses the fact that an electrified 
body exerts an action on bodies in the space about it. This 
space is called its electrical field of force. It can be shown, 
too, that the magnitude of the force exerted depends on the 
material filling the space. For instance, if the electrified body 
is immersed in petroleum the force it exerts on another body 
is only about one half that in air. Indeed it is believed that 
the force exhibited is due to actions in the surrounding 
medium, which is known as the dielectric. 

447. Nature of Induced Electrification. Let A and B 
(Fig. 465) be two metallic bodies placed near together on 
. well-insulated supports.* Charge 
^H £ !^ A positively by rubbing over it a 

glass rod rubbed with silk. 

Fio. 465.— Explaining induced tt i ^ i < 

electrification. t irst, touch A With a proot plane 

and carry it to the electroscope. The leaves will show a 
separation. Repeat and get a greater separation. Next, 
touch the proof plane to a, tliat end of B nearest A, and carry 
it to the electroscope. The leaves come closer together, show- 
ing that the charge on the end a is negative, that is, of the 
opposite kind to that on A. 

Next, touch the proof-plane to the end h, which is farthest 
from A, and convey the charge to the electroscope. It makes 
the leaves diverge further, showing that the charge is of the 
same kind as that on A. 

We find, therefore, that the two ends have charges of 
opposite signs, the charge on the end of B nearest to A being 

*The bodies may be of wood covered with tin-foil, and may rest on blocks of parafHn. 





INDUCED CHARGES ARE EQUAL 385 

of the opposite sign to that on ^4. It is to he ohserved, also, 
that the electrification on B does not in any way diminish the 
charge on A. 

448, Induced Charges are Equal. Place two insulated 
conductors A and B in contact and hold a positively charged 
rod near (Fig. 466). The conductor A will 
be charged negatively and B positively. 
While the rod is in position separate the 
conductors, and then remove the rod. The 
body A is now charged with negative and 
B with positive electricity. 

Bring them together carefully. A spark p,,^. 46^wo^ai 
will be heard to pass between them and Si " The'cllS 
they will be entirely discharged. The two °" '^ ^'"^ ^ '""^ '^'i"'*'- 
charges have neutralized each other, M'hich shows that they 
must have been equal. 

443. Charging by Induction. Let an electrified rod be 
brought near an insulated conductor (Fig. 467). A negative 

charge will be induced on the 

V ^ x ) end a and a positive charge will 

be repelled to the end h. Suppose 
now the conductor is touched with 

Fio. 467.— How to charge by induction. ,1 ,-. . . . , , . , m, 

the finger or is jonied to earth* 
by a wire (see § 455). We must now consider the conductor 
and the earth to be a single conductor, and while the negative 
charge will remain on a, " bound " to the charge on the rod 
the "free" positive charge will escape to the earth. Now 
remove the finger and then the rod. The conductor will be 
charged negatively. 

In this way it is easy to give a charge of any desired kind 
and magnitude to an electroscope. Suppo.se we wish to 
give a positive charge. Rub an ebonite rod with cat's fur 



* Connect to a gas or water-pipe. Connection may be made to any part of the conductor. 



386 



ELECTRICITY AT REST 




and bring it towards the knob of the electroscope. The knob 
will be charged positively and the leaves negatively by 
induction. Now touch the electroscope rod with the finger ; 
the negative charge will escape. Then remove the finger and 
after that the ebonite rod. The positive charge will remain 
on the electroscope, producing a separation of the leaves. 

450. Charges Reside on the Outer Surface. Place a tall 
metal vessel on a good insulator (Fig. 468), and electrify it 

either by an ebonite rod or by an electrical 
machine (§ 461). Disconnect from the 
machine. Lower a metal ball, suspended 
by a silk thread, into the vessel and let it 
touch the inner surface. Then apply the 
ball to the electroscope ; it shows no change. 
„ ^„ . . „ , , Next, touch the ball to the outside of the 

Fig. 468. - A tall metal ves- ' 

sei joined to an electrical vesscl and tcst with the electroscoDC. It 

machine. Reniovmg the 1 

wire disconnects it. ^^^^ shows a cliargc. Finally charge the 

ball by the machine, then lower it into the metal vessel and 
touch the inner surface with it. Then test it with the 
electroscope. It will be found that its charge is entirely 
gone ; it was given to the metal vessel, on the outer surface 
of which it now is. 

In Fig. 4G9 is shown a metal sphere on an insulating stand, 
and two hemispheres with in.sulating 
handles whicli just fit over it. First, 
charge the sphere as strongly as 
possible. Then, taking hold of the 
insulating handles, fit the hemispheres 
over it, and then remove them. If 
now the sphere is tested with the 
electroscope no trace of electricity will 
be found on it. 

451. Distribution of the Charge ; the Action of Points. 
Though the electric charge resides only on the outer surface 




Fio. 469.— Apparatus to show 
that the charge resides only 
on the surface of a conductor. 




LIGHTNING RODS 387 

of a conductor it is not always e([ually dense all over it. The 
distribution depends on the 

shape of the conductoi', and /"""^ !'"?' 1"""^% Z'""''''^---. 
experiment shows that the V..^ -O ^.. "- ~^ .y' S-^^*^^'" 

Charore is greater at Shai'p Km. 470.— showing the distribution of an electric 
° ° charge on conductors of different shapes. 

edges. 

On a sphere the char^^c is uniformly distributed over the 
surface {a. Fig. 470). On a cylinder with rounded ends the 
charge is denser at the ends than at the middle (/j, Fig. 470) ; 
and on a pear-shaped conductor it is much denser at the 
small end. 

The force with which a charge tends to escape from a con- 
ductor increases with the density of the charge, and it is for 
this reason that a pointed con- -^^v^ ^ ^ ^ 

ductor soon loses its charge. I 

If a pointed wire is placed on \\ 

a conductor attached to an ; 3ZlZii^^ 
., ^, ,. electrical machine the elec- fio. 472 -The " eiec- 

FiG. 471. — Electric trie whirr rotates 

wind-froni a pointed trifled air particles streaming; \y "the reaction 

conductor blowingaside ' " from the electric 

a candle flame. f^.Q^ it may blow asidc a ^''"'^■" 

candle flame (Fig. 471); or an "electric whirl" (Fig. 472) 
nicely balanced on a sharp point when placed on an electrical 
machine is made to rotate by the reaction as the air-particles 
are pushed away from the points. It rotates like a lawn- 
sprinkler. 

452. Lightning Rods. In a thunderstorm the clouds 
become charged with electricity and by induction a cnarge of 
the opposite sign appears on the surface of the earth just 
beneath. The points on the lightning rods, in the place where 
this charge is, allow the induced charge to escape quietly into 
the air. It is evident, then, that the lower end of a lightning- 
rod should be buried deep enough to be in moist earth always, 
since dry earth is a poor conductor. 



388 



ELECTRICITY AT REST 



453. Electrical Potential. Let us take two insulated con- 
ductors A and B, two metal balls on silk threads, for instance, 
and let one of them be charged and the otlier not, or let one 
be charged to a greater degree than the other. Then when 
they are brought together there is some action between them, 
and we describe it by saying that there has been a Jloiv of 
electricity from one to the other. We wish to learn on what 
this Jloiv depends. 

It can best be explained by considering analogies in other 
branches of science. 

Water will flow from the tank A to the tank B (Fig. 473) 
through the pipe G connecting them if the water is at a higher 

level in A than in B; or, what 
amounts to the same thing, if 
the hydrostatic pressure at a is 
greater than that at h. The 
tank B may already have more 
w^ater in it, but the flow does 
not depend on that. It is regu- 
lated by the diflference between 
the pressures at the two ends of the pipe and it Avill continue 
until these pressures become equal. 

Or, consider what happens when two gas-bags filled with 
compressed air are joined by a tube in which is a stop-cock. 
If the pressure of the air is the same in each there will be no 
flow from one to the other on opening the stop-cock. If there 
is a difference, there will be a flow from the bag at high 
pressure to that at low. 

Again, when two bodies at different temperatures are 
brought together, there is a flow of heat from the one at the 
higher temperature to that at the lower temperature. 

Corresponding to pressure in hydrostatics and to tempera- 
ture in the science of heat, in electricity we use the term 




Fig. 473. — Water flows from the higher level 
in A to the lower level in B. 



NATURE OF ELECTRICITY 389 

potential, (or sometimes livessure). If two points of a con- 
ductor are at different potentials there will be a flow from 
the point at high potential to that at low potential. This 
potential difference (for which P.D. is an abbreviation), is 
usually measured in volts, a definition of which will be given 
in the next chapter (§ 471). 

454. Nature of Electricity. So far no reference has been 
made to the nature of electricity ; indeed it is very difficult to 
make a hypothesis which will explain satisfactorily all the 
observed phenomena. 

We speak of a flow of electricity, but certainly nothing of 
the nature of ordinary matter moves, though just as certainly 
there is a transference of energy. In the case of conduction 
of heat we do not know the precise nature of heat, but here 
again we are sure that there is a transference of energy. 

But we have electricity of two kinds, which appear simply 
to neutralize each other. In considering t\\Q flow of electricity 
it is usual to confine our attention to the positive electricity. 
A flow of negative electricity in one direction in a conductor 
is equivalent to the flow of an equal amount of positive 
electricity in the opposite direction. 

It is best, however, not to be too fixed in our views as to 
the precise nature ot electricity, though we can be sure that 
when we say there is a flow of electricity, there is a transfer 
of energy. It is well to remember, too, that the electrical 
energy is not all within the conductor. On the other hand, it 
has been demonstrated that the energy resides chiefly in the 
surrounding space and that the conductor simply acts as a 
guide to it. 

455. Zero of Potential. In stating levels or heights we 
usually refer them to the level of the sea. The ocean is- so 
large that all the rain which it receives does not appreciably 



390 



ELECTRICITY AT REST 




alter its level. In a somewhat similar way, the earth is so 
large that all the electrical charges M'hich we can give it do 
not appreciably alter its electrical level or potential, and so we 
take the earth to be our zero of potential. 

Lake Superior is 602 feet above the level of the sea, and the 
Dead Sea, in Palestine, is 1,300 feet below it. There is a 
continual flow from Lake Superior to the ocean ; and if a tube 
joined the two, there would be a flow from the ocean to the 
Dead Sea. 

Bodies which are charged positively are considered to be at 
a potential higher than that of the earth, and those charged 

negatively to be at a potential 
below that of the earth. 

Consider the four tanks in 
Fig. 474. The levels of A and 
B are above, and those of C and 
D below that of the earth. A 
flow would take place from A 

or B to the earth, or from the earth to C or D, or from any 

one tank to another at lower level. 

456. Electrical Capacity. On pouring the same quantity 
of water into different vessels we observe that it rises to 
different levels ; and that vessel into which we must pour the 
most water in order to raise its level by any amount, say 1 
cm., is said to have the greatest capacity. If a vessel has a 
small cross-section, like a narrow tube, it will not take much 
water to make a great change in its level ; and its capacity is 
small. 

There is something analogous in the science of elec- 
tricity. It requires different amounts of electricity to raise 
the potentials of different conductors by one unit, and so 
we say there is a difference in the electrical capacities of 
conductors. 



Fig. 4V4.— Four tanks with water at different 
levels. 



ELECTRICAL CONDENSER 



391 







A 


+ 


- 


B 


'S^ 


+ 


+ 
+ 


- 


- 


f\ 


m 


N. + 


+ 


- 


- 


1 

h 


1 '*' 


+ 
+ 


~ 


- 




\ A 


+ 


- 


ir^* 




^w^ 






#.^^ 



Fia. 475. — A and B are two metal plates on insu- 
lating; bases. A is joined to an electroscope and 
B to earth. 



Continue 



457. Electrical Condenser, In Fig. 475 ^4 {ind 7i me two 
metal plates on insulating bases. They may be of tin-plate 
about 10 or 12 inches 
square, bent at the bottom 
and resting on- paraffin 
blocks, G, C, with metal 
blocks Z), D, to keep 
them in place. First let 
B be at some distance 
from A, and charge A. 
The greater the charge, 
the higher rises the 

potential and the wider diverge the gold-leaves 
charging until the leaves are far apart. 

Then, with the plate B joined to earth (simply keeping a 
finger on it will do), push it up towards A. As the plates 
get nearer together the leaves begin to fall, showing that the 
potential of xi has fallen through the presence of B. If now 
we add positive electricity to A by means of a proof plane 
we shall find that several times the original amount of 
electricity must be added to A in order to obtain the 
original separation of the leaves, that is, to ruise it to the 
original potential. 

The two plates and the air between them constitute a 
condenser. 

The explanation of the action of the condenser is as follows. 
Let the charge on A be positive. When the plate B is brought 
up the charge on A induces on B a negative charge repelling 
the equal positive charge to earth. The attraction of the 
charge on B draws the chai'ge on A to the face nearest B, 
thus reducing the amount on the electroscope and making 
room for additional charges. The two charges on the plates 
A and B are " bound " charges. 



392 



ELECTRICITY AT REST 



458. The Dielectric in a Condenser. Push the plates A 
and B (Fig. 475) near together, and charge the plate A until 
the separation of the leaves is quite decided. Now insert 
between A and B a sheet of thick plate glass, sliding it along 
B, being careful not to touch A, and observe the effect on the 
electroscope. The leaves come closer together, showing that 
the potential has fallen and the capacity has increased. 
Ebonite or paraffin may be used as a dielectric instead of 
the glass, but the effect will not be so pronounced. 

459. Leyden Jar. This is the most usual kind of con- 
denser. It consists of a wide-mouthed bottle 
(Fig. 476), the sides and bottom of which, 
both within and without, are coated with tin- 
foil to within a short distance from the neck. 
The glass above the tin-foil is varnished to 
maintain the insulation. Through a wooden 
stopper passes a brass rod, the upper end of 
which carries a knob, the lower a chain which 
touches the inner coating of the jar. Tlie two 

coatings form the two plates of the condenser, the glass being 
the dielectric. 

To charge the jar the outer coating is connected to earth (or 
held in the hand), and the knob is joined to 
an electrical machine. To discharge it, con- 
nection is made between the inner and outer 
coatings by discharging tongs (Fig. 477). 
Usually the discharge is accompanied by a 
brilliant sjiark and a loud report. (It is wisest 
not to pass the discharge through the body.) 

Condensers used in electrical experiments 
are often made of a number of sheets of 
tin-foil separated from each other by sheets 
of paraffined paper or mica. Alterna^te sheets of the tin-foil 
are connected together. 




Fig. 476. — A Leyden 
Jar. 




Fig. 477.— Discharg- 
ing tongs. The 
handles are of 
glass or of ebonite. 



THE ELECTROPHORUS 



393 




460. The ElectrophorUS. By means of this instrument, which 
was invented by Volta, in 1775, we can electrify a conductor without 
using up its charge. 

It consists of a cake A of ebonite or of resi- 
nous wax resting on a metal plate, and a metal 
cover* B, of rather smaller diameter, pro- 
vided with an insulating handle. (Fig. 478.) 

First, the cake is rubbed with cat's fur, 
and thus it obtains a negative charge. Then 
the cover is put on and touched with the 
finger. If it is lifted up by the handle it 
will be found to be positively charged, and 
on presenting it to the knuckle a spark, ^lo. 478.-The eiectrophorus. 
sometimes half-an-inch long, is obtained, and the cover is discharged. 
The gas may be lighted witli this spark ; and if the cover is pre- 
sented to the knob of an electroscope the latter will be charged. 
The process may be repeated any number of times without renewing 
the charge on the cake. 

Query. — Every time the cover is discharged energy disappears ; where 
did it come from ? 

The action is explained thus : — 
When the cover is placed on the cake, 
which is a non-conductor, it rests upon 
it on a few points only and so does not 
remove its charge. But the negative 
charge on A induces on the lower face 
oi JJ a. "bound" positive charge, re- 
pelling to the upper face a " free " 
negative charge, which escapes when 
the finger touches it. When the cover 
is lifted the positive charge becomes 
" free " and spreads over its surface. 

461. Wimshurst Influence 

Machine. The electrical machines 
in common use are simply convenient 
arrangements for utilizing the prin- 
ciple of influence so well illustrated in 
the eiectrophorus. 

In Fig. 479 is shown a Wimshurst 
machine. It consists of two varnished 
glass plates a, a, placed as close together as possible and driven by 

* This may be a wooden disc covered with tin-foil. 




Fig. 479. 



-The Wimshurst electrical 
machine. 



394 



ELECTRICITY AT REST 



belts b, h' in opposite directions. Each plate has an even number of 
metal sectors cemented on its outer face. A neutralizing conductor 
c, c is fixed diametrically across each plate and fine wire brushes on 
the ends just touch the metal sectors as the plates rotate. These 
conductors are set almost at right angles to each other. 

Two collecting combs e, e' with their teeth turned towards the 
rotating discs encircle them at each side of the machine. These 
are insulated from the frame of the machine by ebonite rods r, r'. 
From them run up a pair of adjustable discharging rods d, d', ending 
in knobs. A pair of Leyden jars j, j are usually added, and when 
these are charged a powerful spark passes. 

462. Explanation of the Action of the Machine. The 

action of the machine can best be explained by a diagram (Fig. 480), 

in which, for greater clearness, 
the two rotating discs are re- 
presented as though they were 
two cylinders of glass, one in- 
side the other and rotating in 
opposite directions as shown by 
the arrows.* The neutralizing 
brushes Wj, n., touch the sectors 
on the back plate, while n^, 7i^ 
touch the front sectors. In the 
diagram a section of the -cylin- 
ders is supposed to be seen, and 
the metal sectors are represented 
by the dark heavy lines on the 
outer and inner surfaces. 

Suppose now that one of the 
sectors x on the front plate (near 
the top of the dicigram) has a slight positive charge. As it rotates 
towards the left it will be brought opposite a sector x on the 
back plate at the moment when this is in contact with the brush 
Wj. This latter sector then acquires by influence a negative charge, 
the sector z at the other end of c receiving a positive charge while 
the sector z opposite it, on the other plate, receives by influence a 
negative charge. 

As the rotation continues the induced negative charges on x and 
z are carried to the right hand comb e by which they are collected, 
the positive charges on x and z to the left-hand comb e, which 
collects them. 




Fig. 480. 



d * - d 

-Diagram of a Wimshurst machine. 



*This method of explanation is due to Prof. S. P. Thompson ; see his Elementary Lessons in 
Electricity and Magnetism, p. 63. 



EXPLANATION OF THP] ACTION OF THE MACHINE 395 

Again, the negative charge on x and the positive charge on z 
are brouglit opposite n.^ and n^, I'espectively, and these are connected 
by c'. The sector which n.,_ touches acquires a positive charge and 
tliat which n^ touches acquires a negative charge, and these are 
carried on to the collecting combs. 

In this way all the sectors become more and more highly charged, 
and the front sectors at the top and the back sectors at the bottom 
are carrying positive charges to the comb e, while the other sectors 
are carrying negative charges to the comb e . 

Thus large charges may be accumulated on the combs and in the 
jars connected with them (not shown in Fig. 480), and powerful 
sparks may be obtained between the knobs on the discharging rods 
d, d'. 



CHAPTER XLIII 
The Electric Current 

463. Nature of the Electric Current. As explained in 
§ 453, when two bodies at different potentials are joined by a 
conductor, there is a passage of electricity from one to the 
other, and this we speak of as an electric current 

The terms we use in dealing with electric currents are 
suggested by a study of the flow of liquids in pipes, but we 
must not push the analogy between the two cases too far. 
As to what electricity really is we are in entire ignorance. 
There may be no actual motion of anything through the con- 
ductor, though recent investigations somewhat favour that 
view, but since the current can do work for us we recognize 
the presence of energy. 

464. An Electric Current Known by the Effects it will 
Produce. The electric current makes the conductor and the 

region surrounding it acquire new 
properties, one of the most striking 
of these being a chanere in magfnetic 
conditions. This is illustrated in 
the following experiment. 

Insert an unmagnetized knitting 
needle into a small glass tube and 
wind copper wire in a coil about it. 
Connect one end of the wire with 
the outer coating of a powerfully charged Leyden jar, and the 
other with a discharger as shown in Fig. 481. Discharge the 
jar through the wire. On testing the knitting needle with 
a magnetic compass it will be found to be magnetized. 
Evidently the coil of wire in carrying the charge had the 
power to magnetize the steel. 

465. The Voltaic Cell. The current in the wire connecting 
the two coatings of the Leyden jar lasts but for an instant, the 

396 




Fia. 481. — The pressure of an electric 
current shown by its power to mag- 
netize steel. 



THE VOI/FAIC CP]LL 



397 



coatings almost at once assuming the same potential. In 
order to produce a continuous current a constant dift'erence 
of potential must be maintained between the ends of the 
conductor. Tliis can be done by means of the Galvanic or 
Voltaic Cell. 

Galvani* discovered by accident that the discharge of an 
electric machine connected with a skinned frog produced con- 
vulsions in the legs ; and on 
further research he found that 
the same effect could be produced 
without the electric machine, but 
simply by touching one end of 
a branched fork of copper and 
silver wires to the muscles in 
the frog's leg, and the other end 
to the lumbar nerves (Fig. 482). 
He attributed the result to 
" animal magnetism." 

Volta, a fellow-countryman, 
conceived that the electric cur- 
rent had its origin, not in the 
frog's legs, but in the contact of 
the metals, and in a series of investigations he was led to 
the invention of the voltaic cell. 

Volta divided conductors into two 
classes : — First, simple substances 
such as the metallic conductors, 
silver, copper, zinc, etc. Second, 
liquids such as dilute acids and solu- 
tions of metallic salts. These are 
now known as electrolytes, and are 
decomposed when an electric current passes through them. 







Alessandro Volta (1745-1827). Professor 
of Physios at the University of Pavia, Italy. 
Invented the voltaic cell. 




Fi0. 482.— Galvani's experiment. 



*Aloisio Galvani (1737-1798), a Physician and Professor of Anatomy in the University of 
Bologna. 



898 



THE ELECTRIC CURRENT 




Fio. 483.— Conductors of the first class con 
nected in a circuit ; no current produced. 




He found that it was impossible to produce a current by 

joining conductors of the first 
class in any order whatever in 
a circuit (Fig. 483) ; but that 
a current was developed when- 
ever a conductor of the second 
class was introduced between 
two different conductors of the 
first class. For example, he found that when discs of copper 
and zinc were separated by a disc of cloth moistened with 
common salt brine, and joined exter- 
nally by a conductor as in Fig. 484, 
a current passed through the circuit. 
Similarly he found that a current p,^. 48l^onductors of the first 
was generated when the plates thus TcirS' ll'^c ^T copper ■ 
connected were immersed in dilute ^. cloth moistened with brine. 

sulphuric acid (Fig. 485). This combination is a voltaic cell 
in its simplest form. 
The essential parts of an ordinary voltaic cell are two different 
conducting plates immersed in an electrolyte 
which acts chemically on one of them. 

466. Plates of a Voltaic Cell Electrically 
Charged. Since an electric current flows 
through a conductor joining the plates of a 
voltaic cell, we would infer that the plates 
are electrically charged when disconnected. 
This can be shown to be the case by means 
of a condensing electroscope, which consists 
of an ordinary gold-leaf electroscope combinei) 
with a suitable condenser. 

A convenient arrangement is illustrated in 
Fig. 486. It is unsatisfactory to work with 
a single voltaic cell. Three or four should be joined "in 
series " as shown at B. These cells may be small glass tubes 



s 


; ; 

z 






S>z'ziz:<iC 




m 


. . . i 

IphurieAi 


M 



Fig. 485.— Simple 
voltaic cell. 



PLATES OF A VOLTAIC CELL 



399 



or bottles containincr dilute sulphuric acid, with strips of 
copper and zinc soldered together and dipping in them. 
The condenser consists of two perfectly flat brass plates. 
The lower one Af is supported on an ebonite stem, and 
the upper one JSf is furnished with a handle. A sheet of 
paraffined paper or dry writing paper or very thin mica is 




e r c z c z 



Fio. 486. — The condensing electroscope. 

placed between the plates. The binding-posts e and / are 
joined to the electroscope, which is the same as shown in 
Fig. 463, with the disc removed. Its binding-post is joined to 
a gas-pipe or other good earth-connection. The end zinc plate 
Z of the battery is joined to a and the end copper plate G 
is joined loosely by the wire lo to the binding post h. 

When the connections have been made as described, there is 
a charge on the gold leaves, but it is so slight that they do 
not diverge appreciably. 

Now by means of a glass or ebonite I'od remove the wire w 
from the binding post h, and then lift off' the iipper plate N of 
the condenser. The leaves now diverge. 

This action may be explained thus : — When the connections 
are as shown in the figure, Z and N are both joined to earth 
and hence are at zero potential. The lower plate M is charged 
positively by the battery. This ' charge attracts a hound 
negative charge to the lower face of N, repelling the corres- 
ponding free charge to earth. Thus there is a considerable 
charge of electricity in the condenser though the potential is 
not high. 



400 THE ELECTRIC CURRENT 

But when vj is removed and the plate iY hfted the plate 31 
is no longer a part of a condenser, but simply an isolated plate 
of much smaller capacity. The charge on it now being free, it 
spreads to the electroscope and causes the leaves to diverge. 

In a voltaic cell the plate which is not attacked chemically 
is always found to have a positive charge, while the active 
plate is always found to have a negative charge. 

467. An Electric Circuit — Explanation of Terms. A 
complete circuit is necessary for a steady flow of electricity. 
This circuit comprises the entire path traversed by the current, 
including the external conductor, the plates, and the electrolyte. 
The current is regarded as flowing from the copper to the zinc 
plate in the external conductor, and from the zinc to the 
copper plate ivithin the fluid (Fig. 485). 

When the plates are joined by a conductor, or a series of 
conductors, without a break, the cell is said to be on a closed 
circuit; when the circuit is interrupted at any point, the cell 
is on an open circuit. By joining together a number of cells 
a more powerful flow of electricity may be obtained, and such 
a combination is called a battery. 

That plate of the cell or battery from which the current is led 
oflfis called the positive pole, the other the negative p>ole. Also, 
in an interrupted circuit, that end from which the current will 
flow when the connection is completed is said to be a positive 
pole or terminal, the other a negative pole or terminal. 

468. Chemical Action of a Voltaic Cell. When plates of 
copper and pure zinc are placed in dilute sulphuric acid to 
form a voltaic cell, the zinc begins to dissolve in the acid, but 
the action is soon checked* by a coating of hydrogen which 
gathers on its surface. If the uj^per ends of the plates are 
connected by a conducting wire, or are touched together, the 
zinc continues to dissolve in the acid, forming zinc sulphate, 
and hydrogen is liberated at the copper plate. 



ELECTROMOTIVE FORCE 40] 

Commercial zinc will dissolve in the acid even when 
unconnected with another plate. The fact that the iinpure 
zinc wastes away in open circuit is possibly explained on the 
theory that the impurities, principally iron and carbon, take 
the place of the copper plate, and as a consequence currents 
are set up between the zinc and the impurities in electrical 
contact with it. 

469. Source of Energy in the Cell. In order to produce a 
flow of electricity energy is required. The commonly accepted 
chemical theory of the action of a cell will be given in the next 
chapter ; but for the present we may think of the cell as a 
kind of furnace in which zinc is burned up chemically in 
order to obtain electric energy. 

When the circuit is open, just enough energy is exerted to 
keep the poles at a certain difference of electrical level or 
potential, but when the poles are connected by a conductor 
the current flows and the zinc is continually consumed. 

470. Electromotive Force. The term electromotive force 
is applied to that which tends to 'produce a transfer of elec- 
tricity. Consider, for example, a voltaic cell on an open 
circuit. Its electromotive force is its power of producing 
electric pressure, and this is obviously equal to the potential 
diflerence between the plates. 

This conception can be illustrated by the analogy to two 
tanks of water maintained at different levels (Fig. 473). Just 
as the difference in level gives rise to a hydrostatic pressure 
which would cause a transfer of water if the tanks -were con- 
nected by a pipe, so a difference of potential in the plates of the 
cell is regarded as producing an electrical pressure, or electro- 
motive force, which would cause a transfer of electricity if the 
plates were connected by a conductor. (Read § 453 again.) 

471. Unit of Electromotive Force. The difference of 
potential between two bodies is measured by the M'ork done 
in transferring a certain quantity of electricity from one to 



402 THE ELECTRIC CURRENT 

the otlier. The practical unit of petential difference, and 
lience ot" electromotive force (E.M. F.), is known as the volt, 
and tliis may be taken as approximately the E.M.F. ot" a zinc- 
copper cell. 

472. Electromotive Force, Current Strength, and Resis- 
tance. The water analogy may assist us still further. 

The strength of the water current, that is, the quantity of 
water which will flow past a point in the pipe in one second, 
obviously depends upon the pressure resulting from differences 
of level, and upon tha resistance which the pipe offers to the 
flow of water. Similarly the strength of the current wdiich 
passes through the conductor joining the plates of a cell 
depends upon tlte electromotive force of the cell and the 
RESISTANCE of the circuit. 

The strength of the current may be increased, either by 
increasinof the electromotive force, or reducing the resistance 
of the circuit. The exact relation between these quantities will 
be discussed at a later stage (§ 546). 

473. The Electromotive Force of a Voltaic Cell. The 
E.M.F of a cell containing a given electrolyte depends on the 
nature of the plates. Thus the E.]\I.F. of the zinc-carbon cell 
is about twice as great as that of the zinc-copper cell, when 
dilute sulphuric acid is the electrolyte. 

When the materials used are constant, the E.M.F. is inde- 
pendent of the size and shape of the plates or their distance 
apart. 

Theoretically, a comparatively large number of substances 
might be selected as plates to construct a voltaic cell. 
Consider, for example, the following elements in the order 
given : — 

Magnesium | Zinc | Lead | Tin | Iron | Copper i Silver | Gold | Platinum | Carbon 

If any two of these elements are used as plates in a voltaic 

cell the current will flow in the outer circuit from the second 



DETECTION OP AN ELECT RIO CURRENT 



403 



to the first named. Moreover, the })otential diffei-ence between 
any pair depends upon their distance apart in the series. 
Such a series is known as an elect rornotive, ov ■potenfial,HQrieB. 

474. Oersted's Experiment. We have referred to the fact 
that an electric current has the power of producing niagnetic 
effects (§ 4()4). This important principle was discovered by 
Oersted* in 1819. In the course of some experiments made 
with the purpose of discovering an identity between electricity 
and magnetism, he chanced to bring the wire joining the 
plates of a voltaic battery over a magnetic needle, and was 
astonished to see the needle turn round and set itself almost 
at right angles to the wire. 
On reversing the direction of 
the current the needle turned 
in the opposite direction (Fig. 
487). If the battery is held 
over the wire the needle is 
deflected, thus showing that 
the current flows through the 
battery too. 

475. Detection of an Electric Current. Oersted's experi- 
ment furnishes a ready means of detecting an electric current, 
A feeble current, flowing in a sinu;le wire over a map^netic 
needle produces but a very slight deflection; but if the wire is 

wound into a coil, and the cur- 
rent made to pass several times 
in the same direction, either over 
or under the needle, or, better 
still, if it passes in one direction 

Fig. 488.-Simple gfalvanoscope The wire q^^^ [^ ^ud in the OppOsite dirCC- 
passesseveral times around the frame, and X i 

its ends are joined to the binding-posts. ^[^^ under it, the cffect will be 

magnified (Fig. 488). Such an arrangement is called a Gal- 
vanoscope. It may be used not only to detect the presence of 

* Hans Christian Oersted (1777-1851), Professor in the University of Oopenhaj^en. 




Fig. 487.— Oersted's experiment. 




404 THE ELECTRIC CDRRENT 

currents, but also to compare roughly their strengths, by 
noting the relative deflections produced. 

476. Local Action. We have noted that a plate of com- 
mercial zinc dissolves when immersed in dilute acid, because 
electric currents are set up between the zinc and the impurities 
in electrical contact with it. Such currents are known as 
local currents, and the action is known as local action. This 
local action is wasteful. It may, to a great extent, be pre- 
vented by amalgamating the zinc. This is done by washing 
the plate in dilute sulphuric acid, and then rubbing mercury 
over its surface. The mercury dissolves the zinc, and forms a 
clean uniform layer of zinc amalgam about the plate. The 
zinc now dissolves only when the circuit is closed. As the 
zinc of the amalgam goes into the solution, the mercury takes 
up more of the zinc from within and the impurities float out 
into the liquid (see § 468). Thus a homogeneous surface 
remains always exposed to the acid. 

477. Polarization of a Cell. If the plates of a zinc-copper 
cell are connected with a galvanoscope the current developed 
by the cell will be seen gradually to grow weaker. It 
will also be observed that the weakening in the current is 
accompanied by the collection of bubbles of hydrogen on the 
copper plate. To show that there is a connection between 
the change in the surface of the plate and the weakening in 
the current, brush away the bubbles and the current will be 
found to grow stronger. A cell is said to be polarized when 
the current becomes feeble from a deposition of a film of 
hydrogen on the plate forming the positive pole. 

The adhesion of the hydrogen to the positive pole weakens 
the current in two ways. First, it decreases the potential 
difference between the plates ; because the potential difference 
between zinc and hydrogen is much less than between zinc and 
copper or carbon. Second, it increases the resistance which 



LEGLANCHfi CELL— DANIELL CELL 



405 



the current encounters within the cell, because it diminishes 
the surface of the plate in contact with the fluid. 

Polarization may be reduced by surrounding the positive 
pole by a chemical agent which will combine with the hydrogen 
and prevent its appearance on the plate. 

478. Varieties of Voltaic Cells. Voltaic cells differ from 
one another mainly in the remedies adopted to prevent 
polarization. Several of the forms connnonly described have 
now only historic interest. Of the cells at present used for 
commercial purposes, the Leclanch^, the Daniell, the Dry and 
the Edison-Lalande are among the most important. 

479. Leclanchd Cell. The construction of the cell is shown 
in Fig. 489. It consists of a zinc rod immersed in a solution 
of ammonic chloride in an outer vessel, 
and a carbon plate surrounded by a 
mixture of small pieces of carbon 
and powdered manganese dioxide in 
an inner porous cup. The zinc dis- 
solves in the anunonic chloride solu- 
tion, and the hydrogen which appears 
at the carbon plate is oxidized by the 
manofanese dioxide. 




Fig. 489.— Lfiolanch6 cell. C, car- 
bon ; D, porous cup ; Z, zinc ; 
Jf, carbon and powdered man- 
ganese ; S, solution of amnionic 
chloride. 



As the reduction of the manganese 
dioxide goes on very slowly, the cell 
soon becomes polarized, but it recovers itself when allowed to 
stand for a few minutes. If used intermittently for a minute 
or two at a time, the cell does not require renewing for 
months. For this reason it is especially adapted for use on 
electric bell and telephone circuits. Its E.M.F. is about 
1.5 volts. 

480. Daniell Cell. The Daniell cell consists of a copper 
plate immersed in a concentrated solution of copper sulphate 



406 



THE ELECTRIC CURRENT 




Fis. 490. — Daniell cell. Z, zinc ; P, porous cup ; 
C, copper ; 4, solution of zinc sulphate; i>, solu- 
tion of copper sulphate. 



contained in an outer vessel and a zinc plate immersed in a 

zinc sulphate solution in an 
inner porous cup (Fig. 490). 

In a form of the Daniell 
cell known as tlie Gravity 
Cell the porous cup is dis- 
pensed with and the solu- 
tions are separated by gravity 
(Fig. 491). The zinc plate, 
w^hicli is usually of the form 
shown in the figure, is sup- 
ported near tlie top of the 
vessel and tlie copper plate 

is placed at the bottom. The copper sulphate being denser 

than the zinc sulphate, sinks to the bottom, while the zinc 

sulphate floats above about the 

zinc plate. The copper sulphate 

solution is kept concentrated by 

placing crystals of the salt in a 

basket in the .outer vessel (Fig. 

490), or at the bottom about the 

copper plate (Fig. 491). 

Tlie Daniell cell is capable of Fio. 491.— Gravity cell. Z, zinc plate; 

. . ..A, zinc sulphate solution; B, copper 

giving a continuous current tor sulphate solution ; C, crystals of copper 

an indefinite period if the materials 

are renewed at regular intervals; but the strength of the cur- 
rent is never very great because the internal resistance is high.. 

These cells are adapted for closed circuit work, when a 
comparatively weak current will suffice. The gravity type has 
been extensively used on telegraph lines, but in the larger 
installations the dynamo and the storage battery plants are 
now taking their place. 

The E.M.F. of the cell is about 1.07 volts. 




CELLS 



407 




N— ^^SL 



481. The Dry Cell. The so-called dry cell is a modified 
form of the Leclanchd cell. The carbon 
plate C (Fig. 492) is closely surrounded 
by a thick paste, A, composed chiefly 
of powdered carbon, manganese dioxide 
and amnionic chloride. This is all con- 
tained in a cylindrical zinc vessel, Z, 
which acts as the negative pole of the 
cell. Melted pitch, P, is poured on 
top in order to prevent evaporation, Fio. 492. -a dry cell. 

i e., to prevent the cell from becoming really dry. 

482. Edison-Lalande Cell. In this cell one plate consists of 
compressed finely -ground copper oxide powder fitted in a light 
copper frame. On each side of this is a plate of zinc well 
amalgamated. The exciting li(]uid consists of one part of 
caustic soda dissolved in three parts by weight of water. To 
prevent it from being acted upon by the carbonic acid of the 
air it is covered with a layer of petroleum. 

The E.M.F. is low, about 0.7 volt, but the internal resistance 
is also low; such a cell can deliver a powerful current (10 to 
20 amperes) for a considerable time ( 1 5 to 30 hours). 

QUESTIONS 
1. The bichromate cell, once very commonly used in laboratories, 
consists of two connected carbon plates G and a zinc plate Z 
between them, immersed in a solution of potassium bichro- 
mate in water mixed with sulphuric acid S. (Fig. 493.) 
Explain the action of the cell. 

2. The Grove cell, used before the dynamo wjis perfected, 
to furnish energetic constant currents, consists of a zinc 
plate immersed in dilute sulphuric acid and a platinum plate 
immersed in nitric acid, the fluids being kept apart by a 
porous cup. Tlie Bunsen's cell differs from the Grove's 
cell in substituting a carbon plate for the platinum one. 
Explain the action of those cells. 




Fio. 493.— Bi- 
ohromate cell. 



CHAPTER XLIV 




Chemical Effects of the Electric Current 

483. Electrolysis. lu the preceding chapter we have dis- 
cussed tlie production of an electric current through the 
action of an electrolyte on two dissimilar plates. If the 
action is reversed and a current from some external 
source is passed through an electrolyte, reactions 
similar to those within the voltaic cell take place. As 
an illustration take the action of an electric current 
on hydrocliloric acid. Con- _^ ^^ 
nect the poles of a voltaic 
battery consisting of three 
or four cells to two carbon 
rods A and B (Fig. 494), 
and immerse these in the 
acid. The current flows in 
the direction indicated by 
the arrows, and the rod A by which it enters the electrolytic 
cell is called the anode, the rod B by which it leaves is called 
the catliode. A and B are spoken of as electrodes. Gases will 
collect at the electrodes. On testing, that liberated at A will 
be found to be chlorine, and that at B, hydrogen. This process 
of decomposition by the electric current is called electrolysis 
(i.e., electric analysis). 

484. Explanation of Electrolysis. According to the theory 
at present most commonly accepted, an electrolytic salt or 
acid, when in solution, becomes more or less completely 
dissociated. The respective parts into which the molecules 
divide are known as ions. When, for example, common salt 
is dissolved in water, a percentage of the molecules (NaCl) 

408 



Fig. 494.— Electrolysis of hydrochloric acid. The 
electrodes A and B are carbon rods fitted in 
rubber stoppers. 



THEORY OF THE ACTION OF A VOLTAIC CELL 409 

break up to form sodium (Na) and chlorine (CI) ions. Simi- 
larly, if sulphuric acid is diluted with water, some of its 
molecules (H^SO^) dissociate into hydrogen (H) ions and 
sulphion (SOJ ions. 

A definite charge of electricity is associated with each ion, 
and wdien it loses this charge it ceases to be an ion. The 
hydrogen and sodium atoms, and the atoms of metals in 
general, as ions, bear positive charges, while chlorine atoms 
and sulphion are tjqjes, respectively, of the elements and 
radicals which bear negative charjres. 

The ionization theory furnishes a simple explanation of the 
typical results described in the preceding section. When 
connected with the terminals of the battery the electrodes 
innnersed in the hydrochloric acid become charged, the anode 
positively, and the cathode negatively. As a consefjuenee, the 
positively charged hydrogen ions are attracted to the cathode, 
and the negatively charged chlorine ions to the anode. This 
'migration' of positively charged ions in one direction, and 
negatively charged ions in the other, constitutes the current in 
the electrolyte. 

The ions give up their charges to the electrodes, and combine 
to form molecules. The gases are, therefore, liberated at these 
centres. 

The positive charges which the hydrogen ions bring to the 
cathode tend to diminish the negative charge of the cathode, 
while the negative charges of the chlorine tend to diminish 
the positive charge of the anode ; but a constant difference of 
potential between the electrodes is kept up by the current 
maintained in the external conductor by the battery. 

485. Theory of the Action of a Voltaic Cell. We have seen 

that chemical changes accompany the production of tlie current in 
the voltaic cell (§ 468). These take place in accordance with the 
same principles as the changes in the electrolytic cell as described in 
sections 483 and 484, the main difference being that in the elec- 
trolytic cell the source of the current is without the cell, while in 



410 CHEMICAL EFFECTS OF THE ELECTRIC CURRENT 

the voltaic cell the current originates within the cell itself. Various 
theories have been proposed to account for the cause of the current 
in the voltaic cell. Possibly the application of the ionization theory 
as proposed by Nernst gives the most plausible explanation of its 



According to this theory every metal immersed in an electrolyte 
has a certain pressure, known as its solution tension, tending to 
project its particles into solution in the form of ions. The magni- 
tude of this pressure is the greater the nearer the metal to the 
positive limit in an electromotive series (§ 473). The metallic ions 
also have a tendency to give up their charges and to deposit them- 
selves on metals immersed in the electrolyte, this tendency being 
the stronger the nearer the metal to the negative limit in an electro- 
motive series. When the former of the forces is the stronger the 
solution about the metal in acquiring positive ions becomes posi- 
tively cliarged in its relation to the metal. On the other hand, 
when the tendency of the ions to deposit themselves is the greater, 
an excess of deposition over solution takes place, and the metal in 
comparison with the solution becomes positively charged. In" the 
first case the metal becomes lower in potential than the solution, 
and in the second case higher. 

To apply this theory to the simple cell in which zinc and copper 
are the plates and dilute sulphuric acid is the electrolyte, consider 

first the zinc plate. Since zinc is near 
"v-rxt- - 7r<^ the positive limit in the electromotive 

series, the tension driving ions into 
solution is greater than the tendency 
towards deposition ; hence zinc ions go 
into solution carrying positive charges. 
By experimental determination the 
zinc is found to be 0.62 volts lower in 
potential than the solution. Now con- 
sider the copper. As copper is towards 
the negative side of the series, the tend- 
ency of the ions to deposit themselves 
is the greater of the forces and the 
plate becomes positively charged by 
^f.: 495.-piagram illustrating the the deposition of positively charged 

theory of the action of a voltaic cell. i i . mi i i 

hj'drogen ions, llie plate can be 
shown to be 0.46 volts higher in potential than the solution. The 
difference in potential, therefore, between the copper and zinc plates 
is 0.46 + 0.62 = 1.08 volts. 




SECONDARY REACTIONS IN ELECTROLYSIS 



411 



"When tlie poles are connected a current flows through the wire 
from the copper to tlie zinc, tending to discharge them ; but, as 
rapidly as they are discharged the zinc throws more ions into solu- 
tion and more hydrogen ions are forced against the copper, retaining 
a permanent diiFerence of potential between the metals and producing 
a continuous flow of electricity until the zinc is all dissolved or the 
hydrogen ions all driven out of the electrolyte. The migration of 
positively charged ions towards the copper plate (cathode) and of 
the negatively charged ions towards the zinc plate (anode) constitute, 
as in the electrolytic cell, the current in the electrolyte. 

486. Secondary Reactions in Electrolysis. If the hydro- 
chloric acid is replaced by a solution of common salt (NaOl), 
chlorine as before appears at the anode, but the sodium atoms, which 
have parted with their charges to the cathode, instead of combining 
to foi*m molecules, displace hydrogen atoms from mole- 
cules of water in order to form sodium hydroxide. Hence, 
hydrogen, and not sodium, is liberated at the cathode. 
The presence of the hydroxide in solution can be 
shown by adding sufficient red litmus to colour the 
solution. As soon as the 
current begins to pass, the 
liquid about the cathode is 
turned blue. The bleaching 
of the litmus about the 
anode indicates the presence 
of chlorine. 

rrii 1 ... Fig. 496. — Electrolj'sis of water, 

ine above expernnent is 

typical of a large number of 

cases of electrolytic decomposition where secondary reactions, depend- 
ing on the chemical relations of elements involved, take place. The 
electrolysis of water, possibly, furnishes another example. 

487. Electrolysis of Water. Insert platinum electrodes 
into the bottom of a vessel of the form sliown in Fig. 49U. 
Partially fill the vessel with water acidulated with a few 
drops of sulphuric acid. Fill two test tubes with acidulated 
water and invert them over the electrodes. Connect the 
electrodes with a battery of tliree or four voltaic cells. Gases 
will be seen to bubble up from the electrodes, displacing the 
water in the test tubes. 




412 CHEMICAL EFFECTS OF THE ELECTRIC CURRENT 



On testing each gas with a lighted splinter, that collected 
at the anode will be found to be oxygen, and that at the 
cathode, hydrogen. It will also be observed that the volume 
of the hydrogen collected is twice that of the oxygen. 

In this case, as in the electrolysis of hydrochloric acid, there is a 
migration of hydrogen ions in the direction of the current, and the 
gas is given off at the cathode ; but the liberation of the oxygen is 
probably due to secondary reactions. The sulphion ^SO^) ions move 
to the anode, where they part with their charges and combine with 
the hydrogen of the water, thus forming again sulphuric acid, and 
liberating oxygen. The quantity of the acid, therefore, remains 
unchanged and water only is decomposed. 

488. Electroplating. Advantage is taken of the deposi- 
tion of a metal from a salt by electrolysis in order to cover 
one metal with a layer of another, the process being known as 
electroplati7ig. 

Consider, as an example, the process of silver-plating. The 
objects to be plated are immersed in a bath containing a 

solution oi a silver salt, usually the 
cyanide (AgCN). A plate of silver is 
also immersed in the bath (Fig. 497). 
A current from a battery or dynamo 
is then passed through the bath, from 
the silver plate (the anode), to the 
objects (the cathode). The positively 
Fig. 497.— Bath and electrical con- charged silver ious are Urged to 

nection for electroplating. i i • i • • i • 

the objects, and on giving up their 
charges, are deposited as a metallic film upon them. Mean- 
while the negatively charged cyanogen (CN) ions migrate 
towards the silver plate, from wliich they attract into solution 
additional silver ions. Tlius the metal is transferred from the 
plate to the objects, while the strength of the solution remains 
constant. 

The process of plating with other metals is similar to 
silver-plating. The electrolyte must always be a solution 




ET.ECTUOTYPINO 413 

of tlie salt of the laotal to l)e decomposed; the anode is 
a plate of that itiotal, and the cathode the object to be 
plated. 

For copper-plating, tlie bath is usually a solution of copper 
sulphate; for gold- and silver-plating, a solution of the cya- 
nides ; and for nickel-plating, a solution of the double sulpliate 
of nickel and anniioniuni. 

489. Electrotyping. Books are now usually printed from 
electrotype plates instead of from type, as the type would soon 
wear away. An impression of the type is made in a wax 
mould, the face of which is then covered with powdered 
plumbago to provide a conducting surface uj)on which the 
metal can be deposited. Tlie mould is then flowed with a 
solution of copper sulphate, and iron filings are sprinkled over 
it. The iron displaces copper from the sulphate, and the 
plumbago surface is thus covered with a thin tilm of copper. 
The iron filings are washed off, and the mould immer.sed in a 
bath of nearly concentrated copper sulphate solution, slightly 
acidulated with sulphuric acid. The copper surface is then 
connected with the negative pole of a battery or dynamo, and 
a copper plate which is connected with the positive pole is 
immersed in the bath. 

WJien the layer of copper has become sufficient!}^ thick it is 
removed from the bath, backed with melted type-metal and 
mounted on a wooden block. The face is an exact repro- 
duction of the type or engraving. 

490. Electrolytic Reduction of Ores ; Electrolysis Applied 

to Manufactures. Electrolytic processes are now extensively used 
for reducing certain metals from their ores. A soluble, or fusible 
salt is formed by the action of chemical reagents, and the metal 
is deposited from it by electrolysis. For example, aluminium is 
reduced in large quantities from a fused mixture of electrolytes. 
Sodium is prepared in a similar manner. 

The metallui'gist also resorts to electrolysis in separating metals 
from their impurities. Copper, for example, is refined in this way. 



414 CHEMICAL EFFECTS OF THE ELECTRIC CURRENT 



M^f 



FiQ. 498.— Electric connection in an 
experiment to illustrate the polari- 
zation of electrodes. 



The unrefined copper is made the anode in a bath of copper sulphate, 
and the pure copper is deposited at the cathode, wliile the impurities 
fall to the bottom of the bath. 

Currents of electricity are also employed in the preparation of 
many chemical products for commercial purposes. Caustic soda 
and bleaching liquors are manufactured on a large scale by . 
electrolytic means. 

491. Polarization of Electrodes. If, in the process of the 
decomposition of water (§ 487), we disconnect the wires from 

the battery when the gases are 
coming off freely, and connect them 
with a galvanoscope, we shall find 
that a current will flow in a 
direction opposite to that which 
liberated the hydrogen and oxygen. 
The experiment may be readily 
performed by connecting the bat- 
tery B, the electrolytic cell A, and 
the galvanoscope G, as shown in Fig. 498, mercury cups or 
keys being provided for opening and closing the circuits at 
G and D. When the circuit is closed at G but open at D the 
electrolysis proceeds, and the galvanoscope indicates the 
direction of the current. If the battery is cut out by 
opening C, and the circuit is closed at D, a momentary 
current is found to pass in a direction opposite to the 
original current. 

The reverse current is explained on the principle that the 
films of hydrogen and oxygen which collect about the elec- 
trodes cause a difference in potential between them, which 
develops an E.M.F. in a direction opposite to tliat which 
prodticed the original current. The electrodes are then said 
to be j)olarized. 

It is obvious that to decompose water, tlie E.M.F, of the 
battery used must be greater than the counter-electromotive 



SECONDARY, OR STORAGE CELLS 415 

force, which is about 1.47 volts, sei up by the difference in 
potential between the electrodes when the gases are being 
liberated. 

492. Storage Cells or Accumulators. If lead electrodes are 
substituted for the platinum in the experiment of the preceding 
section, and the battery current is made to pass through 
dilute sulphuric acid (1 of acid to 10 of water) for a few 
minutes, hydrogen will be liberated as before at the 
cathode, and the other lead plate, tlie anode, will be 
observed to turn a dark brown, but no oxygen will be 
set free at its surface. 

On cutting out the battery by opening the circuit at G, and 
connecting tlie lead plates with tlie galvanoscope by closing 
the circuit at D, a reverse current, much stronger than that 
generated by the polarization of the platinum electrodes, will 
pass through the galvanoscope. Moreover, this current will 
last much longer. 

This experiment illustrates the principle of action of all 
storage cells or acciiniidatovfi. 

Wlien tlie current is passed through the dilute acid from 
one plate to the other, the oxygen freed at the anode unites 
with the lead, forming oxide of lead. The composition of 
the anode is thus made to differ from the cathode, and in 
consequence there arises a difference in potential between 
them which causes a current to flow in the opposite direction 
when the plates are joined by a conductor. 

This current will continue to flow until the plates again 
become alike in composition, and hence in potential. 

493. Construction of Lead Cell and Edison Cell. Instead 

of using plates of solid lead, perforated plates or "grids" made of 
lead, or some alloy of lead, are frequently employed. The holes in 
the plates are filled with a paste of lead oxides (red lead on the 
positive, litharge on the negative plate), which forms the active 



416 CHEMICAL EFFECTS. OF THE ELECTRIC CURRENT 




Fig. 499. — A storage cell, 
with one positive and 
two negative plates. 
Two positive and three 
negative, three positive 
and four negative, or 
even more plates may 
be used. 



material (Fig. 499). "When the plates are immersed in the dilute 
sulphuric acid and the current passed through the cell, these oxides 
are changed to peroxide (PbOg) in the positive 
plates and reduced to spongy lead in the negative. 
During the process of discharge both the 
plates are converted into lead sulphate, and a 
part of the sulphuric acid disappears, thus 
lowering the density of the electrolyte. When 
the cell is being charged, the sulphion ions 
combine with lead sulphate and water to form 
the lead peroxide and sulphuric acid, and the 
hydrogen ions react upon the lead sulphate 
forming spongy lead and sulphuric acid. 

In the Edison storage battery, which has 
recently obtained some prominence, the positive 
plate consists of perforated steel tubes heavily 
nickel-plated, filled with alternate layers of 
nickel hydroxide and pure metallic nickel in 
very thin flakes. Tlie negative plate is a grid 
of nickel-plated steel holding a number of rec- 
tangular pockets filled with powdered iron 
oxide. The electrolyte is a 21 per cent, solution of caustic potash 
in distilled water, with a small percentage of lithia. The battery 
jar is made from nickel -plated steel. Its voltage is 1.2 and it 
weighs about one-half as much as a lead battery of equal capacity. 

494. Laws of Electrolysis. Faraday discovered the Laws of 
Electrolysis and formulated thein in 1833. They may be 
summed up in the following statements : — 

1. The amount of an ion liberated at an electrode in a 
given time is proportional to the strength of the current. 

2. T}ie weights of the elements separated from the electrolyte 
by the saine electric current are in the proportion of their 
chemical equivalents. 

495. Measurement of Current Strength by Electrolysis. 
In accordance with the laws of electrolysis the amount of the 
ions liberated per unit time may be taken as an exact measure 
of the strength of a current passing through an electrolyte. 

Tlie practical unit of current strength is called the ampere 
and is defined as the current ivhich deposits silver at the rate 
of 0.001118 grains per second (see § 547). 



VOLTAMETERS 



417 



Tlie same current deposits copper at the rate of 0.000328 
grams, and hydrogen at the rate of 0.000010884 gram.s per 
second. 

Other elements may be used in defining the unit, but in 
practice wlien the strength of a current is to be estimated by 
electrolysis, it is usually determined by ascertaining tlie 
amount of silver, copper, or hydrogen which is deposited in a 
specified time. If W-^^, W.^, W^ is the mass in grams of 
silver, copper and liydrogen, respectively, deposited in t 
seconds, and G the strength of the current in amperes. Then 



G = 



W„ 



IF, 



t X 0.001118 t X 0.000328 t x 0.000010384 




496. Voltameters. An electrolytic cell used for the purpose 
of measuring the strength of an electric 
current is called a voltameter. 

For silver, tlie cell consists of a platinum 
bowl, partially filled with a solution of 
silver nitrate in which is suspended a silver 
disc (Fig. 500). When the voltameter is 
placed in the circuit, the platinum bowl is 
made the cathode and the silver disc the 
anode. When the current has been passed 
through the solution for the specified time 
the silver disc is removed, the solution 
poured off, and the bowl washed, dried and 
weighed. The increase in weight gives 
the mass deposited. 

The copper voltameter consists of two 
copper electrodes immersed in a solution 
of copper sulphate. The cathode is weiglied before and after 
the passing of the current. Tlie diflference in weight gives the 
amount of copper deposited in the given time. 



Fio. 500. — A standard silver 
voltameter. Cathode, a 
platinum bowl not less 
than 6 cm. in diameter 
and 4 cm. deep. It rests 
on a metal ring to ensure 
good connection. Anode, 
a disc of pure silver 
supported by a silver 
rod riveted through its 
centre. Electrolyte, 15 
parts by weight of silver 
nitrate to 8.5 parts of 
water. Filter paper is 
wrapped about the anode 
to prevent loose particles 
of silver from falling on 
the cathode. 



418 CHEMICAL EFFECTS OF THE ELECTRIC CURRENT 

Tlie hydrogen, or water, voltameter is simply the apparatus 
used for the decomposition of water (§ 487). For the purpose 
of measuring the current, the hydrogen alone is collected in a 
graduated tube. The current to be measured is passed through 
tlie acidulated water until the liquid in the tube stands at the 
same level as the liquid in the vessel. The time during which 
the current was passing is then noted. The temperature of the 
gas and the barometric pressure are also taken. The volume 
of the hydrogen liberated is read from tlie graduated tube, 
reduced to standard pressure and temperature, and the mass 
corresponding to this volume calculated. 

The process of measuring the strength of a current by a volta- 
meter is slow. We shall discuss in tlie next chapter a more 
convenient method by the use of galvanometers. Voltameters 
are now used mainly in standardizing these instruments. 

QUESTIONS AND PROBLEMS 

1. Why can a single Daniell cell not be used to decompose water ? 

2. Plates of copper and platinum are dipped into a solution of copper 
sulphate, and a current is passed through the cell from the copper to tlie 
platinum. Describe the effects produced, also what happens when the 
current is reversed. 

3. How long will it take a current of one ampere to deposit one gram 
of copper from a solution of copper sulphate ? 

4. A constant current is passed through a silver voltameter for a period 
of 20 minutes and it is found that 6.708 grams of silver have been 
deposited. What is the strength of the current ? 

5. The same current is passed through three electrolytic cells, the first 
containing acidulated water, the second a solution of copper sulphate, 
and the third a s<jlution of silvor nitrate. What weight of hydrogen and 
what weight of oxygen will be liberated at the first cell ; and what weight 
of copper will be deposited at the cathode of the second cell ; when 11.18 
grams of silver are deposited on the cathode of the third cell ? 

6. What transformations t)f energy take place (1) in charging a storage 
cell, (2) in discharging it ? Is anything "stored up" in the cell ? If so, what? 

7. Why is it possible to get a much stronger current from a storage cell 
than from a Daniell cell ? 



CHAPTER XLV 



Magnetic Relations of the Current 

497. Discovery of Electromagnetic Phenomena. The dis- 
covery by Oersted of tb.e effect of an eh^ctric current on the 
magnetic needle (§ 474) gave a decided impetus to tlie study of 
electromagnetic phenomena. The investigations of Arago, 
Ampere, Davy, Faraday and otliers during the next ten years 
led to the discovery of practically all the principles tliat have 
had important applications in modern electrical development. 

498. Magnetic Field Due to an Electric Current. In 1820, 
a year after Oersted's great discovery, Arago proved tliat a wire 
carrying a strong current had tlie power to lift iron filings, and 
hence concluded that such a wire must be refjarded as a magnet. 
Two years later Davy showed that the apparent attraction was 
due to the fact that the particles of iron became magnets under 
the influence of the current, and that on account of the mutual 
attractions of the opposite poles they fcn-med chains about the 
wire. 

The action of the current on the filings may be shown by 
passing a thick wire vertically up 
through a hole in a card, and sprink- 
lino' iron filintrs from a muslin bao; on 
the card. If tlie card is gently tapped 
wliile a strong current is passing 
througli the « 

wire, the filings / ^ a; v 

arrange them- /^^ ^ ^§i-\ 
selves in con- / i^^, \ 

centric rings H 

about it. (Fig. 501.) 

If a small jeweler's compass is placed 

on the card, and moved from point to 

point about tlie wire, it is found that in every position the 

needle tends to set itself with its axis tangent to a circle whose 

419 




Fio. !501. — The presence of a mag- 
netic field about a wire carrying 
an electric current shown by 
action on iron filings. 



Fio. 502. —The presence of a 
magnetic field about a wire 
carrying an electric current 
shown by the action on a 
compass needle. 



420 



MAGNETIC RELATIONS OP THE CURRENT 




Fig. 503 — Direction of lines of 
force about a conductor. 



centre is the wire (Fig. 502). On reversing the direction of the 
current the direction in wliich the needle points is also reversed. 
These experiments show that a wire through which an 
electric current is flowing is surrounded by a magnetic field, 
the lines of force of which form circles around it. Thus the 
wire throughout its entire length is surrounded by a " sort of 
enveloping magnetic whirl." 

The dir.ection in which a pole of the magnetic needle tends 
to turn depends on the direction of the current in the wire. 
Several rules for remembering the relation between the direc- 
tion of the current and the behaviour of the needle have been 
given, two of them being as follows : — 

1. Suppose the right hand to grasp 
the ivire carrying the current (Fig. 
503) so that the thumh points in the 
direction of its flow ; then the N-pole 
tvill he urged in the direction in which 
the fingers p)oint. 
2. Imagine a man swimming in the wire with the current 
and that he turns so as to face the needle; then the N-p>ole of 
the needle ivill he deflected towards his left hand. 
499. Magnetic Field about a Circular Conductor. Since 
the lines of force en- 
circle a conductor, it 
would appear that a 
wire in the form of a 
circular loop, carrying 
a current (Fig. 604) 
should act as a disc of 
steel magnetized so as 
to have one face a iY- 
pole, the other a /S-pole. That such is 
the case can be demonstrated by a simple 
experiment. Take a piece of copper wire and bend it- into ihe 




Fig. 504.— Lines of force 
about a circular loop. 




t rfMliir^ ru 



IG. 505. — Experiment to 
show that a circular loop 
carrying a current behaves 
as a disc magnet. 



MAGNETIC CONDITIONS OF A HELIX 421 

form shown in Fig. 505, making the circle aboiit 20 cm. in 
diameter. Suspend the wire by a long thread, and allow its ends 
to dip into mercury held in receptacles made in a wooden block 
of the form shown in the figure. (The inner receptacle should 
be about 2 cm. in diameter and the outer one 2 cm. wide with 
a space of 1 cm. of wood between them.) Pass a current 
through the circular conductor by connecting the poles of a 
battery with the mercury in the receptacles. For convenience 
in making connections, the receptacles should be connected by 
iron wires with binding posts screwed into the block. 

Now, if a bar-magnet is brought near the face of the loop, 
the latter will be attracted or repelled by its poles, and behave 
in every way as if it were a flat magnetic disc with poles at 
its faces. Indeed, if the current is strong, and the ends of the 
wire moves freely in the mercury, it will set itself with its 
faces north and south under the influence of the earth's 
magnetic field. 

In taking this position it obeys the general law that a 
magnet when placed in the field of force of another magnet 
always tends to set itself in such a position that the line 
joining its poles will be parallel to the lines of force of the 
field in which it is placed. 

To fulfil this condition the plane of the coil must become 
perpendicular to the direction of the lines of force of the field. 
A coil carrying a current, therefore, always tends to set itself 
in the position in which the maximum number of lines of 
force ivillpass through it. 

500. Magnetic Conditions of a Helix. Ampere showed that 
the magnetic power of a wire carrying a current could be 
intensified by winding it into the form of a sj^iral. The 
magnetic properties of such a coil can be demonstrated by 
simple experiments. 

Make a helix, or coil of wire, about three inches long, by 
winding insulated copper wire (No. 16 or 18) about a 



422 



MAGNETIC RELATIONS OF THE CURRENT 




Fig. 50u. — A helix carr^'ing a current be- 
haves like a bar-magnet. 



lead-pencil. Connect the ends of the wire with the poles of a 

voltaic cell, and with a mag- 
netic needle explore the region 
surrounding it. 

Next make a hehx some- 
what larger in diameter, say- 
about three-quarters of an inch, 
and place it in a rectangular 
opening made in a sheet of 
cardboard (Fig. 506). This can be done by cutting out two 
sides and an end of a rectangle of the proper size and then 
passing the free end of the strij) lengthwise through the 
helix, and replacing the strip in position. Sprinkle iron filings 
from a muslin bag- on the cardboard around the helix and 
wathin it. Attach the ends of the wire to the poles of a 
battery and gently tap the cardboard. 

In these experiments the helix through which the current 
is passing behaves exactly like a magnet, having W and 8 
poles and a neutral equatorial region. The field, as shown by 
the action of the needle and the iron filings, resembles that of 
a bar-magnet. (Compare § 429.) 

501. Polarity of the Helix and Direction of the Current. 

There is a fixed relation between the poles 
of the coil and the direction of the cm'rent 
passing through the wire. Looking at the 
south j)ole of the helix, the electric cur- fig.507.— Relation of poiar- 

,' 7 ,7 •? • .7 7* /• ity of helix to the direction 

rent pauses through the coils %n the direction of the current— clock rule. 

of the hands of a clock (Fig. 507) ; or, we can give a " right- 
hand " rule similar to that in § 498 as 
follows : — If the helix is grasped in the 
rigid hand, as shown in Fig. 508, with 
the fingers pointi^ig in the direction in 
which the current is moving in the coils, 
tJie thumb will point to the N-pole. 




N 




Fio. 608.— Relation of polar- 
ity of heli.x to direction of 
current— right-hand rule. 



ELECTROMAGNET 



423 




^a 



jY 



502. Electromagnet. Arago und Ampere magnetized steel 
needles by placing them within a coil 
of wire carrying a current. Sturgeon, 
in 1825, w^as the first to show tliat if 
a core of soft-iron is introduced into f,o. 509._The essential parts 

such a coil (Fig. 500) the magnetic effect of an electromagnet. 

is increased, and that tlie core loses, its magnetism when tlie 
circuit is opened. The combination of the lielix of insulated 
wire and a soft-iron core is called an electroviagnet. 

503. Why an Electromagnet is More Powerful than a 
Helix without a Core. When the helix is used without a 
core, the greater number of the lines of force pass in circles 
around the individual turns of wire, comparatively few running 
through the helix from end to end and back again outside the 
coil ; but when the iron core is inserted the greater number of 
lines of force pass in this latter way, because the permeability 
of iron is very much greater than that of air. Whenever a 
turn of wire is near the core, the lines of force, instead of 
passing in closed curves around the ware, change their shape 
and pass from end to end of the core. The effect of the core, 
therefore, is to inci-ease the number of lines of force which 
are concentrated at the different poles, and conser^uently to 
increase the power of the magnet. 

The strength of the magnet may be still further increased 
by bringing the poles 
close together so that 
the lines of force may 
pass within iron 
throughout their whole 
course. This is done 
either by bending the 

core into 

form, as shown in 
Fig. 510, or by joining two magnets by a 'yoke' as shown in 





Fio. 510.— An electro- 
magnet — horseshoe 
form. 



Tir-ivcA «lir»P Fia. 511.— An electromagnet 
iiuibe j>uuB —joke form. 



424 



MAGNETIC RELATIONS OF THE CURRENT 



Fig. 511. The lines of force thus pass from one pole to the 
other through the iron body held against them. 

504. Strength of an Electromagnet. The strength of an 
electromagnet depends equally on tlie strength of the current 
and on the number of turns of wire which encircle the core. 

This law is generally expressed 
by saying that the strength is 
proportional to the am'pere- 
tiirns which surround the core, 
meaning that the strength varies 
as the product of the number of 
turns of wire about the core 
and the streno^th of the current 
measured in amperes. 

This law is true only when 
the iron core is not near to 
being magnetized to saturation. 
It should also be observed 
that when an electromagnet is 
used with a battery, or other 
source of current where the ends of the wire are kept at a con- 
stant difference of potential, an increase in the number of turns 
of the wire may not necessarily add to the strength of the mag- 
net, because the loss in magnetizing force tlirough loss in current 
caused by increased resistance may more than counterbalance 
the srain throuo'h the increased number of turns of wire. 

Query. — In what circuit should a "long coil" electromagnet (one with 
a great number of turns of fine wire) be used, — one in which the remain- 
ing resistance is great or small as compared with the resistance of the 
magnet? (See § 510.) 

505. Action of one Electric Current on Another. — Ampere's 
Laws. Oersted's discovery of the action of an electric current 
on the magnetic needle (§ 474) led Ampere to investigate the 
actions of currents on one another. Tlie results of his obser- 
vations are formulated in two statements, generally known as 
Ampere's Laws. 




Andr]6 Marie Ampere (1775-1836). Bom 
at Lyons, France. Discovered the action 
of one current upon another. 



ACTION OF ONE ELECTRIC CURRENT ON ANOTHER 425 




1, Parallel currents in the same direction attract each 
other ; parallel currents in crpposite directions repel each 
other. 

2. Angular currents tend to become parallel and to jioiv in 
the sam^e direction. 

The laws may be verified in a simple manner by the 

following experiments : — 

Wind insulated magnet wire (No. 20) into coils of the forms 

A and B in Fig. 512. A is about 25 cm. square and contains 

five convolutions of wnre. It may 

be made by winding the wire 

around the edge of a scpiare board, 

tying the strands togcsther at a 

number of points with thread, and 

removing the board. B may be 

made in a similar manner. It is 

rectangular, 20 cm. by 10 cm. and ^Tor'^To'^n^tS".' lllfpSl^S 

contains also five convolutions. t^on'attact'' ea^h othen """ ''"'°- 

Suspend A by a long thread and allow the ends of the wire 

to dip into the mercury receptacles, as shown in Fig. 505. 

Connect the wires as shown in Fig. 512 so that a current 

from a battery of three or four cells will pass in one continuous 

current through the two coils. 

Bring one edge of B near one of 
the vertical edges of A with the 
planes of the coils at right angles to 
each other, in such a position that 
the current in the adjacent portions 
of the two coils will flow (1) in the 
same direction (Fig. 512); (2) in 
the opposite direction (Fig. 513). 
In the first position the coils 

attract each other and in the second they repel each other. 




Fio. 513. — Connection for demonstrating 
Anipfere's Laws. Parallel currents in 
opposite directions repel each other. 



426 



MAGNETIC RELATIONS OF THE CURRENT 





Fio. 514. — Connections 
for demonstrating Am- 
pfere'a Laws. Angular 
currents tend to be- 







Now, hold B within A as shown in Fig. 514, arranging the 

connecting wires in such a way that A is free to turn round. 

The coil A turns about and tends to set itself in the 

position in which the 

currents are parallel 

and flow in the same 

direction. 

The reason for the 

behaviour of the coils 

is obvious. When the 

currents flow in the 

same direction, their 

come parallel and flow . . n i i j. j 

in the same direction. magnetic neldS tend 

to merge, and the action in the medium 
which surrounds the wires tends to 
draw them tofj'ether, but when the FiG,5i5.—Ma^etic field of two cur- 

^ . T 1 • rents in the same direction. 

currents flow m opposite directions 

these actions tend to push the wires 
further apart (see § 499). The direc- 
tions of the lines of force in the fields 
may be shown by passing two wires 
through the card as in the experiment 
of § 498, and causing the current 
to pass (1) in the same direction 
through each wire (Fig. 515); (2) 

Pig. 5i6.-Magnetic field of currents in Opposite directions (Fig. 516). 

in opposite directions. 

506. Practical Applications of the Magnetic Effects of the 
Current. No sooner were the principles of electromagnetism 
made known by the researches of the early investigators than 
their practical applications began to be recognized. 

Schweigger modified Oersted's experiment by bending the 
wires in coils about the magnetic needle, and applied the device 
to detecting electric currents and comparing their strengths. 




THE ELECTRIC TELEGRAPH— TELEGRAPH KEY 427 

Amp^-e, in 1821, suggested the possibility of transmitting 
signals by electromagnetic action. Joseph Henry used an 
electromagnet at Albany, in 1831, for pi'oducing audible signals. 
In 1837, Morse devised the system by which dots and dashes, 
representing letters of the alphabet, were made on a strip of 
moving paper by the action of an electromagnet. About the 
same period, also, the possibility of producing rotary motion 
by the action of electromagnets was demonstrated by the 
experiments of Henry, Jacobi, Davenport, and others. At the 
present time electromagnets are used for a great variety of 
practical purposes. The following sections contain descriptions 
of some of the more common applications. 

507. The Electric Telegraph. The electric telegraph in its 
simplest form is an electromagnet operated at a distance by 
a battery and connecting wires. The circuit is opened and 
closed by a hey. The electromagnet, fitted to give signals, is 
called a sounder. When the current in the circuit is not 
sufficiently strong, on account of the resistance of the line, to 
work a sounder, a more sensitive electromagnet called a relay 
is introduced which closes a local circuit containing a battery 
directly connected with the sounder. 

508. The Telegraph Key. The key is an instrument for 
closing and breaking tlie circuit. Fig. 517 shows its construc- 
tion. Two platinum contact points, 

P, are connected with the binding 

posts A and B, the lower one being 

connected by the bolt G which is 

insulated from the frame, and the ^^^ ^ 

upper one being mounted on the lever y^q. 517.— Telegraph key. 

L which is connected with the binding 

post B by means of the frame. The key is placed in the circuit 

by connecting the ends of the wire to the binding posts. 

When the lever is pressed down, the platinum points are 
brought into contact and the circuit is completed. When the 




428 



MAGNETIC RELATIONS OF THE CURRENT 




lever is nob depressed, a spring iY keeps the points apart. A 
switch S is used to connect tlie binding po3ts, and close the 
circuit when the instrument is not in use. 

509. The Telegraph Sounder. Fig. 518 shows the construc- 
tion of th sounder. It consists of an 
electromagne'. E, above the poles of 
which is a soft-iron armature ^, mounted 
on a pivoted beam B. The beam is 
raised and the armature held by a 
spring S, above the poles of the magnet 

FIG. 6i8.-Teiegraph sounder. ^^ ^ distance regulated by the screws 

G and D. The ends of the wire of tlie magnet are connected 
with the binding posts. 

510. The Telegraph Relay. The relay is an instrument 
for closing automatically a local circuit in an ofRce, w^hen 
the current in the main circuit, 

on account of the great resistance 

of the line, is too weak to work 

the sounder. It is a key w^orked 

by an electromagnet instead of 

by hand. Fig. 519 shows its 

construction. It consists of a 

" long coil " electromagnet B,, 

in front of the poles of which is a pivoted lever L carrying 

a soft-iron armature, which is held a little distance from tlie 

poles by the spring S. Platinum contact points, P, are 

connected with the lever L and the screw C. The ends of the 

wire of the electromagnet are connected with the binding 

posts B, B, and the lever L and the screw G are electrically 

connected with the binding posts B^, Bi. 

Whenever the magnet R is magnetized the armature is 
drawai toward the poles and tlie contact points P are brought 
together and the local circuit completed. 




Fig. 519.— Telegraph relay. 



INSTRUMENTS IN A TELEGRAPH SYSTEM 



429 



511. Connection of Instruments in a Telegraph System. 

Fig. 520 shows a telograpli line passing through three offices 



^gaf. 




M^ 



%^ 



rl**L 



2*4=1* 





P 



W A B C - 

Earfh Earth 

Pig. 520. — Connection of instruments in a telegraph circuit. 

A, B, and C, and indicates how the connections are made in 
eacli office. 

When the line is not in use the switch on each key K is 
closed and the current in the main circuit flows from the positive 
pole of the main battery at A, across the switches of the keys, 
and through the electromagnets of the relays, to the negative 
pole of the main battery at G, and thence through the battery 
to the ground, which forms the return circuit, to tlie negative 
pole of the main battery at A. The magnets R, R, R, are 
magnetized, the local circuits completed by the relays, and 
the current from each local battery flows through the magnet 
E of the sounder. 

When the line is being used by an operator in any office A, 
the switch of his key is opened. The circuit is thus bi'oken 
and the armature of the relay and of the sounder in each of 
the offices is released. 

When the operator depresses the key and completes the main 
circuit, the armature of the relay in each office is drawn in, 
and the local circuit is completed. The screw D of each 
sounder is then drawn down against the frame, producing a 
'click.' When he breaks the circuit at the key, the local 



430 



MAGNETIC RELATIONS OF THE CURRENT 



circuit is again opened and tlio l)eani of each sounder is drawn 
up ]»y the spring against the screw C, producing another 
'chck' of different sound. If the circuit- is completed and 
broken quickly by the operator, the two ' clicks ' are very 
close together, and a "dot" is formed; but if an interval 
intervenes between the ' clicks ' the effect is called a " dash." 
Different combinations of dots and dashes form different 
letters. The transmitting operator at A is thus able to make 
himself understood by the receiving operator at B or G. 

512. The Electric Bell. Electric bells are of various kinds. 
Fig. 52 L shows the construction of one of 
the most common forms. It consists of an 
electromagnet M,M,E, in fi-ont of the poles 
of which is supported an armature A by 
a spring >S^. At the end of the armature 
is attached a hammer H, placed in such a 
position that it will strike a bell B when 
the armature is drawn to the poles of 
the magnet. A current breaker, consisting 
of a platinum-tipped spring D, attached to the 
armature, is placed in the circuit as shown in the 
figure. 

When tlie circuit is completed by a push- 
button P, the current from the battery passes 
from the screw G to spring D and 




Fio. 521. — Electric bell and its connections. 
At G is shown a section of the push- 
button. The figure shows the bell when 
the button is not pressed. The current 
may pass in either direction through the 
bell. 




through the electromagnet to the battery. The armature 
is drawn in and the bell struck by the hammer ; but by the 



GALVANOMETERS— THE TANGENT GALVANOMETER 481 



luovenieiifc of tlie armature the spring I) is separated from the 
screw C, and the circuit is broken at this point. The magnet 
then released, tlie armature with its spring S causes the 
hammer to fall back into its original position when the circuit 
is again completed. The action goes on as before and a con- 
tinuous ringing is thus kept up. 

513. Galvanometers. Since the magnetic effect of the 
current varies as its strength, the strengths of different 
currents may be compared by comparing their magnetic 
actions. Instruments for this purpose are called Galvano- 
meters. There are two main types of the instrument. 

In the first type the strength of the current is measured by 
the deflection of a magnetic needle within a fixed coil, made 
to carry the current to be measured ; in the second, the 
strength is measured by the deflection of a movable coil 
suspended between the poles of a permanent magnet. 

The Galvanoscope described in § 475 is of the first type. 

514. The Tangent Galvanometer. A more useful instru- 
ment of the first type is the tangent galvanometer. It 
consists of a short magnetic needle, 
not exceeding one inch in length, 
suspended, or poised at the centre 
of a large open ring or circular coil 
of copper wire not less than ten 
inches in diameter. A light pointer 
is usually attached to the needle, 
and its deflection is read on a 
circular scale placed under the 
pointer (Fig. 522). 

This is called a ' tangent ' gal- 
vanometer because when the coil 
is placed parallel with the earth's 
magnetic meridian and a current passed through it the 




Fio. 522. — Tangent galvanometer. 



432 



MAGNETIC RELATIONS OP THE CURRENT 



intensity of the eivrrent will vary as the ' tangent ' of the 
angle of deflection of the needle. 

Thus, if the current corresponding to any angle of deflection, 
say one ampere, is known, the current corresponding to any 
other angle of deflection can be determined by referring to a 
table for the tangent of the angle, and making the necessary 
calculations. 

515. The D'Arsonval Galvanometer. Galvanometers of the 
second type are generally known as D' Arsonval galvanometers. 

In this form the permanent magnet remains 
stationary, and a suspended coil rotates 
through the action of the current in the 
field of the permanent magnet. Fig. 523 
shows the essential parts of the instrument, 
and in Fig. 527 a complete instrument ifi 
seen. N and S are the poles of a permanent 
magnet of the horse-shoe type. G is an 
elongated coil suspended by the wires A 
and B, which lead the current to and from 
the coil. The deflection of the coil is 
indicated either by a light pointer and a 
scale, or by a mirror D attached to the upper part of the coil 
to reflect a beam of light, which serves as a pointer to indicate 
the extent of the rotation. 

The coil is brought to the zero by the torsion of the 
suspension wires.. When the current is passed through it, 
the coil tends to turn in such a position as to include as 
many as possible of the lines of force of the field of the 
permanent magnet, and the deflection is approximately pro- 
portional to the strength of the current. Instruments of this 
type may be made exceedingly sensitive. 

516. Ammeters and Voltmeters. A galvanometer with a 
scale graduated to read amperes is called an ammeter. The 




Fig. 523. — The es- 
sential parts of a 
D'Arsonval galvano- 
meter. 



AMMETERS AND VOLTMETERS 



433 



coils are of low resistance, in order that tlie instrument may 
be placed directly in the circuit witliout sensibly affecting the 
strength of the current. 

If the galvanometer is to be used to measure potential 
differences between points in a circuit it sliould have high 
resistance (why ?) ; and if the scale is graduated to read 
directly in volts, the instrument is called a voltmeter. 

The best portable voltmeters and ammeters used for com- 
mei'cial purposes are 
of the movable coil 
type. Fig. 524 shows 
an instrument of this 
class. The coil C, hav- 
ing a soft-iron cylinder 
within it, is pivoted 
on jewel bearings, and 
is held between the 
poles N" and S oi a 
permanent magnet of 
great constancy. It is 
brought to the zero 
position by a coil spring sp. 

When the current is passed through the instrument, the 
coil, to which a pointer p is attached, reacts against the 
spring and turns about within the field of the magnet. 

Each instrument is calibrated by comparison with a standard 
instrument i^laced simultaneously in the same circuit with it. 

QUESTIONS 

1. If you were given a voltaic cell, wire with an insulating covering, 
and a bar of soft-iron, one end of wliich was marked, state exactly what 
arrangements you would make in order to magnetize tlie iron so that the 
marked end might be a iV^-pole. Give diagram. 

2. A current is flowing through a rigid copper rod. How would you 
place a small piece of iron wire with respect to it so that the iron may be 
magnetized in the direction of its length ? Assuming the direction of the 
current, state which end of the wire will be a A^-pole. 




Fig. 524.— Ammeter or voltmeter. C, movable coil ; sp, one 
of the springs; N, S, poles of the permanent magnet; 
p, pointer. 



43 i MAGNETIC RELATIONS OF THE CURRENT 

3. A telegraph wire runs north and south along the magnetic meridian. 
A magnetic needle free to turn in all directions is placed over the wire. 
How wiU this needle act when a current is sent through the wire from 
south to north ? Supposing the wire to run east and west, how would 
you detect the direction of the current with a magnetic needle ? 

4. An insulated wire is wound round a wooden cylinder from one end 
A to the other end B. How would you wind it back from B to A (1) so 
as to increase, (2) so as to diminish, the magnetic effects which it produces 
when a current is passed through it ? Illustrate your answer by a diagram 
drawn on the assumption that you are looking at the end B. 

5. A small coil is suspended between the poles of a powerful horse-shoe 
magnet, and a current is made to flow through it. How will the coil 
behave (1) when its axis is in the line joining the poles of the magnet ? 
(2) when it points at right angles to that line ? 

6. If it were true that the earth's magnetism is due to currents 
traversing the earth's surface, show what would be their general 
direction. 

7. An elastic spiral wire hangs so that its lower end just dips into a 
vessel of mercury. When the top of the spiral is connected with one 
pole of a battery, and the mercury with the otlier, it vibrates, alternately 
breaking and closing the circuit at the j)oint of contact of the end of the 
wire and the mercury. Explain this action. 



CHAPTER XLVI 







Induced Currents 

517. Faraday's Experiments. Much of tlie life of the 
great investigator Faraday was occupied in endeavours to 
trace relations between the various " forces of nature," — gi-avi- 
tation, chemical affinity, heat, light, electricity and magnetism. 
Seeing that magnetic effects could be produced by an electric 
current, he felt sure that an electric « current could be obtained 
by means of a magnet. During seven years (1824-31), he 
devoted considerable time to securing experimental proof of 
this, and at last, in August, 1881, was successful. 

He took a ring of soft-iron and on it wound two coils A, B, 
of wire. The ends of one coil he 
joined to the terminals of a battery 
C, the ends of the other to a galvano- 
meter G (Fig. 525). He noticed that 

on closing the battery circuit the Fiq. 525.-Current induced in a cir- 
° •' cuit bj' opening or closing another 

needle of the galvanometer was de- circuit. 

fleeted, but that after oscillating a while it returned again to 

its zero. However, just when the circuit was opened the 
needle was again deflected, settling down to 
rest as before after a few oscillations. 

On September 23rd he wrote, " I am busy 
just now again on electromagnetism, and 
tliink I have got hold of a good thing, but 
can't say. It may be a weed instead of a fish 
that I may at last pull up." The following 
day he placed a coil of wire wound over an 
iron core, with its ends connected to a gdl- 
fieldof i''^jrml"nent vauometcr, between the poles of bar-magnets 
magnet. ^^ shown in Fio:. 526. Whenever the magnetic 

contact at N and ^ was made or broken the needle of the 

galvanometer G was disturbed. 

435 




Fig. 526.— Current in- 
duced in a circuit by 



436 INDUCED CURRENTS 

On October Isfc lie again modified his exj)eriments by 
winding two coils of insulated wire on the same block of 
wood, connecting one with the galvanometer, and the other 
with the battery. As before, he found that whenever the 
batteiy circuit was closed or opened a current was produced 
in the galvanometer circuit, and that the needle was deflected 
in one direction on closing the circuit, in the opposite on 
opening it ; but that in this case, as in his previous experi- 
ments, the current in the galvanometer circuit was only 
momentary. 

It remained only to invent a method of making these 
momentary currents continuous. This has been worked out 
by others and has given us the dynamo. Thus, in the 
discovery of the principle of producing a current by induction, 
Faraday made possible all the modern ajDplications of elec- 
tricity in industrial development. 

518. Production of Induced Currents. Faraday's dis- 
coveries may be summed up in the following statement : — 
Whenever, from any cause, the niiinher of magnetic lines of 
force passing throiogh a closed circuit is changed, an electric 
current is produced in that circuit. 

Such a current is known as an induced current. 

519. Illustrations of Induced Currents. Faraday's original 
experiments are simple and can be performed by anyone 
without difficulty. The coils connected with the galvanometer 
should be wound with many tui-ns of fine insulated wire, 
and the galvanometer used should be sensitive ; one of the 
D'Arsonval (§ 515) type answers well. 

A great variety of experiments might be added to illustrate 
the phenomena of induced currents, because any device what- 
ever which will alter the number of lines of force passing 
through a coil will induce a current in it. 



EXPLANATION OF TERMS 



437 



Let us take a coil of very fine insulated M'ire wound on a 
liollow spool of the form shown in Fig. 527 and connect 
the ends of the wire to the gal- 
vanometer. Thrust the pole of a 
bar-magnet into it, and then with- 
draw it ; slip the coil over one pole 
of a horse-shoe magnet, and then 
remove it. In both cases the gal- 
vanometer indicates a current, in 
one direction when the pole passes 
within the coil, and in the opposite 
direction when it is witiidrawn, 
but in each cshHe.the current lasts 
only while the magnet and coil 
are in motion relative to each other. 




Fig. 527.— Apparatus for showing that 
when a magnet is thrust into or with- 
drawn from a closed coil a current ig 
induced in the coil. 



If the coil used in the preceding experiments is slipped over 
the polo of an electromagnet connected with a battery, as 
shown in Fig. 528 and then Avithdrawn, effects similar to 
those observed in the case of the permanent magnet will be 
seen. 

520. Explanation of Terms. The coil connected with the 
battery is called the ^)7"i7H«ri/ coil, and the 
current which flows through it is called the 
jyriniary current; the coil connected with 
the galvanometer is called the secondary 
coil, and the momentary currents made to 
flow in it, secondary currents. When the 
secondary currents flow in the same direc- 
tion as the primary, they are said to be 
direct, or to flow in a positive direction; 
but when the secondary currents flow in the opposite direc- 
tion, they are said to be inverse, or to flow in a negative 
direction. 




Fig. 528.— Currents in- 
duced in a closed coil 
by moving it in the 
field of an electro- 
magnet. 



438 INDUCED CURRENTS 

521. Laws of Induced Currents. Let us repeat the last 
experiment, and take care to trace the relative directions of 
the primary and secondary currents when the number of 
magnetic lines of force passing through the space inclosed by 
the secondary coil is («) increasing, (h) decreasing. It will be 
found that whenever a decrease in the number of lines of 
force which pass through a closed circuit takes place, a 
current is induced in this circuit, flowing in the same direc- 
tion as that which would he required to produce this magnetic 
field, that is, a direct current is produced ; and that when- 
ever an INCREASE in the number of lines of force takes place, 
the current induced is such as would hy itself produce afield 
opposite in direction to that acting, that is, an inverse 
current is p>roda.iced. 

Remember therefore, 

A decrease gives a direct current. 
An increase gives an inverse current. 

Also, by moving the coil up to the pole of the magnet, at 
one time rapidly, and at anotlier slowly, and observing the 
effects on the galvanometer of the change in the rate of the 
motion, it has been shown that tlie total electromotive force 
induced in any circuit at a given instant, is equal to the 
time-rate of the variation of the floiv of magnetic lines of 
force through that circuit. 

It is evident that when a circuit is not closed it is impossible 
to produce a current in it by a change in the number of lines 
of force which pass through it ; but it should be observed 
that, as in the case of a voltaic cell in open circuit, a potential 
difference is established between the terminals of the con- 
ductor. In other words, an electromotive force is developed 
in the circuit. 

It should be noted, also, that the motion of a conductor 
within a magnetic field does not necessarily develop an 




LENZ'S LAW- SELF-INDUCTION 439 

E.M.F. in it. It does so only when it cuts the hnes of force, 

and it is obvious that it does not do so when tlie conductor is 

moved in the direction parallel with the lines of force of the 

field. This may be shown by connecting the 

coil used in the previous exjjeriments with 

the galvanometer and moving it in various 

directions about the poles of a horse-shoe 

magnet. The needle is undisturbed when the 

coil is moved to and fro between the poles, 

in the position shown in Fig. 529 ; but if the 

coil is moved up and down, or placed between fiq. 529.^change in 

.1 1 II T 1 1. 1 • L ^ the number of lines 

tlie poles and turned about a horizontal or a of force cutting a 

, . ■, . T . . , coil necessary to 

vertical axis, or moved in any otlier way the production of 

,., ., 7 /»7- y/- induced currents. 

which causes the number of lines of force 
'passing throitgJi it to change, a current is generated. 

522. Lenz's Law. We have found {a) that parallel currents 
in the same direction attract each other (§ 505), (J>) that on 
moving a current from a conducting circuit an induced 
current is produced in the secondary in the same direction 
as the primary, (§521). We have also found {a) that parallel 
currents in opposite directions repel each other, and (6) that 
on movinof a current towards a conductiiip^ circuit an induced 
current is produced in the secondary in the opposite direction 
to that in the primary. 

Hence, in all cases of electromagnetic induction, the direc- 
tion of the induced ciirrent is cduxiys such that it ijrodiices 
a magnetic field luhich cypj)oses the motion or change which 
induces the current. This is knowm as Lenz's Law. 

523. Self-induction. If an electromagnet containing many 
turns of wire is connected with a battery and the circuit 
closed and opened by touching the two ends of the connecting 
wires together and then separating them, a spark will be 
observed at the ends of the wires ^Yhen they are separated, 



440 INDUCED CURRENTS 

and if the hands are in contact with the bare wires, a shock 
will possibly be felt. 

The effects observed are due to what is known as self- 
induction. 

We have seen that, in the case of two distinct coils of wire 
near each other, when a current is started or stopped in one 
a current is induced in the otlier. This is due to the fact that 
the number of magnetic lines of force passing through the 
second coil is thereby altered. But we can have this induc- 
tive effect with a single coil. Each turn of the wire of the 
coil will exert an inductive action on all the other turns. 

The magnetic lines of force surrounding a current, in circu- 
lating around a wire, pass, especially when the wire is coiled, 
across contiguous parts of the same circuit, and any variation 
in the strength of the current causes the current to act 
inductively on itself. On completing the circuit, this current 
is inverse ; and on breaking it, direct. 

The direct induced current in the primary wire itself, which 
tends to strengthen the current when the circuit is broken, 
is called the extra current. 

This self-induced current is of high E.M.F., and therefore 
jumps across the air space as the wires are separated, thus 
producing the spark. 

QUESTIONS 

1. You have a metal hoop. By means of a diagram describe some 
arrangement by which, without touching the hoop, you can make electric 
currents pass around it, first one way, and then the other. 

2. A coil about one foot in diameter, made of 400 or 500 turns of fine 
insulated wire, is connected with a sensitive galvanometer. When it is 
held with its plane facing north and south, and then turned over quickly, 
the needle of the galvanometer is disturbed. Give the reason for this. 

3. A bar of perfectly soft-iron is thrust into the interior of a coil of 
wire whose terminals are connected with a galvanometer. An induced 
current is observed. Could the coil and bar be placed in such a position 
that the above action might nearly or entirely disappear ? Explain fully. 



SELF-INDUCTION 441 

4. Around tlie outside of <a doep cylindrical jar are coiled two separate 
pieces of fine silk-covered wire, each consisting of many turns. The ends 
of one coil are joined to a battery, those of the other to a sensitive 
galvanometer. When an iron bar is thrust into the jar a momentary 
current is observed in the galvanometer coils, and when it is drawn out 
another momentary current (but in an opposite direction) is observed. 
Account for these results. 

5. A small battery was joined in circuit with a coil of fine wire and a 
galvanometer, in which the current was found to produce a steady but 
small deflection. An unmagnetized iron bar was now plunged into the 
hollow of the coil and then withdrawn. The galvanometer needle was 
observed to recede momentarily from its first position, then to return 
and to swing beyond it with a wider arc than before, and finally to settle 
down to its original deflection. Explain these actions, and state what 
was the source of the energy that moved the needle. 

6. The poles of a voltaic battery are connected with two mercury cups. 
These cups are connected successively by : — (I) A long straight wire. 
(2) The same wire arranged in a close spiral, the wire being covered with 
some insulating material. (3) The sani3 wire coiled around a soft-iron 
core. Describe and discuss what happens in each case when the circuit 
is broken. 



CHAPTER XLVII 

Applications of Induced Currents 

524. The Principle of the Dynamo. In its simplest form, a 
dynamo is a coil of wire rotated about an axis in a magnetic 
field. The principle may be illustrated by connecting to the 
galvanometer the coil used in the experiments on current 
induction and rotating it about a vertical axis between the 
poles of a horse-shoe magnet. Continuous rotation in one 
direction is prevented by the twisting of the connecting wires 
about each other. In a working dynamo this difficulty is 
overcome by joining the ends of tlie wires to rings, from 

which the current is 

taken by brushes bear- 
ing upon them. A 

study of Figs. 530-533 

will show how the 

current is generated 

in the coil and how it 

Tin c Pig. 531. —Principle of the 

IS made to now irom dynamo: 

brush to brush through the external conductor. 

Let ahcd be a coil of wire, having one end attached to the 
ring A and tlie other to the ring B ; and suppose the coil to 
rotate about a horizontal axis between the poles N and S. 

Now the maximum number of lines of force pass through 

the coil when it is in the position shown in Fig. 530 and 532, 

and the minimum number when it is in-the position shown in 

Figs. 531 and 533. In the first quarter-turn, that is, in the 

change from the position shown in Fig. 530 to the position 

shown in Fig. 531, the number of lines of force passing 

through the coil is decreasing, and a direct current (flowing 

clockwise viewed from N) is induced in it. During the next 

442 





Fio. .530.— Principle of the 
d) nanio. 



THE ARMATURE OF THE DYNAMO 



443 





Fig. 532.— Principle of tiie 
dynamo. 



Fig. 533.— Principle of the 
(Ivnanio. 



quarter-turn (Figs. 531 and 532) the number of lines of force 
through the coil is increasing, and an inverse current (counter- 
clockwise viewed from 
N) is induced in it; 
but as the opposite 
face of the coil (viewed 
from N) is presented 
to the view, it is evi- 
dent that the current 
flows in the same 
absolute direction in the coil as during the first quarter-turn. 
In the same way it can be shown that the current continues to 
flow in one direction in the coil during the second half-turn 
(Figs. 532, 533, 531). But as the sides ab and cd of the coil have 
changed places, this direction will be opposite to that of the 
current in the coil during the first half-turn. The current in 
the coil, therefore, changes direction at the end of each half 
revolution, but the complete circuit includes the wires joining 
the brushes bearing on A and B; hence a current which 
changes direction at regular intervals is produced in the 
external conductor. Such is known as an alternating current. 
525. The Armature of the Dynamo. We have, for simpli- 
city, considered in the preceding section the case of the 
revolution of a single coil within the magnetic field. In 
ordinary practice a number of coils are connected to the same 
collecting rings or plates. These coils are wound about a 
soft-iron core, which serves to hold them in place and to 
increase the number of lines of force passing through the 
space inclosed by them. The coils and core with the attached 
connections constitute the aTmature of the dynamo. 

The armatures vary in type with the form of the core and 
the winding of the coils. A single coil wound in a groove 
about a soft-iron cylinder (Fig. 534) forms a shuttle armature; 
when a number of coils are similarly wound about the same 



444 



APPLICATIONS OF INDUCED CURRENTS 



an iron rinfj. 



iron cylinder the armature is said to be of the drum type. 

Fig. 535 shows a Grainine-ring armature, 

in which a series of coils are wound about 
To prevent the generation 
of " eddy cur- 
rents," within 
the iron itstdf, 
which are waste- 
ful of energy and 

overheat the macliine, the armature core 

is built up of thin soft-iron discs insulated from one another. 





Fia. 534. — Shuttle armature. 



Fig. 535.^Gramme-ring 
armature. (Invented 
by Gramme in 186S.) 





526. Field Magnets. In small generators, used to develop 
high tension (or po- 
tential) currents, per- 
manent maoiiets are 
sometimes used to 
supply the fields. 
The machine is then 
called a magneto. In 
all ordinary dynamos 

FIG. 536.-Bipolar field. the field is fumishcd F'O- 537. -Multipolar field. 

by electromagnets known technically as field-mxignets. These 
magnets are either bipolar (Fig. 536) or multipolar (Fig. 537). 
In the multipolar type two or more pairs of poles are arranged 
in a ring about a circular yoke A. 

527. The Alternating Current Dynamo. When an alter- 
nating current is used for electric lighting or power 
transmission, the alternations range from 25 to 60 per second. 
Now such a current cannot be generated in a bipolar field 
except by unduly increasing the rapidity of the revolutions 
of the armature, because the current clianges direction but 
twice. each revolution. The requisite number of alternations 
is secured by increasing the number of pole-pieces in the 



THE ALTERNATING CURRENT DYNAMO 



445 




Kio. 538. — Essential parts and electrical 
connections in the alternating- current 
dynamo. 



fieid-itiagnets. Tu LIk^ ;i,1 ten m tors in couimon use, the arma- 
ture coils A, A... (Fii,^ 5;]>S) 

revolve in a muliipolar licld. They 

are wound in alternate directions 

and connected in series with the 

two free ends of the wire brought 

to two collecting rings, C and D, 

as shown in the figure. 

To study the action, suppose the 

ring of armature coils to be opposite 

to the ring of the field coils, and to be 

revolving in either direction. Since 

the armature coils leaving positions opposite iV^-poles in the 

field have currents induced 
in them opposite in direc- 
tion to those in tlie coils 
leaving ^'-poles, and since 
these coils are wound alter- 
nately to the right and the 
left, it is evident that the 
induced current in each coil 
will be in such a direction 
as to produce a continuous 
current in the whole series, 
which will fl(jw from one 
collecting ring to tl'.e other. 
It is evident, also, that tlie 

FiQ. 539.— A self-excitinff alternating current dy- rli"i-(»f>f ir>n r\f fliia /^nvT-onf 
namo, driven by the pulley P. There are four '-"^♦-^Lauu Ui tlUb CUlieno 

f!''-Att'e :n;a'tu;e:'''^rthis'ts;^ h S; ^vlU be reversed the instant 

consists of two armatures wound together. One fl,„ fialrl anrl QT-mofnT'O r»r>ila 

is joined to a commutator rf, on which rest four ^^^*^ ^^^^^^ '^"^ «*' mature COHS 

brushes 6, b, b (one not seen). This generates a ^.^.^.'^ f.ipa panTi nflipr 

direct current (see next section) which is used to "-g'^m -iciuc Cctcii uuuei. 
excite the field-magnets. The other armature is £~^. ., , p i, 

joined to the three collecting rings c, c, c, from OlUCe the number Ot altcr- 

which the three-phase alternating current is led off. . p ,i • , o 

nations or tins current tor 
each revolution of the armature ec^uals the number of poles in 




446 



INDUCED CURRENTS 



the lield-magnet, the numl)er of alternations per minute is 
equal to the number of poles in the field-magnet multiplied 
by the number of revolutions made by the armature per 
minute. 

528. Production of a Direct Current— The Commutator. 

When an electric current flows continuously in one direction 
it is said to be a direct current. The current in an armature 
coil changes direction, as we have seen, at regular periods. To 
produce a direct current with a dynamo it is necessary to 
provide a device for commuting the alternating into a direct 
current. This is done by means of a coininiitator. It con- 
sists of a collecting ring made of segments called comTYiuiator 
plates, or bars, insulated from one another. The terminals of 
the coils are connected in order with the successive plates of 
the ring. Take, for example, the case of a single coil 
revolved in a bipolar field, as considered in (§ 524). The 

commutator consists of two 
a semi-circular plates, (Figs. 
540 and 541), and the 
brushes are so placed that 
they rest upon the insulat- 
ing material between the 
plates at the instant the 
cuirent is changing direc- 
tion in the coil. Then 
since the commutator plates 
change position every time the current changes direction in 
the coil, the current always flows in the same direction from 
brush to brash in the external circuit. 

529. Direct Current Dynamo. The essential parts of a 
direct current dynamo with ' ring ' armature and bipolar field 
are shown in Fig. 542. The coils ai-e wound continuously in 
one direction about the core, and are connected with commutator 




Fio. 540. 



Pio. 541. 



Arrang-ements for transforming the alternatiriif 
current in the arinalure into a direct current 
in the external circuit. 



DIRECT CURRENT DYNAMO 



447 




Fia. 542. — Essential parts and electrical con- 
nections in the direct current dynamo. 



plates P, P,. . . . as indic^ate'l. I'^oi- simplicity, suppose that 
the riug contains but four coils, (f^, 6'^, C'j, 64, and that tiny 

aie in the typical positions 
shown in the figure. 

Consider the conditions of 
the coils as viewed from one 
point, say iV, along the lines of 
force in the direction jY to >S'. 

The maximum number of 
lines of force pass tlirough a 
coil when it is crossing the line 
AB, and the minimum when it 
is crossing a line drawn from 
i\r to S; hence, if the ring is 
revolving clockwise, as shown 
by the arrows, observe : — 

1. The number of lines of force passing through the space 
inclosed by the coil C\ is decreasing, and a direct (clockwise) 
current is induced in it. 

2. The number of lines of force through the coil C^ is 
increasing, and an inverse (contra-clockwise) current is induced 
in it ; but as the coils present opposite ends when viewed from 
iV, it is evident that the current flows in the same absolute 
direction in C^ and Co. 

3. The number of lines of force through the coil 63 is 
decreasing, and a direct (clockwise) current is induced in it. 

4. The number of lines of force through the coil C^ is 
increasing, and an inverse current (contra-clockwise) is induced 
in it; but as C3 and C^ present opposite ends when viewed 
fi'om iV", the currents flow in the same absolute direction in 
each, but in a direction opposite to that in the coils C^ and C.-,. 

Similarly with any number of coils, the currents in all coils on 
one side of the line AB flow in one direction while those, in the 
coils on the other side of AB flow in the opposite direction. 



448 



INDUCED CURRENTS 




Fig. 543.— Modern direct-current dynamo. A, Drum 
armature ; B, multipolar field ; C, dynamo complete. 



Hence, it' tlie eiuls of tlu^ wires oi" the coils are connected to 
tlie coininutator plates, and the brushes bear upon these plates 
at the points E and F as shown in the figure, a direct, or 
continuous, current will flow from F to E through a conductor 

which joins the brushes. 
The action in a 'drum' 
armature is similar. The 
coils are so wound that 
the currents on both 
sides flow in the arma- 
ture away from one 
brush and to the other 
brush. 

It is obvious that in 
a multipolar field, there 
must be as many pairs 
of collecting brushes as 
there are pairs of poles. Fig. 543 shows a modern direct- 
current dynamo with drum armature and multipolar field. 

530. Excitation of Fields in a Dynamo. In the alternating- 
current dynamo the electromagnets which form the fields are 
sometimes excited by a small direct-cur- 
rent dynamo belted to the shaft of the 
machine (see also Fig. 539) ; in the direct- 
current dynamo the fields are magnetized 
by a current taken from the dynamo 
itself. When the full current generated in 
the armature (Fig. 544) passes through the 
field-magnets, which are wound with coarse 
wire, the dynamo is said to be series-ivound. 
A dynamo of this class is used when a 
constant current is required, as in arc 
lighting. When the fields are energized by a small fraction 
of the current, which passes directly from brush to brush 




Pig. 544.— Series-wound 
dynamo. 



THE ELECTRIC MOTOR 



449 




Fio. 545.— Shunt -wound 
dynamo. 



tlirougli many turns of line wii-i; in tlui field coils, while the 
main current does work in the external circuit (Fig. 545), 
the dynamo is t^JiADit-ivowtid. This type is used where the 
output of current required is continually 
changing, but where the potential differ- 
ence between the bruslies must be kept 
constant, as in incandescent lighting, 
power distributing, etc. The regulation 
is accomplished by suitable resistance 
placed in the shunt circuit to vary the 
amount of the exciting current. 

The regulation is more nearly auto- 
matic in the compound-wound dynamo. 
In this form the fields contain both series 
and shunt coils. 

The field-magnets, of course, lose their strength when the 
current ceases to flow, but the cores contain sufficient residual 

magnetism to cause the ma- 
chine to develop sufficient 
current to "pick up" on the 
start. 



531. The Electric Motor. 

The purpose of the electric 
motor is to transform the 
energy of the electric current 
into mechanical motion. Its 
construction is similar to that 
of the dynamo. In fact, any 
direct-current dynamo may be 
used as a motor. Consider, 
for example, a shunt-wound 




FiQ. 546.— Essential parts and electrical connec- 
tions in the direct-current electric motor. 



bipolar machine with Gramme-ring armature (Fig. 546) con- 
nected with an external power circuit. 



450 INDUCED CURRENTS 

Tlie C'4irfent supplied to tlie motor divides at c?, part flows 
througli the fleld-iuagiiet coils, and part enters the armature 
coils by tlie brush B at the point b, where it divides, one 
portion passing through the coils on one side of the ring, and 
another through the coils on the other side. The currents 
through the armature coils re-unite at a, pass out by the brush 
7?i, and are joined at e by the part of the main current which 
flows througli the field- magnet coils. 

Both the field-magnet and the armature cores are thus 
magnetized, and the poles are formed according to the law 
stated in | 501. The poles of the field-magnet are as indicated 
in the figure. Each half of the iron core of the armature will 
be an electromagnet of the horse-shoe type, having a >S-pole 
at s and a iV-pole at n. The mutual attractions and repulsions ■ 
between the poles of the armature and of the field-magnet 
cause the armature to revolve. 

532. Counter-Electromotive Force in the Motor. As the 

armature of the motor is revolved it will, as in the dynamo, 
develop an E M.F. opposite to that of the current causing the 
motion. The higher the velocity of the armature, the greater 
is this counter-E.M.F. The electric motor is, therefore, self 
regulating for different loads. When the load is light, the 
speed becomes high and the increase in the counter-E.M.F. 
reduces the amount of current passing through the motor ; on 
the other hand, when the load is heavy the velocity is decreased 
and the counter-E.M.F. is lessened, allowing a greater current 
for increased work. 

When the motor starts from rest there is, at the beginning, 
no counter-E.M.F., and the current must be admitted to the 
armature coils gradually through a rheostat, (a set of resist- 
ance coils) to prevent the overheating of the wires and the 
burning' of the insulation. 



THE TRANSFORMER 451 

QUESTIONS AND PROBLEMS 

1. Upon wliab is the pntoutial diUbrence between tho brushes of a 
dynaiao dependent 'i 

2. To what is the internal resistance of a dynamo due ? 

3. How shoukl a dynamo be wound to produce (1) currents of high 
E.M.F. ; (2) a current for electrophiting ? 

4. A dynamo is running at constant speed ; what effect will be pro- 
duced on the strength of the field-magnets by decreasing the resistance 
in the external circuit («) when the dynauKj is series-wound ; (/>) when it 
is sliunt-wound ? 

5. What would be the effect of short-circuiting (1) a series-dynamo ; 
(2) a shunt-dynamo? Explain. (A dynamo may be short-circuited by 
joining the brushes, or the main wires fi'om them, by a conductor of low 
resistance.) 

6. An alternating current dynamo has 16 poles, and its armature 
makes 300 revolutions per min. ; find the number of alternations per sec. 

7. Why would an armature made of coils wound on a wooden core not 
be as effective as one with an iron core ? 

8. What would be the effect upon the potential difference between 
the brushes of a dynamo of moving them backward and forward around 
the ring of commutator plates ? Explain. 

9. What would be the effect upon the working of a dynamo, of 
connecting the commutator plates by binding a bare copper wire around 
them, (1) if the field-magnets are in a shunt circuit ; (2) if the field- 
magnet is excited by a separate dynamo ? Would a current be generated 
in either of these cases ? If so, where would it flow ? 

533. The Transformer. If two independent coils are wound 
about the same iron core, as in Faraday's original experiment 
on induced currents (§ 517), it is obvious that an alternating 
current in one coil will produce an alternating current in the 
other if it is closed, because the core becomes magnetized in 
one direction, then demagnetized, and magnetized in the 
opposite direction at each change in the direction of the 
current in the primary circuit ; linos of force are thus made 
to pass through the secondary coil in alternate directions. 



452 INDUCED CURRENTS 

This is the principle of tlio transt'ornier, a device for 
changing an alternating current of one electromotive force 
to that of another. 

Wlien the change is from low E.M.F. to high, the trans- 
former is called a step-up transformer, and when from high to 
low, a step-down transformer. There are many forms of tliis 
instrument but the essential parts are all tlie same — two coils 
and a laminated soft-iron core, so placed that as many as 
possible of the lines of force produced by the current in one 
coil will pass through the space inclosed by tlie other. 

In transformers used for commercial purposes, the coils 
are usually wound about a core shaped in 
the form of CD . The inner coils (Fig. 547) 
are tlie primary, and the outer the secondary. 
The electromotive force of the current gen- 
erated in the secondary coil is to that of 
the primary current nearly in the ratio of 
the number of turns of wire in the secondary 

Fia. 547.— The trans- -i i. ^i i, • ii 

former. coiJ to tlic numDcr lu tlic pmuary. 

534. Uses of the Alternating Current. On account of 
the facility with which the E.M.F. of an alternating current 
may be changed by a transformer, alternating currents are 
now usually employed whenever it is found necessary or 
convenient to change the tension of a current. The most 
common illustrations are to be found in the case of the long 
distance transmission of electricity, where the currents 
generated by the dynamos are transformed into currents of 
very high E.iM.F. to overcome tlie resistance of the trans- 
mission wires,* and again into currents of lower tension for use 
at the centres of distribution; and in the case of incandescent 
lighting, where it is advisable to have currents of fairly high 

* There is also less waste through the heating of the conducting wire when high tension is 
used. If the tension is hi^h the current is small, and the heating is proportional to the square 
of the current (see § 538). 




THE INDUCTION COIL 



453 



tension on tlio .street wires but, for tlie .sake of safety and 
economy, currents of low E. M. F. in the lamps and house 
connections. 

In the Hydro-electric system whicli supplies many centres 
of Ontario with electric energy, the current when first gener- 
ated at Niagara Falls is at a potential of 12,000 volts. It is 
then transformed to 110,000 volts and transmitted over 
well-insulated lines. On arriving at its destination it is 
transformed doAvn again for use in lighting, power and 
heating. 

535. The Induction Coil* In the induction coil currents 
of very high electromotive force are 
produced by the inductive action of 
an interrupted current. (Fig. 548.) 

Tlie essential parts of the instru- 
ment are shown in Fig. 549. It 
differs from an ordinary trans- 
former mainly in having added to the primary circuit a 

current-breaker and a condenser. 
The primary coil consists of a 
few turns of stout insulated wire 
wound about a soft-iron core. The 
secondary coil, consisting of a great 
number of turrs of very fine insu- 
lated wire, surrounds the primary 
coil. Its terminals are attached to 
binding posts placed above the coil. 
The current-breaker is usually of the type illustrated in the 
electric bell (§ 512), but other forms are often employed. The 
condenser CC is made up of alternate layers of tinfoil and 
paraffined paper or mica, connected with the spring A and 




Fig. 548.— The induction coil. 




Fio. 549.— Tlie essential parts and 
electrical connections in the induc- 
tion coil. 



*The induction coil was greatly improved by RuhmkorflE (1803-1877), a famous manufacturer 
of scientific apparatus in Paris, and is often called the Ruhmkorff coil. 



454 INDUCED CURRENTS 

screw B of the current-breaker in such a manner that one of 
these is joined to the even sheets of the foil, the other to the 
odd ones. The core is a bundle of soft-iron wires insulated 
fi-om one another by shellac. Such a core can be magnetized 
and demagnetized more easily than one of solid iron. 

533. Explanation of the Action of the Coil. When the 
prhnary circuit is completed the battery current passes through 
the coil and magnetizes the core. This draws in the hammer 
H, and the circuit is broken between tiie spring A and the 
screw B. The hammer then flies back, the circuit is again 
completed and the»action is repeated. An interrupted current 
is thus sent through the primary coil, which induces currents 
of high electromotive force in the secondary. 

Self-induced currents in the primary circuit interfere with 
the action of the coil. On completing the primary circuit, the 
current due to self-induction opposes the rise of the primary 
currents and thus diminishes the inductive effect. Similarly, 
the extra-current induced in the primary coil when the circuit 
is broken passes across the break in the form of a spark and 
prolongs the time of fall of the primary current, again lessen- 
ing the inductive action. The condenser is introduced to 
prevent this latter injurious effect. When the circuit, is 
broken the extra-current flows into the condenser and charges 
it, but as the two coatings are joined between A and B througli 
the primary coil and the battery, the condenser is immediately 
discharged, giving rise to a current in the opposite direction 
which flows back through the primary coil and instantaneously 
demagnetizes the soft-iron core. The direct current induced 
in the primary coil, therefore, becomes shorter and more 
intense. 

The potential difference between the terminals of the sec- 
ondary coil can thus be made sufficiently great to cause a 
spark to pass between them, the length of the spark depending. 



TELEPHONE 



455 



oil tlie capacity of the coil. Coils giving sparks from 18 to 24 
inches are frecjueiitly manufactured. 

The smaller coils are used extensively for physiological pur- 
poses and for gas engine ignition (see § 308), and the larger for 
exciting vacuum tubes and for wireless telegraphy (see § 575). 

537. Telephone. The telephone, as invented by Alexander 
Graham Bell, employs the principle of induced currents for 
reproducing sound waves. 

The transmitter and receiver first used were alike. Each 
consisted of an iron diaphragm C, supported in front of one 
end of a permanent bar-magnet A, about which was wound a 
coil of fine insulated wire B, as shown in Fig. 550. 



I 




Fig. 550.— The essential parts and electrical connections in the original Bell telephone. 

The terminals of the transmitter and receiver coils are con- 
nected by the line wires. The sound waves falling upon the 
diaphragm of the transmitter cause it to vibrate, and these 
vibrations produce fluctuations in the number of lines of force 
passing through the coil, which cause induced currents to 
surge to and fro in the circuit. The currents alternately 
strengthen and weaken the magnet of the receiver and thus 
set up vibrations in the diaphragm 
similar to those in the diaphragm of 
the transmitter. 

The Bell receiver is very sensitive and 
is still used on all telephone systems, but 
a mag-net of the horse-shoe type is now 
usually emplo3^ed instead of the bar- 
magnet used in the original form. The 
transmitter was not found satisfactory, 
especially on long distance lines, and has been replaced by 
one of the microphone type (Fig. 551). 




Fie. 551.— The microphone 
transmitter used in the 
Bell system. 



456 



INDUCED CURRENTS 



At the back of the mouthpiece is a metallic diaphragm 
D, B is a, carbon button attached to the diaphragm, and B' 
another carbon button attached to the frame of the instru- 
ment, opposite to B. The space between the carbon buttons 
is loosely packed with coarse granulated carbon. (See upper 
small figure.) 

The connections of the instruments in the complete circuit 
are shown in Fig. 552. The transmitter acts on the principle 




Fi8. 552. — Electrical connections in telephone circuit. V, mouthpiece of 
transmitter; B, B,, carbon buttons; D, diaphragm of receiver, and M its 
permanent bar- magnet. T is a transformer. 



that the conductivity of the granular carbon varies with the 
varying pressure exerted upon it by tlie button B, as the 
diaphragm vibrates under the action of the sound waves. The 
current passing from the battery through the primary coil of a 
transformer T will, therefore, be fluctuating in character and 
will induce a current of varying strength and varying direc- 
tion, but of higher electromotive force, in the secondary coil 
which is connected in the main line with the receiver. This 
current will cause corresponding variations in the magnetic 
state of tlie electromagnet of the receiver and thus set 
up vibrations in its diaphragm, which will reproduce the 
sound waves that caused the diaphragm of the transmitter 
to vibrate. 



CHAPTER XL VIII 
Heating and Lighting Effects of the Electric Current 

538. Heat Developed by a.ii Electric Current. In discuss- 
ing the sources of heat (§§ 242-245) we referred to the fact 
that whenever an electric current meets with resistance in a 
conductor heat results. Now, as no body is a perfect con- 
ductor of electricity, a certain amount of the energy of the 
electric current is always transformed into the energy of 
molecular motion. Joule, who investigated this subject, found 
by comparing the results of numerous experiments that in a 
given time the niimher of Jiedt units developed in a conductor 
varies as its resistance and as the square of tJce strength of 
the current. 

539. Practical Applications. Resistance wires heated by 
an electric current are used for various purposes, such as 
performing surgical operations, igniting fuses, cooking, heattng 
electric cars, etc. In electric toasters and flat-irons tlie resis- 
tance wire is an alloy of nickel and chromium. This can be 
kept at a red heat for weeks without injury, whereas an iron 
wire would soon deteriorate. 

540. Electric Furnace. In Fig. 553 is shown one kind of 
electric furnace. Carbon rods C, G pass 
iohrough the asbestos walls of a chamber 
about 4 in. long, 2| in. wide and 1| 
in. high. Between them is a small 
crucible, and the space about is packed 
with granular carbi^n (arc lamp carbon rods broken into 
pieces about as large as coarse granulated sugar). The 

457 




Fig. 55:i. — Eluelric rtsistance 
tiiriiace. 



458 HEATING AND LIGHTING EFFECTS 

furnace is joined to an electric-lighting circuit through a 
rheostat. The resistance of the granulated carbon is con- 
siderable, and sufficient heat can be generated to melt pieces 
of copper in the crucible. This is a resistance furnace. 
Carborundum is produced from cokf sand, salt and sawdust in 
a furnace of this type. 

In the a7'C furnace the heat is produced at a break in the 
circuit, as illustrated in the arc lamp (| 544). 

541. Electric Welding. Rods of metal are welded by 
pressing them together witli sufficient force while a strong 
current of electricity is passed through them. Heat is devel- 
oped at the point of junction, at which place the resistance 
is greatest, and the metals are softened and become welded 
together. But the most important application 
of the heating effects of the electric current is 
Ja to be found in electric lighting. 

542, Incandescent Lamp. The construc- 
tion of the incandescent lamp in common use 
Fio. 554.— The incan- is sliown in Fig. 554. A carbou filament 

descent lamp. A, -, ■ • ,i i /• i i 

carbon filament ; £, made by caroonizmg a thread or bamboo or 

conducting wires . , 

fused in glass; c, cottou fibre at a vcry high temperature, is 

brass base to which , . . 

one wire is soldered, attached to Conducting wires and inclosed in 
a pear-shaped globe, from which the air is then exhausted. 
The conducting wires where they are fused into the glass are 
of platinum. When a sufficiently strong current is passed 
thi'ough the carbon filament, which has a high resistance, it 
is heated to incandescence and yields a bright steady light. 
The carbon is infusible, and does not burn for lack of oxygen 
to unite with it. 

Lamps are now also being used in whicli tlie filament is 
fine wire of the metal tungsten. 




GROUPING OP LAMPS 459 

The Nonist lamp differ.s from the ordinary incandescent 
lamp in that the subHtance made incandescent consists of a 
small rod known as a gloiver, composed of oxides of the 
rare earths. Since these oxides are incombustible the 
gl6wer is not inclosed in an exhausted globe. Its chief 
drawback is tliat the glower is a non-conductor when cold, 
and must be heated before the current will pass through 
it. Both the tungsten and Nernst lamps give inuch more 
light than the ordinary carbon filament lamp for the same 
current. 

543. Grouping of Lamps. All the incandescent lamps to 
be used in the same circuit are so constructed as to give their 
proper candle power when the same potential-difference is 
maintained between their terminals. This is generally from 
100 to 110 volts. The lamps are connected in Tnultiple, or 
paralld, that is, the current from the leading wires divides, 
and a pirt flows through each lamp, as shown in Fig. 545. 
The dynamo is i-egulated to maintain a constant potential 
difference between the leading wires. 

544. The Arc Light. If two carbon rods, connected by 
conductors to the })olos of a sufficiently powerful battery 
or dynamo, are touched together and then separated a shorts 
distance the current continues to flow across the gap, 
developiiig intense heat and raising the terminals to incan- 
descence, thus producing a powerful light, generally known 
as the arc light. 

When the carbon points are separated by air only, the 
potential difterence between them, when connected with the 
poles of an ordinary arc-light dynamo, is not sufficient to cause 
a spark to pass, even when they are very close together ; but 
if they are in contact and then separated while the current is 



460 



HEATING AND LIGHTING EFFECTS 



passing ilirougli them, the " extra-current" spark produced on 
separation (§ 523) volatilizes a small quantity of the carbon 
between the points, and a conducting medium, consisting of 
carbon vapour and heated air, is thus produced, through which 
the current continues to flow. 

Since this medium has a higli resistance, 
intense heat is developed and the carbon 
points become vividly incandescent and 
burn away slowly in tlie air. When a 
direct current is used, the point of the 
positive carbon becomes hollowed out in the 
form of a crater, and the negative one 
becomes pointed, as shown in Fig. 555. 
The greater part of the light is radiated 
from tlie carbon points, the jDOsitive one 
being the brighter. 




Fig, 555.— The arc light. 



545. The Inclosed Arc— The Arc-light Automatic Feed. 

The open arc is now being largely superseded by the 
"inclosed arc," a form in which the carbon points are 
inclosfed in .a glass or porcelain globe with an air-tight 
joint at the bottom (Fig. 556), and with but sufficient 
opening at the top to give the upper carbon freedom. 
Since the oxygen in the globe soon becomes exhausted, 
and the absence of draft prevents its renewal, the carbons 
of the inclosed arc burn away very slowly. Ordinarily 
they last about ten times as long as when burning in the 
open air. 

In Figs. 556, 557, A and B are tlie terminals by wliich the 
current enters and leaves tlie lamp. Let it enter at A, and 
suppose the switch to be open so that it cainiot pass along x 
directly to B. The current goes to B by two paths. In the 



THE INCLOSED ARC 



461 



first, it p;issns i1ii-()n(;li Mm in;i«4iic't m, down througli the 
cjirltdiis II. jiikI 
/, ;iii(l then to 
/>' by way of <j. 
Ill tlie second, 
it traverses 
the magnet n 
and then goes 
on to B. The 
strength of 
current in each 
case will de- 
pend on the re- 
sistance oi* the 
path. 

When on is 
magnetized tlie 
plunger c is 
drawn up, and 
this raises d 

1 • 1 • , Fio. 557. — Diaofram showing- the connections 

Wmcn IS at- jn the inclosed arc lamp. The lamp 

iiici:iuniiaiii ui tiic iii- J- I 3 i ilhisti'aterl in this and (he last figure is 

closed an: lamp. The taClieU. tO One intended to he joined in series with others 

automatic feed is much -, £ ±\ on an alternating current circuit, but they 

the same in all arc end. OI tllC are all similar in principle, 
lamps. . . 

rocking-arni o\ 
This again lifts the clutch e Avhich raises the upper carbon u. 
If tlie carbons get too far apart the resistance increases and 
more current passes through n, which draws up its plunger /. 
This raises the other end of r, sets free the clutch, and the 
carbon drops. In this way the carbons are kept at the 
proper distance apart. 

The resistance s carries some of the current on startinor; 
when d rises it is cut out. An almost air-tight plunger in h 
prevents too abrupt motions of c. 





Fig. 556.— Showing the 
mechanism of the in 



CHAPTER XLIX 




Electrical Measurements 

546. Ohm's Law. We have learned that the strength of a 
current, or the quantity of electricity which flows past a 

point in a circuit in one second, 
depends on the E.M.F. of the 
current and the resistance of 
the circuit. The exact rela- 
tion which exists between these 
quantities w^as first enunciated 
by G. S. Ohm in 1826. It may 
be thus stated : — 

Tlie current varies directly as 
the electrcmiotive force and in- 
versely as the resistance of the 
circuit. From a practical point 
of view this is one of the 
most important generalizations 
in electrical science. It is known as Ohm's Law. 

547. Practical Electrical Units. It is evident that if units 
of any two of the three quantities involved in the relation 
stated in Ohm's Law are adopted and defined, the unit of the 
third quantity is also determined. This was the procedure 
followed at the International Congress on Electrical Units 
which met in London in 1908. 

The following definitions of units were adopted: — 

The Unit of Resistance. The International Ohm is the 
resistance offered to an unvarying current hy a column of 
mercury at the temperature of melting ice, 14-.4-521 grams in 
mass, of a constant cross-sectional area, and of a length cf 
106.300 cm. 462 



Georg Simon Ohm (1789-l&5t). Born at 
Erliingen ; died at Munich. Discoverer of 
Ohm's Law. 



PRACTICAL ELEOTllICAL UNITS 463 

Unit of Curuext Strength. TJie Infernafiovdl Ainj)ere 
is the V/iivaryi iKj c'lrctrtc, current, ivhich v>Ji,fih juisxed tJirovgh 
asoluAlunofffllrrr vi/ra/e iiiuIpt certain stated conditions, 
deposits silver at the rate of 0.00111800 grams per second. 

Unit of Electromotive Force. The International Volt 
■19 the electrical i^res'.svM"*? which when steadily applied to a 
ci)iidiict(jr, whose resistance is one International Ohm, ivill 
pfoduce a current of one International Ampere. 

Then, if (7 is the measure of a current in amperes; 7^, tlie 
resistance of the circuit in ohms; and E, the electromotive 
force in volts, Ohm's Law may be expressed as follows : — 

E 

PROBLEMS 

1. The electromotive force of a l)attery is 10 volts, the resistance of the 
cells 10 oliiiis, and the resistance of the external circuit 20 ohms. What 
is the current ? 

2. The difference in potential between a trolley wire and the rail is 500 
volts. What current will tlow througli a conductt)r which joins them if 
the total resistance is 1000 ohms ? 

3. The potential difference between the terminals of an incandescent 
lamp i:5 104 volts when one-half an ampere of current is passing through 
the filament. What is the resistance ? 

4. A dynamo, the E.M.F. of which is 4 volts, is used for the purpose of 
copper-plating. If the resistance of the dynamo is y^^f of an ohm, what 
is the resistance of the bath and its connections when a current of 20 
amperes is passing through it ? 

5. What must be the E.M.F. of a battery in order to ring an electric 
bell which re([uires a current of ^^ ampere, if the resistance of the bell 
and connection is 200 ohms, and the resistance of the battery 20 ohms? 

6. What must be the E.M.F. of a battery required to send a curi-ent 
of yJu of an ampere through a telegraph line 100 miles long if the resis- 
tance of the Avires is 10 ohms to the mile, the resistance of the instruments 
being 300 ohms, and of the battery 50 ohms, if the return current through 
the earth meets with no appreciable resistance ? 



464 ELECTRICAL MEASUREMENTS 

7. The potential difference l)et\veen tlie carbons of an arc lamp is 50 volts 
and the resistance of the arc 2 ohms. If the arc exerts an opposing K M.F. 
of its own of 30 volts, what is the current passing through the carbons ? 

8. A dynamo, of which the E.M.F. is 3 volts, is used to decompose 
water. What is the total resistance in the circuit when a current of one- 
half an ampere passos through it, if the counter electromotive force ot 
polarization of the electrodes is 1.5 volts ? 

548. Fall of Potential in a Circuit. If a battery or dynamo 
is o-eneratino" a current in a circuit, it is evident that the 
E.M.F. required to maintain this current in the whole circuit 
is greater than that required to overcome the resistance of 
only a part of the circuit. For example, if the total resistance 
is 100 ohms, and the E.M.F. is 1000 volts, the current in 
the circuit is 10 amperes. Here an E.M.F. of 1000 volts is 
required to maintain a current of 10 amperes against a total 
resistance of 100 ohms; manifestly to maintain this current in 
the part of the circuit of which the resistance is, say 60 ohms, 
an E.M.F. of but 500 volts will be required. This is usually 
expre.ssed by saying that there is a fall in potential of 500 
volts in the part of the circuit whose resistance is 50 ohms. 

In general, if there is a closed circuit through which a cur- 
rent is flowing, the fall in potential in any portion of the circuit 
is proportional to the resistance of that portion of the circuit. 

PROBLEMS 

1. The end A of the wire ABG is connected with the earth, and the 
diflference in potential between the other end (7 and the earth is 100 volts. 
If the resistance of the portion AB is 9.6 ohms and that of BC 2.4, what 
current will flow along the wire, and what will be the potential difference 
between the point B and the earth ? 

2. The i)ole3 of a battei-y are connected by a wire 8 metres long, having 
a resistance of one-half ohm per metre. If the E.M.F. of the battery is 
7 volts and the internal resistance 10 ohms, find the distance between two 
points on the wire such that the potential difference between them is 
1 volt. What is the current in the wire 1 

3. The potential difference between the brushes of a dynamo supplying 
current to an incandescent lamp is 104 volts. If the resistance in the 



QUANTITY OF Ef.ECTRICITY 465 

wires on the street leading from Mio dyiranio io the lumse is 2 oliins, that of 
the wires in the liouse 2 ohms, and that of the ]am[) 204 olims, wliat is the 
fall in potential in (1) the wires on the street, (2) the wires in the house, 
and what is the potential difference between the terminals of the lamp ? 

4. A dynamo is used to light an incandescent lamp wliich requires a 
curi-ent of 0.6 ampere and a potential difTerence between its terminals of 
110 volts. If the wires connecting the dynamo with the lamp have a 
resistance of 5 ohms, find the potential difTeronces which must be main- 
tained between the terminals of the dynamo to light the lamp properly 1 

5. A cell has an internal resistance of 0.3 ohm, and its E.IM.F. on open 
circuit is 1.8 volts. If the poles are connected by a conductor whose 
resistance is 1.2 ohms, what is the current pi'oduced, and what is the 
potential difference between the poles of the cell ? 

6. If the E.M.F. of a cell is 1.75 volts, and its resistance 3 ohms, find 
the internal drop in potential when the circuit is closed by a wire whose 
resistance is (a) 4 ohms, (b) 32 ohms. 

549. Quantity of Electricity. Let us refer again to tlie flow 
of water tlirougli a pipe (§ 453). The current strength is the 
rate of floiv. It depends upon the difference of pressure at the 
ends of the pipe, and the resistance of the pipe. But we often 
wish to know the quantity of water passing in a given time. 
Obviously we have the relation, 

Quantity = rate of flow x time of flow. 

We miglit measure rate of flow in gallons-per-second, and 
quantity in gallons. 

In electrical measurements there is something similar. We 
may think of the quantity of electricity passing a cross-section 
of a circuit in a given time, and as before we have the relation, 
Quantity of electricity = current strength x the time. 

If we measure current strength in amperes, and time in 
seconds, the quantity will be given in coulombs; and we 
have the definition: — A Coulomb is the amount of electricity 
wliich passes a point in a circuit in one second when the 
strength of the current is one ampere. 

The ampere corresponds to gallons-per-second, the coulomb 
to gallons. 



466 ELECTRICAL MEASUREMENTS 

If the strength of a current is 6' amperes and (lie quantity 
flowing past a point in (he circuit in t seconds is Q coulombs, 
then Q = Ct. 

Practical electricians frecjuently employ the anq>ere-Jtour 
as the unit quantity, as for exani])le, in estimating the capacity 
of a storage cell. A battery contains 100 ampere-hours, when 
it will furnish a current of one ampere for 100 hours, or 2 
amperes for 50 hours, etc. 

550. Work Done in an Electric Circuit. The water analogy 

will assist us again in getting a clearer grasp of the principle by 
which the energy expended in an electric circuit may be expressed. 

Just as the work done by a stream depends on the quantity of 
water and the distance through which it falls, so the work clone in 
any portion of an electric circuit depends on the quantity of electri- 
city which passes through it and the difference in potential between 
its terminals. One joule, or 10^ ergs, of work is done, when one 
coulomb of electricity falls through one volt. 

Hence, if Q is the quantity of electricity passing through a wire 



Fig. 558. — Portion of an electric circuit. 

AB (Fig. 558) and F denotes the fall in potential from A to B, the 
work done by the current = QV = CVf. 

551. Rate at Which Work is Done in an Electric Circuit. 

The power or i-ate at which work is done in an electric circuit is 
estimated in joules per sec, that i.s, in watts !§ 71). 

Thus if a cun-ent of C amperes flovvs through a circuit in which 
there is a drop of potential of V volts, energy is being delivered at 
the rate of VG watts. 

Hence W (power in watts) = fall in potential (in volts) x 
current (in amperes). 

Since one horse-power = 746 watts (§ 71). 

T, ,. , , Potential diff. (in volts) x current (in amperes) 
Power (m horse-power) = ^ -~- ^ 

'■ ' 746 

552. Relation Between Heat Energy and the Energy of 

the Electric Current. The meclnuiical equivalent of heat is 4.2 
joules per calorie, that is one calorie = 0.24 joules. Hence if an 
electric current of C amperes is flowing in a circuit in which there 
is a fall in potential of Y volts, and all the energy of the current is 



WORK DONE IN AN ELECTRIC LAMP 467 

transformed into heat, f x (' x 0.24 calories will l)e developed 
every second. 

More frecjuently, however, the quAintitij of heat produced V)y a 
current is expressed in terms of the current and the resistance. 15y 
Ohm's Law, F = C x // ; therefore the heat developed in a circuit, 
whose resistance is li Ohms by a current of C amperes is C'-R x 0.24 
calories per second, or in t seconds the heat produced = C'Ht x 0.24 
calories. This accords with results determined experimentally by 
Joule (§ 538). 

553, Work Done in an Electric Lamp. The efficiency of an 

electric lamp is usually determined in watts per candle power. 

Thus if a 16-candle power incandescent lamp rerjuires a current of 

h ampere in a 110 volt circuit, its efficiency is — S or 3.4 watts 

per candle power. •'•" 

For commercial purposes, the energy consumed by a lamp in a 
given time is usually measured in tvatt-houis. For example, if a 
customer has a lamp of the above desciiption burning for 100 hours 
per month, lie pays monthly for 55 x 100, or 5500 watt-hours of 
energy. 

PROBLEMS 

1. A current of 10 anii)ere3 flows through an arc light circuit. What 
quantity of electricity will pass across the arc of one of the lamps in a 
night of 10 hours ? 

2. The difference in potential between a trolley wire and the rail which 
carries the return circuit is 5U0 volts, and the motor of a car takes an 
average current of 25 amperes. How much work is done each hour in 
the circuit joining the trolley wire and the rail 1 

3. Find the horse power necessary to run an electric light installation 
taking 125 amperes at 110 volts. 

4. The resistance of the filament of an incandescent lamp is 200 ohms 
and it carries a current of 6 amperes. Find the amount of heat (in 
calories) developed in this filament per minute. 

5. A 25-candle power tungsten lamp, when used in a 25-volt circuit 
takes one ampere of current. Find its efficiency. 

6. The potential difference between the wires entering a house is 104 
volts, and an average current of 8 amperes flows through them for 4 hours 
per day. How many watt-hours of energy nnist the householder pay for 
in a month of 30 days ? Find the cost at 8 cents per kilowatt-hour. 
(1 kilowatt = 1000 watts.) 




468 ELECTRICAL MEASUREMENTS 

. 554. Resistance Boxes. The standavd resistance was defined 
in § 5-17.. It is obvious that for (he purpose of comparing 
resistances it would be incon\"enient to use mercury columns 
in ordinary experiments. In practical work resistance coils 
are used for this purpose. Lengths of wii'e of known resist- 
ance are wound on bobbins and connected in sets in resistance 
boxes. Fig. 559 shows the common method of joining the 
coils. A current in passing from A to 
B meets with practically no resistance 
from the heavy metallic bar when all 
the plugs are inserted. To introduce a 
given resistance, tlie plug short-circuiting 
Fia. 559.-c^nn^tioM in a the proper coil is removed and the current 
resistance box. j^ ^^^.^^|^ ^^ travcrse the resistance wire. 

For convenience in calculation the coils are usually grouped 
very much as weights are arranged in boxes. For example, 
a set of coils of 1, 2, 2, 5, 10, 10, 20, 50, 100, 100, 200, 500 
ohms may be combined to give any resistance from 1 to 1000 
ohms. 

555. Determination of Resistance; Method of Substitution. 

If the current strength and electromotive force of a current 
are known or can be determined with an ammeter and a volt- 
meter, the resistance in the circuit can be calculated from 
Ohm's Law R = E/G. 

To determine an unknown resistance, when these factors 
are not known, the conductor is placed in a circuit with a cell 
of constant E.M.F. and a sensitive galvanometer. The deflec- 
tion of the needle of the galvanometer is noted, and the 
unknown resistance then replaced by a resistance box. The 
coils are adjusted so as to bring the needle to its former 
position. The resistance thus placed in the circuit is evidently 
the resistance of the conductor. 

This method, which is usually known as the method of 
substitution, was employed by Ohm in his first experiments. 



THE WHEATSTOXE BRIDGE 



469 



Obviously vjiriaiions in the E.M.F. of the cell used will 
introduce errors in the determination. 

556. The Wheatstone Bridge. Wheatstone, who wan a con- 
temporary of Olun and had followed his experiments, invented 
what is known as the " Wlieat^tone Bridge/' an arrangement 
of coils which makes the determination independent of changes 
in the E. M. F. of the cell. The coils are arranged in three sets 
A, B, and C, with connections for a battery, a galvanometer 
and the resistance to be measured, as shown in Fig. 560. 




Fig. 560. —Electrical connections in the Wheatstone Bridge. 

They are mounted in a box and the changes in the resist- 
ance are made in the usual way, by inserting or withdrawing 
conducting plugs, as shown in Fig. 559. 

The branches A. and G usually have three coils each, the 
resistances of which are respectively 10, 100 and 1000 ohms, 
and the bi'anch B has a combination of coils, which will give 
any number of units of resistance from 1 to 11,110 ohms. 
The conductor, whose resistance X is to be measured is 
inserted in the fourth branch of the In-idge (Fig. 560), and the 
resistances yl, B and C adjusted until the galvanonu'ter con- 
necting M and X stan<ls at zero when the keys are closed. 

Then the cm-rent from the battery is flowing from P, partly 
through X and C, and partly through B and A to Q, and since 



470 ELECTRICAL MEASUREMENTS 

no current flows from 31 to N, the potential of M must be the 
same as that of N; therefore the fall in potential from P to A^ 
in the circuit PNQ is tlie same as the fall from P to 1/ in the 
circuit PMQ ; but the fall in potential in a part of a circuit is 
proportional to the resistance of that portion of the circuit. 

Hence, ^~ ^ or A = 

C A A 

The resistances A, B and C are read from the instrument, 
and the value of A'^ is calculated from the formula. 

557. Laws of Resistance. The resistances of conductors 
under varying conditions have been determined by various 
investigators with great care. The general results are given 
in the following laws : — 

1. The 7'esistance of a conductor varieHi directly as its length. 

2. The resistance of a conductor varies inversely as the area of its 
cross-section. In a round conductor, therefore, the resistance varies 
inversely as the square of the diameter. 

3. The resistaiice of a conductor of given length and cross-section 
depends upon the material of which it is made. 

Hence, if I denotes the length of a conductor, A the area of 
its cross-section and R its resistance, 

where ^ is a constant depending on the material of the con- 
ductor and the units of measurement used. The constant p is 
known as tlie Specific Resistance of the material. For 
scientific purposes tlie specific resistances is usually expres.sed 
as tlie resistance in microhms or millionths of an olim, of a 
cube of this material, whose edge is one centimetre in length, 
wlien a current is made to flow parallel to one of its edges. 

The following table gives the specific resistances in microhms 
of some well-known substances at 0°C. 



EESISTANCE AND TEMPERATUllE 
Table of Resistances at O^C. 



471 



Aluminium wire . 2.01 

Copper wire (annealed). . . 1.58 
Carbon (lamp filament) . . 4000 

Mercury 94.07 

Nickel wire (annealed).. . .12.43 



Platinum wire (annealed). 9.04 

German Silver wire 20.89 

Iron (telegraph wire) 9.70 

Silver wire (annealed) .... 1.4G 
Steel (rails) 12.00 



558. Resistance and Temperature. If we connect a piece 
of fine iron or platinum wire in a circuit with a voltaic cell 
and a galvanometer and note the deflection of the needle, we 
shall find on heating the wire with a lamp that tlie galvano- 
meter indicates a weakening in the current. The rise in the 
temperature of this wire must, therefore, have been accom- 
panied by an increase in its resistance. This action is typical 
of metals in general. 

The resistance of nearly all pure metals increases about 0.4 
per cent, for each rise in temperature of 1° C. The resis- 
tance of carbon on the other hand diminishes on heating. The 
filament of an incandescent lamp, for instance, has when hot 
only about one-half the re.sistance which it has when cold. 
The resistance of an electrolyte also decreases with a rise in 
temperature. 

QUESTIONS AND PROBLEMS 

1. What is the resistance of a column of mercury 2 metres long and 0.6 
of a Sf^uare millimetre in cross-section at 0° C 'i 

2. The resistance at 0° of a column of mercury 1 metre in length and 
1 sij. mm. in cross-section is called a "Siemens' Unit." Find the value 
of this unit in terms of the ohm. 

3. Copper wire ^\^ inch in diameter has a resistance of 8 ojims per mile. 
What is the resistance of a mile of copper wire the diameter of which 
is ^jr inch ? 

4. A mile of telegraph wire 2 mm. in diameter offers a resistance of 13 
olnns. What is the resistance of 440 yards of wire 0.8 mm. in diameter 
made of tlie same material ? 

.5. What length of copper wire, having a diameter of 3 mm., hat, the 
same resistance as 10 metres of copper wire having a diameter of 2 mm.? 



472 ELECTRICAL MEASUREMENTS 

6. Oil measuring the resistance of a piece of No. 30 B.W.G. (covered) 
copjier wire 18.12 yards long I found it to have a resistance of 3.02 ohms. 
Another coil of the same wire had a resistance of 22.65 ohms. What 
length of wire was there in the coil ? 

7. Two wires of the same length and material are found to have resis- 
tances of 4 and 9 ohms respectively. If the diameter of the first is 1 mm., 
what is the diameter of the second ? 

8. What must be the thickness of copper wire, which, taking equal 
lengths, gives the same resistance as iron wire 6.5 mm. in diameter, the 
specific resistance of iron being six times that of copper ? 

9. Find the length of an iron wire -^^ inch in diameter which will have 
the same resistance as a copper wire -^^ inch in diameter and 720 yards 
long, the conducting power of copper being six times that of iron. 

10. A wire made of platinoid is found to have a resistance of 0.203 
ohm per metre. The cross-section of the Avire is 0.016 sq. cm. Express 
the specific resistance of platinoid in microhms. 

11. Taking the specific resistance of copper as 1.58, calculate (1) the 
resistance of a kilometre of copper wire whose diameter is 1 mm., (2) the 
resistance of a copper conductor 1 sq. cm. in area of cross-section, and 
long enough to reach from Niagara to New York, reckoning this distance 
as 480 kilometres. 

12. A current flows through a copper wire, which is thicker at one end 
than the other. If there is any difi"ereiice either (1) in the strength of 
the current at, or (2) in the temperature of, the two ends of the wire, 
state how they diff'er from each other, and why. 

559. Resistance in a Divided Circuit. When a current is 

divided and made to flow from a conductor A to another B 

through two parallel circuits (Fig. 561), 

it is often necessary to determine the 

resistance of a single wire, which will 

.— ivi e circui . ^^ equivalent to the two in parallel, and 

to find the fraction of the total current which flows through 

each wire. 

Let E denote tlie diflerence in potential between A and B 
and Rj^ and R,^ the resistances of the wires. 



SHUNTS .473 

W 
Then the current throuf^h the first wire = — (Ohm's Law), 

and " " " second " = _. 

w w 

Total current through the two wires = — _^ — -. 

R^ R.2 

E 

But the total current = -— , where R is the resistance of a 

it 

single wire equivalent to the two. 

E E E 
Therefore ^ = ^ + ^. 

,, , . 11 1 

that IS — — h ^-• 

R R^ R.2 

Again, the fraction of tlic total current in the first wire 

_ R, _ R, 



E^ E^ R, + R,^ 

R^ i?2 
Similarly, the fraction of the total cuirent in the second wire 

i^i + R-z 

560. Shunts. When it is undesirable to send the whole 
current to be measured through a galvanometer or other 
current-measuring instrument, a definite 
fractional part of the current is diverted , ^ 



R 

by making the instrument one of two 

parallel conductors in tlie circuit, as F'O- 562.— Galvanometer and 
^ . . ' shunt. 

shown in Fig. 562. 

The conductor R " in parallel " with the galvanometer G is 
called a shunt. 



474 ELECTRICAL MEASUREMENTS 

If G is the resistance of the galvanometer, R the resistance 
of the shunt, and C the total current, the amount of current 

~D 

through the galvanometer = — x C (§ 559). 

Lt -\- -ti 

For the sake of facility in calculation, it is usual to make R 
^, yV, or -^\-^ of G, when, by the above formula, the current 
through the galvanometer will be yV» yJir' or y^T' respectively, 
of the total current to be measured. 

PROBLEMS 

1. The poles of a voltaic battery are connected by two wires in parallel. 
If the resistance of one is 10 ohms and that of the other 20 ohms, find 
(1) the resistance of a single wire equivalent to the two in parallel ; (2) 
the proportion of the total current passing through each wire. 

2. Find the total resistance when the following resistances are joined 
in series : — 3^ ohms, 2^ ohms, 2j ohms. What would be the joint 
resistance if the resistances were joined in parallel ? 

3. What must be the resistance of a wire joined in parallel with a wire 
whose resistance is 12 ohms, if their joint resistance is 3 ohms 1 

4. The joint resistance of ten similar incandescent lamps connected in 
multiple is 10 ohms. What is the resistance of a single lamp ? 

5. Four incandescent lamps are joined in parallel on a 100-volt circuit. 
If the resistances of the lamps are respectively 100 ohms, 200 ohms, 300 
ohms and 400 ohms, find (1) the total current passing through the group 
of lamps ; (2) the proportion of the total current passing' through the first 
lamp ; (3) the resistance of a single lamp which would take the same 
current as the group. 

6. A galvanometer whose resistance is 1000 ohms is used with a shunt. 
If j"j of the total current passes through the galvanometer, what is the 
resistance of the shunt ? 

7. If the shunt of a galvanometer has a resistance of 1/n of tlie galvano- 
meter, what fraction of the total current passes through the galvanometer ? 

8. The internal resistance of a Daniell's cell is 1 ohm ; its terminals are 
connected («) by a wire whose resistance is 4 ohms, {h) by two wires in 
parallel, one of the wires having a resistance of 4 ohms, the resistance of 
the other wire being 1 ohm. Compare the currents through the cell in 
the two cases. 



SHUNTS 



475 



561. Grouping of Cells or Dynamos. Electrical generators 
may be connected in various ways to give a 
current in the same circuit. , 

They are connected in series or tandem when 
the negative terminal of one is connected with 
the positive terminal of the next (Fig. 563), and 
in multiple, or parallel, when all 
the positive terminals are con- 
nected to one conductor and all 
the negatives to another (Fig. 564). 
Sometimes combinations of these 
methods of arrangement are employed as shown in Figs. 
565, 566. jl 

562. Current Given by A il H 

Series Arrangement. If n ^^\^ 





Fig. 563.— Cells con- 
nected in series. 



Fio. 664.— Cells 
connected in 
multiple. 




jk.>->v.» *-'![ * ■ >■■ ■ l l * ' * ' 7 * »- 



cells are arrantred in series, '^■"" '^ ^^ 

. . ° . Fig. 50.5. KiQ. 51)0. 

and r IS the internal resist- Cells connected in inultiple-series. 

ance of each cell, it is evident that the resistance of the 
group = nr, because the current has to pass through a liquid 
conductor n times as long as that between the plates of a 
single cell. 

If the potential-difference between the plates of a single cell 
(Fig. 563) is e, the potential-difference between Z^ and C^ is e ; 
but when C\ and Z.2 are connected by a short thick conductor 
there is practically no fall in potential between them, there- 
fore the potential-difference between Z^^ and Z.^ is e. Again, 
the potential-difference between Z.^ and C.^ is e, therefore the 
potential-difference between Z^ and Cj is 2e. Similarly, 
for 3, 4, etc., cells the potential-differences are respectively Se, 
4<e, etc. Hence, the E. M. F. of n cells in series is ne. 

Let E denote the E. M. F. and R the resistance of this 
group, and let R^ denote the external resistance in this 
circuit. 



476 ELECTRICAL MEASUREMENTS 





By 


Ohm's Law, 


C' = 


E 
R' 


E 


= lie, and R = 


nr + R^ 


> 






Hence 


G= — 


lie 



nr + R^ 

563. Current Given by Multiple Arrangement. If n cells 
are arranged in multiple, and r is the internal resistance of 

a single cell, the internal resistance of the group = — , because 

n 

the current in passing through the liquid from one set of 
plates to the other has n paths opened up to it, and therefore 
the sectional area of the column of liquid traversed is n times 

that of one cell, hence the resistance is only — of that of one 

n 

cell (§ 557). When all the positive plates are connected they 
are at the same potential ; for a similar reason all the negative 
plates are at tlie same potential, hence the E.M.F. of n cells 
in multiple is the same as that of one cell. 

This method of grouping is equivalent to transforming a 
number of single cells into one large cell, the Z plates being 
united to form one large Z plate, and the C plates to form one 
large G plate. It must be remembered that the potential- 
difference between the plates of a cell is independent of the 
size of the plates. (§ 473.) 

If E is the E.M.F. , R the resistance of the group, and 
R^ the external resistance, 

E e 



C = 



R + R, ^^ 

n 



564. Current Given by Multiple-Series Arrangement. Fin- 
ally let us consider an arrangement of the cells, partly in series 
and partly in parallel. Suppose them to be divided equally 
into sets, and let the cells in a set be joined in series while the 
sets themselves are arranged in parallel (see Figs. 565, 566). 



BEST ARRANGEMENT OF CELLS 477 

Let each set contain n cells, and let there be m sets. There 
are mn cells in all. 

Let e volts be the E.M.F. of each cell, r ohms its internal 
resistance, and R^ ohms the external resistance of the 
circuit. 

Then since n cells are joined in series, the E.M.F. of each 
set is ne volts. The internal resistance of each set is nr 
ohms, but as there are m sets arranged in parallel, the total 

resistance of the battery is — of this, that is, _ ohms. 

Hence the resistance of the entire circuit is — + Ri ohms, 
and the 

Current C = amperes. 

565. Best Arrangement of Cells. It is manifest that when 
the external resistance is very great as compared with the 
internal resistance, in order to overcome the resistance the 
electromotive force must be increased, even at the expense of 
increasing the internal resistance, and the series arrangement 
of cells is the best. When'the external resistance is very low 
as compared with the internal resistance, the object of the 
grouping is to lower as far as possible the internal resistance, 
and the multiple arrangement is the best. Between these 
extremes of high and low external resistance some form of 
multiple-series grouping gives the strongest current. 

It can be shown that for a given external resistance the 
maximum current from a given number of cells is obtained 
when the cells are so connected that the internal resistance of 
tlie battery is as nearly as possible equal to the external 
resistance. 



478 ELECTRICAL MEASUREMENTS 

PROBLEMS 

1. If the E.M.F. of a Grove cell is 1.8 volts and its internal resistance 
is 0.3 ohm, calculate the strength of current when 50 Grove cells are 
united in series and the circuit is completed by a wire whose resistance is 
15 ohms. 

2. If 6 cells, each with J ohm internal resistance, and 1.1 volts E.M.F., 
are connected (a) all in series, (b) all in parallel, (c) in two parallel sets of 
thi-ee cells each (Fig. 565) ; calculate the current sent in each case through 
a wire of resistance 0.8 ohm. 

3. Ten voltaic cells, each of internal resistance 2 ohms and E.M.F. 1.5 
volts, are connected («) in a single series, (fe) in two series of five each, 
the like ends of the two series being joined together. If the terminals 
are in each case connected by a wire whose resistance is 10 ohms, find the 
strength of the current in the wire in each case. 

4. The current from a battery of 4 similar cells is sent through a 
tangent galvanometer, the resistance of which, together with the attached 
wires, is exactly equal to that of a single cell. Show that the galvano- 
meter deflection will be the same whether the cells are arranged all in 
multiple or all in series. 

5. Calculate the number of cells required to produce a current of 50 
milli-amperes (1 milli-ampere = loW ampere), through a line 114 miles 
long, whose resistance is 12^ ohms per mile, tlie available cells of the 
battery having each an internal resistance of 1.5 ohms, and an E.M.F. of 
1.5 volts. 

6. You have a battery of 48 Daniell cells, each of 6 ohms internal 
resistance, and wish to send the strongest possible current through an 
external resistance of 15 ohms. By means of diagrams show various ways 
of arranging the cells and calculate the strength of current in each case. 
Find also in each case the difference of potential between the poles of the 
battery, assuming that the E.M.F. of a Daniell cell is 1.07 volts. 

7. A circuit is formed of 6 similar cells in scries and a wire of 10 ohms 
resistance. The E.M.F. of each cell is 1 volt and its resistance 5 ohms. 
Determine the diff"erence of potential between the positive and the 
negative pole of any one of the cells. 



CHAPTER L 
Other Forms of Radiant Energy 

566. Beyond the Visible Spectrum. As has been pointed 
out (Chap. XXXIX), when white light is passed through a 
prism it is thereby separated into its constituent parts, and on 
a screen placed in its patli (see Fig. 402), we observe a spectrum, 
with its colours ranging from violet at one end to red at the 
other. The wave-length of the extreme red is 0.000,8 mm. or 
about so^oo inch ; that of the extreme violet is 0.000,4 mm. 
or about -g-g-lFo- inch. If we considered these waves as we 
do sound waves we would say that the visible radiation 
corresponds to one octave. 

The question arises, are there radiations beyond those which 
give rise to the red and the violet sensations ? 

567. Waves beyond the Violet. In order to investigate 
this question let us receive the spectrum upon a j)hotographic 
plate. Upon developing it we find that while it has been 
scarcely affected by the red and the yellow light, the blue 
and the violet have produced strong action, and further, that 
decided action has been produced beyond the violet. By 
suitable means photographic action has been traced to wave- 
lengths not greater than 0.000,1 mm., that is, to about two 
* octaves ' above the violet. 

568. Beyond the Red. If we wish to explore beyond the 

red we must use a sensitive detector of heat. Let us obtain 

the spectrum of the sun, and then through it, going from blue 

to red, pass an air thermoscope (Fig. 264), the bulb of which 

has been coated with lamp-black. The thermoscope will show 

a heating effect which increases as we go towards the red, but 

the heating does not cease there. Beyond the red the effect is 

479 



480 OTHER FORMS OF RADIANT ENERGY 

still pronounced. By means of special instruments heat waves 
0.061 mm. long have been detected and measured. Such 
waves are about seven ' octaves ' below the longest red 
waves. 

Bodies at ordinary temperatures emit heat waves, and as 
the temperature is raised they give out, in addition, those 
waves which affect the eye. 

569. Radiant Energy. These waves of various lengths are 
simply undulations of the ether. They are all forms of radiant 
energy. While passing from one place to another they all 
travel with the speed of light, and it is only when they fall 
upon some form of matter that their energy is transformed 
into those physical effects which we recognize as heat, light, 
and in other ways. It is to be observed that the space free 
from matter through which these waves pass is not heated 
by their passage. 

Another form of radiant energy is seen in electric waves, 
referred to in the following sections. 

570. Absorption and Radiation. When ether waves fall 
upon a body, more or less of their energy is absorbed and the 
temperature of the body rises. Some bodies have higher 
absorbing powers than others. A surface coated with lamp- 
black or platinum-black absorbs practically all the ether waves 
which fall upon it, and may be taken as a perfect absorber. 
On the other hand, a polished metal surface has a low absorb- 
ing power. Much of the ether energy which falls upon it is 
reflected from the surface instead of being absorbed by it. 

This can easily be tested experimentally. Take two pieces 
of bright tin-plate about 4 inches square, and coat a face of 
one with lamp-black. Then stand them parallel to each other 
and about 5 inches apart. They may conveniently be sup- 
ported in saw-cuts in a board, and the blackened face should 
be turned towards the other plate. Attach with wax a bullet 



ABSORPTION AND RADIATION 



481 




Fia. 567.— The blackened 
half of the vessel radi- 
ates more than the 
polished half. 



to the centre of the outer face of eacli plate. Now place 
midway between the plates a hot metal ball. Soon the bullet 
on the blackened plate will drop off while the other remains 
unaffected. If the blackened plate is touched with the finger 
it will be found unpleasantly hot, while the 
other one will show a comparatively small 
rise in temperature. 

On the other hand, a blackened surface 
is a good radiator while a polished surface 
is a bad one. To show this experimentally 
use an apparatus like that illustrated in Fig. 
567. It consists of two blackened bulbs 
connected to a U-tube in which is coloured 
water. Now place between the bulbs a 
well-polished vessel, one half of which is 
blackened, and fill it with hot water. On 
observing the change in the level of the coloured water it 
will be seen that the blackened surface is radiating much 
more heat than the polished half. 

QUESTIONS 

1. Explain why a sheet of zinc protects woodwork from a stove better 
than a sheet of asbestos. Would bright tin-plate be better still ? 

2. A kettle to be heated by being hung before a fire-place should have 
one side blackened and the other polished. Why ? 

3. A sign consisted of gold-leaf letters on a board painted black. It 
was found, after a fire on the opposite side of the street, that the wood 
between the letters was charred while that under them was uninjured. 
Explain this phenomenon. 

4. Why is a frost more to be feared with a clear sky than with a 
cloudy one ? 

5. Why is there a greater deposition of dew on grass than upon bare 
ground ? 

6. In the Sahara the cold at night and the heat by day are equally 
painful to bear. Explain why. 

7. Covering a plant with paper often prevents it being frozen. Why ? 




482 OTHER FORMS OF RADIANT ENERGY 

571. Phenomenon of the Electric Spark. Let A and B (Fig. 
568) be two knobs attached to an induction coil or an influence 
machine. On putting the apparatus in 
operation the potential of one knob 
rises until a spark passes between the 
knobs. Ordinarily one thinks simply 
that a quantity of electricity has 
lumped from one knob to the other in 

Fig. 568.— Diagram illustrating "^ '■ 

how the electric waves spread order to amiul the difference of poten- 

out from a spark gap. -i 

tial between A and B. But there is 
more in the phenomenon than that. As a matter of fact 
there is a rush across from A to B, then one back from B to 
A, then another from A to B, and so on, until the energy of 
the charge is dissipated. Thus, instead of a .single spark there 
is a series of sparks between A and B. This has been 
demonstrated by photographing their images in a rapidly 
rotating mirror. 

If a pail of water be quickly dumped into one end of a 
trousfh, the water rushes to the other end where it is 
reflected. It then returns to the first and is reflected. 
After travelling back and forth for some time the motion 
dies away through friction and the water all comes to the 
same level. 

When a tuning-fork is vibrated, air- waves spread out in all 
directions, and if a unison fork is placed not too far away 
(Fig. 238) the incident waves will excite easily observed 
vibrations in it (see § 229). 

In a similar way the electrical surgings from knob to knob 
excite a disturbance in the surrounding ether, and ether- 
waves spread out in all directions (indicated by the wavy 
lines in Fig. 568). 



SYMPATHETIC ELECTRICAL OSCILLATIONS 



483 




Fig. 569.— Arrangement to show electrical 
resonance. 



572. Sympathetic Electrical Oscillations. It is pos.sible to 
exhibit electrical resonance quite analogous to that obtained 
with the unison tuning- 
forks. Let us take two 
precisely similar Leyden 
jars A and B (Fig. 569), 
and let a wire run from the 
outer coating of A and end 
in a knob c' near to the 
knob c which is attached to 
the inner coating. Join 
these knobs to an influence machine or an induction coil. 

Al.so let the inner and outer coats of B be connected by a 
wire loop Bdef, the portion de being so arranged that by 
sliding it along the other wires the area inclosed by 
the wire Bdef may be made equal to that of the fixed 
loop on the other jar. From the inner coating of B a 
strip of tin-foil is brought down to s within about 1 mm. 
of the outer coating. 

Now cause sparks to pass between the knobs c, c. Then if 
the two wire loops are equal in area there will be a little 
spark at s whenever a spark passes at c, c'. If the wire de is 
slid back or forth the equality of the areas will be destroyed 
and the sparks will cease at s. 

When the spark pa.sses at c, c' there are electrical surgings 
back and forth between the outer and inner coatings of A. 
These cause disturbances in the surrounding ether which 
spread out and set up oscillations in the similar circuit 
attached to the other jar. The natural period of the two 
circuits must be equal (or nearly so) for the sympathetic 
oscillations to be set up. 

In such an arrangement, as here described the number of 
oscillations is ordinarily several millions per second. 



484 OTHER FORMS OF RADIANT ENERGY 

573. Electric Waves. As early as 18G4 Maxwell*, by 
mathematical reasoning based on experimental results obtained 
by Faraday, showed tliat electric waves in the ether must 
exist ; but they were first detected experimentally by Hertz,-{- a 
young German physicist. Hertz showed that they are real 
ether-waves travelling through space with the speed of light, 
that they can be reflected and refracted, and that they also 
possess other properties similar to those possessed by light- 
waves. 

It is now firmly established that the short photographic 
waves, the waves which produce the colours of the spectrum, 
the longer heat-waves and the still lono'er electric weaves are 
all of the same nature. They are all undulations of the ether, 
differing only in wave-length. 

574. The Coherer. Various methods besides that illustrated 
in § 572 have been devised for detecting the presence of electric 
waves. The simplest of these is the coherer. Let us take a 
glass tube 6 or 8 inches long and | inch in diameter, fill it 
loosely with turnings of cast-iron or other metal, and through 
corks in each end insert copper wires. Then join the tube in 

series with a dry cell B, and a 
sensitive galvanometer G (Fig. 
570). Ordinarily the resistance 
of the turnings is so high that 
the needle of the g-al vanometer 

Fig. 570.— r is a tube filled with iron , • i i i ri j. i Ti; 

turnings, Gr la a galvanometer and fi IS not notlCCablv deflected. It 

a battery. • n i • -i 

now an influence machine be 
operated in the neighbourhood the galvanometer at once shows 
a deflection. The bits of metal, when the electric waves aroused 
by the machine fall upon them, appear to cohere, the resistance 
at once decreases and a current flows through the galvanometer. 

* James Clerk Maxwell, a very distins:ui8hed physicist. Born in Scotland 1831, died 1879. 
t Ileinrich Hertz died on January 1, 1894, in his 37th year. 




WIRELESS TELEGRAPHY 



485 




By .simply tapping tlio tube the filings are decohered and 
are ready for action again. 

In the coherer shown in Fig. 571 
the tube is about 3 inches long and 
has an internal diameter of about ^ 
inch. The plugs P, P snugly slide 
in the tube, and a small amount of 

filings is placed between them. Marconi has used a mixture 
of 95 per cent, nickel and 5 per cent, silver. 



571. — A form of coherer intro- 
duced by Marconi. 



Fig. 572.— Simple form of apparatus to illustrate wireless 
teleffraphy. The transmitter is on the left, the receiver 
on the right. 

575. Wireless Telegraphy. By means 
of electric waves it is possible to send 
signals from one place to another without 
connecting wires. A simple arrangement 
for doing this is shown in Fig. 572. C is 
an induction coil, n, n 
being knobs on the ends 
of its secondary. A wire 
A runs np in the air from 
one knob while the other 
is joined to earth. 7) is a 
battery and K a key in 
series with the primary of 
the coil. On depressing K 
W^ sparks pass between -)?, -7?' 
and violent surg;ini{s of 
electricity up and down A are produced. These 
disturbances in tlie surro'ilnding ether, the energy of 
is carried by ether -waves in all directions. 





excite 
which 



486 



OTHER FORMS OF RADIANT ENERGY 



At some distance away is the receiving apparatus. ^ is a 
coherer. From one pole of it a wire B runs up in the air; 
from the other pole a wire leads to earth. In circuit with the 
coherer are a battery F and an electric bell 0. The electric 
waves travel from A with the speed of light and on reaching 
B they excite oscillations in it. These cause the resistance of 
the coherer to fall, and the bell responds. 

576. Arrangement of the Receiving Apparatus. In 

actual experimenting the simple receiving apparatus shown in 
Fig. 572 is not satisfactory. A better arrangement is illus- 
trated in Fig. 573. 

The coherer C is joined in 
series with a battery B and 
a sensitive relay E (§ 510). 
When the resistance of the 
coherer falls, the armature F 
of the relay is drawn over 
against the stop S. Tliis com- 
pletes a circuit, in which are the 
battery H and the electric bell 
G, which is so placed that the hammer, besides striking the 
bell, taps the coherer and decoheres the filings, making them 
ready for 9,nother signal. 

For sending si^jnals across a room or from one room to 
another only a small coil and wires but a few feet high are 
required ; but if the distance to be covered is great verj^ 
powerful transmitters and very delicate receivers must 
be used. 

Wireless telegraphy is very useful in communicating signals 
from the shore to a ship or from one ship to another. By 
means of it many lives and much property have been 
saved. 




FlQ. 573. 



-Receiving apparatus for wireless 
telegrapliy. 



PASSAGE OF ELECTRICITY THROU-^JH GASES 487 

577. Passage of Electricity through Gases. In investigating 
this subject the gas is usually contained in a glass tube 
(Fig. 574) into the ends of c^^ ^j 

which platinum wires are fi ^-^. ",1 .7....!^I"^!!Z.!^!".".""^ 

sealed. ^-<^ n n' \^ 

1 he termnialS n, n or an f,q_ 574.— Arran8:ement to study the passage 

induction coil are joined to a °' '''"'""''' through a gas. 

and c, the electrodes of the tube. Let the electricity enter 
the tube at a and leave at c; these are, then, the anode 
and cathode, respectively. Sometimes one electrode has an 
aluminium disc upon it. By connecting a side tube 6 to a 
good air-pump the air can be exhausted from the tube. 

At first, when the air in the tube is under ordinary atmos- 
pheric pressure, the discharge passes between n and n', but as 
the pressure is reduced it begins to pass between a and c ; and 
as the exhaustion is continued some very beautiful effects are- 
produced. 

If, however, the exhaustion is pushed still further, until the 
pressure within the tube is about one millionth of an atmos- 
phere, phenomena of a different class are produced. As Sir 
William Crookes was the first to study these phenomena in 
great detail, these very highly exhausted tubes are known as 
Crookes Tubes. 

From the cathode something is shot off which travels 
through the tube in straight lines and with great speed. This 
has been shown to consist of very small particles charo-ed 
with negative electricity, and the streams of these particles are 
known as cathode rays. 

578, Rontgen Rays. In 1895, Rontgen, a German physicist, 
while experimenting with Crookes tubes, discovered a new 
kind of radiation, which he called X-rays, but which is more 
often known as Rontge.n rays. 



488 



OTHER FORMS OF RADIANT ENERGY 




Fig. 575.— a Rontgen ray tube. 



In Fi^. 575 is shown a tube suitable for producing the 
Rontgen rays. The electrodes a and 
G are joined to a large induction coil. 
From the concave surface of the 
cathode e the cathode rays are pro- 
jected, and when they strike the 
platinum plate ini (or any other 
solid body) they give rise to the 
Rontgen rays, which spread out as 
shown in the figure, easily passing 
through the walls of the tube. 

579. Photographs with Rontgen Rays. The Rontgen rays 
can affect a photographic plate just as light does. They can 
also pass through substances quite opaque to 

light, such as wood, cardboard, leather, flesh, 
but they do not so easily penetrate denser 
substances such as lead, iron and brass. If 
the hand be held close to a photographic plate 
and then exposed to the Rontgen rays, the 
rays easily pass through the flesh but are 
considerably hindered by the bones. Conse- 
quently when the plate is developed that part 
which was behind the flesh is much more 
blackened than that behind the bones. When 
a print is made from the ' negative ' we obtain 
a picture like that in Fig. 576. 

In place of a photographic plate we may use a paper screen 
coated with crystals of barium-platino-cyanide. When the 
rays fall upon this it shines with a peculiar yellow-green 
shimmering light. It is said to fiaoresce. The shadow of an 
opaque body is clearly seen by this light. 

580. Other Properties of the Rontgen Rays. If the 

hand or any other portion of the body is continually exposed 
to the Rontgen rays serious injury may result. 




Fig. 576.— From an X- 
ray photograph of 
the human hand. 



CONDUCTION OF ELECTRICITY THROUGH AIR 



489 



Another striking cliaracteristic of the rays is their ability 
to discharge an electritieJ body. If the air is thoroughly dry 
a well-insulated electroscope (§ 445) will hold its charge for 
many hours; but if it is placed in the path of the Rontgen 
rays the charge at once leaks away. For this to take place 
the air suiTOunding the gold leaves must become a conductor 
of electricity. 

581. Conduction of Electricity through Air. It is believed 
that electricity is conducted through a gas much as it is 
through a liquid. The latter was explained in § 484. 

Let C and 7) (Fig. 577) be two parallel metal plates placed a 
few cm. apart, and let G be joined to one pole of a battery, the 
other pole being joined to earth. E is an electrometer. This 
is a delicate instrument which measures the electrical charge 
given to it. First, suppose the tube T not to be inaction; 



r^YW 




Fig. 577. — An arrangement to exhibit the conduction of electricity by air. 
X-rays ionize the air. 



The 



the needle of the electrometer will be at rest. Then let the 
tube be started, and let the Rontgen rays pass into the air 
between the plates G and D. At once the electrometer begins 
to receive a charge, showing that electricity has passed across 
from G to D and thence by the wire w to the electrometer. 

When the X-rays pass through a gas they cause the mole- 
cules of the gas to be broken up into positively and negatively 
charged carriers of electricity called ions. This process is 
called ioniz'ition. When a molecule is ionized it is broken up 
into two ions, the electrical charges of which are equal in 



490 _ OTHER FORMS OF RADIANT ENERGY 

magnitude but of opposite sign. The positive ions are repelled 
from G to D and the negative ions are attracted by the plate 
C. In this way the electricity is transferred from C to D. 

582. Radio-activity. In 1896, a French physicist named 
Becquerel discovered that the element uranium and its various 
compounds emitted a I'adiation which could affect a photo- 
graphic plate ; and soon afterwards it was shown that, like 
the X-rays, it could ionize the air. A little later it was dis- 
covered that thorium and its compounds acted in the same 
way. Thorium is the chief constituent of Welsbach mantles. 
All such bodies are said to be radio-active. 

In searching for other radio-active bodies, Madame Curie 
observed that pitchblende, a mineral containing uranium, was 
more radio-active than pure uranium. After a very laborious 
chemical research she succeeded in separating from several 
tons of pitchblende a few milligrams of a substance which 
was more than a million times as radio-active as uranium. To 
this substance the name of radium was given. 

In experimenting pure radium is not used, but radium 
bromide. Other radio-active substances liave been discovered, 
polonium and actinium being the names given to two of the 
most powerful. 

It is easy to illustrate radio-activity. Lay some crystals of 
a salt of uranium or tliorium (uranium nitrate or thorium 
nitrate, for instance,) upon a photographic plate securely 
wrapped in black paper and allow them to remain there for 
some hours. When the plate is developed it will be found to 
be fogged. Or if the substance be held near a charged electro- 
scope the charge will at once leak away. 

583. Different Kinds of Rays. Rutherford has shown that 
there are three types of rays emitted by radio-active bodies 
(see §107). These he named the a (alpha), the ^ (beta) and 
the y (gamma) rays. The a rays are powerful ionizers of a 



DIFFERENT KINDS OF KAYS 491 

f^as, and it is now believed that the a particles are positively- 
charged atoms of helium. It takes very little to stop them. 
A sheet of aluminium -gV mm. thick completely cuts them off. 
The ^ rays are much more active photo f^raphically than 
the a rays, but not so powerful in ionizing a gas. They 
consist of negatively-charged particles and behave much like 
cathode rays. The y niys can pass through great thicknesses 
of solid matter, but their precise nature has not yet been 
determined. They resemble Rontgen rays. 

During recent years investigations into radio-activity have led 
to new views regarding the nature of atoms, regarding the rela- 
tions between electricity and matter, and regarding the maimer 
in which one substance is disintegrated and another is formed. 



ANSWERS TO NUMERICAL PROBLEMS 



Part I — Introduction 

Page 7. I. 2,500,000 mm. 2. 299,804.97 km. 3. 32,400,000 sq. cm. 

4. 29.921 in. 5. 1 cu. m. = 1,000 1. = 1,000,000 c.c. 6. 183.49 m. 7. 65.4 
cents. 8. 9697.5 kg. 9. The former. 10. 4.79 mm. 

Pageie. I. 1.47 kg. 2. 54.05C.C. 3. 519.75 grams. 4. 21.59 ; 46.318 c.c. 

5. 2.7 grams per c.c. 6. 12 kg. 7. 0.77 gm. per c.c. 8. 1.99 mm. 9. 283.5, 
0.5, 1.9, 7.1, 14.3 grams; 1814.4, 453.6, 141.7, 14.2, 85.0, 28.3 grams. (Correct 
to first decimal place ; accurate enough for photography). 

Part II — Mechanics of Solids 

Page 19- I. 88 ft. per sec. 2. 103 km. per hr. 3. 11 miles per day. 
4. 1 mile per day. 

Page 20. I. 2i| cm. per sec. per sec. 2. - ^V ft- P^r sec. per sec. 3. 
32. 185 ft. per sec. per sec. 

Page 27- l- 4 ft. per sec. 2. 1000 cm. per sec. 3. 576 ft. or 176.4 m. 
4. 190 cm. per sec. 5. 128 ft. per sec. 6. 7.82 sec; 4.37 sec. (approx.). 
7. 759§ ft. ; 33| sec. 8. 4 ft. per sec. per sec. 9. 4 sec. ; 1 sec. ; 78.4 m. 
10. 144 ft. or 44.1 m. 11. 15 sec. 12. Yes; 29^ ft. to spare. 

Page 31- 2. 14, 8, 11.4 ft. per sec. 4. 62.45 cm. per sec. ; 68.06 cm. 
per sec. 5. 7.55 ft. per sec. 

Page 34. 3- 125 : 3. 

Page 39. I. 5 cm. per sec. per sec. ; 25 cm. per sec. ; 10,000 units. 2. 5 
grams ; 2 cm. per sec. per sec. 3. 200 dynes. 4. 75 ft. per sec. ; 5 ft. per 
sec. per sec ; 750 units. 

Page 41- 2. 1,250 m. per sec. 3. 19.6 m. j)er sec. ; 1,250.15 m. per sec. 

Page 43- 4. 11 72 (nearly) ft. per sec. 

Page 46 l. 16 J pounds. 3. 3 feet. 

Page 53. I. Doul)led. 2. 44J, 25, 16 kg. 3. 0.37 pounds. 

Page 56. i. 100,000 ergs. 2. 1,800 ft.-pds. 3. .^0,000 ft.-pds. 4. ^y 
kg.-m. 5. 150,000 ft.-pds. 6. 528,000 ft.-pds. 

Page 63. 5- 5 ft. 

Page 66. 3- 45 pounds. 

Page 70. I. U pounds. 2. 90 pounds, 120 pounds. 3, 37^ pounds. 
4. 225 pounds. 

Page 73. I. Twice as great ; twice as long. 2. 4. 3. J. 4. 60 pounds. 
Page 77. I. 26§ pounds. 2. 6,400 pounds. 

Page 80. 2. 2()| pounds. 3. 4if pounds. 4. -f J jr pound ; s^ts pound. 

49S> 



ANSWERS TO NUMERICAL PROBLEMS 493 

Part III — Mechanics of Fluids 
Page 91. I. 312ig. 2.800kg. 3. II, .550 pounds. 4.10,000. 5.36 kg. 
6. 184.87 ft. nearly. 

Page 94. l. 62.3 pounds (at62'' F.) ; 97.7 pounds. 2. 4.57 pounds. 3. 2.5 kg. 

4. 4 9 kg. 5. 600 g. 6. i. 7. 1,557.5 pounds. 8. 133^ c.c. 12. 22.3 pounds. 
Page 99. l. f g- per c.c. 2. ig. per c.c. 3. 1.2 g. per c.c. 4. § g. per 

c.c. 5. 20 c.c. ; 6 g. per c.c. ; 0.8 g. per c.c. 6. |- g. per c.c. 7. S.g. = § ; 
s.g. = j; 6i inches. 8. 1.072 (nearly) g. per c.c. 9. Gold, 386.4 g. ; silver, 
21.04 g. 

Page 104. 6. 1.291 g. 

Page 115. I. 6§ c. ft. 2, 22.85 1. 3. 75,314.7 c. in. 4, 4S3fs in. of 
mercury. 5. 562^ mm. 6. 174 in. of mercury. 7. 0.0001259 (nearly) per 
c.c. 8. 101.34 g. 9, $3.60. 

Page 118. 4- 2908.75 kg. 

Page 128. i. i; ^t- 2. |. 3. 1^. 4. 12.92 m. 

Page 130. I. (b) 13.6 times ht. of mercury barometer. 2. 219J in. 

Part V — Wave-Motion and Sound 

Page 178. l. 335,338,356 m. per sec. 2. 1024.3 ft. per sec. 3. 5,595 
ft. 4. 3,490.2 ft. 5. 3.81 sec. (nearly). 9. 1,678.5 ft. 10. 4,707.4 ft. 
per sec. 11. 11,404 ft. per sec. {t = 20° C). 12. 4,290.2 ft. per sec. 

Page 186. 2. 4J0, 500. 3. 2,685.6. 5. 4,698. 6. 321, 65i, 130^, 261, 
522, 1,044, 2,088, 4,176. 7. 271.2. 8. G', E". 9. 69.2, 46.1, 31.1, 20.8 in. 
(approx. ). 

Page 198. 5. 6.49 in. 6. 4,064 m. per sec. 7. 36 poumls. 9. v^2 : 1. 
10. 10.38 in. if closed at one end ; 20.76 in. if open. 

Page 207. I. C", E" counting G as the first. 
Part VI— Heat 

Page 228. i. 9, 32.4, 48.6, 117. 2. 11 J, 15, 20, 525. 3. 117. 4. 153 

5. - 17r, - 121°, 0°, 7r, 37r. - sir, - 40°. 6. 50°, 68°, 89.6°, 167°, - 4°, 
- 40°, - 459.4°. 7. 3S§ cent. deg. 8. (a) 9.6°, - S°, - 12°, 1?°. {f>) 20° C, 

68° F. ; 31i° C, 88}° F. ; -7|° C, 18^° F. 

Page 232- I. 4.0002 ft. 2. 1.000 342 m. 3. 1-20.0216 sq. in. (nearly). 
4. 57.69 cm. (nearly). 5. 762.84 mm. ; 762.55 mm. 6. 761.07 mm. 

Page 236. 3. 28.55 1. 4. 107.59 c.c. (nearly). 5. 155.1 pds. per sq. in. 

6. 17.53 pds. per sq. in. (nearly). 7. 1.127 g. (nearly). 8. 32°.8 C, - 22°.8 C. 
9. 27.3° C. II. 108.87 1. (nearly). 12. 322| c.c. 13. 0.837 g. 14. 0.0000760 
g. per cm. (nearly). 

Page 239. I. 1,625 cal. 2. 3,000 cal. 3. 23° C. 4. 10 cent. deg. 5. 66i°C. 

Page 242. 1. 5.6 cal. 2. Mercury, 2.244 cal.; water, 2 cal. 3. .36 cal. 
4. 0.094. 5. 0.694. 6. 9,600 cal. 7. 950.16 cal. 8. 226,000 cal. 9. 27.9 
cal. 10. 3.17° 0. (nearly). 11. Sp. ht. 0.113 (nearly); iron. 12. 0.113 
(nearly). 13. 30,225 cal. 14. 47.0° C. (nearly). 15.0.748. 



494 ANSWERS TO NUMERICAL PROBLEMS 

Page 2i7. 6. 2,800 cal. 7. 1,200,000 cal. 8, 59 rV C. 9. 1,11H grams. 

10. 80 grams. II. 2,185 cal. 12. 166.15 grams. 13. 12.05 (nearly) grams. 
14. 0.09. 15. 79.38. 

Page 255- 5. 19,832 cal. 6. 182,240 cal. 7. 27,945 cal. 8. 230,680 cal. 

9. 44.37° C. 10. 10.07 g. (nearly). 11. 3.14 g. 12. 21,705 cal. 13. 

432,500 cal. 14. 536.4 cal. per gram (nearly). 

Page 273. i. («) 2,500 ft.-pds. ; 3.21 B. T. U. 2. .3,736,250 1. 3. 

2,388.34 cal. 4. 77,763.5 B. T. U. 5. 78.064 kg. 6. 1,038.77 lbs. 

Pakt VII — Light 

Page 293. I. 2.4 inches. 5. 869,159 ; 5,791 miles (nearly). 6, 105.4 miles. 

Page 299. 2. 4:25. 3. 25:9. 4. 14.15 c.p. 5. 4 ft. 6. 2 ft. from the 
candle towards the gas-flame and 6 ft. from the candle in opposite direction. 

Page 308. 2. 60°. 5. 40, 80, 120 inches. 

Page 318. 5. 15 cm. from vertex, in front of mirror ; 2.5 cm. higli. 6. 40 
cm. from vertex, behind mirror ; 25 cm. high. 7- 1*^ '^^^- {""om vertex, behind 
mirror ; virtual ; 4 cm. high. 

Page 329. I. 0.405 nearly. 2. 139,500 mi. per sec. ; 124,000 mi. per sec. ; 
9/8. 8. m°- 9- 1-52. 

Page 355. 4. 30 cm. 

Part VIII — Electricity and Magnetism 

Page 418. 3. 3,049 sec. (nearly). 4. 5 amp. 5. H, 0. 10.384 g.; 0, 0.83072 g.; 
Cu., 3.28 g. 

Page 451. 6. 80 per sec. 

Page 463. l. h amp. 2. J amp. 3. 208 ohms. 4. 0.19 ohm. 5. 22 
volts. 6. 13.5 volts. 7. 10 amp. 8. 3 ohms. 

Page 464. I. 8^ amp ; 80 volts. 2. J amp. ; 4 m. 3. 1 volt, 1 volt, 
102 volts. 4. 113 volts. 5. li amp., ^\ volt. 6. | volt, ^ volt. 

Page 467. i. 360,000 coulombs. 2. 45,000,000 joules. 3. 13.75 K.W. = 
18.43 H.-P. 4. 103,680 cal. 5. 1 c.p. per watt. 6. 99,840 watt-hours ; $7.99. 

Page 471. l. 3. 13 ohms. 2. 0.9407 ohms. 3. 72 ohms. 4. 20.31 ohms. 
5. 22.5 m. 6. 1.35.9 yds. 7. 0.6 mm. 8. 2.653 mm. 9. 1,080 yds. 10. 3.04. 

11. 20. 1 ohms; 75.84 ohms. 

Page 474. I. 6§ ohms ; §, J. 2. 8rVohms; S|ohms. 3. 4 ohms. 4. 100 
ohms. 5. 2 fV amp.; H amp.; 48 ohms. 6. 100 ohms. 7. _J_. 8.9:25. 

Page 478. I. 3 amp. 2. IH amp. ; lifamp. ; 2^\a.\np. 3. ^ amp. in each 
case. 5. 50 cells. 6. Let »i = No. of cells in a group, m = No. of groups in 
parallel. For n = l, ?re = 48, C=0.071 amp., P. D. =0.009 volt ; n = 2, m = 24, 
C=0.1.38, P.Z>.=0.069; Ji = .3, to=16, C=0.199, P.D.=0.224; n = 4, m = 12, 
C=0.252, P.Z).=0.504; n = 6, to = 8, C=0.329, P.D.^IAS; n=S, m=6, 
(7=0.372, P.Z).=2.98; n=12, m=4, C=0.3S9, P.D. = 7.00; n=16, m=3, 
C=0.364, P.Z). = 11.69; ?i = 24, m=2, (7=0.295, P.Z>.=21.24; n=48, w=l, 
C=0.169. P.i). =48.67. 7. 0.75 volt. 



INDEX 



Aberrution, 310 ; chromatic, 347. 

Absolute temperature, 234. 

Absorption, of light, 341; of radiant 
energy, 480. 

Acceleration, definition of, 20 ; uni- 
form, 20. 

Accelerations, composition of, 32. 

Accumulators, 415. 

Achromatic lenses, 34G. 

Actinium, radio-activity of, 490. 

Adhesion, 142. 

Agonic line, 37G. 

Air, weight of, 101 ; pressure of, 
101 ; variations in pressure of, 
107 ; compressibility and expansi- 
bility of, 112 ; the uses of com- 
pressed, 123. 

Air-brakes, 124. 

Air-pump, 119 ; the Geryk, 120 ; 
the mercury, 121 ; the Bunsen 
jet, 121. 

Alternating current, uses of, 452. 

Alternating current dynamo, 444. 

Ammeters, 432. 

Ampere, the international, 463. 

Ampere's laws of currents, 424. 

Aperture of mirror, 309. 

Archimedes' principle, 93. 

Arc lamp, 459 ; the inclosed, 4G0 ; 
regulation of, 461. 

Armature, of a dynamo, 443 ; 
shuttle, 443 ; Gramme-ring, 444 ; 
drum, 444. 



495 



Artesian wells, 90. 
Atmosphere, variations and pres- 
sure of, 107 ; height of the, 111. 
Automobile 'honk,' 211. 
Axis of mirror, 309. 

B 

Balance, description of, 11. 

Balloons, 117. 

Barometer, the, 105 ; the cistern, 
105 ; the siphon, 106 ; the ane- 
roid, 106 ; practical uses of, 
107. 

Beats, 203 ; tuning l)y means of, 
205. 

Bell, electric, 430. 

Boiling point, 251 
sure on, 251. 

Boyle's law, 113 
135. 

Brittleness, 146. 

Bugle, 212. 

Buoyancy, nature of, 92 ; to de- 
termine force of, 93 ; of gases, 
116. 

c 

Caissons, pneumatic, 125. 

Camera, the pin-hole, 290 ; the 

photographic, 359. 
Capacity, electrical, 390. 
Capillary action, 152 ; explanation 

of, 154 ; illustrations of, 155. 



effect of pres- 
explanation of, 



496 



INDEX 



Cell, the voltaic, 396 ; Leclanch^, 

405 ; Dan.iell, 405 ; gravity, 400 ; 

the dry, 407 ; Edison-Lalande, 

407. 
Centre of curvature of mirror, 309. 
Centre of gravity, definition of, GO ; 

to find, experimentally, GO ; of 

some bodies of simple form, 61. 
Charges, induced, equal, 385 ; reside 

on outer surface, 386. 
Charles' law, 232, 235. 
Chords, musical, 182, 184. 
Clarinet, 211. 
Clouds, 264. 
Coefficient, of expansion of solids, 

229 ; of expansion of liquids, 230 ; 

of expansion of gases, 232. 
Coherer, the, 484. 
Cohesion, 142. 
Cold storage, 258. 
Colladon's fountain of fire, 327. 
Colours, by dispersion, 339 ; of 

natural objects, 341. 
Complementary colours, 345. 
Compressed air, uses of, 123. 
Condensation of water-vapour of 

the air, 261. 
Condenser, the air, 123 ; the steam, 

269 ; electrical, 391. 
Conduction of heat, 274 ; in solids, 

274 ; in liquids, 275 ; in gases, 

276 ; practical significance of, in 

bodies, 276. 
Conductors, electrical, 381. 
Conjugate foci, of mirror, 313 ; of 

lens, 333. 
Conservation of mass and energy, 58. 
Convection currents, 279 ; in gases, 

280 ; applications of, 281. 
Cooling by vaporization, 256, 257. 



Cornet, 212. 

Coulomb, 465. 

Couple, 46, 

Critical angle, 326 ; values of, 326. 

Critical temperature, 259. 

D 

Daniell's cell, 405. 

D'Arsonval galvanometer, 432. 

Declination, magnetic, 376. 

Densities, table of, 14. 

Density, definition of, 13 ; measure- 
ment of, 14 ; relation to specific 
gravity, 15 ; of a solid heavier 
than water, 96 ; of a lighter than 
water, 97 ; of a liquid by the 
specific gravity bottle, 97 ; of a 
liquid by Archimedes' principle, 
98 ; of a liquid by means of a 
hydrometer, 98. 

Dew, 264. 

Dew-point, 261. 

Diatonic scale, 183. 

Diffusion, of gases, 133 ; of liquids 
and solids, 134. 

Dip, magnetic, 378. 

Direct current dynamo, 446. 

Direct vision, 350. 

Dispersion of light, 339. 

Displacement, definition of, 18 : 
resultant, 18 ; component, 18. 

Distillation, 265. 

Diving bells and diving suits, 124. 

Doppler's principle, 207. 

D17 cell, 407. 

Ductility, 146. 

Dynamo, the principle of, 442 ; the 
armature of, 443 ; field magnets 
of, 444 ; the alternating current, 
444 ; direct current, 446. 

Dyne, the, 38. 



INDEX 



497 



Earth, a magnet, 375 ; magnetic 

field about, 378. 
Ebullition, 248, 251. 
Echoes, 175. 

Edison-Lalande cell, 407. 
Efficiency of heat engines, 272. 
Elasticity, definition of, 143 ; meas- 
urement of, 143 ; of various 
metals, 144. 
Electricity, nature of, 389 ; quan- 
tity of, 465 ; passage of, through 
gases, 487. 
Electrical, attraction, 380 ; repul- 
sion, 381 ; law of attraction and 
repulsion, 381 ; potential, 388 ; 
capacity, 390 ; condenser, 391. 
Electrical units, 462. 
Electric bell, 430. 
Electric circuit, explanation of 

terms, 400 ; work done in, 466. 
Electric current, nature of the, 396; 
known by itseffects,396; detection 
of, 403 ; heat developed by, 457. 
Electric furnace, 457. 
Electric lamps, 458, 459. 
Electric motor, 449; counter electro- 
motive iorce in, 450. 
Electric spark, phenomenon of, 482. 
Electric telegraph, 427. 
Electric waves, 484. 
Electric welding, 458. 
Electrification, kinds of, 381 ; by 

induction, 383. 
Electrolysis, 403 ; explanation of, 
408 ; secondary reactions in, 411 ; 
of water, 411 ; applied to manu- 
factures, 413 ; laws of, 416 ; 
measurement of current strength 
by, 416 



Electromagnet, 423 ; strength of, 
424. 

Electromotive force, 401 ; unit of, 
401 ; of a voltaic cell, 402. 

Electrophorous, the, 393. 

Electroplating, 412. 

Electroscope, the gold-leaf, 382. 

Electrotyping, 413. 

Energy, definition of, 56 ; trans- 
formations of, 57 ; measurement 
of, 57 ; conservation of, 58. 

Equilibrium, conditions for, 62 ; 
three states of, 62. 

Erg, the, 55. 

Ether, 288. 

Evaporation, 248 ; rate of, 248 ; 
molecular explanation of, 249 ; 
into air, 250 ; cold by, 256. 

Expansion, of solids by heat, 217 ; 
of liquids and gases by heat, 218 ; 
applications of, 218 ; coefficient 
of, of solids, 229 ; coefficient of, 
of liquids, 230 ; of water, 231 ; 
coefficient of, of gases, 232. 

Eye, construction of the, 356 ; image 
on the retina of, 357 ; accommo- 
dation of, 357 ; defects of, 358. 



Faraday's experiments, 435. 

Field glass, 305 ; the prism binoc- 
ular, 366. 

Field magnets, of a dynamo, 444 ; 
excitation of, 448. 

Field of force, 370 ; due to electric 
cui'rent, 419 ; about a circular 
conductor, 420. 

Flotation, principle of, 94. 

Flute, 210 



498 



INDEX 



Focal length of mirror, 310 ; deter- 

miuatiou of, 311. 
Focus of mirror, 310. 
Fog, 264. 
Force, definition of, 36 ; units of, 

37 ; gravitation units of, 39 ; 

moment of a, 44. 
Forces, composition and resolution 

of, 40 ; composition of parallel, 

45 ; parallelogram of, 47 ; triangle 

of, 48 ; polygon of, 48 ; at the 

surface of a liquid, 150. 
Freezing mixtures, 247. 
French horn, 212. 
Friction, definition of, 64 ; laws of 

sliding, 65 ; rolling, 65. 
Frost, 264. 
Fusion, 243 ; change of volume in, 

244 ; heat of, 245. 

G 

Galvanometer, 431 ; the tangent, 
431 ; the D'Arsonval, 432. 

Galvanoscope, 403. 

Gases, buoyancy of, 116 ; diffusion 
of, 133. 

Gas engines, 270. 

Gas thermometer, 234. 

Gay-Lussac's law, 232. 

Gravitation, law of, 50. 

Gravity cell, 406. 

H 

Hail, 264. 

Hardness, 146. 

Harmonics, 186 ; in a string, 190 ; 

in an organ pipe, 197. 
Heat, nature of, 214 ; source of, 

215 ; unit of, 238 ; specific, 239 ; 

given out in solidification, 246 ; 

absorbed in solution, 247. 



Heating, by hot water, 282 ; by 
steam, 283 ; by hot-air furnaces, 
283. 

Heat of fusion, 245 ; determination 
of, of ice, 246. 

Heat of vaporization, 254 ; deter- 
mination of, 254. 

Helix, magnetic conditions of a, 421; 
polarity of the, 422. 

Hooke's law, 144. 

Horse-power, 59. 

Hot-water heating, 282. 

Humidity, 262 ; relation of, to 
health, 263. 

Hydraulic air compressor, the Tay- 
lor, 121. 

Hydraulic elevator, the, 84. 

Hydraulic lift-lock, the, 86. 

Hydraulic press, the, 84. 

Hydrometer, the, 98. 

Hydrostatic paradox, 88. 

Hygrometer, 263. 



Ice-making machine, 258. 

Images, in plane mirror, 302, 306 ; 
in parallel mirrors, 307 ; in in- 
clined mirrors, 307 ; to draw, 
in curved mirrors, 314 ; relative 
sizes of image and object in curved 
min'ors, 315 ; to draw, in lenses, 
337. 

Incandescent electric lamp, 458. 

Inclination, magnetic, 378. 

Inclined plane, the, 77. 

Induced currents, production of, 
436 ; illustrations of, 436 ; laws 
of, 438. 

Induced magnetism, 369r 



INDEX 



499 



Induction, magnetization by, 3(59 ; 

electrification by, 38.'} ; electrical 

charging by, 385. 
Induction coil, 453 ; explanation of 

the action of, 454. 
Inertia, definition of, 33. 
Intensity, of sound, 172 ; of light, 

294. 
Interference of sound-waves, 205 ; 

with resonators, 200. 
Intervals of the major diatonic 

scale, 183. 
Isogonic lines, 376. 



Joule, the, 267, 466. 



Kaleidoscope, 307. 

Kilogram, standard, 8 ; prototype, 9. 



Lantern, the projection, 360. 

Latent heat, 245. 

Lateral inversion by a mirror, 300. 

Leclanch^ cell, 405. 

Length, standards of, 2. 

Lens, 330 ; principal axis of, 330 ; 
action of, 330 ; focus of, 331 ; 
focal length of, 331 ; power of, 
331 ; determination of focal length 
of, 331 ; conjugate foci of, 333 ; 
magnification by, 338. 

Lenses, kinds of, 330 ; combina- 
tions of, 332 ; achromatic, 346 

Lenz's law, 439. 

Lever, the first class, 67 ; second 
class, 68 ; third class, 70. 

Leyden jar, 392. 



Light, radiation, 287 ; how trans- 
mitted, 287 ; waves and rays of, 
289 ; travels in straight line", 
290 ; determination of velocity 
of, 300, 301 ; illustrations of velo- 
city of, 301 ; velocity in liquids 
and solids, 301 ; laws of reflec- 
tion of, 302 ; refraction of, 319 ; 
laws of refraction of, 322 ; total 
reflection of, 325 ; dispersion of, 
339 ; absorption of, 341. 

Lightning rods, 387. 

Lines of force, properties of, 372. 

Liquid, surface of, in connecting 
tubes, 89 ; diffusion of, 134 ; 
distinction between liquids and 
solids, 141. 

Liquefaction of air, 260. 

Local action in a cell, 404. 

Loops, 166 ; in a vibrating string, 
189. 

Luxfer prisms, 327. 

M 

Machine, object of a, 67. 

Magnet, natural, 367 ; artificial, 

367 ; poles of a, 307 ; retentive 

power of, 370 ; field of force 

about, 370 ; the earth a, 375. 
Magnetic, laws of, attraction and 

repulsion, 368 ; substances, 369 ; 

shielding, 372 ; permeability, 373; 

declination, 376 ; inclination, 378. 
Magnetism, induced, 369. 
Magnetization, explanation of, 373; 

effects of heat on, 375. 
Magnification by lens 338. 
Malleability, 145. 
Mariner's compass, 375. 



500 



INDEX 



Mariotte's law, 115. 

Mass, standards of, 7 ; definition of, 
7, 33. 

Matter, molecular theory of, 131. 

Maximum density of water, 231. 

Maximum thermometers, 227. 

Measurement, of a quantity, 2 ; 
of length, 10 ; of mass, 11 ; of 
density, 14 ; of acceleration due 
to gravity, 24 ; of weight, 51 ; 
of work, 55 ; of energy, 57 ; 
of elasticity, 143 ; of current 
strength, 416, 

Mechanical equivalent of heat, de- 
termination of, 267. 

Melting point, 243 ; influence of 
pressure on, 244. 

Metre, the standard, 3 ; the proto- 
type, 4 ; sub-divisions of, 6 ; 
relation to yard, 6. 

Microscope, the simple, 361 ; mag- 
nifying power of, 362 ; the 
compound, 362. 

Minimum thermometers, 227. 

Mirrors, plane, 302 ; curved, 309 ; 
centre of curvature of, 309 ; 
radius of curvature of, 309 ; ap- 
erture of, 309 ; axis of, 309 ; 
focus of, 310 ; parabolic, 317 ; 
conjugate foci of, 313. 

Molecules, description of, 131 ; evi- 
dence suggesting, 131 ; motions 
of, 134 ; velocities of, 136 ; 
motions in liquids, 138 ; motions 
in solids, 139 ; size of, 146 ; 
nature of, 148. 

Moment of a force, 44. 

Moments, law of, 45. 

Momentum, definition of, 34. 



Motion, 18 ; under gravity, 22 ; 
in a circle, 28 ; translation and 
rotation, 28 ; Newton's first law 
of, 35 ; Newton's second law of, 
36 ; Newton's third law of, 42. 

Multiple arrangement of cells or 
dynamos, 475. 

Musical sounds and noises, 179 

N 

Nodes, 166 ; in a vibrating string, 

189. 
Non-conductors, electrical, 381. 



Oboe, 211. 
Octave, the, 182. 
Oersted's experiment, 403. 
Ohm, the international, 462. 
Ohm's law, 462. 
Opaque bodies, 292. 
Optical bench, 336 
Organ pipes, 196. 
Osmosis, 139. 

Overtones, in a string, 190 ; in an 
organ pipe, 197. 



Parabolic mirrors, 317. 

Pascal's principle, 83. 

Permeability, magnetic, 373. 

Phonograph, 213. 

Photometer, Rumford's, 295 ; the 

Bunsen, 296 ; Joly's diff'usion, 

297. 
Piccolo, 210. 
Pipe organ, 210. 

Pitch, 180 ; determination of, 180. 
Plasticity, 145. 



INDEX 



501 



Point, position of. a, 17. 

Polarization, of a cell, 404 ; of elec- 
trodes, 414. 

Poles of a magnet, 367. 

Polonium, radio-activity of, 490 

Position, of a point, 17. 

Potential, electrical, 388 ; zero of, 
389 ; fall of, in a circuit, 464. 

Pound, standard, 8. 

Poundal, the, 40. 

Power, definition of, 59 ; units of, 
59. 

Pressure, transmission of , by fluids, 
82 ; due to weight, 86, 88 ; rela- 
tion between pressure and depth, 
87 ; equal in all directions at the 
same depth, 87. 

Primary currents, 437. 

Pulley, the, 71 ; a single movable, 
72 ; differential, 76. 

Pulleys, systems of, 72. 

Pumps, lift-pump, 126; force-pump, 
127 ; double action force-pump, 
128. 

Q 

Quality of sound, 200. 
Quantities, physical, 1. 
Quantity, measuring a, 2. 
Quantity of electricity, unit of, 465. 



Radiant energy, forms of, 216, 287, 

479. 
Radiation, transference of, by heat, 

285 ; of light, 287, 480. 
Radio-activity, 490. 
Radium, radio-activity of, 490. 
Radius of curvature of mirror, 309. 



Rain, 264. 

Rainbow, 348. 

Recomposition of white light, 343. 

Reflection of light, laws of, 302 ; 
regular and irregular, 305 ; from 
parallel mirrors, .307 ; from in- 
clined mirrors, 307 ; total, 325. 

Reflection of sound, 175. 

Refraction of light, meaning of, 319; 
experiments illustrating, 319 ; ex- 
planation of, by means of waves, 
320 ; laws of, 322 ; table of in- 
dices of, 323 ; through a plate, 
324 ; atmospheric, 327 ; through 
prisms, 328. 

Regelation, 245. 

Resistance, determination of, 468 ; 
laws of, 470 ; specific, 470 ; and 
temperature, 471 ; in a divided 
circuit, 472. 

Resistance boxes, 468. 

Resi.stances, table of, 471. 

Resonance, 193 ; of an open tube, 
195. 

Resonators, forms of, 194. 

Rontgen rays, 487 ; photographs 
with, 488 ; properties of, 488. 



Saxaphone, 211. 

Scale, diatonic, 183 ; of equal tem- 
perament, 184 ; the harmonic, 
185. 

Screw, the, 78. 

Secondary currents, 437. 

Self-induction, 439. 

Series arrangement of cells or 
dynamos, 475. 

Shadows, theory of, 291. 



502 



INDEX 



Shunts, 473. 

Siphon, 129 ; the aspirating, 129. 

Snow, 264. 

Solidification, 243. 

Solids, distinction between liquids 
and solids, 141. 

Sonometer, the, 187. 

Sound, origin of, 168 ; conveyance 
of, 168 ; velocity of, in air, 169 ; 
intensity of, 172 ; transmission 
of, by tubes, 173 ; velocity of, in 
solids, 173 ; velocity in different 
gases, 175 ; reflection of, 175 ; 
determination of velocity of, by 
resonance, 194 ; quality of, 200. 

Sound-waves, nature of, 170 ; in- 
terference of, 205. 

Specific heat, 239 ; of water, 240 ; 
determination of, by method of 
mixtures, 240. 

Specific heats of some common sub- 
stances, 241. 

Specific resistance, 470. 

Spectra, kinds of, 350 ; continuous, 
351 ; discontinuous, 351 ; absorp- 
tion, 351. 

Spectroscope, 348. 

Spectrum, 339 ; a pure, 340 ; ana- 
lysis of, 351 ; the solar, 352 ; 
meaning of dark lines of, 352. 

Standards, of length, 2 ; national, 
5 ; of mass, 7 ; of light, 298. 

Steam-engine, 268 ; high and low 
pressure, 269 ; the compound, 
269 ; the turbine, 269. 

Steam heating, 283. 

Storage cells, 415. 

Strain, 143 ; Shearing, 145 

Stresses, 143. 

Stringed instruments, 209. 



Sublimation, 140. 

Submarine bell, 177. 

Surface tension, 151 ; illustrations 
of, 155. 

Sympathetic electrical oscillations, 
483. 

Sympathetic vibrations, 202 ; illus- 
trations of, 203. 



Tangent galvanometer, 431. 

Telegraph, the electric, 427 ; key, 
427 ; sounder, 428 ; relay, 428 ; 
wireless, 485. 

Telegraph system, connection of 
instruments in, 429. 

Telephone, 455 ; transmitter, 455 ; 
receiver, 455. 

Telephone circuit, connection of 
instruments in, 456. 

Telescope, the astronomical, 363 ; 
objectives and eyepieces, 365 ; 
the terrestrial, 366. 

Temperature, nature of, 222 ; and 
quantity of heat, 222 ; determina- 
tion of, 222 ; absolute, 234 ; 
critical, 259. 

Thermal capacity, 239. 

Thermometer, Galileo's, 223 ; con- 
struction of a mercury, 224 ; 
determination of the fixed points 
of, 225 ; graduation of, 225 ; com- 
parison of scales of, 226 ; gas, 234. 

Thermometers, maximum and mini- 
mum, 227. 

Thermostats, 220. 

Time, unit of, 9. 

Tones, musical, 180 ; simultaneous 
production of, 190 ; fundamental, 
186; fundamental in a string, 188. 



INDEX 



603 



Torricellian experiment, 102. 
Total reflection, of light, 325 ; 

prisms, 326. 
Transference of heat, by conduction, 

274 ; by convection, 270 ; by 

radiation, 285. 
Transformer, the, 451. 
Translucent bodies, 292. 
Transparent bodies, 292. 
Trombone, 212. 
Tuning-fork, 191. 
Turbine engine, 269. 



Units, fundamental, 2 ; derived, 7 ; 
of time, 9 ; the English and the 
C.G.S. system, 10 ; of force, 37 ; 
of work, 64 ; of power, 59 ; of 
heat, 238 ; of electromotive force, 
401, 463 ; of resistance, 4G2 ; of 
current strength, 463 ; of quan- 
tity of electricity, 465. 

Uranium, radio-activity of, 490. 



Vaporization, 248. 

Vapour, pressure of, 249 ; satu- 
rated, 250. 

Velocities, composition of, 29 ; reso- 
lution of, 30 ; triangle and 
polygon of, 31. 

Velocity, definition of, 18; uniform, 
19 ; average, 21 ; of sound in air, 
169 ; of sound in solids, 173 ; of 
sound in gases, 175 ; determina- 
tions of, of light, 300, 301 ; illus- 
ti-ations of, of light, 301 ; of light 
in liquids and solids, 301. 



Ventilation, 284. 

Vertex of a mirror, 309. 

Vibrating flames, 200. 

Vibration number, 164. 

Vibrations, period of, 164 ; fre- 
quency of, 164 ; laws of, of a 
string, 188 ; of rods, 190 ; of 
plates, 192 ; of air columns, 193 ; 
mode of, in an open tube, 196 ; 
sympathetic, 202. 

Viscosity, 140. 

Volt, the international, 463. 

Voltaic cell, 396 ; plates of a, elec- 
trically charged, 398 ; chemical 
action in, 400 ; source of energy 
in, 401 ; electromotive force of, 
402 ; polarization of, 404 ; theory 
of the action of, 409 ; grouping 
of, 475. 

Voltameters, 417. 

Voltmeters, 432. 

w 

Watt, the, 59, 466. 

Watt-hour, the, 467, 

Wave-length, definition of, 160 ; 
relation among wave-length, velo- 
city, and frequency, 164. 

Wave-motion, characteristics of, 
157. 

Waves, cause of, on water, 158 ; 
speed of, on water, 160 ; speed 
dependent on depth, 161 ; refrac- 
tion of, 162 ; reflection of, 162 ; 
transverse and longitudinal, 164 ; 
in a cord, 163 ; method of study- 
ing standing, 167. 

Weather, elementary principles of 
forecasting, 110. 

Weather map, 107. 



504 



INDEX 



Wedge, the, 78. 

Weight, definition of, 12 ; measure- 
ment of, 51. 

Weights, 12 ; metric, 13. 

Wheatstone bridge, 469. 

Wheel and axle, the, 74 ; examples 
of, 75 ; difierential, 75. 

Wimshurst, influence machine, 393 ; 
explanation of action of, 394. 

Winds, 28a 



Wireless telegraphy, 485. 
Work, definition of, 54 ; units of, 
54 ; measurement of, 55. 



X-rays, 487. 



Yard, standard, 2, 



8 



.1