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UNIVERSITY OF CALIFORNIA
LIBRARY
OF THE
Accessions Afo...^.-2'..o... Book No.. .....
NATUKAL
PHILOSOPHY
BY
ISAAC SHARPLESS, Sc.D.,
PROFESSOR OF MATHEMATICS AND ASTRONOMY IN HAVERFORD COLLEGE,
AND
GEO. MORRIS PHILIPS, PH.D.,
PRINCIPAL OF STATE NORMAL SCHOOL, WEST CHESTER PA.
**-*?
JTf
o*
PHILADELPHIA:
J. B. LIPPINCOTT COMPANY.
JOSEPH A. HOFMANN,
Bookseller & Stationer,
208 MONTCOMERY ST..
San Francisco, Cal.
,
Copyright, 1883, by J. B. LIPPINCOTT & Co.
PREFACE.
THIS Treatise on Natural Philosophy differs from others
in the large number of practical experiments and exercises
which it contains. The authors believe that students of
science should be, as far as possible, investigators, and, to
encourage the spirit of research, they have given sugges-
tions tending to lead them on in this way. The experi-
ments can nearly .all be performed with very simple and
inexpensive materials, such as any school or home can
furnish. More elaborate instruments are described for the
benefit of classes which have access to them. The book
can also be used by classes which have not time to perform
the experiments. Yet it is strongly recommended that as
many as possible be tried.
Two sizes of type are used through the book. The
matter printed in large type will form a complete ele-
mentary course, and the whole book a more exhaustive
one. Those who take the former are advised to include
as many as convenient of the experiments, exercises, and
questions. The large number given will allow the teacher
to make selections suited to the ability of the class.
The use of technical terms, except where they seemed
necessary to the better comprehension of the subject, has
been avoided. It has been recognized that the majority
673234 3
PREFACE.
of students of natural philosophy have no use for these
terms. What they want is a practical knowledge of the
subject and the cultivation of scientific habits of mind.
The methods of the leading scientific men of the present
time have been incorporated, and their instruments de-
scribed and figured. In any treatise on the subject which
embraces an account of these methods, the doctrine of the
conservation of energy must have a prominent place. The
great advances in practical science within the last few
years, especially in sound, electricity, and meteorology,
have also been utilized so far as they seem to bear on the
principles.
The work has been greatly benefited by the criticisms
and suggestions of C. Canby Balderston, of Westtown
School, Pennsylvania. The chapters on Magnetism and
Electricity were written by him.
CONTENTS.
PREFACE 3
CHAPTER I. Matter 7
II. Motion and Force 19
Gravity and Stability 35
Falling Bodies 40
The Pendulum 44
Machines ........ 47
III. Liquids 63
Hydrostatics . . . . . . .63
Specific Gravity 78
Hydraulics 83
Water-Machines 87
IV. Gases 95
The Atmosphere 100
Pneumatic Machines ..... 103
V. Sound 120
Cause and Phenomena ..... 120
Musical Sound 129
Musical Instruments 133
Music 150
VI. Light 162
Keflection 169
Refraction 177
Dispersion 188
Polarization ....... 202
Optical Instruments 205
VII. Heat 213
Conduction 234
Convection 236
Steam-Engine 237
VIII. Magnetism 244
1* 5
CONTENTS.
PAGE
CHAPTER IX. Electricity 255
Fractional Electricity 255
Current Electricity 277
Electro-Magnetism . . . . .289
Magneto-Electricity 304
Kadiant Matter 313
X. Meteorology 319
The Atmosphere 322
APPENDIX I. The Metric System 343
II. Table of Specific Gravities . . . .345
INDEX 346
NATURAL PHILOSOPHY.
CHAPTEE I: , ,,
v , >B /, ' i j.. ,'-.-:'
MATTER.
1. What is Matter? All the bodies which occupy space,
the stars and the planets, rocks, water, and air, and
everything we can see or feel, are embraced under the
term matter.
We can crumble a rock or divide a quantity of water
into smaller portions. These can again be subdivided, and
all the fragments will resemble the original in their prop-
erties. There is a practical limit to this subdivision,
arising from the imperfection of our senses or our tools,
but we may suppose it carried on till the very smallest
possible fragments remain which possess the properties of
the substance.
2. Molecules. To these fragments we give the name
molecules. They are definite quantities of matter, which
have size and weight.
Hence a molecule is the smallest portion of any substance
in which its properties reside* All matter is made up of
molecules. We know that molecules must be extremely
small. Sixteen ounces of gold, which in the form of a cube
would not measure an inch and a quarter on a side, can be
spread out so that it would gild silver wire sufficient to
reach around the earth. Its thickness must then be at least
1 The properties of matter are those qualities which are peculiar to
it, which belong to it and to nothing else.
7
8 NATURAL PHILOSOPHY.
one molecule, and is doubtless many. In odors, which
produce sensation by invisible particles, the molecules
scatter about through the atmosphere for years without
apparently diminishing the size of the substance from
which they are separated. Microscopists have found ani-
mals so minute that four million of them would not be so
large as & slti.glcr grin of sand, yet each has its organs and
its circulating fluids. .,
3. Siz of a Mpkenle.- The methods of attaining an idea of the
actual dize of a molecule "are too abstruse for explanation here, but
the figures, derived from experiments of different kinds, point to
UTo'.TJ'oir.irUTF f an i nc h as the mean diameter. This is too minute
a quantity for comprehension, and may be better understood by the
illustration of Sir William Thomson : "If we conceive a sphere of
water of the size of a pea to be magnified to the size of the earth,
each molecule being magnified to the same extent, the magnified
structure would be coarser-grained than a heap of small lead shot,
but less coarse-grained than a heap of cricket-balls."
The molecules of hydrogen gas are about 7,-jnri.TnnF of an i nc h
apart, so that the spaces between are much greater than the molecules
themselves.
4. Atoms. When the division is carried any further
than molecules, a form of matter with new properties is
produced. It is not possible to divide a molecule by me-
chanical means, but heat or chemical agents can separate
it into two or more portions. Each of these is called an
atom. An atom cannot be further divided by any means
known to us.
Hence an atom is the smallest possible portion of matter.
Experiment i. Put a piece of marble or chalk (not a crayon)
into a vessel, and pour on it some good vinegar. Bubbles of gas will
arise through the water.
A molecule of marble is composed of a number of atoms of dif-
ferent substances. The acid in the vinegar causes a division of the
molecule, forming new substances. One of these substances (carbonic
acid) is a gas, which passes off into the air. The others remain in
the vessel.
5. Constitution of Molecules. The molecules of some
MATTER. 9
substances are made up of two or more similar atoms. A
molecule of hydrogen gas contains two atoms exactly alike.
On the other hand, a molecule of common salt contains one
atom of sodium and one of chlorine, which are widely
different from each other and from salt. In their ordinary
state, sodium is a soft inflammable solid, and chlorine a
greenish gas. A molecule of sugar is composed of forty-
five atoms of three different kinds, carbon, which we can
see as charcoal, and hydrogen and oxygen, which are color-
less invisible gases.
Experiment 2. In a vessel heat a small portion of sugar over a
fire. A black substance will remain.
In this case heat effected a separation of the atoms of
the molecules ; the gases passed off into the air, and the
solid carbon remained.
6. Elements. If the molecules of a substance are com-
posed of one kind of atoms only, it is said to be an element.
Sixty-five elements have been discovered on the earth.
Iron, copper, carbon, are elements. "Water and air are
not.
7. Matter Indestructible. If the escaping gases and the
carbon of the last experiment could be weighed, the sum of
the weights would be found to be just equal to the weight
of the original sugar. Hence we arrive at an important
property of matter, it is indestructible.
There are many cases of the apparent destruction of
matter in combustion and chemical action, but all that is
done is to change its form. The molecules are divided,
and the atoms form new combinations, some or all of which
are invisible. In all the various changes continually going
on, in our furnaces and laboratories, and in nature, not a
new atom is ever created. According to the best of our
knowledge, the amount of matter in the universe has re-
mained unchanged since the original creation.
8. Matter Porous. The molecules of matter do not fit
10 NATURAL PHILOSOPHY.
closely together. Hence open spaces, or pores, are left
between them. We then arrive at a property of matter
which is believed to be universal, it is porous.
Experiment 3. Fill a tumbler with cotton-wool, pressing it down
so firmly that the vessel will hold no more. Now remove the cotton
and fill the vessel with alcohol. With care, the cotton may all be
replaced without spilling the alcohol. The cotton has gone into the
?ores of the alcohol, and the alcohol into the pores of the cotton,
t is impossible to conceive that the molecules of both substances
occupy the same space.
9. Matter can be Expanded and Compressed. As a result
of the porosity of matter, it is possible to expand or to com-
press it. The molecules are not changed in form or size,
but they are further separated in expansion, and crowded
together in contraction, so that the substance becomes more
porous in one case and less so in the other. Heat in general
separates the molecules from one another. A ball that will
just go through a ring when cold will not do so when heated.
The mercury in a thermometer-tube rises in hot weather
because the heat separates the molecules and there is no
chance for expansion in any other direction. The ends
of the rails of a railroad-track which touch each other in
summer are separated in winter. A nail can be driven
into wood because it causes a compression of the molecules
around to make a place for it.
Experiment 4. On a cork
floating on water place a shav-
ing. Set it on fire, and put over
it an inverted tumbler. The heat
of the combustion will expand
the air in the tumbler and force
FIG. l EXPANSION BY HEAT. it out under the edge ; what is
left will quickly cool and con-
tract, so that almost immediately the water will rise into the tumbler.
10. Expansion by Cold. Heat does not always expand
bodies.
Experiment 5. Fill a bottle with water, and cork tightly. Leave
in a cold place till the water is frozen. The bottle will be cracked.
The cold here caused expansion. At 39.2 Fahrenheit a
MATTER.
given weight of pure water takes up least room and ex-
pands with a change of temperature either way.
11. Some Bodies can be Hammered into Plates and
Drawn into Wires, When certain solid bodies are ham-
mered out into plates or drawn into wires the molecules
slide past one another and arrange themselves differently.
This motion of the molecules is not possible in all solid
bodies, and some possess it in a much higher degree than
others. Gold may be hammered out into sheets less than
2"f)oYoo~o f an mc ^ i n thickness. Copper, silver, and tin
can also be beaten out into very thin foil. One of the
substances which may most readily be drawn out into
wires is glass.
Experiment 6. Heat in an alcohol flame, or hot gas flame, a small
glass rod or tube. When red and soft, it may be drawn out into a
very fine thread.
Metal wire is made by drawing the soft metal through
holes, each one smaller than the preceding. Platinum wire
can be reduced so that it will be finer than the finest hair.
12. Matter Elastic. All bodies are more or less elastic.
By this it is meant that when compressed within certain
limits the molecules tend to come back to their original
position with respect to one another.
When a ball is allowed to fall on a hard floor, there is a
compression of the molecules of the ball near the point of
contact with the floor. The elasticity of the ball causes
an immediate restoration to the original form of the ball,
and this produces the rebound. When gases are com-
pressed, they recover their former state immediately when
the pressure is withdrawn. They are said to be perfectly
elastic. Although liquids can be compressed but slightly,
they are also perfectly elastic.
13. Tenacity. When the molecules of a solid adhere
so closely that they strongly resist a force tending to
pull them apart, it is said to be tenacious. The amount
of tenacity depends on the structure of the substance.
12 NATURAL PHILOSOPHY.
"Wrought iron, being fibrous, has much more tenacity than
cast iron, which is granular. Steel is very tenacious. A
bundle of wires will support much more weight than the
same material in solid form. Hence the cables of suspen-
sion-bridges, which have to hold up immense weights, are
usually made up of bundles of fine steel wire.
Experiment 7. Place a piece of stick on two supports some dis-
tance apart, and break it by a weight applied in the middle. Ex-
amine the fracture. The lower fibres will be found to be separated.
14. Bridges. When a weight rests on a bridge, it has to stand
the same kind of strain as the stick. The tendency is to pull it apart
at the bottom. Hence an iron bridge has its lower " chord" made of
tenacious wrought iron rather than of cast iron. The upper chord is
compressed, and as cast iron will stand more compression than
wrought iron, it is frequently used there.
15. Hardness. Hardness is another property of solid
bodies, depending on the closeness with which the mole-
cules stick together and resist the entrance of another
body which tends to penetrate them. Hard bodies are not
always tenacious. Diamond is the hardest of substances,
being able to scratch everything else. This, ability to
scratch is the test of hardness.
Experiment 8. Scratch a piece of glass with the edge of a quartz
crystal or piece of flint. Attempt to do the same with a penknife-
blade. Quartz is harder than glass, and glass is harder than steel.
16. Density. There is more matter in the same space in
some bodies than in others. This is either because the
molecules are closer together, or because each molecule
contains more matter. We express this by saying that
some bodies are more dense than others.
17. Volume. The volume of a body is the amount of
space it occupies.
18. Mass. The mass of a body is the quantity of mat-
ter which it contains. If a gas be heated so as to expand
it, the mass remains the same, as no new molecules are
formed, but the density decreases. The mass therefore de-
pends on two things, the volume and the density. The
MATTER. 13
number of molecules in a unit (as a cubic inch) of a body
multiplied by the number of cubic inches gives the whole
number of molecules. In other words, the product of the
volume by the density gives the mass, or
Mass = volume X density.
19. Unit of Length. The English units of length are
the inch, the foot, and the yard ; the French are the metre
and its decimal divisions. It is convenient to remember
that a metre is about 40 inches, a decimetre about 4 inches,
a centimetre about -^ of an inch, and a millimetre -^ of an
inch. 1
20. Unit of Surface. For square measure we have in
English the square inch, square foot, and square yard, and
in French the square metre, square decimetre, and square
centimetre. The cubic units are derived in the same way.
21. Unit of Mass. The unit of mass in the English
system is the pound avoirdupois ; in the French it is the
mass of a cubic centimetre of water at its greatest density,
39.2 F. This is called a gram, and is about 15 i grains.
This is divided and multiplied decimally for smaller and
larger weights.
22. Unit of Density. The unit of density for solids and
liquids is the density of water at 39.2 F.
23. Affinity, Cohesion, Attraction. The force which
holds together the atoms in a molecule is called affinity.
The force which holds together the molecules in a body
is called cohesion.
The force which holds together the different bodies of
the universe is called attraction.
Hence affinity makes substances ; cohesion makes bodies;
attraction makes systems.
Attraction is also used to express the force which draws
one body to another, as in the case of magnets, etc.
1 The metric system possesses great advantages, especially for scien-
tific people. Appendix I. gives it in part, and should be studied.
2
14 NATURAL PHILOSOPHY.
24. Solids. In solid bodies the molecules preserve their
positions with considerable firmness, resisting attempts to
displace them. Hence these retain their form and size.
The force of cohesion in them is strong.
25. Liquids. In liquid bodies there is perfect freedom
of the molecules among themselves, so that the bodies
adapt their form to the surrounding vessel. They retain
their size, but change their form with the slightest force
exerted upon them. The force of cohesion in them is
weak.
26. Gases. In gaseous bodies there is no cohesion, the
molecules have a repellent action upon one another, so that
an unrestrained gas will expand indefinitely.
27. Motion of Molecules. The molecules of all bodies are be-
lieved to be in rapid motion. In solids this is restrained by cohesion,
so that a molecule has only a short vibratory motion. In liquids the
molecules slide over one another without resistance, restrained only
when they reach the sides of the enclosing vessel. This contact pro-
duces the pressure against the sides. In gases the molecules are
strongly repelled from one another, and dash about with great ve-
locity. Hence there are constant collisions among them and with
other bodies. Our bodies are subject to this incessant battering by
the little molecules of the atmosphere, but, the force being the same
on both sides of the tissues, we do not notice it.
28. Adhesion. Adhesion differs from cohesion in that
it acts between molecules of different bodies. The force
which causes mortar to stick to bricks, which causes a
pencil to leave a mark on paper, which enables glues and
pastes to be effective, is adhesion. It is also something
like adhesion which causes water to rise in a small tube
or on the side of a glass plate.
29. Weight. The weight of bodies results from attrac-
tion. All bodies attract all other bodies. The more mole-
cules a body contains, the greater is its attraction for others,
and the attraction of others for it. The pull of all the par-
ticles of the earth on the objects on its surface is the same
as if one strong pull drew them to its centre. Hence a
MATTER. 15
plumb-line points to the centre of the earth, 1 and different
plumb-lines are not parallel, but converge downward.
30. Gravity, The attraction of the earth is called
gravity.
31. Weight Proportional to Mass. The earth pulls every
particle of a body. If we suppose a string attached to
each molecule, and all the strings pulled by equal forces,
we would have the case of attraction. Hence the more
molecules the greater the attraction. But the mass is
determined by the number of molecules. Hence we have
the law,
Under the same conditions the weights of bodies (or the
total attractions) are proportioned to their masses.
32. Weight Inversely Proportional to Square of Distance.
The position of the body affects the weight. The attrac-
tion diminishes as the bodies recede from each other. If
the distance doubles, the attraction is only one-fourth, and
if the distance trebles, one-ninth, of the original amount.
We express this by saying, The attraction varies inversely as
the square of the distance.
33. Mass Constant. The position of the body does not
affect the mass. It might be removed far from the earth
and the mass would be the same. The number of mole-
cules i.e., the mass would be constant if carried to the
sun ; but as there is so much more mass in the sun than
in the earth, the attraction, and consequently the weight
of the body, would be greatly increased.
34. Unit of Weight. The unit of weight is the same as
the unit of mass, the gram.
35. Mobility and Inertia. Bodies will not move unless
some force is exerted on them from without, and they yield
to the slightest force impressed which is not counter-
balanced by some other force. This brings us to two other
1 This is very slightly modified by the fact that the earth is not a
perfect sphere.
16 NATURAL PHILOSOPHY.
properties of matter, mobility, which induces it to yield
freely to impressed forces, and inertia, which prevents it
from moving itself, or from changing any motion which
may be given it. Matter has no power to move or to resist
an unbalanced force.
Examples of inertia are numerous. It requires more
force to start a car than to keep it in motion. When sud-
denly stopped by another force, the contents are thrown
forward by their inertia. A ball projected upward stops,
not because it has power to stop itself, but because another
force, gravity, is constantly pulling against its motion. A
marble thrown swiftly through a pane of glass will make
a small round hole, because the inertia of the other parts
of the glass prevents them from yielding to the sudden
impression.
Experiment 9. Place a card on the end of a finger, and a cent on
the card. By a quick stroke with the forefinger of the other hand
the card may be shot out, leaving the cent resting on the finger.
36. Ether. We have spoken of the three forms of
matter, solid, liquid, and gaseous ; we have also said that
the molecules of matter do not fill up the whole space, but
that pores, which are large compared with the size of the
molecules themselves, exist in all substances. This inter-
molecular space is supposed to be filled with something
called ether, which is as far separated from gases by its
properties as gases are from liquids. It also fills the pores
of the air, and the spaces between the planets and between
the stars, outside the bounds of the atmospheres which
surround them. It is highly elastic, without weight or
color, or any other properties which can be perceived by
the senses. It is supposed to be the agent which by its
vibratory motion conveys the rays of light from the sun
to the earth, and which carries them between the molecules
through transparent substances.
37. Radiant Matter. Dr. William Crookes 1 has found
1 An English scientist, now living (1883).
MATTER. 17
that by exhausting the air in a tube so as to leave not more
than one-millionth the ordinary amount, the remaining sub-
stance has such peculiar properties that he feels justified
in giving it a new name. He calls it radiant matter, and
considers it to be the fourth form. Solid, liquid, gaseous,
and radiant would then be the four aggregate states, each
having properties which widely separate it from the others.
By passing electric sparks through radiant matter some of
its properties have been determined. 1 Of the properties
of ether we know nothing by direct experiment, but it is
considered likely that it is a form of radiant matter.
38. Summary. Matter is made up of a countless number
of minute molecules. It is perfectly inert, but each par-
ticle possesses the property of attracting every other
particle. It has extension in three directions, and has
three (probably four) forms of aggregation.
39. Natural Philosophy. Natural Philosophy treats of
the laws of cohesion, the molecular properties of matter,
and the effects of the action of forces upon matter.
40. Astronomy. Astronomy treats of matter in large
masses, and of the laws of gravitation.
41. Chemistry. Chemistry treats of the atomic proper-
ties of matter, and of the laws of affinity.
Exercises. 1. Is matter destroyed when water is dried up? when
gunpowder explodes ? when house gas burns ? Where does it go to?
2. To what property of matter do blotting-pads owe their utility ?
rubber bands ? watch-springs ? pop-guns ? putty ? hammers ? piano-
strings ? water-filters ?
3. Why does not the addition of a little sugar to a full cup of
coffee cause it to overflow ?
4. When we fix the head of a hammer on the handle by striking
the end of the handle on a block, what property do we use?
5. Why does a foot-ball, nearly empty, become full when we ex-
haust the air from around it ? why does it soon collapse ?
6. One sixteen-thousandth of a cubic inch of indigo dissolved in
sulphuric acid can color two gallons of water. What property of
matter is here shown ?
7. How would you test the relative hardness of two minerals ?
1 These will be further explained, page 314.
b 2*
18 NATURAL PHILOSOPHY.
8. When water is converted into steam, are the molecules enlarged
or separated? is its mass increased or diminished? its density? its
weight ? its volume ?
9. Name a substance which is often found in all three forms.
10. If you knew the volume and mass of a solid, how would you
obtain its density ? if you knew its mass and density, how would you
obtain its volume?
11. Give an instance of a hard body which has little cohesion.
12. Why does not a large stone fall to the earth more rapidly than
a small one ?
13. If a body were removed to a distance of 8000 miles from the
surface of the earth, how much less would it weigh than at the sur-
face? Ans. ^ as much.
14. What would a 100-pound weight weigh if moved to the dis-
tance of the moon (60 radii of the earth) ? Ans. ^ pound.
15. Suppose a sphere were one-half the diameter of the earth and
of the same density, what would a body which weighed 100 pounds
on the earth weigh at its surface? Ans. 50 pounds.
Note. Its mass would be one-eighth that of the earth, and dis-
tance of the body from its centre one-half.
MOTION AND FORCE.
19
CHAPTER II.
MOTION AND FORCE.
42. Rest and Motion. A body is at rest when it does not
change its place. It is in motion when it does change its
place.
No body with which we are acquainted is at rest. The
earth and all that is on it move with great velocity. The
sun moves, and so do the stars. But when a book lies on the
table it does not move with respect to the surrounding bodies
or the earth. It is at relative rest, but in absolute motion.
43. Kinds of Motion. When a body in motion passes
over equal spaces in equal times, its motion is uniform.
When it passes over unequal spaces in equal times, its
motion is varied. When the spaces in successive times
become greater, its motion is accelerated, and when less, re-
tarded. This acceleration or retardation may also be uni-
form or varied.
44. Velocity. The velocity of a motion is the space
traversed in the unit of time. It may be in miles per
hour, feet per second, etc.
Feet moved in Successive Seconds.
Kinds of Motion.
30
30
30
30
Uniform.
10
15
20
25
Uniformly accelerated.
20
18
16
14
Uniformly retarded.
20
14
16
4
Varied, not uniformly.
Questions. When a train starts from a station, what kind of
motion is it ? when stopping ? when a ball is thrown upward ? when
it falls ? What kind of motion in the hands of a watch ? in the cur-
rent of a river ? in the winds ?
45. Force. Force is anything which tends to produce, change,
20 NATURAL PHILOSOPHY.
or destroy motion. If it acts on a body at rest, it produces
motion. If it acts on a body in motion, it may change the
direction or velocity of the motion, or destroy it. Two or
more forces may act on a body at rest so as to balance each
other and cause no motion. But each one tends to produce
motion. In bridges and buildings we have cases of bal-
anced forces. Gravity is a force always acting upon them,
and upon everything they sustain. This produces other
forces acting along the various timbers and pieces. If the
structure is well built, the strains from these forces are
exactly balanced, every part is sufficiently strong to do its
work, and there is no motion except such as is due to the
elasticity of the materials.
46. Kinds of Force. A force may act for an instant and
then cease, in which case it is said to be an impulsive force ;
or it may act for some time, when it is a continuous force.
The striking of a ball by a bat is an example of an impul-
srve force, and the pulling of a train by a locomotive, of a
continuous force.
47. Impulsive Force produces Uniform Motion. An im-
pulsive force tends to produce uniform motion, and a continuous
force accelerated motion. This would seem to be contradicted
by experience. For the motion of a ball is soon destroyed,
and the, continual pull of the engine may only keep the
train moving uniformly. But the force of the bat or
of the locomotive does not act alone. Were it not for
gravity, the resistance of the air, and friction, which are
modifying forces, the ball would move on forever with
uniform velocity, and the velocity of the train would be
accelerated so long as the engine pulled it ever so slightly.
48. Newton's Laws of Motion. All the circumstances
of motion are embraced in three laws, first enunciated by
Sir Isaac Newton. These cannot be proved mathemati-
cally. They should be looked upon as fundamental prin-
ciples, which depend on the properties of matter, and which
may be shown to be true by experiment.
MOTION AND FORCE. 21
1. A body at rest remains at rest, and a body in motion con-
tinues to move forward in a straight line, until acted on by
force external to it.
2. Motion or change of motion is proportional to the force
impressed, and is in the straight line in which the force acts.
3. When bodies act on each other, action and reaction are
equal and in opposite directions.
The first law is the result of the inertia of matter, and
the second, of its mobility. The first says matter can do
nothing itself, and the second, that the slightest force will
have its corresponding effect.
The third law may be made clear by some illustrations.
The earth attracts an apple and causes it to fall. The
apple attracts the earth just as strongly, and the earth
moves to meet it, but the greater mass of the earth makes
it move so little that the motion is not noticed. When you
hold up a body in your hand, the hand presses up just as
hard as the body presses down. The reaction of the wfcjer
on the oar, and on the fins of a fish, causes the boat or the
fish to advance ; the reaction of the air on the wings causes
the bird to sustain itself and to move forward.
49. Momentum. Momentum is the quantity of motion. The
momentum of the earth was the same as the momentum
of the apple. For while its velocity was less, its mass was
as many times greater. Hence mass and velocity together
make up momentum. A body weighing two pounds has
twice the motion of one of one pound which has the same
velocity ; a body with twice the velocity of another has
twice the motion, the mass being the same. In general we
have the equation,
Momentum = mass X velocity.
50. Measure of Forces. We may measure forces in two
ways. One way is by the pressure necessary to resist
them, weighing the forces, as it were. The unit would
then be in the English system the pound, and in the French
system the gram. These would vary as gravity varied,
22
NATURAL PHILOSOPHY.
being greater nearer the level of the sea. A better way
to measure forces is by the velocity they would produce.
We have here also two systems.
In the English, the unit of force is the force which, acting
for one second, will cause a pound of matter to have a
velocity of a foot a second.
In the French, it is the force which, acting for one second,
will cause a gram of matter to have a velocity of a centi-
metre a second. This unit is called the dyne (pronounced
dine), and is coming into general use among scientific men.
51. Acceleration. The velocity which a force would
produce in a unit of mass in a second is
called its acceleration.
52. Illustrations. We will now illus-
trate some of these terms. If a body
weighing 20 grams has a velocity of 10
centimetres a second, its momentum is
200. (This is not foot-pounds or grams
or centimetres; the unit of momentum
has no name.)
If this momentum is produced by a
force acting for 1 second, it is a force
of 200 dynes; if for 5 seconds, it is a
force of 40 dynes.
53. Acceleration a Measure of Force.
If a force acting on the body for 1
second will give it a velocity of 10 cen-
timetres, the acceleration is 10. During
every succeeding second which it acts, it
adds 10 centimetres to its velocity. As
its inertia keeps the body moving at its
former velocity, this continual force constantly increases
its velocity. The greater the force, the greater will be
the velocity produced the first second. The acceleration is
a measure of the force.
54. Dynamometer. A practical way of measuring some
FIG. 2. DYNAMOMETER.
MOTION AND FORCE. 23
forces is by a spring-balance placed in the line through
which the force must act. A dynamometer (Fig. 2) is an
instrument of the same kind, registering the amount of
force expended. It is used to determine the resistance to
motion of a train, wagon, plough, or other instrument.
If a body be hung on a spring-balance, we weigh the
force of 'gravity. If a spring-balance or dynamometer is
placed between a horse and a plough, we weigh in the
same manner the force of the pull of the horse. If the
horse pulls with a force of 200 pounds, this means that the
connection with the plough is strained just as a rope would
be if sustaining a weight of 200 pounds.
Questions. 1. What kind of force is gravity? what kind of
force drives the bullet from the gun ? what kinds of motion would
they produce if unmodified ?
2. Which of Newton's laws are illustrated by the breaking of an
egg against a table ? by the tendency of a train to be thrown out-
ward over a curve ? in the throwing of a ball ? in the fact that it is
more difficult to start a train than to keep it in motion ?
3. A body weighing 20 pounds has a momentum of 400: what is
its velocity in feet per second ?
4. Two bodies, one of 20 and one of 2 pounds, are drawn together
by their mutual attractions : which will move the faster, and how
much ?
5. A body of 20 grams and a velocity of 10 centimetres per second
meets another body of 40 grams moving in the opposite direction
with a velocity of 4 centimetres per second : in what direction will
the bodies move after impact ? Ans. In the direction of the first.
6. How many dynes of force are required to produce a velocity of
500 centimetres per second in a body of 200 grams weight in 5
seconds? Ans. 20,000.
7. What would be the mass if 20 dynes of force would produce in
5 seconds a velocity of 5 centimetres per second ? Ans. 20.
8. In how many seconds would a force of 40 dynes produce a
momentum of 400 units ? Ans. 10.
55. Representation of Forces. A force may be repre-
sented by a straight b
line. Thus, the line ab
indicates that the force acts on a body at a in the direction
ab. The length of the line may also represent the mag-
nitude of the force. A line twice as long would represent
twice as great a force.
24 NATURAL PHILOSOPHY.
56. Resultant. The resultant of two or more forces is
the name given to a single force which would produce the
same effects.
If two forces, one of 2 pounds and one of 4, act on a
FIG. 3. FORCES IN A LINE.
body at a in the same direction, their resultant is evidently
a force of 6 pounds acting in the same direction. If they
act in opposite directions, their resultant is the difference
of their forces (2 pounds), and acts in the direction of the
greater. !By considering one direction as positive and the
other as negative, we express both of these cases by a
single law.
57. Resultant of Parallel Forces. The resultant of two
or more parallel forces is their algebraic sum.
If in one direction we have forces of 6, 2, 4, and in the
other 3, 7, 1, the resultant is 6 -f 2 -f 4 3 7 1 = 4-1.
The resultant is 1, and acts in the direction of the plus
forces.
58. Parallelogram of Forces. If the forces do not act
in the same line, they may still
-have a single resultant.
Let the forces p and q act on
a at the same time in the direc-
tions given in the figure. Ac-
cording to Newton's second law,
f the
FIG. ^.-PARALLELOGRAM OF FORCES.
full effect on the body. The
force p would carry it somewhere in the line ab, but the
force q is such as to take it over the space ac. Hence it
would bring it into the line cd, parallel to ab. By the same
reasoning the body would be shown to be brought into the
line bd, parallel to ac. If it is brought into both of these
MOTION AND FORCE. 25
lines it must be brought to their place of meeting at d.
The figure abdc is a parallelogram, and is called in this
case the parallelogram of forces. The body would move in
a straight line, ad, which is the diagonal of the parallelo-
gram, and its motion would be the same as if acted on by
the single force r. Hence r is the resultant of p and q.
59. Triangle of Forces. If we consider the forces with-
out reference to their point of application, ab, bd, and ad
will represent them, and will form a triangle. A force act-
ing at a, equal and opposite to ad, will balance ad. Hence
the three forces ab, bd, and da (notice the order of the
letters) will form a system which is balanced. We have
a general truth that if three forces are represented in mag-
nitude and direction by the sides of a triangle taken in
order, the system is balanced.
60. Resultant of any Number of Forces. If more than
two forces act on one point, we must find the resultant of
two of them ; then of this resultant and a third force ; and
so on.
If ab, ac, ad, and ae are forces acting at a, then the re-
sultant of ab and ac is ar ; of ar and
ad, ar' ; and of ar' and ae, ar". It
will be observed that abrr'r" is
polygon, four of the sides of which
are parallel to the forces, and the
fifth represents the resultant. --- dT
61. Polygon of Forces. This prin-
. -i i , , , , 7 FIG. 5. POLYGON OF FORCES.
ciple is called the polygon of forces,
and may be stated as follows : If a figure be constructed
having the sides equal and parallel to the forces, the line
necessary to close this polygon, drawn from the starting-
point, will represent the magnitude and direction of the
resultant.
Also, if the forces acting on a body be represented in
magnitude and direction by the sides of a polygon taken
in order, the system is balanced.
B 3
It i
a
h -
26
NATURAL PHILOSOPHY.
62. Forces not in a Plane. If the forces are not all in
one plane, the method would produce the outlines of a
solid body.
If ab, ac, ad be three forces not in one plane, ar is the
resultant of the first two, and ar' the final resultant. 1
b
FIQ. 6. PARALLELOPIPED OF FORCES.
Fio. 7. RESOLUTION OP FORCES.
63. Composition and Resolution. The force ar may be
divided into two forces, ab and ac, or into ae and of, or, in
general, into any two which with it would make a triangle.
Combining forces so as to get a resultant is called the
composition of forces, and separating single forces into sev-
eral parts is called the resolution of forces. The parts are
called components.
Experiment 10. Fasten two pulleys against a vertical board so
that they will turn freely. Arrange
cords as in the figure, making the
knot at a so as not to slip. Hang
weights p, <7, and r, being careful not
to get r greater than p and q com-
bined. Measure off ab and ac pro-
portional to the weights p and q, and
draw lines on the board to complete
the parallelogram abdc. Measure ad,
and it will be found to be equal to r
on the same scale that ab and ac were
made ; also the point d will be found to be directly over a.
This shows that the diagonal ad represents the resultant
in magnitude and direction.
FIG. 8. RESOLUTION OF FORCES.
1 If the forces do not all act on the same point in the body the
problem becomes too complex for this treatise.
MOTION AND FORCE.
27
between a
FIG. 9. CROSSING A CURRENT.
Experiment n. Place spring balances in the strings
and the pulleys, and measure the forces in this way.
64. Rowing across a Current. If a man undertakes to
row straight across a river 6 f
in which there is a current,
his course will be oblique.
For let ab represent the
force of his rowing, and ac
the force of the current.
Then the resultant ad will be the direction of his course,
and he will land at / instead of at e. If he wants to go
straight across, he will steer in the direction a'b', so that
a'b' combined with a'c' will have a resultant in the direc-
tion a'e'.
65. Sailing a Boat. In sailing a boat we have a good
illustration of the resolution of forces. Let
ab be the keel, cd the direction of the sail,
and fe the force of the wind, fe may be
resolved into two forces, fg, parallel to the
sail, which would have no effect in driving
the vessel forward, and ge, perpendicular
to it. The force ge may again be resolved
into gh, perpendicular to the keel, and he,
in its direction. This latter force is all that is effective in
propelling the boat. The force gh tends to upset it. In a
complete analysis of forces the action of the rudder must
also be taken into account.
66. Component Forces greater than the Original. It is
possible to resolve a force into two components each of
which shall be much greater than the original force. If in
Fig. 8 the weight r should be very small, the line between
the pulleys would be nearly straight, and by constructing
the parallelogram it would be seen that the components
along ab and ac would be much greater than r. The same
principle is shown in the knee-joint (Fig. 11). This consists
of a pair of levers, jointed together at b. One of them is
Fia. 10. SAILING A
BOAT.
28 NATURAL PHILOSOPHY.
firmly fixed at the end a, the other is attached to a movable
6 slide. Any force, p, acting verti-
cally on the joint will be resolved
into two, one along each lever.
The more obtuse the angle at
FIG. H.-KNEE-JOINT. the joint, the greater will be the
component forces as compared
with the applied force.
Experiment 12. Stretch a string tightly between two fastenings.
Tie a weaker string to its middle point. By pulling this the stronger
string breaks first For the component pull is stronger than the
original.
67. Centrifugal Force. When a body is swung around
by a string there are two forces acting
on it. One is its inertia, which would
tend to cause it to move in a line, ab,
touching the curve. The other is #c, the
pull of the string. The tendency would
be to move in the diagonal ad. But as this
pull is acting continuously, and the direc-
tion continually changing, the line is a
Fw ' 12< "CVE ION IN A curve - These are the forces which keep
the earth and all the planets in their orbits.
The outward pull on a string, which is the result of the
inertia of the body tending to cause it to get farther from
the centre, is centrifugal force. It is always opposite and
equal to the force drawing towards the centre.
68. Centrifugal Force Apparatus. Its effect is shown in
the centrifugal force apparatus of Fig. 13. Here the flexible
bands are put in rapid rotation, and the centrifugal force
makes them assume the form indicated by the dotted line.
69. Effects of Centrifugal Force. There are many other
illustrations of centrifugal force. When the earth was a
soft body, the centrifugal force caused by its rotation on its
axis probably produced the bulging at the equator which we
now notice. The centrifugal force is greater at the equator
MOTION AND FORCE.
29
than elsewhere, because of the greater velocity of the earth
there. Hence bodies are lighter there than at the poles.
An equestrian leans inward in riding around a curve, to
FIG. 13. CENTRIFUGAL FORCE APPARATUS.
balance the centrifugal force. It is this force which causes
mud to fly off moving carriage-wheels, or water from a
grindstone, and which sometimes breaks a rapidly-revolv-
ing fly-wheel. In sugar-refineries
the syrup is separated from the
crystals by being thrown outward,
the sugar being retained by a wire
gauze. Clothes are dried by a simi-
lar arrangement. In a bicycle in
motion the centrifugal force causes
the particles to continue to move in the same plane. Hence
the faster it is going the more difficult it is to overturn.
70. Moment of a Force. The moment of a force is its
ability to produce rotation. If be be a lever attached to a
body which has power to rotate about an axis at a, and a
3*
FIG. 14. MOMENT OF A FORCE.
30 NATURAL PHILOSOPHY.
force be applied at b, in the direction of the arrow-head, it
will tend to produce rotation. This ability will depend on
the magnitude of the force and the length of its lever-
arm, and is equal to their product. Thus, the moment of
p=pX ab.
1. A force of 10 pounds has a lever-arm of 2 feet: what is its
moment?
Ans. 20 foot-pounds.
2. A force of 16 grams has a lever-arm of 200 metres : what is its
moment in kilogram-metres ?
If a man attempt to overturn a heavy pillar, he will push
against it some distance above the base ; for in this case
his lever-arm will be greater, and consequently the mo-
ment of the force which he exerts. It is familiar to every
one how much is gained by a long lever in producing an
effect ; that this effect is increased not only by increasing
the force, but also by increasing the length of the arm
through which it acts. Seeing that this was the case,
Archimedes is reported to have said that with a lever
long enough he could move the world.
Exercises. 1. A current flows east at the rate of 4 miles an
hour, and a vessel heads north at the rate of 10 miles an hour : draw
a diagram showing the true direction and velocity of the vessel.
2. Four men pull at a rope with forces of 40, 50, 25, and 60 pounds
in the same direction : what is the resultant pull ? If the two latter
pull in an opposite direction from the others, what is the intensity
and direction of the resultant ?
3. Two men carry a basket ; one pulls upward with a force of 20
pounds, and the other with a force of 40 pounds: what is their re-
sultant and the weight of the basket?
4. A body is given simultaneously three blows, one eastward at
the rate of 40 feet per second, one northward, 28 feet per second, one
westward, 32 feet per second : which way does it move, and with
what velocity ?
71. Work. Work consists in moving against resistance.
A horse or an engine does work when it pulls a load, a
bird when it propels itself through the air, a man when
he lifts up a weight.
Let us take the latter case. When a load is lifted, a cer-
MOTION AND FORCE. 31
tain amount of work is done ; when it is lifted twice as high,
twice as much work is done, or when the weight is twice
as great, twice as much work is done when twice as great
a weight is lifted through three times the height, six times
the work is done ; or,
"Work done = weight X height.
In general, the work done by any force is the product
of the force and the distance through which the point of
application is moved.
72. Unit of Work. A unit of work is the work done in
raising a unit of weight through a unit of height. In the
English system the units are the foot and the pound, and
the unit of work is called the foot-pound; in the French
system the kilogram and metre are used, and the unit of
work is the kilogram-metre.
73. Horse-Power. For large engines a larger unit is
used, the horse-power. This is equivalent to 33,000 foot-
pounds per minute. 1 An engine capable of lifting 33,000
pounds 1 foot in 1 minute, or 66,000 pounds 1 foot in 2
minutes, or 11,000 pounds 6 feet in 2 minutes, is an engine
of 1 horse-power. Multiply weight in pounds by height
in feet, divide by the number of minutes and by 33,000,
and we have the horse-power.
74. Erg. As these units depend on gravity, which is
variable, another, based on the French system, has been
employed, called the* erg; the erg is the work done by a
force of one dyne acting through one centimetre.
Exercises. 1. How many foot-pounds of work are done in lifting
20 pounds through 10 feet ? how many kilogram-metres ?
2. An engine can lift 2 tons 20 feet in 40 seconds: what is its horse-
power ?
3. An engine can lift 20 kilograms 20 metres in 20 seconds : what
is its horse-power ?
4. How many ergs of work are done by a force of one dyne acting
through a metre?
5. A force gives to a decagram of matter a velocity of 2 centimetres
1 The element of time enters into horse-power, but not into foot-
pounds.
32 NATURAL PHILOSOPHY.
a second. If this force acts through a metre, how many ergs of work
are done ?
75. Energy. Energy is ability to do work. A moving
body has this ability, hence it has energy. A body lifted
up has this ability, hence it has energy. The units of
energy are the same as the units of work.
76. Potential Energy. A weight held up by the hand
has the power by virtue of its position to fall, and hence do
work, if its support be withdrawn. A body of water held
up by a dam has the power to do work on a water-wheel,
if allowed to fall upon it. A wound-up spring has power
to perform work in turning the machinery of a clock.
This kind of energy is called energy of position, or potential
energy.
77. Actual Energy. A weight descending, water falling
on a wheel, a spring uncoiling, a bullet moving through
the air, a muscle in use, have energy, energy of motion, or
actual energy.
78. Formula for Potential Energy. The formula for potential
energy is w X ^, where w represents the weight of a body, and h the
height to which it is raised. For it is evident that increasing either
of these quantities will proportionately increase the ability of the
body to do work.
79. Formula for Actual Energy. The formula for actual en-
ergy is ?m> 2 u where ra represents the mass, and v the velocity of the
moving body. For its momentum is mv (Art. 49). Now, suppose
it to be moving against a resistance which takes one unit from its
momentum each second, it will then require mv seconds to bring it to
rest, and its mean velocity will be %v, for it diminishes uniformly
from v to nothing. The distance through which the body would
move is mv X \v = %mv z . It therefore does \mv l units of work upon
the resistance (for the resistance is supposed to be a unit of force), and
its actual energy is %mv z .
80. Energy of a Projectile. When a ball is thrown up-
ward, its energy of motion becomes gradually less and
less, and its energy of position greater and greater. At its
highest point the one is nothing, the other is the greatest
possible. During the fall the conditions are reversed. We
MOTION AND FORCE.
say that the energy of motion is converted into energy of
position in the ascent, and converted back in the descent.
81. Potential and Actual Energy equal. We have proved
the two formulae,
Potential Energy = wh.
Actual Energy $mv*.
In the section on falling bodies we will prove other formulae, which
will show that the energy of motion which a body has at the begin-
ning of its ascent is just equal to the energy of position at its highest
point ; that is, that under these conditions wh -= $mv*.
82. Conservation of Energy. This brings us to the very
important doctrine of the conservation of energy. This says
that energy is always conserved or preserved ; that it is
never destroyed, but may be converted into energy of an-
other form ; that the sum of the energies of the universe,
like the sum of the matter of the universe, is constant ; that
energy is indestructible, as matter is. We cannot follow
energy through all its transformations, any more than we
can follow matter, but we have the best of grounds for
believing in the truth of the theory.
We will show in future chapters that heat, light, and
electricity are motions of the particles of bodies or of the
ether; hence we have other forms of energy in them.
These are all convertible, without loss, into one another and
into the two forms mentioned above. When a nail is struck
by a hammer, it becomes hot, for the force of the blow is
changed into heat, and sometimes, when sparks are struck,
into light. When water falls on a wheel from a pond, its
energy of position, first converted into energy of motion,
moves the wheel ; but part of this energy produces heat
by striking the wheel, part produces heat in the bearings,
and part runs the machinery. If an electrical machine be
connected with it, some of the energy will be converted
into electricity with its attendant light.
In a steam-engine the energy of position of the mole-
cules of coal is converted into heat, and the heat finally
into motion of the piston.
c
34 NATURAL PHILOSOPHY.
83. Correlation and Conservation. The principle that
one force can be converted into another is the correlation
of forces, while the principle that in this correlation no
energy is lost is the conservation of energy. These are long
names, but they express truths which are of great im-
portance in modern science, and should be thoroughly
understood.
Exercises. 1. How many foot-pounds of energy of position has
a weight of 20 pounds 8 feet above the floor, with respect to the
floor ? a table 3 feet high stands on the floor : how much has the
weight with respect to this table ? Ans. 160, 100.
2. A bullet of 1 ounce is shot from a 20-pound gun with a velocity
of 1600 feet per second : has the motion of the bullet or the recoil of
the gun greater energy ? and how much ?
Note. Because the momentum of the bullet equals the momentum
of the gun,
1600 X xV = 20 X velocity of recoil.
Velocity of recoil = 5 feet per second.
W
Energy of motion = \ mv 2 = J v 2 .
For the bullet = $ X oifex (1600) 2 = 2484. -f .
20
For the gun = J X X 5 2 = 7.7 +.
Note. From this we see the diiference between momentum and
energy. It is the energy, not the momentum, which gives the power
to the ball to penetrate bodies and to do harm. As we increase the
velocity, we increase the momentum in the same proportion, but we
increase the energy in the square ratio. As velocity is doubled, mo-
mentum is doubled, but energy is quadrupled. As velocity is trebled,
momentum is trebled, but energy is increased ninefold.
Perhaps we can understand this better if we consider that as it goes
twice as fast it will meet twice as many particles in the same time,
and it will crowd them away twice as fast ; that is, it has four times
the effect ; if it has three times the velocity, it will have nine times
the effect ; and so on.
3. State what transformations of energy take place in sliding a
body down a plane, in the electric light, in ringing a bell, in lighting
a match, in a clock running down, in a pendulum swinging.
4. Which would be preferable, to carry a 40-pound trunk up 20
feet or a 60-pound trunk up 15 feet ?
5. How many pounds of water per minute will a 20 horse-power
engine raise through 200 feet ? Ans. 3300.
MOTION AND FORCE, 35
GKAYITY AND STABILITY.
84. Effects of Attraction, The earth attracts every par-
ticle of matter towards itself. This gives us the phenom-
ena of falling bodies, causes matter to have weight, makes
the surface of still water level, and constantly operates in
many ways we do not notice.
f 85. How Attraction Acts. It does not require any time
'I for this force to act. Attraction traverses the great space
Ibetween the sun and the earth, to the best of our knowledge,
instantaneously. Nor does the interposition of another
body affect it in any way. We can cut off sound or heat
or light by the interposition of a wall, but attraction acts
through it without diminution. Nor does the kind of mat-
ter make any difference. Every molecule is attracted alike,
the number of molecules determining the total attraction.
86. Law of Attraction. The law of gravity, which was
discovered by Newton, is that every portion of matter in the
universe attracts every other portion with a force directly pro-
portional to the masses, and inversely proportional to the square
of the distance between them.
Questions. How much is the attraction between two masses
changed by doubling the distance between them ? by increasing it 5
times? by doubling one mass? by doubling one mass, trebling the
other, and trebling the distance between them ?
87. Decrease of Gravity Downward. The gravity is
greatest at the surface of the earth. When we go down
into the earth the gravity decreases, because some of the
matter of the earth is attracting us upward. Were we to
get half-way to the centre we should only have half the
weight that we have at the surface. At the centre we should
have no weight, being equally attracted in all directions.
Were it possible for a body to fall freely towards the
centre, it would increase its velocity continually and fly to
the surface on the other side, thence back again. Were
there no resistance, this would go on forever. Otherwise,
36 NATURAL PHILOSOPHY.
the vibrations would become smaller and smaller, and the
body would finally settle at the centre.
88. Centre of Gravity. The centre of gravity of a body
is the point about which it will balance in every position.
If a body has a uniform figure and the same structure
throughout, the centre of gravity is in t.he centre of the
figure, and is readily found. The centre of gravity of a
homogeneous sphere is at its centre ; of a cylinder, at the
centre of its axis ; of a uniform ring, not in the mass of the
ring, but in the space in the centre ; of a rectangular block,
where its- diagonals intersect.
89. How to find the Centre of Gravity. If a body is hung
up by a string, the
centre of gravity
will be in the line
of the string pro-
longed down-
ward. If a new
point of suspen-
sion be taken,
and the line pro-
Fia. 17. CENTRE OF GRAVITY. ,
longed down-
ward, it will cut the first line in the centre of gravity.
This enables us to find the centre of gravity in certain
cases. In the case of a thin body, we may balance it over
a ruler in two directions, or over the edge of a table, as in
Fig. 17. If the lines of the ruler or the edge of the table be
marked on it, their intersection will be the centre of gravity.
In general, its position has to be found mathematically.
Experiment 13. Lay a thin board on a ruler, and find its centre
of gravity as described. Bore a hole here and insert an awl. Notice
how the board is balanced in every position.
Experiment 14. Bore a hole in a board, and insert an awl, on
which hang a plumb-line. Mark the path of the line on the board.
Do this again from some other point. The intersection of the lines
is the centre of gravity.
90. Representation of Weight as a Force. A line down-
MOTION AND FORCE. 37
ward from the centre of gravity of a body may represent
its weight; that is, it will be the resultant of all the
parallel pulls of the earth on its different particles. Hence
in treating of the weight of a body as a force we must
represent it by a line, in the direction of a plumb-line,
downward from its centre of gravity.
91. Base of Support and Centre of Gravity. If a body
rests on a support, and a line from the centre of gravity
downward meets this support within the base of the body,
it will remain in position ; if not, it will slide or overturn,
for the downward pull meets with no resistance.
Experiment 15. Find the centre of a board, as in Experiment 14.
Tilt it sidewise, and notice that when the centre is exactly over the
FIG. 18. CENTRE OF FIG. 19. CENTRE OF GRAVITY.
GRAVITY AND BASE OF
SUPPORT.
point of support a, as indicated by a plumb-line, the body is just
ready to turn either way.
Experiment 16. Place a light piece of stick, a>, with one end
resting on a table. At b notch it so that another stick, be, may fit in
the notch and press against the handle of a bucket under the table.
A string, cd, must also be attached to the handle. A great weight
may now be placed in the bucket, for the centre of gravity of the
weight comes under the support at a. If b is depressed, it raises the
centre of gravity, and hence b is again quickly raised.
A wagon at rest will overturn when the line drawn
from the centre of gravity falls outside the wheels. The
tower of Pisa * could be made to overturn by building it
higher, for the centre of gravity would thus be thrown
farther out.
When a man stands erect, the line from his centre of
1 Where is this, and how constructed?
4
38
NATURAL PHILOSOPHY.
gravity falls between his feet. In beginyiing to walk, he
throws his body forward, so as to bring his centre of gravity
FIG. 20. LINE FROM CENTRE OF GRAVITY MUST FALL INSIDE THE WHEELS.
in front of his feet. He would now fall did he not catch
himself by throwing one foot forward. The operation is
then repeated with the other foot. He also throws his
body from side to side, so as to keep the centre of gravity
over the foot which is on the ground. In carrying a
FIG. 21. UNSTABLE, NEUTRAL, AND STABLE EQUILIBRIUM.
weight on his back, he leans forward, and in carrying it
in one hand he leans sidewise, for the same reason.
92. Stability. The position of a body is stable when any
MOTION AND FORCE. 39
overturning force beginning to act will tend to cause its
centre of gravity to rise, as a brick lying flat ; for then it will
of itself return to its original position when the force is
withdrawn. It is unstable when the slightest overturning
force causes its centre of gravity to fall, as a cane bal-
anced on end, in which case it will not recover its position,
but will go farther from it. It is neutral when the over-
turning force causes motion in a horizontal line, as a ball on
a floor; then it will come to rest in any position.
93. Measure of Stability. The more the centre of gravity
has to rise in overturning, the
more stable the body is. A brick
on its flat side is more stable
than a brick on end. To over-
turn it the centre of gravity has
to be raised through the verti-
cal height ab, which is a much Fm 22- _ STABIUTY .
greater distance in one case than
in the other, and therefore a much greater force is required.
The work done in overturning is the weight multiplied
by ab.
Exercises. 1. When will a body slide, and when roll, down an
inclined plane?
2. In rising from a chair, why do we lean the body forward ?
3. Why is it easier to walk on a fence with a long stick in the
hand?
4. When is a pendulum in stable equilibrium ?
5. A cone balanced on its apex is in what kind of equilibrium ?
on its base ? on its side ?
6. Why cannot a person pick up an object from the floor in front
of him when standing with his heels against a vertical wall ?
7. Should the centre of gravity of a ship be high or low ? of a
wagon ?
8. Why is it easier to suspend an iron ring on a nail on the inside
than to balance it on the outside ?
9. What would a 200-pound man weigh if moved to within 1000
miles of the centre of the earth ? Ann. 50 pounds.
40 NATURAL PHILOSOPHY.
FALLING BODIES.
94. How much a Body will Fall in a Second. The attrac-
tion of the earth is such that it will cause a body starting
from rest to fall about 16.1 feet (about 4.9 metres) in one
second. Its velocity at the beginning was nothing, and it in-
creased uniformly during the second. Hence at the end it
is moving at the rate of 32.2 feet (9.8 metres) ; that is, it
has acquired a velocity which if continued uniformly would
carry it over 32.2 feet (9.8 metres) the second second. But
during this second second it has also the pull of the earth,
adding 16.1 feet more to the space passed over, making
48.3 feet, or three times 16.1 feet, in that second. The third
second it has an acquired velocity of 64.4 feet, and an
additional pull of 16.1 feet, making 80.5 feet, or five times
16.1 feet, as the fall during the third second.
In general, the fall through any second is found by
taking the series of odd numbers, 1, 3, 5, 7, etc., and mul-
tiplying 16.1 by the number in the series corresponding to
the given second.
Let it be required to find the fall during the sixth sec-
ond. The sixth number of the series is 11.
11 X 16.1 = 177.1 feet.
The space fallen through in the first three seconds will
evidently be (1 -f 3 -f 5) X 16.1 ; in the first five, (1 + 3
_j_ 5 _f_ 7 _|_ 9) x 16.1 ; and so on.
The sum of the numbers in the parenthesis is found by
adding the end terms, and multiplying by half the number
of terms, or the number of seconds. 1
1 If the ninth second is given, we find the odd number correspond-
ing by multiplying 9 by 2 and subtracting 1. If we add the first
two odd numbers, it gives the square of 2 ; if the first three, the
square of 3; and so on. Thus, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5
+ 7 = 16. We thus see a reason for the rule, to be announced farther
on, that the spaces passed over vary as the squares of the times.
MOTION AND FORCE. 41
To find the space through which a body would fall in nine
seconds, we add the end terms 1 and 17, and multiply by -|
and by 16.1, or
(17 + 1) X f X 16.1 = 1304.1 feet.
95. Formulae for Falling Bodies. But it is better to
work out some general formulas.
Let s represent the space passed over ;
" t " " time;
" v " " velocity;
" g " " acceleration produced by gravity in
one second = 32.2 feet = 9.8 metres, which is taken as the
measure of gravity. As g is the velocity acquired in one
second, in t seconds we will have
v = gt. (1)
But as the velocity uniformly increases from nothing to
gtj the mean velocity is J gt, and the space passed over in
t seconds with this velocity is
= }0fX* = Iff?. (2)
From(l), t=l (3)
Substitute in (2),
= l<rxjHor (4)
(5)
From (2)
9
Note. We said (page 33) that the potential energy which a hody
has when raised above a plane is equal to the actual energy of its
motion when it falls to that plane ; in other words, that
ws = \mv i .
We can now prove this. The weight of a hody is equal to the
number of its particles multiplied by the pull on each, or
w = mg.
Also, from (4), s=--.
Multiplying these together, we have ws trig Xs~ wv2 ) which
is what we wanted to prove.
4*
42 NATURAL PHILOSOPHY.
These formulsB enable us to work out all possible cases
of falling bodies. We seek for one in which the desired
quantity constitutes the first member, and in which the
last member is all known.
Exercises. 1. How far will a body fall in 8 seconds? We want
s, and have given t and g : hence use formula (2).
2. How long will it take a body to fall through 200 metres ? Use
(6).
3. What velocity would a body acquire in each of the last cases ?
4. A body has a velocity of 400 feet per second : through what
space and how long has it been falling?
5. A body has a velocity of 40 metres a second : through what
space and how long has it been falling?
96. Projection Upward. When a body is projected up-
ward, the attraction of the earth takes away from its
energy of motion, and when it falls it gives it back again.
It has the same velocity in coming down that it had in
going up at the same height. The circumstances of the
motion are just reversed.
1. How high will a body rise by an upward impulse of 80 metres
per second ?
Use formula (4).
6400
2. A bullet is shot up with a velocity of 1600 feet per second : how
high will it go?
3. A body rises to the height of 300 metres : how long did it take it ?
97. Resistance of Air. All the above is on the supposi-
tion that the motion is in a vacuum. The resistance of
the air very materially alters the results in real cases. A
body will not rise as high as it otherwise would, nor will
it fall with nearly the velocity with which it was projected.
98. Parabola of a Projectile. In the case of bodies pro-
jected not vertically, were there no resistance the body
would move in a symmetrical curve called a parabola* and
1 A parabola is a curve every point of which is equally distant
from a point/, Fig. 24, and from a straight line ec. When a gun is
MOTION AND FORCE.
43
would have equal velocities at equal heights. In practice,
it descends more steeply than it rises. The curve is some-
thing like that represented in Fig. 23.
FIG. 23. CURVE OF A BALL.
Fro. 24. PARABOLA.
Experiment 17. Get one of your friends to knock a ball, and
take a side view of the curve.
If a body were projected horizontally from the top of a
tower, it would reach the level at the
same time as if it were dropped.
Moreover, it would reach the level
at the same time whatever its ve-
locity of projection. For gravity
is the only downward force acting,
and a horizontal impulse will not
change the circumstances of its
motion vertically. It is a general
law that a force at right angles to the motion of a body
cannot change its velocity, though it may its direction.
The range, bd, of a projectile is equal to the velocity of
discharge multiplied by the time it is moving. For the
discharge is caused by an impulsive force, which tends to
produce uniform velocity. Gravity acting at right angles
does not cause any change in this horizontal velocity. The
projectile moves faster, but it does not get along in a hori-
zontal direction any faster in one part of its flight than in
FIG.
25. PROJECTION
ZONTALLY.
shot horizontally, the curve, except for the resistance of the air, would
be a semi-parabola, ab.
44 NATURAL PHILOSOPHY.
another. The same is true if it be projected from the
ground at an angle upward.
THE PENDULUM.
99. What is a Pendulum ? The pendulum is a body sus-
pended by a flexible cord, so that it may
freely vibrate. When drawn aside from
a vertical line, the weight is raised and
gravity causes it to descend. Its inertia
will then carry it up the other side, and
were it not for friction and the resistance
of the air it would rise to the height from
which it fell, and swing back and forth
forever. On account of these resistances
,,, 9R p . it does not rise so high, but makes shorter
HIQ. Zb. PENDULUM.
and shorter vibrations, and is finally
brought to rest.
100. Energy of a Pendulum. "When drawn aside, it has
energy of position equal to its weight multiplied by ab ;
this is converted into energy of motion in the fall, and this
is reconverted to energy of position in the ascent, except
such portion of it as appears as heat in point of suspension
and in the air. Finally the whole energy is converted
into heat, and the pendulum remains at rest.
101. Simple Pendulum. The laws of pendulums are in-
vestigated mathematically by considering an ideal pendu-
lum of which the bob is a single point without size, yet
with weight, and the string perfectly inelastic and without
breadth, the whole moving without any resistance. This
arrangement is called a simple pendulum. The real pendu-
lum, the compound pendulum, approaches in its motions to
this. The longer and finer the string, the more nearly do
its motions conform to those of the simple pendulum.
102. Equation Of Pendulum. The following equation has been
found to give the circumstances of the motion of a simple pendulum :
MOTION AND FORCE. 45
In which
T= time of complete vibration ;
1=2 length of pendulum ;
g force of gravity ;
it = 3.1416 = ratio of circumference to diameter of a circle.
From this equation 1 we have the following laws :
103. Laws of the Pendulum. 1. The times of all pendulums
of the same length at the same place are independent of the ex-
tent of the vibration. A long swing will be performed in
nearly the same time as a short one.
This is only approximately true in the case of the or-
dinary pendulum ; a pendulum can be so arranged that it
will be strictly true.
2. The times of different pendulums at the same place are
proportional to the square roots of their lengths. The time of
vibration of a pendulum four times as long as another is
twice as great.
3. The times of pendulums of the same length are inversely
proportional to the square root of the intensity of gravity.
To find the intensity of gravity at any place, we should
measure the length of a pendulum, count the time of its
vibration, and then in the formula T=7ti/^ we have all
the terms but g, which may be readily found. This sup-
poses that we have a simple pendulum. If we have a
compound pendulum, we must exhaust the air around it,
diminish the friction at its point of support, increase the
flexibility of the cord as much as possible, and make cer-
tain allowance for the size of the bob.
These laws are independent of the nature of the mate-
rial of the bob.
Experiment 18. Procure pendulums made of some heavy mate-
rial, as lead, suspended by long silk cords to the ceiling.
1 The equation is proved by Higher Mathematics.
46
NATURAL PHILOSOPHY.
1. Take two of them of the same length, draw one aside farther
than the other, and let them go at the same instant. Notice the
equality of their times. Or take a long pendulum and count its vi-
brations in a minute when the vibrations are long and when they are
short.
2. Make one just four times as long as the other ; notice that the
short one swings twice while the long one swings once.
3. Change the length till you have it vibrating once in a second;
measure this length, and compare it with that obtained from the
formula by making T= 1, # = 32.2, and TT= 3.1416.
A pendulum which vibrates once in a second is called a seconds
pendulum.
104. Pendulum for Clocks. The utility of a pendulum
for clocks may be explained by Fig. 27. The pendulum
swings between two arms a, and is connected with the
rod o and the escapement mn. The pallets
of this work into the teeth of the escape-
ment-wheel E. When the pendulum swings,
one of the teeth of the wheel escapes from
the pallet m, and the weight, which acts
on R, falls a little, and moves the train of
machinery. But directly the pallet n
catches and holds it again. So the pendu-
lum simply regulates the motion of the
machinery. Swift vibrations make the
clock go faster, and slow vibrations make
it go slower. As a long pendulum swings
slower than a short one, by lengthening
the pendulum the rate of the clock is di-
minished, and vice versa. As heat pro-
duces this result in a metal bar, it is neces-
sary to compensate for this. This may be
done by a gridiron pendulum so arranged
that when some of the bars expand down-
ward and lengthen the pendulum, the
others expand upward and shorten it. By
making these of different materials the
expansion in one direction may be made
just to balance that in the other.
FIG. 27. PENDULUM
BOR CLOCKS.
MOTION AND FORCE.
47
MACHINES.
105. The Mechanical Powers. All machines, however
complex, are combinations of one or more of the six me-
chanical powers, viz., the lever, wheel and axle, pulley, in-
clined plane, wedge, and screw.
THE LEVER.
106. The Lever. The lever is a bar which can be turned
about a support. This support is called the fulcrum. The
power and the weight act on this bar at different points.
The relative positions of fulcrum, power, and weight deter-
mine the kind of the lever.
Fia. 29. LEVER OF THE SECOND KIND.
107. Kinds of Lever. A lever of the first kind has the
48
NATURAL PHILOSOPHY.
fulcrum between the power and the weight, as in a steel-
yard or a crow-bar.
A lever of the second kind has the weight between the
power and the fulcrum, as in a nut-cracker or an oar, or in
a crow-bar used as in Fig. 29.
FIG. 30. LEVER or THE THIRD KIND.
A lever of the third kind has the power between the
weight and the fulcrum, as in the treadle of a lathe.
Questions. What kind of lever is a balance ? a see-saw ? a pair
of scissors ? a ladder raised by a man near its base ? the forearm of a
man ? a pair of tongs ? pincers ? a wheelbarrow ? sheep-shears ? the
handle of a water-pump ? a claw-hammer used in drawing a nail ?
the rudder of a ship ?
Where is the fulcrum in each case ?
108. law of the Lever. The law of the lever in equi-
librium is that the moment of the power is equal to the
moment of the weight ; that is (Figs. 28, 29, 30),
p x ab = w X <w.
In this equation, if we know any three terms, the re-
maining one can be found.
MOTION AND FORCE. 49
Exercises. 1. Given p = 20, ab =8, ac = 6. Find w.
2. Given p = 18, ab = 8, w = 240. Find ac.
3. Given JB = 5, w =- 200, aft = 400. Find ac.
4. Given ab = 40, ac = 80, w = 200. Find p.
5. Given ac = 20, p = 2, 10 = 50. Find length of lever.
Experiment 19. Take a rod and mark it off in inches. Place a
fulcrum near one end, and a 5-pound weight 2 inches from the ful-
crum. Balance it with a 1-pound weight. It will have to be just
10 inches from the fulcrum. Vary the weights and the distances.
109. Ratio of Power and Weight. Whenever the lever-
arm of the uower is greater than the lever-arm of the
weight, the power is less than the weight. In levers of the
first kind the power may be greater or less than the weight ;
in the second kind it is always less ; and in the third kind
it is always greater.
110. Spaces vary inversely as Forces. The space through
which the power and weight act is always proportioned to
their lever-arms, and hence in inverse ratio to their mag-
nitudes. In order to lift w tow?,p has to move toy, a dis-
tance just as many times greater
than ww' as w is greater than ,
,,
or as ap is greater than aw.
We gain power, but we have to
move through a greater space
and with greater velocity. It F IG . SI.THE LEVEE.
is a general law in machinery
that the distances through which the power and the
weight move are inversely proportional to their magni-
tudes, and since by " work done" we mean the force mul-
tiplied by the distance through which it moves, we have
another law for the lever, the work done by the power is
equal to the work done by the weight.
111. The Balance. The balance is a lever of the first
kind. Its accuracy will depend on the exact equality of the
two arms, and may be tested by first weighing a substance,
then reversing weights and substance. If they still bal-
ance, it is correct. By its sensitiveness we mean the
c d 5
50
NATURAL PHILOSOPHY.
amount of weight which, placed in either pan, after being
exactly balanced, will cause it to turn. The smaller this
weight, the more sen-
sitive it is. The sensi-
tiveness is increased by
diminishing friction at
the points of turning,
by placing the centre
of gravity of the beam
near the point of sup-
port, and* by making
the beam long and
light. The first is ac-
complished by making
the fulcrum of a piece
Fio.32.-THE BALANCE. of steel called a knife-
edge.
112. Bent Levers. If the lever is bent, and the forces are not
parallel, the general law still holds. But we must measure the lever-
Fia. 33. ARM OF A DELICATE BALANCE.
arms from the fulcrum perpendicular to the direction of the force.
In the figure (34) the arms are ab and ac.
U m v c.noi i i w
DEPARTMENT OF PHYSICS
MOTION AND FORCE.
51
113. Compound Levers. If one lever acts on a second, as in
Fig. 35, the power of the second lever is the weight of the first. If
FIG. 34. BENT LEVEE.
FIQ. 35. COMPOUND LEVEE.
a6 = 6, ac = 2, cd=5, de=l, and a power of 10 is applied at b.
Then in the first lever,
6 X 10 = 2 X weight at c.
Weight at c 30.
And in the second lever,
This is also obtained by multiplying the power by the product of
the lever-arms of the powers and dividing by the product of the lever-
arms of the weights, or
10X6X5-^-2X1=150.
THE WHEEL AND AXLE.
114. The Wheel and Axle. The principle of the wheel
and axle is the same as that of
the lever.
The radius of the wheel ab is
the lever-arm of the power, and the
radius of the axle ac is the lever-
arm of the weight. There is equi-
librium when
p x ab = w X ac.
Having given any three of these,
the fourth can be found as in the
case of the lever.
The power is applied by means
of a handle, or of a cord wrapped around the wheel, and the
Fio. 36. WHEEL AND AXLE.
52
NATURAL PHILOSOPHY.
weight is attached by a cord around the axle. The power
may act at any angle with the line of the weight, as p', so
that the wheel and axle is used for the transmission of force
FIG. 37. WINDLASS.
FIG. 38. CAPSTAN.
in different directions. If they are of the same diameter,
there is nothing gained except the change of direction.
The windlass (Fig. 37) and capstan (Fig. 38) are ex-
amples of the wheel and axle.
115. Cog- Wheels, If the wheel or the axle has teeth which
work into similar teeth in other
wheels, we will have a train of
cog-wheels. The law of equi-
librium of such a train is : the
weight multiplied by the product
of all the radii of the axles is
equal to the power multiplied by
the product of all the radii of the
wheels.
Since the teeth of a small wheel
are the same distance from one
FIG. 39. TEAIN OF WHEELS. another as the teeth of a larger
wheel in which it works, when it
makes a complete revolution the larger one has only turned part
way round. If one has half as many teeth as the other, it will make
two revolutions to one of the other. It will, therefore, travel twice
as fast. But the number of teeth is proportional to the circumfer-
ences, and hence to the radii, of the wheels. Hence we have the prin-
MOTION AND FORCE. 53
ciple that the velocity of connected wheels is inversely proportional
to their radii.
116. Train Of Wheels. An axle with cogs is called a pinion.
If a power turns a wheel the pinion of which works in another wheel,
the pinion of this in another wheel, and so on, we have great increase
of power, but we lose velocity. If we apply our power to the other
end of the train, the last wheel, we gain great velocity when we reach
the first pinion, but we lose power in the same proportion. The first
method is used when we want a small power to move a heavy weight,
and the latter when we want to gain a great velocity.
Wheels may also be connected by means of belts. The circum-
stances of motion are the same as in a train of cog-wheels. In this
case the friction between the belt and the surface of the wheel takes
the place of the cogs, and the advantage is that power can be commu-
nicated through a long distance.
Exercises. In the following examples let R stand for the radius
of the wheel and r for the radius of the axle.
1. Given R = 20, r = 5, and P= 200, to find W.
2. Given R = 20, P= 100, and W= 1000, to find r.
3. Given R = 20, r = $, and W= 500, to find P.
4. Given r = \, W=1QQO, and P=40, to find R.
5. In lifting an anchor which weighs 1000 pounds, four men work
a capstan having a radius of 2 feet, by bars the outer ends of
which are 6 feet from the centre of the barrel. How much force does
each exert ? Ans. 83.3+ pounds.
6. A power of 5 pounds acts on a wheel with a radius of 1 foot.
The pinion (2 inches radius) acts in a wheel of 1 foot radius. This
is repeated 3 times. "What weight may be lifted ? Ans. 1080 pounds
THE PULLEY.
117. Fixed Pulley. The pulley consists of a wheel work-
ing in a block. In its simplest form it is used to change
the direction of a force. In this case there is no power
gained ; a little is lost by friction and by the rigidity of
the rope ; but, except these, it is carried over without loss
or gain. In the figure the downward force becomes an
upward one, and can be applied to lifting weights. Such
a pulley is called a fixed pulley.
118. Movable Pulley. The case is different when we
have a pulley such as is shown in Fig. 41. Here the
weight is supported by both branches of the cord above
54
NATURAL PHILOSOPHY.
the pulley, hence the tension on each need be but half
W
Fio. 40. FIXED PULLEY.
W
FIG. 41. MOVABLE PULLEY.
the weight; that is, for equilibrium, W must be twice P.
A pulley of this kind will, therefore, enable
a power of one pound to lift a weight of two
pounds. Such a pulley is called a movable
pulley.
119. Work done. Since, when W is lifted any
distance, the pulley is elevated the same amount,
the ropes at both a and b will be shortened, and P
will have to rise through twice this distance.
Hence, as in the lever, in order to gain the advan-
tage of the movable pulley, we lose space and time.
The work done by the power is equal to the work
done by the weight.
120. Combination of Pulleys. In the
combination of pulleys of Fig. 42, the three
upper ones are fixed pulleys, and only
change direction. The three lower are
movable pulleys, and each doubles the ef-
fective force applied to it, so that a power
can lift a weight six times its own weight.
The general rule for pulleys is that a power
w
FIG. 42. COMBINA
JJON OF PULLEYS.
MOTION AND FORCE.
55
can lift a weight as many times greater than itself as twice
the number of movable pulleys.
How would this rule be affected if the rope began at the upper
movable pulley ?
Exercises. 1. In Fig. 43, how much weight will a power of 20
pounds lift ?
2. If the power moves through 30 feet, how far will the weight
move ?
3. How much power will be required to lift a weight of 1 kilogram
through 1 metre, and through what distance will it move ?
FIG. 43. PULLETS.
FIG. 44. PULLEY AND WINDLASS.
4. In a system of pulleys, a power of 2 pounds balances a weight
of 24 pounds : how many movable pulleys are employed ?
5. In the combination of pulley and windlass of Fig. 44, ab is 2
feet, ac 6 inches. A power of 30 pounds is applied at b : how much
weight can be lifted ?
6. How many turns will be required to lift the weight through 3
feet?
THE INCLINED PLANE.
121. Law of the Inclined Plane. Less power is required
to roll a body up an inclined plane than F
to lift it through the height of the plane.
Hence we gain by its use.
Let A be a body resting on an inclined "/^J )o
plane, EF. Let the weight of the body E
be represented by the line AB, directly FIG. 45.-iNCLiN ED PLANE.
downward. Let this be resolved into two
forces, AC, perpendicular to the plane, and AD, parallel
56
NATURAL PHILOSOPHY.
to it. Then AC makes pressure against the plane, and AD
tends to make the body roll or slide down ; and if a force
parallel to EF, and equal and opposite to AD, be applied to
the body, it will be in equilibrium.
By geometry we readily prove the proportion that
AD : AB :: FG : EF,
or, as the force required to hold the body on the plane, which
we may call the power, is to the weight of the body, so is
the height of the plane to its length. When the power acts
parallel to the plane, we have then for equilibrium,
Power : Weight : : Height of Plane : Length,
or, the weight is as many times greater than the power as
the length is greater than the height of the plane.
Exercises. In the above case, 1. Given EF = 10, FG = 5, W~
200. Find P.
2. Given EF = 10, FG = 5, P = 40. Find W.
3. Given EG = 4, FG = 3, W= 200. Find P.
FIG. 46. COMBINATION OF POWERS.
4. In the combination of lever, inclined plane, and pulley of Fig.
46, AB =10 feet, AC=2 feet, DF = 20 feet, EF=8 feet, P=100
pounds : how large a weight can be lifted ?
5. How much power will be needed to lift a ton ?
6. How far will P have to move to drag W through 1 foot ?
THE WEDGE AND SCKEW.
122. The Wedge. If the inclined plane is pushed under
the body, it becomes a wedge, and the same rules for equi-
librium hold good. The height of the plane is now the
back of the wedge, and the weight is as many times greater
than the power as the length exceeds the back of the wedge.
Wedges are used for splitting timber, for raising heavy
MOTION AND FORCE.
57
weights, for cutting and piercing. Knives, scissors, awls,
chisels, pins, needles, are wedges.
123. The Screw. A screw is an inclined plane wound
around a cylinder.
Experiment 20. Take a triangle of
paper, as in Fig. 47, and wind it around a
round piece of wood ; it will illustrate how
an inclined plane can be made into ascrew. 1
FIG. 47. SCREW AND IN-
CLINED PLANE.
124. Law of the Screw, One com-
plete turn of the screw will lift the
weight through the distance which
separates the threads. The law of the screw is, there-
fore, that the weight is as
many times greater than the
power as the circumference
described by the power is
greater than the distance be-
tween the threads.
Exercise. A power of 30
pounds applied at the end of a
lever 2 feet long acts on a screw,
the distance between the threads
of which is ^ of an inch : how
much weight can be lifted ?
In the common screw, propelled by a screw-driver, the
weight is the resistance of the material penetrated, and the
circumference described by the power is the circle through
which the largest part of the handle travels. 2
125. Friction. All the laws of machines are modified
by friction. Friction is roughness at the point of contact
of two surfaces, which prevents them from sliding freely
on each other. In levers there is friction at the fulcrum,
in the wheel and axle and pulley at the bearings, on the
1 Such a curve is a helix, and not a spiral, as often stated. A spiral
is a curve in one plane.
2 The distance between the threads of a fine screw is best obtained
by measuring an inch along it and counting the number of threads.
FIG. 48. THE SCREW.
58 NATURAL PHILOSOPHY.
inclined plane, wedge, and screw at their surfaces. In all
these cases this represents so much resistance, to overcome
which additional power is required. It is important to as-
certain the amount of friction be-
tween surfaces of different kinds, so
that its effect may be accurately
taken into account in our theories
of machines. The following will
afford a means of testing its amount.
Experiment 21. Fasten a pulley to the
table, as in Fig. 49. Place a block on the
FIG. 49. DETERMINING FRIG- table and attach the pulley-cord to it. On
TION - the other end of the cord apply weights till
the block begins to move. The amount of
these weights will measure the friction between the block and the
table.
Experiment 22. Place a brick on end, then on face on the table.
The friction will be the same in both cases.
Place a second brick on top of the first, the friction will be doubled.
126. Laws of Friction. By some such arrangement as
this it has been found,
1. That friction is less between metals of different kinds
than between metals of the same kind. Hence the advan-
tage of brass bearings for iron axles.
2. That it is proportional to the weight (or pressure),
and does not depend on extent of surface in contact.
3. That it is greater at the start than after motion has
commenced. A part of the weight may be removed from
the cord, and it will continue to descend. The object of
lubricants is to diminish friction.
127. Friction Essential. Friction should not be looked
upon as a resistance merely : it is indispensable to our wel-
fare. It is the friction between our feet and the ground
v/hich saves us from falling at every step. It is the friction
between the particles of dirt and the rocks which prevents
all the hills from crumbling down and everything being re-
duced to a dead level. It is the friction of nails and screws
which gives them their utility and .prevents all our struc-
MOTION AND FORCE. 59
tures from falling in ruins. It enables the engine to draw
us on the track ; it gives to belted wheels their value ; it
enables long ropes to be made out of short strands, and
keeps knots tied ; it causes the rivers to flow gently along
their beds.
128. Machines do not create Energy. We have seen both
in the lever and in the pulley that the work done by the
power is equal to the work done by or upon the weight or
resistance. This is a general law of machines. Whenever
we gain power we lose speed, and when we gain speed we
lose power. A machine cannot create any energy. It
transmits that which is applied to it by an external power.
The power does work upon it, and it does work upon the
resistance. This work may be of a different kind, but is
the same in amount.
129. Uses of Machines. The question then comes up,
What do we gain by machines ? Sometimes we gain only
a change of direction, as in the fixed pulley ; sometimes it
is an advantage to gain power at the expense of velocity,
as in a lever or pulley used to raise a heavy weight ; and
sometimes it is an advantage to gain velocity at the ex-
pense of power, as in the case of a clock, where the slow
falling of the weight, or uncoiling of the spring, may cause
rapid motion of the hands ; or in the sewing- or mowing-
machines. Sometimes it is a gain to change the character
of the power, as in the steam-engine, where heat produces
mechanical motion, or in electric lighting-machines, where
heat and motion produce electricity and light. Machines
are also a great gain in enabling us to use the power of the
wind, of steam, of falling water, and of animals.
130. Perpetual Motion. These examples will show the
character of the gains of machinery. In no case is the
energy increased by the machine itself. We see, then, the
folly of all perpetual-motion machines, machines which will
keep themselves running without the addition of any ex-
ternal energy. Any such machine would have to create
60 NATURAL PHILOSOPHY.
energy. Let us suppose that water falling on a wheel
would cause such motion of the wheel as would, applied to
a pump, force the water up to the level from which it fell.
This would be a perpetual-motion machine, for it would
keep itself going forever without any new supplies of
force. But it requires just as much energy to lift the
water up to its level as is given out by the fall. But part
of the energy of the fall is required to overcome the fric-
tion of the machinery and the resistance of the air, hence
there cannot be enough left to raise the water to its old
level. If machines could be constructed so as to run with-
out any resistance, perpetual motion would be possible, and
under no other circumstances.
Such a machine would be useless for any practical pur-
poses, for if any machinery were connected with it, it would
soon bring it to rest, and a new supply of power would
be needed.
General Exercises. 1 1. The minute-hand of a watch is twice as
long as the second-hand : show that the end of the second-hand moves
thirty times as fast as the end of the minute-hand.
2. Find the space described in the fifth second by a falling body.
3. If a body falls for a quarter of a minute, show that at the end of
that time it would be moving at the rate of 483 feet per second, and
ascertain what this velocity will be, expressed in miles per hour.
4. A stone dropped into a well is heard to strike the water in two
seconds and a half; find the depth of the well. Ans. 100 feet.
5. An express train, 66 yards long, moving at the rate of 40 miles
an hour, meets a slow train, 110 yards long, moving at the rate of 20
miles an hour ; find how long a man in the express train takes to
pass the slow train, and how long the express train takes in completely
passing the slow train. Ans. -fa minute, fa minute.
6. A river, one mile broad, is running downward at the rate of 4
miles an hour ; a steamer can go up the river at the rate of 6 miles
per hour ; find at what rate it can go down the river. Ans. 14.
7. A moving body is observed to increase its velocity by a velocity
of 8 feet per second in every second ; find how far the body would
move from rest in 5 seconds. Ans. 100 feet.
1 In these and other exercises at the ends of the chapters a great
variety is given in quality and hardness. The teacher should make a
selection adapted to the class. Many classes had better omit all of
them, while some would be benefited by working them all.
MOTION AND FORCE. 61
8. A body is moving at a given instant with a velocity of 40 feet
per second ; from this instant a constant force is made to act on it in
a direction opposite to that of the motion which brings it to rest
after it has described 20 feet ; find the proportion which this force
bears to the weight of the body. Am. About 1 times.
9. A man jumps suddenly off a platform with a 20-pound weight
in his hand : find the pressure of the weight on his hand while he is
in the air.
10. Forces represented by 4, 5, and 10 pounds respectively act on a
particle : show that they cannot keep it at rest.
11. A, B, C, D is a square. A force of 4 pounds acts from A to
B, a force of 6 pounds from B to C, and a force of 10 pounds from C
to D : find their resultant. Ans. 8:48.
12. It is required to substitute for a given vertical force two others,
one horizontal and one inclined at an angle of 45 degrees to the ver-
tical : determine by a diagram the magnitude of these two forces.
13. A weight of 24 pounds is suspended by two strings, one of
which is horizontal, and the other is inclined at an angle of 45 de-
grees to the vertical direction : find by a diagram the tension of each
string.
14. A straight rod is bent at right angles, so that one part is twice
as long as the other : show how the centre of gravity of the bent rod
can be determined.
15. Show that a cylinder, if placed on its flat end, will be in stable
equilibrium, but, if placed on its curved surface, in neutral equilib-
rium.
16. A triangular board is hung by a string attached to one corner :
find what point in the opposite side will be in a line with the string.
17. Find where the fulcrum must be placed that 2 pounds and 8
pounds may balance at the extremities of a lever 5 feet long.
18. The arms of a lever are respectively 15 and 16 inches : find
what weight at the end of the short arm will balance 30 pounds at
the end of the long arm, and what weight at the end of the long arm
will balance 30 pounds at the end of the short arm.
19. A straight lever, 6 feet long, and heavier towards one end than
the other, is found to balance on a fulcrum 2 feet from the heavier
end, but when placed on a fulcrum at the middle it requires a weight
of 3 pounds hung at the lighter end to keep it horizontal : find the
weight of the lever. Ans. 9 Ibs.
20. Two men, A and B, carry a weight of 200 pounds on a pole
between them ; the men are 5 feet apart, and the weight is at a dis-
tance of 2 feet from A : find the weight which each man has to bear.
21. Suppose that a body which really weighs 1 pound appears in
a balance to weigh 1 pound 1 ounce : find the proportion of the length
of the arms.
22. A substance is weighed from both arms of a false balance, and
its apparent weights are 9 and 4 pounds : find the true weight.
23. The radius of the axle of a capstan is 1 foot : if four men push
each with a force of 100 pounds on spokes 5 feet long, show that on
the whole a tension of 2000 pounds can be produced on the rope which
passes around the axle.
24. A wheel and axle is used to raise a bucket from a well ; the
6
62 NATURAL PHILOSOPHY.
circumference of the wheel is 60 inches, and while the wheel makes
three revolutions the bucket, which weighs 30 pounds, rises one foot :
find the smallest force which can turn the wheel.
25. Suppose the power to act parallel to the plane, and that the
height of the plane is to its base as 5 is to 12 : if the weight is 65
pounds, find the power.
26. Find the relation between the power and the weight in a screw
which has 10 threads to an inch, and is moved by a power acting at
right angles to an arm at the distance of 1 foot from the centre.
27. A pendulum vibrates 65 times in a minute : how much must it
be lengthened to vibrate once in a second ?
Solution. Time of one vibration = if second.
Hence, from formula if = 3.1416 V ' ^
(ilfOTe) 2 ^ From this we fi ^ d !
In a seconds pendulum we have 1 = 3.1416 Kgy The difference
between the two values of 1 will be the answer.
28. In what time would a seconds pendulum vibrate at a height of
4000 miles above the earth's surface ? at a depth of 2000 miles under
ground ?
29. How long is a pendulum which vibrates 40 times a minute ?
30. A seconds pendulum, carried up a mountain,, vibrates 58 times
a minute : what is the force of gravity ?
LIQUIDS. 63
CHAPTEE III.
LIQUIDS.
SECTION I. HYDROSTATICS,
131. Definitions. In Art. 25 we were taught that liquids
are substances in which there is perfect freedom of the
molecules among themselves, and that they change their
form with the slightest force. No liquid fulfils these con-
ditions perfectly, but many do this near enough for all
practical purposes. Water is commonly used as the typi-
cal liquid, and will be so used here.
Liquids will be treated under two heads, liquids at rest
and liquids in motion. Hydrostatics is the science which
treats of liquids at rest.
132. Liquids almost Incompressible. Liquids can scarcely
be compressed even if subjected to the greatest pressure.
Indeed, it was formerly thought that they could not be
compressed at all. Many years ago some philosophers in
Florence filled a hollow silver ball with water, and, after
closing the opening, squeezed the sides together by great
pressure. This pressed the ball out of its spherical shape,
and, as this would make the cavity smaller, 1 they hoped to
1 It is proved in higher mathematics that a hollow sphere has a
greater capacity than a vessel of any other shape which is enclosed
hy the same surface. Hence, when the shape of the silver vessel was
changed, its shell would not hold so much water ; but, as indicated
above, instead of shrinking to fit its smaller quarters, the water
oozed through the sides.
Tyndall calls attention to the fact that Bacon performed this ex-
periment fifty years before it was performed in Florence ; but this
fact is generally unknown, and Bacon seldom gets credit for it.
64
NATURAL PHILOSOPHY.
compress the water. But, instead of shrinking in bulk, the
water came through the thick silver sides, and spread over
the outside like dew.
But by using better apparatus modern experimenters
have been able to compress water and other liquids slightly.
To compress a quantity of water whose upper surface is a
foot square into a bulk only yi^- less would require a pile
of iron weights, each 1 foot square, more than i of a mile
high. For all practical purposes, therefore, water is incom-
pressible. This property of liquids will be illustrated
presently in water machinery, and is of great use to us
there.
133. Liquids perfectly Elastic. If liquids are compressed,
and even if kept compressed for a great length of time,
they always expand to their original bulk when the press-
ure is removed. Hence we infer that they are perfectly
elastic.
Experiment 23. Throw a flat
stone very slantingly on the sur-
face of a pond of still water, and
notice how it rebounds or " skips"
again and again. What causes
it? Does a stone skip so well on
smooth ice ? Why not ?
134. Liquids transmit Press-
ure equally in all Directions.
The most remarkable and
important fact about liquids
is that whenever any press-
ure is put upon one, the liquid
presses out with the same force
in every direction.
FIG. 50. THE PRESSURE OF LIQUIDS THE
SAME IN EVERY DIRECTION. In Fig. 50, the piston A presses
down upon one square inch of
water with a force of 1 pound. This force is transmitted to every part
of the surface, and the liquid therefore presses with the force of 1 pound
upon each square inch of the surface of the vessel, as is shown by its
sustaining the weights at B, C, D, and E.
To which class does the lever at C belong? at D ? at E? Has
LIQUIDS.
the weight of the water been taken into account here ? "Would it
make any difference ?
135. The transmitted Pressure proportional to the Sur-
face In Fig. 51, if the small tube is 1 inch square and
the large one 4, then the area
of the water pressing on the
large piston is 16 times 1 as great
as upon the small one, and with
an upward pressure of 1 pound
upon each square inch of B,the
whole upward pressure then is 16
pounds. This is called the hydro-
static paradox, because it seems
paradoxical (or beyond belief)
that 1 pound Should balance 16 ^ FIG. 51. THE HYDROSTATIC
pounds.
136. The Hydrostatic Press. If more than a pound be
placed upon C (Fig. 51), the piston A will be forced down
and D will be raised. In this way a small weight can be
made to raise a very large one. This is the principle of
the hydrostatic press, which is shown in Fig. 52. In order
that all of the parts, and the manner of working, may be
seen, the figure represents the press cut open through the
middle, or in section, as this is called. The raising of the
piston p sucks up water from m. When the handle HE
is pushed down again, a valve keeps the water from going
back into m, and it is forced through the narrow tube into
M, and the large piston P is raised and pressed against the
cotton-bale C with great force. If p is 1 inch in diameter,
and P 10 inches, for every pound down upon p there is a
pressure of 100 pounds upon the cotton-bale. This force is
usually further increased by using a lever, GE (which
class ?), to increase the pressure upon p.
1 The student will not forget that the areas of similar surfaces vary
according to the squares of their like dimensions.
e 6*
66
NATURAL PHILOSOPHY.
137. The Hydrostatic Press creates no New Force. The
hydrostatic press may seem to contradict Art. 130, where
it is said that power is never created by machinery. But
FIG. 52.--THE HYDROSTATIC PRESS.
the surface of the water which presses up against P is
100 times as great as that pressed upon by p, and therefore
when the small piston has been forced down 1 foot P has
been raised only yj-g- of a foot. So that our force of 1 pound
moving through 1 foot has been changed to a force 100
times as great, but moving through only y^- of a foot, and
therefore exactly equivalent to the first force.
The loss of power by friction has not been taken into
account here, and less power is lost by it in this machine
than in almost any other. 1 On this account, and because
1 About 10 per cent, of the power is usually lost by friction. The
principle of the hydrostatic press has been known for more than two
hundred years, but no way of making the joints tight enough to resist
the enormous pressure of the water was found until Bramah, an Eng-
lish inventor, about the beginning of the present century, invented a
curved leather collar for this purpose, shown in Fig. 52, at a and b.
LiqviDS. 67
by enlarging P almost any power can be accumulated there,
this machine is in common use where great force is needed.
138. Pressure on the Bottom of a Vessel, In a vessel
whose bottom is level and sides perpendicular, the pressure
of the water upon the bottom is evidently equal to its
weight, as in Fig. 53, A. If, now, a vessel with a narrow
stem, but widening into a broad base, as in Fig. 53, B, be
filled with water, the water at a, being pressed upon by
the weight of the column of water above it, transmits this
pressure equally in every direction to the water surround-
ing it. This does the same in turn, so that the pressure on
every part of the bottom of the vessel is the same as on
the part under the column. Then, in Fig. 53 C, the press-
ure at E is equal to that at D, and therefore the pressure
at F (or at H), is the same as it would be at / if the first
joint of the pipe were extended straight down to /. And
also the pressure at M or O is the same as it would be at
FIG. 53. PRESSURE VARIES WITH THE DEPTH.
m. If the tubes were curved, or had any other shape, the
pressure on the bottom would be the same. Hence the fol-
lowing important principle : In a vessel of any shape what-
ever, the pressure of a liquid upon the bottom is the same as
if the sides rose perpendicularly around the bottom, and it were
filled with the liquid to the same height as at present. 1
The space underneath this collar is connected with M, so that the
water presses the collar tighter above the piston as the pressure in M
grows greater, and prevents the water from leaking there. From this
discovery the hydrostatic press is sometimes called Bramah's press.
1 The bottom of the vessel is understood to be horizontal, that is,
68
NATURAL PHILOSOPHY.
A cubic foot of water weighs 1000 ounces, or 62 pounds. 1
Therefore, to find the pressure of water on the bottom of a
vessel, find the number of cubic feet in a column of water
whose base is the bottom 2 of the vessel and whose height
is the perpendicular height of the surface of the water above
the base, and multiply 62J pounds by this number.
139. Pascal's Experiment with the Vases, The apparatus
FIG. 54. PASCAL'S VASES.
shown in Fig. 54 was devised by Pascal 3 to prove these truths ex-
level. For the pressure upon the bottom when it is not horizontal,
see Art. 140.
1 More exactly, a cubic foot of pure, fresh water at 32 F. (what
does that mean?) weighs 62&o pounds, and slightly less at higher
temperatures. A cubic foot of sea-water weighs about 64J pounds.
2 Should the outside or the inside area of the bottom be taken ?
3 Pascal (Pascal) was born in France in 1623, and died there in
LIQUIDS. 69
perimentally. The bottom of the glass tube ca is loose, and hangs by
a string from one arm of a balance. Small weights are put on the othei
arm until they balance the bottom and the string. The glass tube
be, whose sides are perpendicular, is screwed on at c, an additional
weight of 1 pound is put into the scale-pan e, and water is poured into
be. The pound-weight holds the bottom close against the end of the
tube until a pound of water has been poured in. Then the water
pushes the bottom down, and runs out as fast as more is poured in,
the marker d having been set so as to show the height of the water
when it began to run out.
If, now, be be unscrewed and m be screwed on in its place, it will
be found that water must be poured in to exactly the same height as
at first before it will loosen the bottom and run out, although, because
of the widening out of m, there may be 2 pounds of water in it then,
thus proving that the pressure on the bottom depends only upon the
area of the bottom and the perpendicular height of the water. If n be
used, perhaps half a pound of water will fill it up to the marker d
and start the flow of water.
140. Pressure on the Sides of a Vessel, Since the press-
ure is transmitted equally in all directions, at the edge of
the bottom of a vessel the pressure of the liquid on the
side is the same as on the bottom. Half-way up to the sur-
face it is the same as the downward pressure at that depth,
or half as great as at the bottom. At the surface there is
no pressure on the side. Therefore the average pressure
per square inch on the side is half as great as on the bot-
tom. If, then, a cubical vessel be full of water, the pressure
upon each of the four sides is one-half that upon the base.
In the above case the sides of the vessel are supposed to be rect-
angles, perpendicular to a horizontal base. In general, the average
pressure upon the perpendicular sides of any shape is the pressure
upon the centre of gravity of the part of that side under water.
If the side of a vessel is not perpendicular, the pressure upon the
part of the side under water is the same as if that part were laid level
and covered with water to the average depth of the water upon the
inclined side, or to the depth of the centre of gravity of the side.
1662. He was a very brilliant scientist, who did much for Natural
Philosophy, especially in the subject we are now considering. He
wrote a book on Conic Sections when in his sixteenth year.
70
NATURAL PHILOSOPHY.
A vessel's base, which is not horizontal, may be considered as an
inclined side, and the pressure upon it found in the same way. This
is a different thing from the downward pressure in such a vessel.
That is the same as the weight of the water, and would be found by
taking a horizontal section through the water and its average depth.
141. Pressure on the Top of a Vessel. There may also be
05 1
Intf. 55. UPWARD PRESSURE OF
LIQUIDS.
an upward pressure upon the top
of a vessel. Thus, in a vessel
shaped as in Fig. 55, the pressure
upward at H or F is just the same
as the pressure downward at B.
Students sometimes cannot see how
the pressure upon the bottom DCE can
be as great as if the sides went up to a
and 6, and yet when put upon scales
and weighed the whole will not weigh
nearly so much as the other vessel of
water would. It is because the press-
ure upward at F and H counterbalances
a part of the pressure downward at D
and E. A foot-ball might be blown so
full that the air would press outward
against the cover with a force of sev-
eral pounds to the square inch, and yet
ordinary scales would not show it to be any heavier than when empty.
The pressure within is as great up as down, and so does not add to
the weight.
142. The Hydrostatic Bellows. Fig. 56 shows a common
piece of apparatus which well illustrates these principles.
FIG. 56. THE HYDROSTATIC BEL-
LIQUIDS. 71
The narrow tube, about six feet long, is screwed into the
bellows, and water poured into the tube will raise a heavy
weight on the bellows. When the bellows are distended,
an additional pound of water may easily sustain 100 pounds
more on the bellows.
Few persons appreciate the amount of pressure caused by a con-
siderable depth of water. Pascal long ago showed that a strong cask
could be burst by screwing into it a long tube and filling cask and
tube with water. Tanks and cisterns would be much less likely to
leak if made wide and shallow, than if made narrow and deep. The
pressure in the water-pipes of cities and towns is often very great.
Exercises. 1. Why are canal-banks and dam-breasts made thicker
below than above ?
2. If water be thrown hard against a wall, will it trickle down the
wall, or fly off? Why?
3. If in the vessel shown in Fig. 51 one side of A is 2 inches and
one side of B 12 inches, and if 5 pounds were put upon C, what
weight upon D would it balance ? Ans. 180 pounds.
4. What weight must be put upon C to balance 396 pounds upon D ?
5. If you should stand upon C, what weight upon D would you
balance ?
6. If you should stand upon D, what weight upon C would balance
you ?
7. What weight must be put upon C to make B stand 1 foot higher
than A? Ans. l$f pounds.
8. What, if B were 6 inches square? Ans. l^f pounds.
9. What, if B were 1 foot square and A 6 inches square ? Ans. 15f
pounds.
10. In a hydrostatic press the diameter of the small piston is 1
inch and that of the large piston 12 inches : how great a weight will
be raised by a downward pressure of 50 pounds upon the small piston ?
Ans. 7200 pounds.
11. If GE (Fig. 52) is 3 feet and GH 6 inches, what weight will be
balanced by 50 pounds at the end of the handle ? Ans. 43,200 pounds.
12. If friction were taken into account, how much would these be
reduced to ? *
13. If a tight cover were put upon B (Fig. 53), and it were turned
upside down, would the pressure of the water upon the new base be
the same as upon the old one ?
14. Would the pressure per square inch be the same ?
15. Would it weigh the same in a pair of scales ?
?.6. There are 2150.4 cubic inches in a bushel : what weight of water
would fill a peck measure? Ans. 19$ pounds.
17. If the room in which you recite these lessons were filled with
water, what would it weigh ?
18. A cubical vessel is full of water : how many times its weight
is the pressure of the water upon the sides and bottom together?
Ans. 3 times.
72 NATURAL PHILOSOPHY.
19. A vessel of water is 2 feet deep : find the pressure upon each
square inch of the bottom.
20. Upon a square inch of the side, 6 inches above the bottom.
Ans. f f pound.
21. Upon a square inch of the side, 18 inches above the bottom.
22. In Fig. 55, if AB is 18 inches, what is the upward pressure
per square inch at F? Ans, i|f pound.
23. If a hydrostatic bellows be 15 inches square, and the tube be 6
feet long, when full of water how much weight will the bellows sus-
tain ? Ans. 585^| pounds.
143. Liquids rise to a Level. In communicating vessels
or tubes, liquids rise to stand at a level. The water-works
of a town illustrate this on a great scale. The water, seek-
ing the level of the reservoir, rises from the underground
pipes up into the highest stories of the houses.
An apparatus consisting of a vase, connected with various crooked
glass tubes, is often used to illustrate this, but a common coffee-pot
is about as good. The coffee stands at the same height in the spout
as in the coffee-pot itself.
144. Fountains, Springs, and Wells. It is water seeking
its level that causes fountains and artesian wells. But in
FIG. 57. A FOUNTAIN.
a fountain the stream never rises quite so high as the level
of the reservoir, on account of friction in the pipe, resist-
ance of the air, and the interference of the falling drops
with the upward stream.
LIQUIDS. 73
When rain falls, it sinks down into the earth until it
comes to a layer of rocks or clay, and flows along this to
an outlet, generally where the surface of the ground sinks
down to the level of the bed of clay or rock. This is a
spring. Where there is no spring, a pit is often dug down
until it reaches one of these small underground streams,
and we have a well.
Artesian wells are small holes only a few inches in diameter, bored
into the earth with a sort of auger. They are often many hundreds
of feet deep, and the water rises in them, sometimes flowing out at
the surface. This is because the well has tapped an underground
stream of water which has flowed down there from high ground.
Fig. 58 makes this clear.
FIG. 58. AN ARTESIAN WELL.
The water has flowed from a under a stratum of clay or rock, be,
through which the water cannot rise anywhere until the well is
reached. These wells have been sunk in all parts of the world, and
from some of them immense quantities of water flow. 1 Many of the
oil-wells in Pennsylvania and elsewhere are artesian wells.
1 These are called artesian because the first one was at Artois (Ar-
twa/) in France.
At Passy (Pas-see'), near Paris, there is an artesian well 1923 feet
deep, which discharges 5,660,000 gallons of water daily.
D 7
74
NATURAL PHILOSOPHY.
145. Water-Level. The surface of a small portion of
water appears to be perfectly level, and is practically so,
but large surfaces of water are found to be perceptibly
convex. 1 This necessarily follows from the fact that the
earth is round, the water taking the shape of the earth.
FIG. 59. DEVIATION OF WATER-LEVEL FROM EXACT LEVEL.
The surface of water or level ground falls from a horizontal line
8 inches at the end of one
mile, but 8 inches multi-
plied by the square of 2 at
the end of two miles, and
by the square of 3 at the
end of three miles, etc.
Why are not the plumb-
lines parallel in Fig. 59?
146. Spirit-Level.
This very common in-
strument is a glass
tube almost filled with alcohol, but with a small air-bubble
left in it, and then sealed up air-tight. The tube looks to
be perfectly straight, as in Fig. 60, but it is really slightly
FIG. 60. A SPIRIT-LEVEL.
1 Do not forget to know clearly what concave and convex mean.
You can remember that a concave surface is hollowed out like a cave,
and that a convex one has just the opposite shape.
LIQUIDS. 75
curved, as shown (but exaggerated) in Fig. 61. When the
ends of the tube are level, the middle is the highest point,
and the light bubble is found there. The spirit-level is
constantly used by carpenters and other mechanics, and is
B
-
A
FIG. 61. THE CURVE OF A SPIRIT-LEVEL (EXAGGERATED).
often attached to telescopes, and to surveying and other
instruments.
Alcohol never freezes at natural temperatures, and is therefore the
best liquid for filling levels.
147. Bodies in Water : three Important Laws.
Experiment 24. Make a cube of wood 1 5 centimetres (2 inches)
on each side, weigh it, then let it float upon a vessel which was full of
water. Weigh the water which ran over, and it will be found to be
the same as the weight of the cube. Therefore,
I. A body floating in water displaces its own weight of the
water.
"When will the vessel weigh more, full of water, or with the wood
floating in it? Try it.
Experiment 25. Drive enough brads or tacks without heads en-
tirely into the wood to sink it in water. Drop the cube into a ves-
sel full of water. Catch the water which runs over in some vessel in
which you can measure its volume. It will be found to be exactly
125 cubic centimetres (8 cubic inches). Therefore,
II. A body immersed in water displaces its own bulk of the
water.
Could this principle be used to find the volume of an irregular
solid, such as a bunch of keys or a watch-chain ? Could you do it
without making the water overflow ?
Experiment 26. Hold a stone by a string in the air, and after-
wards in water ; notice how much lighter it is in the water ; or, more
exactly, hang the weighted wooden cube by a thread to one arm of a
1 Any piece of wood will do equally well for this experiment, but
this cube will be most convenient for the succeeding ones, hence the
recommendation. In order to make the experiment entirely satis-
factory, the wood ought to be coated with varnish, oil, paraffin, or
something of the sort, to keep it from absorbing water.
76
NATURAL PHILOSOPHY.
balance and weigh it. Then let it hang immersed in water and weigh
it again. Its weight will be 125 grams (4J| ounces), the weight of a
cube of water 5 centimetres, or 2 inches, on each side. Therefore,
III". A body immersed in water is lightened by the weight of
its bulk of water.
Let ABDC represent a solid block
immersed in water. It is pressed
upward at CD with a pressure equal
to the weight of the column of water
NCDN, and downward at AB by only
the weight of NABN ; therefore on
the whole the block is pressed up-
FlG - 62 - ward, or lightened, by the weight of
the difference of these two columns, or ABDC.
FIQ. 63. THE CYLINDER AND BUCKET EXPERIMENT.
Fig. 63 shows a piece of apparatus which illustrates this beautifully.
The cylinder p is of solid metal, and fits into the bucket c exactly.
The two are weighed at first with no water in the jar. Water is then
poured into the jar to cover p, when it will be lightened, and the
scale-pan P with the weights will fall. But if c be filled with water,
the scales will balance again. Explain this.
148. Floating Bodies. We see, then, that a body lighter
than water floats because a part of it displaces enough
LIQUIDS.
77
water to equal in weight the whole of the body. Material
much heavier than water can be floated, if it is thin and
hollowed out enough. A saucer or tin basin w r ill float,
although china and tin are heavier than water, because
to sink it would have to displace a bulk of water equal to
the shell and inside together, and this would be heavier
than the shell of china or tin. It is on this principle that
almost all large ships are now made of iron, and they not
only float, but carry immense loads of freight.
In mechanics (Art. 93) we learfied that a body stands
most stable when its centre of gravity is lowest ; and the
same is true with a floating body. The keels of ships are
often heavily weighted with metal ; the heaviest part of the
cargo is put in the bottom of the ship. And a ship never
goes to sea empty ; if no cargo can be got, it is loaded with
stones for ballast.
"Why is a row-boat much more apt to upset when you stand up
than when you sit down in it ?
The heavier a liquid, the better will a body float in it.
Iron, and even lead, will float upon mercury, just as wood
lillllllllllllllllllllllllllillllllllilllllillllillllllllll
Fia. 64. EGG FLOATING IN BRINE.
floats upon water. Sea-water is heavier than fresh water,
so that a vessel sinks lower when it comes into a fresh-
78 NATURAL PHILOSOPHY.
water river from the ocean. And in the intensely salt
water of the Dead Sea a man cannot sink if he wants to.
Experiment 27. Fill ajar, such as is shown in Fig. 64, half full
of fresh water, an egg will sink to the bottom : why ?
Fill a second jar half full of strong brine, the egg will float : why ?
Pour the fresh water carefully upon the brine, and the egg will
sink about half-way and float there : why ? Would it do to pour
the salt water in upon the fresh ? Try it.
SPECIFIC GRAVITY.
149. Definitions. The specific gravity of a solid or a liquid
is its weight divided by the 'weight of an equal bulk of water.
A cubic inch of iron weighs 4.06 ounces, and a cubic inch of water
.58 ounce". The specific gravity of the iron is 4.06 -=-.58, or 7. A cubic
inch of alcohol weighs .522 ounce : what is its specific gravity?
Pure water at 39 F., the temperature at which it is densest, is the
exact standard of specific gravity for solids and liquids.
The specific gravity of a gas is its weight divided by the
weight of an equal bulk of air, or hydrogen, at a temperature
of 32 F.
To find the Specific Gravity of a Solid.
Experiment 28. Hang a thick screw or other small piece of iron
from one scale of a delicate balance by a fine thread ; weigh it care-
fully : suppose its weight is found to be 350 grains. Set a glass of water
under it, and let the screw hang in the water ; weigh it there : suppose
its weight is 300 grains. According to Art. 147, 350 grains, less 300
grains, or 50 grains, is the weight of an equal bulk of water, and, there-
fore, 350 grains -r- 50 grains, or 7, is the specific gravity of the screw.
Hence the specific gravity of a solid heavier than water can
be found by dividing its weight by its loss of weight when
weighed in water.
150. To find the Specific Gravity of a Solid lighter than
Water.
Experiment 29. Take a small cork, weighing, perhaps, 10 grains.
Fasten it to the screw used before, and weigh the two. They will
weigh 360 grains. Weigh them in the water. They will weigh less
than the screw weighed in the water, perhaps 270 grains. The cork
loses all of its own weight (10 grains) and buoys up 30 grains of the
weight of the screw. Hence, according to Art. 147, the weight of the
water equal to the cork in bulk is 40 grains. And the specific gravity
of the cork is 10 grains -r- 40 grains, or ^.
Hence the specific gravity of a solid lighter than water can
LIQUIDS.
79
be found by dividing its weight by its weight added to what it
buoys up a heavy solid previously weighed in water.
151. The Specific Gravity of Liquids. The specific gravity
of a liquid can be found by dividing the weight of a quantity
of the liquid by the weight of an equal quantity of water. Try
it with strong brine, with coal-oil.
Specific gravity flasks which will hold a certain known weight of
pure water at 39, say 1000 grains, are often used to find the specific
gravity of liquids. The flask is filled with the liquid whose specific
gravity is to be found, and weighed. The weight of the empty flask
being subtracted, the remainder is the weight of the liquid, and this
divided by 1000 grains gives the specific gravity of the liquid.
Experiment 30. Take a heavy solid, say the screw used in Exper-
iment 28, and weigh it, then weigh it in water : suppose the weights to
be 350 and 270 grains as before. Weigh
it also in strong brine : suppose its
weight then is found to be 256 grains.
From its losses of weight in the water
and brine can you find the specific
gravity of the brine ? How does the
result compare with the specific grav-
ity which you found for the brine be-
fore? Test coal-oil again in this way.
152. Hydrometers. Experiment
31. Get a piece of light wood about a
foot long, and an inch square all the
way along. Mark the inches and
quarters of inches on one side. Bore
a half-inch hole in one end, and pour
it full; of melted lead. Smooth the
end off with knife or file, and varnish
or oil the stick so that it will not ab-
sorb water. You have made a hy-
drometer. 1 Put it in water, and it will
stand upright, sinking to a certain
point. It will be convenient to make
it sink to some inch-mark by cutting
a little off one end. (If the water-
mark is at first a little above an inch-
mark, which end will you cut off?
If below, which one ? Why ?) Suppose it sinks in water to the
8-inch mark. Put it in the brine. It will stand at 6| inches. (Why
should it rise higher in the brine than in water ? Do not be satisfied
FIG. 65. HYDBOMETER.
1 Hydrom'eter, from Greek hudor, water, and metron, measure.
80
NATURAL PHILOSOPHY.
until you can give the reason clearly.^ Then 6| cubic inches of the
brine must weigh as much as 8 cubic inches of water, or 1 cubic inch
of brine 1.2 times as much as 1 cubic inch of water, and the specific
gravity of the brine is 1.2. With this hydrometer the specific grav-
ities of other liquids can be quite accurately found. Try it with
coal-oil or other oils, milk, or any other convenient liquid. Glass
hydrometers, as represented in Fig. 65, are in common use. They
are commonly weighted with mercury. Special instruments of this
sort are often used to test milk, alcohol, acids, etc.
153. Specific Gravity of Gases. The specific gravity of
a gas can be found by weighing equal quantities of it and
of air, and dividing the first by the second.
154. Capillary Attraction. We learned in Art. 143 that
liquids seek a level ; but there is a very
curious exception to this law. If we
notice the edge of the water in a glass
vessel, we see that it rises up in a curve.
If there is a corner in the vessel (as in
a square inkstand), it rises higher there.
If two glass plates are held in water
P arallel and close together, the water
will be higher between them than out-
side ; and if the plates be brought together at one end, the
water will rise higher towards this end in a peculiarly
shaped curve, 1 as in Fig. 66. But if the
end of a very small glass tube be put into
water, it will rise in it best of all. It is
from this fact that this phenomenon takes
its name of capillary attraction, from a
Latin word (capil'lus) meaning a hair.
FIG. 67. CAPILLARY AT-
TRACTION IN TUBES. Its cause has DQQii given in Art. 28.
Experiment 32. Color some water with a small quantity of indigo.
Put the end of a fine glass tube (a broken thermometer tube will be
good) into it, and the water will rise. If you have another finer
tube, the water will rise higher in it. And if you have the simple
1 It is proved by higher mathematics that this curve is an hyperbola,
a curve very familiar to mathematicians, and treated of in Analyt-
ical Geometry.
LIQUIDS.
81
piece of apparatus shown in Fig. 67, you will notice that the water
rises higher and higher as the tubes grow finer. And careful experi-
ment shows that in fine tubes the height to which a liquid will rise is
just in proportion to the fineness of the bore.
It is capillary attraction that causes a sponge to absorb
water, a blotter to absorb ink, a lamp-wick to draw up oil,
a towel to dry your face and hands when they are wet.
If a lamp-wick or rag have one end in a basin of water
and the other hanging over the side of the basin, it will
slowly drain all the water out of the basin ; but any im-
purity in the water will remain in the basin.
155. Capillary Repulsion. In all the cases of capillary
FIG. 68. NEEDLES FLOATING ON WATER.
FIG. 09. CROSS-SECTION OF A FLOATING
NEEDLE.
attraction mentioned above, it will be found that the water
wet the substance that drew it up. And whenever there
is capillary attraction,
it will be .found that
the liquid wets the
solid. But if a glass
plate be greased or
waxed and dipped
into Water, the SUr- FIG. 70. INSECT WALKINO ON WATEB.
face water around it
will be pushed away. And if the inner surface of a capil-
lary tube be oiled, water will sink in it below the level of
the water around it. You will notice that the water does
not wet the glass ; and whenever a liquid will not wet a solid,
f
82 NATURAL PHILOSOPHY.
there is capillary repulsion. This is very well shown with
glass tubes and mercury.
If a fine needle be greased (which can generally be done simply by
drawing it between the thumb and finger), and laid carefully upon
the surface of water, it will float. Fig. 68, which shows a cross-section
of the needle floating upon water, explains this. The water will not
wet the greased needle, but is repulsed from it, forming a trough
around the needle. And the needle really displaces as much water as
would fill the trough, which would weigh as much as the needle, or it
displaces its own weight of water. In the same way we can explain
how certain insects walk upon the surface of water.
Exercises. 1. Why do doors and window-frames swell in damp
weather ?
2. Why does water keep wooden buckets and tubs from falling
apart ?
3. In Fig. 51, B is 9 inches square, A 4 inches square. There are 4
pounds upon A, and it is level with B : what weight is upon J5?
Ans. 20^ pounds. How much additional weight upon B will make
it stand 8 inches lower than A ? Ans. 23 pounds 7 ounces. If, when
they are at the same height, 8 pounds be put upon -4, how high will
B stand above A ? Ans. 13ff inches.
4. If B is 15 centimetres square, and A is 6 centimetres square,
with 24 kilograms upon B, what must be upon A to balance it ? How
much additional weight upon A will make it stand 12 centimetres
lower than J5? If, when they are at the same height, 6 kilograms be
put upon B, how far will it stand below A ?
5. A dam-breast is 1000 metres long, it slopes from the surface of
the water to a depth of 12 metres, and the breadth of the part under
water, measured slopingly, is 15 metres : what weight of water in kilo-
grams rests upon the breast ? Ans. 54,000 cubic metres = 54,000,000
kilograms.
6. A box 4 feet long, 2 feet wide, and 3 feet high is full of water :
what is its weight? What is the pressure per square inch upon its
bottom ? Ans. Iff pounds. What at the bottom of one side ? What
half-way up one side ? Ans. |~|f pounds. Half-way up one end ?
Ans. 4|| pounds.
7. Suppose a piece of sheet-iron, 2 feet wide, is run from the lower
part of one end to the top of the other, in the box described in the
last problem : what is the downward pressure upon the sheet-iron ? the
upward pressure ? What is the downward pressure upon each square
inch of the sheet-iron ? Ans. || pound.
8. When a hose is attached to a hydrant, why will it not throw a
stream of water as high as the town reservoir ? If the end of the
hose is carried high enough, will the water rise in the hose as high as
the reservoir ?
9. Why are springs generally on hill-sides or in low places ?
10. How many metres must a man's eye be from the ground to see
5 kilometres over water ? to see 100 kilometres? Ana. 196-J-, 784.63.
LIQUIDS.
11. How far out at sea could a light-house 200 feet high be seen ?
Ans. 17.32 miles. How far off could it be seen from the top of a
vessel's mast 100 feet high ? Ans. 29.56 miles. (How far towards
the light-house could the surface of the water be seen from the top of
the mast? Then, if one's eye were placed there, how much farther
would it be to the light-house ?)
12. Why is it easier to lift a stone under water than to lift the
stone in the air ?
13. The specific gravity of quartz (commonly called flint) is about
2.5. A boy can lift 120 pounds : how heavy a quartz rock can he
raise to the surface of a creek ? Ans. 200 pounds.
14. A piece of copper weighs 1100 grams, and in water it weighs
975 grams : find its specific gravity.
15. A piece of wood weighs 3 ounces ; a bit of lead weighing 2
ounces in water will just keep the wood totally immersed : find the
specific gravity of the wood. Ans. .6.
16. A water-tight box is 6 inches long and 3 inches wide. A
bunch of keys raises the water in it \ inch : what is the volume of
the keys ? If your hand raises the water ^ inch, what is its volume ?
17. A cylindrical cork floats vertically with 1 inch above the water
and T 3 Q of an inch below : find the specific gravity.
18. The specific gravity of a body is 17 : find the volume of 89
ounces of it.
19. A cup when empty weighs 6 ounces ; when full of water it
weighs 16 ounces ; when full of coal-oil it weighs 14| ounces : find
the specific gravity of the coal-oil.
20. A wooden hydrometer, 1 inch square, sinks 9 inches in water,
but 11 inches in oil : find the specific gravity of the oil.
21. A boat in a river displaces 8000 cubic feet of water ; on reach-
ing the ocean it rises so as to displace only 7800 cubic feet: find the
specific gravity of sea- water and the weight of the boat. Answers,
1.026-. 250 tons.
22. The specific gravity of cork is .24 : what is the volume and
what the weight of a cork that must be attached to a piece of lead
weighing 5 ounces in water, in order that both in the water may
weigh ?
23. A flask weighs 960 grains, and it will hold 2000 grains of water.
Some powdered chalk weighs 50 grains in the air. When placed in
the flask and the flask filled up with water, its weight is 2990 grains.
Find the specific gravity of the chalk.
SECTION II. HYDRAULICS.
156. Flow of Liquids through Openings. We have learned
in Art. 96 that, discarding the resistance of the air, a body
which has fallen from any height has just the velocity with
which a body would have to be sent upward to reach that
height. And we also know that a fountain, if the resist-
ance of the air and friction did not hinder it, would rise to
84
NATURAL PHILOSOPHY.
the level of the water in the reservoir. It must be true,
then, that water flows out of an opening with the same velocity
that it would acquire in falling from the level of the water to
the opening.
Therefore the formula v = 1/2*75" (Art. 95) gives the ve-
locity of discharge. This velocity does not increase, then,
in proportion to the depth, but in proportion to the square
root of the depth. In order that the liquid may flow out
D C B A
FIG. 71. VELOCITY OF JETS.
twice as fast, the second opening must be 4 times as deep as
the first, and 9 times as deep if it is to flow 3 times as fast. 1
If an opening be made in the side or bottom of a
vessel containing water, the stream which runs out
will grow narrower for a little way after it leaves
the opening, and then spread out again. The nar-
rowest part of the stream is called the vena con-
tracta (Latin, contracted vein). Its cause may be
seen by scattering a little chalk-dust in the vessel,
which will be carried along by the currents of water
FIG. 72. FLOW OF and show that these currents rush towards the
LIQUIDS THROUGH . 11 :_ 1*1 T -rt- wo
AN OPENING. opening from all directions, as shown in Fig. 72.
And they keep on converging a little way beyond
the opening and make the vena contracta there. On this account the
quantity of water which ought to be discharged at a certain opening
1 Before the invention of clocks, time was almost universally meas-
ured by the descent of water in a tall vessel which had a small open-
ing at the bottom. This was called a clepsydra. If the opening is
LIQUIDS. 85
is never reached in practice, nor is the calculated velocity ever quite
reached, on account of the friction. The range of the spouting liquid
may be found by multiplying the velocity of discharge by the number
of seconds which it has to flow before striking the ground. This last
is the same as the time in which a body would fall to the ground
from the height of the opening. For example, in Fig. 71 the water
flows from the middle orifice with a velocity of 9.8 feet per second.
As this orifice is 3 feet from the ground, the time of falling from
there to the ground is, by Art. 95,
.-. the range = 9.8 feet X .45= 4.410 feet (=ad in Fig. 71).
The range from the opening 1 foot above the middle one is
2 X 4
32.2
For the one 1 foot below the middle one we have
8 feet X A/ = 8 feet X -50 = 4 feet.
\
11.4 feet X x/ 2X2 = H.4 feet X -35 = 4 feet.
Y' 32.2
We find here that the jet which spouts out half-way up the column
of water has the greatest range of all, and the two spouting out at
equal distances above and below the middle one have the same range. 1
These are universal laws, and can be rigidly demonstrated.
157. Flow through Pipes. A very short pipe discharges
more water from a vessel than an opening in the side of
the vessel without the pipe, for the water tends to follow
the side of the pipe, and the vena contracta is not so small.
But a long pipe greatly retards the flow. A long hose-pipe
made just large enough to empty the vessel, after it has been filled 1
inch deep, in an hour, it must be 4 inches deep to run 2 hours, 9
inches deep to run 3 hours, 16 inches deep to run 4 hours, etc. Or
the lowest hour-mark would be 1 inch high, the next 3 inches above
that, the third 5 inches above that, etc., the spaces between the hour-
marks increasing as the odd numbers. This depends upon the prin-
ciple of falling bodies, given in Art. 94.
1 The student may have found that, if carried out, the second
decimal places in the second and third results will not agree. This is
because the decimal places in the velocity and time of fall were not
carried out far enough. If carried out, they will agree exactly. Will
the resistance of the air interfere with the above conclusions ?
8
NATURAL PHILOSOPHY.
illustrates this well. Bends in a pipe check the flow very
much, and a sharp corner much more than a curved bend.
158. Flow of Streams, The friction of the sides and bot-
tom retards streams very much, otherwise all our streams
would be raging torrents. Small streams may fall rapidly,
but the great rivers of the world have a fall of only a few
inches per mile, and flow from 2 to 5 miles per hour.
The Mississippi l from its source to its mouth has an average fall
of but 7 inches to the mile, and in the lower half of its length of
about half of this. In the last 3000 miles of its course the Amazon
falls less than 1 inch per mile.
159. Waves. Throw a pebble into a still pond or a pud-
dle of water, and a wave is made which runs to the shore.
The most important fact to be noticed about this wave is
that, while the wave moves forward, the particles of water do
not move forward, but each particle in its turn simply moves up
and down. This can be seen by watching a chip floating
in the water at some little distance from the edge. The
chip will rise and fall with the water, but will not come to
the shore. If, however, the chip be only a few inches from
a sloping edge of the pond, it will presently be driven
ashore, for the water growing shallower causes some for-
ward motion along the shore.
It may not be easy to see how the wave can move for-
ward while the water only moves up and down. If you
will take a piece of rope and tie one end to a nail, or let a
1 A question which is both interesting and profitable is often asked
as to whether the Mississippi flows up-hill. As this river is in the
northern hemisphere and flows from north to south, on account of
the bulging out of the earth as we approach the equator (or its flat-
tening towards and at the poles), its mouth is 2J miles farther from
the centre of the earth than its source, and is therefore that much
higher than the source. But the mouth of the river is on a much
larger circle of latitude than the source, and must therefore revolve
through a considerably larger circle in the twenty-four hours. This
causes greater centrifugal force at the mouth, which compensates for
its greater distance from the centre of the earth.
LIQUIDS. 87
companion hold it, and, holding the other end in your
hand, give it a jerk, just such a wave as has been described
above will run along the rope, while each particle of the
hemp has moved only up and down. And very likely you
have often seen a wave, caused by the wind, run across a
field of grass or standing grain, which you see must be
caused in this way. The great waves of the ocean, some-
times thirty feet high, are caused by the action of the wind
upon the surface of the water. Like the waves in the
pond, they are, out at sea, only upward and downward mo-
tions of the water ; along a sloping shore they get a for-
ward motion, and become breakers. The highest part of a
wave is called its crest. The hollow is the trough. The
distance from crest to crest, or from any part of a wave to
the corresponding part of the next one (called correspond-
ing phases), is the length of the wave. 1
If two waves were to meet each other so that the two
crests met, one would be piled upon the other, and a crest
higher than either would be formed. But if the crest of
one meets the trough of the other it will fill the trough,
and, if the waves are of the same size, smooth water will be
the result.
WATEK MACHINES.
160. Water- Wheels. These familiar machines are of
great value. In all cases their power is caused by water
falling from a higher to a lower level. In the dam, or head-
race, 2 which may be twenty feet above the tail-race, 2 the
water has potential energy. In falling, its energy is actual,
and this it communicates to the wheel, and thence to the
machinery. 3 Four kinds of water-wheels are usually de-
scribed.
1 It is important that what is said here about waves should be
clearly understood, for they play an important part later in the
book.
2 Find out what these are, if you do not know.
3 Does the water ever get back to the dam again ?
88
NATURAL PHILOSOPHY.
161. The Overshot-Wheel. This is probably the most
common of all the water-wheels. As shown in Fig. 73, in
the circumference of the wheel are what are called buckets,
into which the water runs from above (hence its name),
and the weight of the
water in the buckets
turns the wheel. Some
of the objections to the
overshot -wheel are its
cumbersomeness, the loss
of water from the buckets
on their way down, and
its liability to freeze up
in winter in Northern
latitudes. Yet very many
manufacturers still prefer
it to any other water-
wheel. Under favorable circumstances, overshot-wheels
may utilize 75 per cent, of the potential energy of the
water.
162. The Breast- Wheel. This wheel is shown in Fig. 74.
It is sometimes used where there is but a short fall of
FIG. 73. OVERSHOT-WHEEL.
FIG. 74. BREAST-WHEEL.
water. Both the weight and the momentum of the water
aid in producing the power. Under the best circumstances,
the breast-wheel utilizes 65 per cent, of the water-power.
LIQUIDS. 89
163. The Undershot-Wheel. This is the most inefficient
of all the water-wheels, generally utilizing only about 30
per cent, of the power. It is only adapted to streams
having a strong current and but little fall, and is seldom
used at all.
FIG. 75. UNDERSHOT-WHEEL. FIG. 76. TURBINE-WHEEL.
164. The Turbine l Water- Wheel. This is a water-wheel
of modern invention, and was first used in France. It is
an iron wheel with curved paddles, as shown in Fig. 76.
This wheel is set into an iron case with its axis vertical. Fig.
77 shows the case with the wheel inside but hidden from
view. The water passes through the openings a, ft, c, etc.,
in this case, and strikes the paddles of the wheel within,
thus driving the wheel around. < After giving all its force
to the wheel, the water drops through a large opening in
the bottom of the case and flows away. Unlike the first
three wheels, the turbine revolves horizontally, not verti-
cally.
The encased wheel is often set in an outer iron case, as
seen in Fig. 78. This is attached to a wooden or iron tube
(Fig. 79), which brings the water from the head-race.
1 Pronounced tur'bin.
8*
90
NATURAL PHILOSOPHY.
Turbine-wheels are all comparatively small. They are
made as small as 1 foot or less in diameter, and are very
seldom more than 6 feet in diameter. The turbine- wheels,
being always entirely under water, do not freeze up in
winter, and they utilize more of the power of the water,
reaching 80 or more per cent, of it. On these accounts
many of them are now in use, and they seem likely to
supplant almost entirely the other forms of water-wheels.
FIG. 77. TURBINE-WHEEL IN ITS INNER CASE.
FIG. 78. THE OUTER CASE.
165. The Hydraulic Ram. This is a machine in common
use for raising water. The way in which it works may be
explained by reference to Fig. 80. A is a large supply-pipe
leading down from a spring or other constant source of
water. At C is a valve which falls down of its own weight
and leaves an opening above it. When the water begins
to flow through A, it escapes at C, but quickly acquires
velocity enough to raise the valve there, and, by pressing it
against the top, to close that opening. As the water in A
is running with considerable momentum, and as the water
LIQUIDS.
91
cannot be compressed in the lower part of the pipe (Art.
FIG. 79. THE TURBINE-WHEEL AT WORK.
131), it lifts the valve B and rushes up into the air-chamber
D, compressing the air into the upper part of the air-cham-
92 NATURAL PHILOSOPHY.
ber until the flow ceases. Then the valve C falls again,
and the same process is repeated. The compressed air in
the air-chamber, by constantly pressing upon the water
below it, drives the water up the small pipe EF in a con-
stant stream. This machine will work for months without
any attention, but the water gradually absorbs and carries
off the air in the air-chamber, so that occasionally a new
FIG. 80. THE HYDRAULIC HAM.
supply must be admitted. The pipe A need have only
a few feet of fall, and water may HI this way be raised
through EF to a considerable height. The repeated shock
and noise caused by the lifting of C has been thought to
resemble the butting of a ram, hence the curious name of
this machine.
166. Barker's Mill. This scientific toy is shown in Fig.
81, It consists of an upright tube, c, near the bottom of
which are two smaller tubes extending out on opposite
sides of the upright tube ; near the ends of these, but on
opposite sides, are two small openings. The pressure from
the column of water in c is relieved at the openings, but it
presses against the sides of the tubes opposite the openings,
LIQUIDS. 93
and hence moves the machine around in that direction, or
opposite to the direction in which the water spouts.
The joints of a cane fishing-pole will furnish excellent material, in
the hands of an ingenious boy, to make a Barker's Mill.
FIG. 81. BARKER'S MILL
Exercises. 1. Verify the velocities of the different jets in Tig. 71.
2. Find the velocity of a jet of water through an opening 10 feet
below the surface ; 20 feet below.
3. Find the range in each case in the preceding problem, if the
surface of the water in the vessel be 30 feet from the ground.
4. Making no allowance for the vena contracta, how much water
would be discharged through the lowest opening in Fig. 71 in 1 min-
ute if the opening is 1 inch square and the surface of the water be
kept at the same 'height?
Solution. 17.9 feet = 214.8 inches, velocity per second.
214.8 X 60 = 12, 888 inches, velocity per minute.
As the jet flows 12,888 inches per minute, a column of water 1 inch
square and 12,888 inches long flows out in 1 minute, that is, 12,888
cubic inches. As there are 231 cubic inches in a gallon,
12,888 -5- 231 = 55$ \ gallons.
5. The area of the vena contracta is usually about | of the orifice :
supposing this to be the true cross-section of the stream, what would
be the flow per minute in Exercise 4 ? Ans. 34f gallons.
6. If in Exercise 2 each opening is a circle 1 inch in diameter,
how many gallons will flow out of each in 1 minute, no allowance
being made for the vena contracta ?
7. What would be the discharge in Exercise 6 if the vena contracta
be allowed for as being f of the area of the orifice ?
8. Why is a stream swifter in the middle than near the banks ?
9. Why does the water of a stream flow so much faster during a
flood than usual ?
94 NATURAL PHILOSOPHY.
10. What would be the effect if the water were allowed to fall
upon an overshot- wheel directly over the axis ?
11. Which side of the point mentioned in Exercise 10 had the water
better be allowed to fall upon ?
12. Why would it not do for the small pipe to open into the top of
the air-chamber of the hydraulic ram ?
GASES. 95
CHAPTEE IV.
GASES.
167. Definition and Properties. As we have before learned
(Art. 26), gas is that form of matter in which the molecules
have a repellent action upon one another. A gas will ex-
pand indefinitely if it has room to do it in. A thimbleful
of air, if put into an absolutely empty room, would fill the
whole room. The force with which a gas tries to expand
is its tension.
All liquids, and even some solids, are constantly, though
perhaps slowly, changing to gas, which disappears by
spreading itself through the air. This is called evaporation,
and the gases into which the solids or liquids turn are
called their vapors. By the application of heat almost
every solid has been liquefied and then changed to vapor
or gas. On the other hand, all the gases have by cold and
pressure been changed into liquids or solids.
Until 1877, air and several other of our most common gases resisted
all efforts to change their gaseous form ; but in that year two European
scientists, by means of great cold and enormous pressure, liquefied or
solidified all of these gases which were formerly called permanent.
168. Compressibility of Gases. We found that liquids
were almost absolutely incompressible. Gases, on the con-
trary, are easily compressed.
Experiment 33. Press a tumbler, top down, into a basin of water.
As it is pushed deeper, the water can be seen to rise somewhat in the
mouth of the tumbler. The pressure of the water is compressing the
air. The resistance you feel is the tension of the compressed air.
169. Mariotte's ' Law. Fig. 82 shows a piece of appa-
1 Ma-re-ot' (1620-1684), a French scientist.
This law was first discovered by an Irish scientist, Kobert Boyle
96 NATURAL PHILOSOPHY.
ratus used for making more careful experiments in com-
pressing air. A little mercury is poured into the open end
of the glass tube, and the air from the short end of the
tube is allowed to escape by tilting the tube
until the mercury stands on a level in both
arms at a. The air in the short arm is now
at its natural density, and is pressed upon
only by the weight of the atmosphere itself.
This weight is equal to about 30 inches of
mercury, as we shall see in the next article.
More mercury is now poured into the long
arm, until it is about 30 inches higher there
than in the short arm, when the air in the
short arm (ab~) will be found to be compressed
into one-half its former bulk (mb). There is
double the pressure upon it (one atmosphere
of air and one of mercury), which has com-
pressed it one-half. If one column be made
60 inches higher than the other, the air in the
short arm will be compressed into the upper
third of ab ; it is pressed down by three atmos-
pheres. 90 inches of mercury (making with
FIG. 82. APPARA- ^ ne a i r f our atmospheres) will compress the
TU8 ILLUSTRAT- r .
ING MARIOTTE'S a | r i n the short arm into one-fourth of its
LAW.
original bulk. Hence we see that the bulk of
a quantity of air is decreased just as the pressure upon it is
increased. This law is substantially true of all the gases.
Questions. When the mercury is 30 inches higher than c, is it 30
inches higher than in the short arm ?
If ab is 6 inches, how much above c will the long column reach
when 30 inches higher than the short one? Ans. 33 inches.
How many inches of mercury must be poured in to raise it as
above? Ans. 36 inches.
What will be the answers of the last two questions if the mercury
in one tube is 60 inches higher than in the other ?
(1626-1691), but was afterwards independently discovered by Mariotte,
and hence usually goes under his name.
GASES.
97
170. Column of Mercury supported by the Air. Experi-
ment 34. Take a glass tube, 1 yard long, | or
of an inch in diameter, one end of which is
closed, fill it with mercury, place the finger over
the open end, and invert it, as shown in Fig. 83.
Lower the tube until the open end is covered
by the mercury in the pan below, then remove
the finger. The mercury in the tube will sink
until it is about 30 inches high, then it will
stand there, being just balanced by the pressure
of the air upon the surface of the mercury in
the basin. We have found that a column of mer-
cury 30 inches high weighs the same as a column
of air of the same thickness, extending from the
surface of the earth to the top of the atmos-
phere. 1
When proper precautions have been taken to
have the mercury pure and to remove all bub-
bles of air from the tube, the space above the
mercury is almost a perfect vacuum. But yet
there is a little vapor of mercury there. An
absolute vacuum has never been made.
Why does the experiment not show that the
column of mercury balances (and therefore
weighs as much as) a column of air as large
around as the basin ? (See Art. 134.)
171. The Barometer. If the glass tube
and the basin of mercury just described
be enclosed in a suitable case, and a scale
of inches and fractions be made on a
part of the upper end of the tube, we
have a barometer, an instrument which
will indicate the changes in the pressure
(i.e., the weight) of the air at that place,
which makes it a very important instru-
ment.
172. Height of Mountains measured
TTT1 -r, i , i FIG. 83. BAROMETER IN
with the Barometer. When Pascal heard ITS SIMPLEST FORM.
1 The height of the column of mercury may vary a little from 30
inches, showing that the weight of a column of the atmosphere
varies.
E
9
9
98
NATURAL PHILOSOPHY.
of the experiment described in Art. 170, he
said that if it was the weight of the air that
held the mercury 30 inches high in the tube,
were he to carry the basin and tube to the
top of a mountain the mercury would fall
below 30 inches, for there would not be so
much air above it there. It was tried, and,
as Pascal expected, as the tube was taken up
the mountain the top of the column of mer-
cury slowly went down, a convincing proof
that it was the weight of the atmosphere
which was supporting the mercury. Bar-
ometers are now very commonly used to
measure the heights of mountains. For low
mountains the mercury falls 1 inch for about
every 900 feet of height. At a height of 3^
miles the mercury is 15 inches high. 1 Half
of the atmosphere is therefore within 3
miles of the surface of the earth.
173. The Barometer and the Weather.
The most common and valuable use of the
barometer is to enable us to foretell the
weather : hence it is often called a weather-
glass. Any sudden change in the height of
the mercury is almost always followed by a
storm, and usually it falls rapidly before a
FIG. 84. THE MER-
CURIAL BAROMETER.
1 The following table shows the height of the
mercury at different distances above the earth :
HEIGHT ABOVE HEIGHT OF
THE EARTH. MERCURY.
1 mile 24.7 inches.
2 miles 20.3
4
5
10
15
20
.16.7 "
13.7 "
.11.3 "
. 4.2 "
. 1.6 "
, 1 inch (or less).
GASES.
99
storm. This will be explained and more fully discussed in
the chapter on Meteorology.
174. The Aneroid Barometer. Fig. 85 shows the aneroid
barometer, very different from the mercurial barometer,
and much used now. It is a thin metal box, from which
the air is partly exhausted and it is then made air-tight.
The top of the box is pressed down more or less, accord-
Fia. 85. THE ANEROID BAROMETER.
ing as the pressure of the atmosphere varies ; this, by
means of levers, causes a hand to move back or forth,
which indicates the pressure. In the figure the metal box
is seen within the outside case and behind the levers. It
is graduated by comparing it with a mercurial barometer.
The aneroid barometer is very convenient to carry and use,
for it is sometimes made no larger than a watch. It is also
-
DEPARTMENT OF PHYS
100 NATURAL PHILOSOPHY.
very delicate, but is liable to get out of order, and should
frequently be compared with a mercurial barometer.
THE ATMOSPHERE.
175. Composition of the Atmosphere. The atmosphere
is composed mainly of two gases, oxygen and nitrogen.
These gases are not chemically united in the atmosphere,
as oxygen and hydrogen are in water, but are simply mixed
together in the proportion of four parts of nitrogen to one
of oxygen. There is always vapor of water also in the
atmosphere, as well as small quantities of other gases.
176. Height of the Atmosphere. The height of the atmos-
phere is unknown. From calculations depending upon the
duration of the twilight it was formerly supposed that the
atmosphere was about 45 miles high. But this only proved
that if there were air above that, it was not dense enough
to cause l twilight. And recent observations of meteors 2
(shooting-stars) show that the atmosphere is at least 100
miles high. One-half of the whole, however, is within the
first 3J miles, and the upper part must be excessively rare.
177. Weight of the Atmosphere. The atmosphere must
weigh as much as an ocean of mercury covering the whole
earth to a depth of 2 feet. This is almost six quadrillion
tons. 8 The air in a room 25 feet long, 20 feet wide, and 10
feet high weighs nearly 400 pounds.
178. Pressure of the Air. A column of mercury 1 inch
1 Twilight is the reflection of the sun's light from the upper part
of the atmosphere. (Sharpless and Philips's Astronomy, p. 116.)
2 Meteors, or shooting-stars, are small solid particles of matter
moving in orbits around the sun. When these strike our atmosphere
their velocity is so great that the heat produced by the blow burns
them up, and it is the flash of this burning that we see. The obser-
vations referred to above show that some of them begin to burn 100
miles or more high : hence the atmosphere must extend to that height.
(See Astronomy, chapter viii.)
8 Verify this, taking 13.6 to be the specific gravity of mercury.
GASES.
101
square and 2 feet high weighs about 15 (14.7) pounds.
Therefore the atmosphere everywhere presses down with
a force of 15 pounds to the square inch. And, as is the case
with water, this pressure is the same in all directions.
Everything about us is subjected to this enormous pressure. The
average human body has a surface of about gOOO square inches, and
therefore sustains a pressure of 15 tons. We! fejfe io = sis^ious ct n6
downward pressure, because the air beneath* presses 3 us" up just the
same. And the human body, largely filled* \utth; liquids =ai<} air, }s;
firm enough to resist the crushing pressur5 J 6f > 'r5*p0aBcis to tho square
inch when distributed all over it.
179. Experiments with the Pressure of the Air. Experi-
ment 35. Dip a tumbler under water in such a way that all the air
may escape and it shall be full of water. Kaise the tumbler partly
out of the water, bottom upward, keeping the edge under water. Is
the part of the tumbler above the water empty ? Explain.
Experiment 36. Fill a tumbler full of water. Cover the top with
a card or piece of heavy paper, and, pressing this tightly against the
top, invert the tumbler. Remove the hand from the card, and the
upward pressure of the air will hold the card
against the inverted tumbler and keep the water
in it.
Experiment 37. Make a "sucker" by taking
a round piece of thick leather, fasten a string to
the middle of it, wet it, and press it tightly
against a brick or flat stone. As the air cannot
get under the sucker, the downward pressure
holds it to the brick, so that both may be lifted up
by the string. Suppose the sucker stuck perfectly
air-tight and had a surface of 4 square inches,
how heavy a stone could be picked up with it ?
Experiment 38. Fig. 86 shows a pipette ; the
opening at the bottom is very small. Fill it with
water and cover the upper opening with the fin-
ger, the water will not run out ; remove the fin-
ger, the water will run or drop out. "Why ?
This is much used for dropping small quantities
of liquids.
Cupping. Physicians, in treating certain dis-
eases, sometimes press a cup to some part of the
body and exhaust part of the air from it, either by
sucking it out through a tube in the bottom of
the cup, or by the burning of a bunch of paper
which has been put into the bottom of the cup
and set on fire before it was applied to the body. The skin and flesh
are sucked up into the tumbler. This shows what an outward press-
9*
FIG. 86. PIPETTE.
J02 NATURAL PHILOSOPHY.
ure the body has, in order to withstand the enormous pressure of the
air. (Ask your family physician to tell you all about cupping, so that
you can answer your teacher's questions about it.)
180. Stream of Air meeting a Surface. When a current
of air strikes a surface, it does not bound off. according to
the law of incidence and reflection, but follows along the
surface. 'This is'dae to the adhesion of the air to the
surface, arrd to ~the resistance of the surrounding air.
. Experiment 3. J - i Bldw' obliquely against a wall, and while doing
so hold a lighted candle so that the current would strike it were the
angle of reflection equal to the angle of incidence. The flame will
not be disturbed. Then hold the candle close to the wall beyond the
place where the current strikes. The flame will be much disturbed,
and may be blown out.
Experiment 40. Bend a quarter of an inch of each end of a card
at right angles to the card. Set the card up on these ends, as legs,
upon a table, and try to blow the card over by blowing against the
table under the card, with the intention of making the air rebound
against the under side of the card. The air will not follow the angle
of reflection, but along the table.
Experiment 41. Take a small bent tube of glass, push one end
just through a wide cork, or a piece of wood, so that the cork forms
a little platform about the end of the tube. Put a pin through a
card, and lay the card upon the cork, letting the pin run into the
tube. Now blow into the other end of the tube. The card will not
be blown off, but will stick tight to the cork, and, if turned upside
down, will stay there as long as the blowing lasts ; when that stops
it will fall off. The air flowing out in all directions between the cork
and the card produces a partial vacuum there, and the pressure of
the air on the other side of the card causes it to stick closer.
181. Buoyancy of the Air. All bodies in the air are
buoyed up by it, just as they are when in water, and are
of course lightened by the weight of the air displaced.
This is about 1 ounce for each cubic foot of the body's
bulk, and is not therefore noticed except with very light
substances, such as feathers and the like.
182. Balloons. These are huge bags of silk, made air-
tight by varnish, and filled with hydrogen or, more com-
monly, with common illuminating gas. As either of these
is much lighter than air, the balloon will ascend and carry
considerable weight with it. In 1862, Mr. Glaisher (gla'-
GASES.
103
sber), of England, ascended in a balloon to the enormous
height of 35,000 feet, or nearly seven miles.
FIG. 87. BALLOON.
PNEUMATIC MACHINES.
183. The Bellows. The common hand-bellows is made
of two tapering boards, joined together around the edges
by flexible leather, and having a nozzle at one end. An
opening in one of the boards is covered on the inside with
a flap of leather fastened only at one end. This is a valve ;
it opens freely inward. When the sides of the bellows are
pushed apart, the air pushes the valve inward and rushes
in. But when the sides are brought together, the air
pushes the valve tight against the side, and, thus closing
that opening, must escape through the nozzle. The stream
of air is not continuous.
104 NATURAL PHILOSOPHY.
Blacksmiths use an improved bellows, which gives a con-
tinuous stream of air. When one lets go of a, the lower
board falls and the air pushes the valve v up and rushes in.
When a is pushed
down and be raised, v
closes and the air is
forced through v' into
an upper chamber.
Upon this there are
weights which con-
stantly force the air
FIG. 88. BLACKSMITHS' BELLOWS. OUt of the nozzle.
184. The Air-Pump.
This very useful machine was invented by Otto Guericke 1
about 1650. Pig. 89 gives a complete view of one of the
simpler forms of the machine, and Fig. 90 shows the inside
of one. In the common ones the rod running up from S' is
wanting, db is a brass cylinder, called the barrel, in which
an air-tight piston, p, moves up and down. When p is raised
from the bottom of the cylinder, a vacuum is formed below
it, and the tension of the air in the receiver E causes it to
rush along the tube below, to push up the valve S', and to fill
the cylinder with rarefied air. When the piston is pushed
down, S' falls, and the air pushes S up in order to escape.
One barrelful has been pumped out of the receiver. The
next time a barrelful of rarer air is taken out, and that
left inEis rarer. This can be kept up until the air in E is
very rare, until it is so rare that its tension is too feeble to
lift the valve S', but it is evident that it can never be en-
tirely exhausted.
Some of the more expensive air-pumps have the rod shown in Fig.
90, by means of which the piston opens and closes the valve S'. As
seen in the figure, the rod passes through the piston, fitting in it
rather tightly. When the piston is pushed down, the rod sticks fast
1 Otto von Guericke (fon ga'rik-eh), a German natural philoso-
pher, 1602-1686.
GASES.
105
in the piston until S' is pushed down, then the piston slips down
FIG. 89. THE AIR-PUMP.
around it. When the piston is raised, it lifts the rod high enough to
open S', but cannot lift it farther, because of the button at the top of
FIG. 90. THE INSIDE OF AN AIR-PUMP.
the rod. Since the action of the valve S' does not depend upon the
106 NATURAL PHILOSOPHY.
tension of the air in the receiver, this pump will produce a more
nearly perfect vacuum ; but it is evident that this could not produce
an absolute vacuum, and the impossibility of making perfect ma-
chinery renders the vacuum appreciably less perfect than in theory it
ought to be.
Air-pumps are often made with two barrels, in order to exhaust the
air more rapidly ; and many different forms of the machine have
been devised for the same purpose.
185. The Air-Pump Gauge. In Fig. 90, F is a gauge to
show how much of the air is exhausted. It is a U-shaped
tube, closed at one end, containing mercury, and enclosed
in an air-tight glass case, into which there is an opening from
the receiver. Before the pump begins to work, the mer-
cury is all standing in the closed end of the tube, which it
fills to the top, and is kept there, of course, by the pressure
of air down the open end, which is the same then as the
pressure of the air outside. When part of the air has
FIG. 91. HAND-GLASS. FIG. 92. THE BURST FIG. 93. MAGDEBURG
BLADDER. HEMISPHERES.
been exhausted, the tension of the air in the pump is not
great enough to hold up the mercury in the closed tube,
and it gradually falls. If a perfect vacuum were made, the
mercury would, of course, stand at the same height in both
tubes. The branches of the tube are usually only a few
inches long, as the gauge is not needed until most of the
air is exhausted.
Another form of gauge is sometimes made by attaching
GASES.
107
a long glass tube to the air-pump by a rubber tube, and
then putting the lower end of the glass tube in a vessel of
mercury. As the air is exhausted, the mercury will rise
in the tube.
How high would it rise if the pump could produce a perfect vacuum ?
186. Experiments with the Air-Pump, Experiment 42.
Take a hand-glass (Fig. 91), and set it upon the brass plate of the air-
pump, in the place of the receiver. 1 Cover the top of the glass closely
with one hand, and work the pump. As the air below is exhausted,
the pressure of the air above is felt, and presently it becomes difficult
to remove the hand from the top of the hand-glass.
Experiment 43. Tie a piece of wet bladder tightly around the top
FIG. 94. THE WEIGHT-LIFTER.
FIG. 95. WEIGHT IN A VACUUM.
of the hand-glass, or around the top of a bladder-glass ; after drying
it thoroughly, put it upon the air-pump, and exhaust the air, the
bladder will burst with a loud report : which way, inward or outward ?
Experiment 44. The Magdeburg hemispheres are two hollow
brass hemispheres, which will fit very closely together. After clean-
ing and greasing the edges, put the hemispheres together, and screw
fast to the air-pump. After exhausting the air, turn the stop-cock,
1 Here, as in all experiments with the air-pump, unless the lower
edge of the glass vessel is carefully ground, it must be coated with
tallow, to keep air from passing between it and the brass plate. The
edge of the glass and the brass plate should be cleaned beforehand.
108
NATURAL PHILOSOPHY.
remove from the air-pump, and screw on the second handle. Two
students will find that they may pull hard, yet not pull the two
hemispheres apart. Turn the stop-cock, and they fall apart : l why?
Experiment 45. Put a foot-ball partly filled with air, or a partly-
blown bladder, under the receiver of an air-pump. Exhaust the air,
and the foot-ball or bladder will swell out : why ? Try the experi-
ment with raisins or a shrivelled apple under the receiver.
FIG. 96. FOUNTAIN IN A VACUUM.
FIG. 97. FEATHER AND COIN.
Experiment 46. " Bursting bombs," air-tight cubes, or flasks of
thin glass may be bought from any dealer in philosophical apparatus.
Put one under the receiver, and exhaust the air. It will burst with
considerable force. Explain.
Experiment 47. Attach the top of the weight-lifter (Fig. 94) to
the air-pump by a rubber tube. Exhaust the air, and the weight
will be drawn up : why ?
Experiment 48. Carefully balance a good-sized light metal ball,
then put it under the receiver, and exhaust the air. The ball will now
be found to be heavier than the weight : why ? (See Art. 181.) For
this experiment a hollow metal ball is commonly used. Should there
be an opening into the ball ? Any light solid or liquid, such as a glass
1 The Magdeburg hemispheres were invented by Otto von Guericke,
the inventor of the air-pump. The hemispheres get their name from
the city in Germany where the inventor lived. He made a very large
pair, and in an exhibition before the Emperor of Germany it is said
that several horses were unable to pull them apart.
GASES.
109
bottle (should it be stoppered ?), may be thus weighed outside and then
inside the vacuum. Why ought the body weighed to be lighter (less
specific gravity) than
the weights used? Sup-
pose it were the same
as the weights ? Sup-
pose it were heavier ?
Experiment 49.
Unscrew the top of the
vacuum fountain ap-
paratus (Fig. 96), screw
it to the air-pump, and
exhaust the air. Turn
the stop-cock crosswise,
and screw it into its
base again. The pan
at the bottom is filled
with water, into which
a tube, running up the
stem, opens. If the stop-
cock be turned, the
water will rush up into
the glass vessel in a
fountain: why?
Experiment 50.
Fig. 97 shows a long,
air-tight glass tube con-
taining a feather and a
small coin. Turn the
tube upside down, and
the coin will fall quickly
to the other end, but
the feather will lag
slowly behind. Ex-
haust the air from the
tube, and try the same
thing. They will fall
together : why ? (Art.
181.)
187. S p r e n g e 1'S FIG. VS. SPRENGEL'S AIR-PDMP.
Air-Pump, The im-
perfections of the common air-pump have already been
mentioned. A very good one will leave y^Vir f tne a * r * n
the receiver. But Fig. 98 represents a much more perfect
kind of air-pump. The funnel A contains mercury. The
long, narrow glass tube cd opens into the funnel and dips
at the lower end into the mercury in the bottle B. The
receiver E, from which the air is to be exhausted, has air-
10
110
NATURAL PHILOSOPHY.
tight connections with the tube. The mercury running
down the tube from the funnel separates into drops, because
its velocity increases as it falls. Each drop is an air-tight
piston, and between the drops are nearly perfect vacuums.
As one of these vacuums comes to x, part of the air in R
rushes out to fill it, and that air is carried down into the
bottle B, where it comes to the surface as a bubble and
disappears. In this way the air is drawn from B until
almost a perfect vacuum is formed there. Under favorable
circumstances, this pump leaves only T>T(r J iinnr ^ tne a ^ r
in the receiver.
As the exhaustion goes on, the mercury stands higher
and higher in the tube, and finally is about 30 inches
above the spout B. (Why?) With no intervening air-
spaces, the opening x must therefore be more than 30 inches
above the spout B. The whole apparatus is commonly
about 6 feet high, and the upright tube is about T ^ of
an inch in diameter. The process is slow, especially if
the receiver be large. It is only
by this pump that the necessary
vacuum can be produced in the
electric lamp of the present day.
188. Air-Condenser, If the two
valves in the barrel of the air-
pump (Fig. 99) were turned the
other way, that is, if both opened
downward instead of upward, it
is clear that every stroke of the
piston would drive air into the
receiver. Such a piece of ap-
IJj paratus is called a condenser.
Draw a section of a condenser show-
ing the position of the two valves while
FIG. 99. THE CONDENSER. the piston is being raised. Draw an-
other showing them while it is being
pushed down. Can you think of any way in which a condenser could
be made with its piston solid, and having then a valve only at the
bottom ?
GASES.
Ill
189. Experiments with the Condenser. If the reservoir
be partially filled with water, and a tube runs from under
the surface of the water into the air, the water may be
forced out by compressing air above it. Many of the ex-
periments with the air-pump may be reversed with the
condenser. A foot-ball or bladder may be shrivelled.
(How ?) A thin cube of glass may be
crushed. The specific gravity of air
or any other gas can be best found by
compressing a considerable quantity of
it in a receiver and then weighing it.
(Art. 168.)
190. The Air-Brake. This very use-
ful invention consists of a powerful con-
"denser attached to a locomotive, and
working by steam. It is connected by
rubber tubes with a reservoir under
each car, and fills these reservoirs with
highly-compressed air. When the en-
gineer wishes to stop the train, he
moves a lever, which allows the com-
pressed air in the reservoir to rush into
a cylinder, also under the car, and, by
driving a piston along this cylinder,
it presses the brakes very strongly
against the wheels.
191. The Common Pump, Fig. 100
shows the common pump. It consists
of a tube (pump-stock), in which works
a piston having in it a valve opening upward. Opening
into the bottom of this there is a narrower tube, which
runs down into the water. At the top of this tube is
another valve, also opening upward. To show how it
works, suppose that no water is standing in the pump.
When the piston moves up from the bottom of the pump-
stock as its valve remains closed, it tends to form a vacuum
FIG. 100. THE COMMON
PUMP.
112 NATURAL PHILOSOPHY.
below it. The atmospheric pressure upon the surface of the
water in the well drives up water, and the air in the tube
above it, to fill this vacuum. When the piston descends, the
lower valve falls, and keeps there the air and water that
have been drawn up from below, and the valve in the piston
opens to allow the piston to pass through this air and water
in the pump-stock. The next stroke of the piston raises
the air and water above it to the spout, and the water rises
from the well as before to fill its place. And at each suc-
cessive stroke the pump-stock full of water is pumped out.
If the valves are tight, the tube and pump-stock are usually stand-
ing full of water, so that the latter begins to flow at the first upward
stroke.
192. Depth from which Water may be raised by the Com-
mon Pump. We have found that the atmosphere will sus*
tain a column of mercury 30 inches high ; and, as mercury
is about 13 times as heavy as water, the atmosphere will
sustain a column of water 13 } times 30 inches high, or
about 34 feet. Since the atmospheric pressure will raise
water 34 feet, if a pump were perfectly made it would
work as long as the upper valve was within that distance
from the bottom of the well. Practically, however, the
upper valve ought never (i.e., at the upper end of the
stroke) to be more than about 25 or 26 feet from the sur-
face of the water. 1 Water can be raised farther than that
by having the upper part of the pump-stock lengthened so
1 It was through the observation of this fact that Galileo (gal-i-
lee'o) (great Italian astronomer and philosopher, 1564-1642) first sug-
gested the true cause of water rising in a pump. It had formerly been
explained by saying that nature abhorred a vacuum and therefore the
water rose to fill the vacuum caused by the piston. The Grand Duke
of Tuscany wished to pump water from a depth of 40 or 50 feet, but
the pumps would not work. Galileo found that the water would rise
but 32 feet, and suggested that it was the weight of the atmosphere
that supported the water at that height. His pupil Torricelli (1608-
1647) afterwards discovered that the atmosphere would support 30
inches of mercury, as explained in Art. 170.
GASES.
113
as to bring the spout some distance above the upper end
of the stroke of the piston. The piston then lifts the
water above it to the spout.
FIQ. 101. A FORCE-PUMP.
FIG. 102. MODEL OF A
FORCE - PUMP WITH
AIR-CHAMBER.
193. The Force-Pump, To raise water higher than 26
feet, force-pumps are often used. Fig. 101 represents a
simple kind. The piston is solid. The up-stroke draws
the water from the well and fills the pump-stock with it.
The down-stroke closes the lower valve and forces the
water through the side-valve and up the pipe seen there.
194. Force-Pump with Air-Chamber. Sometimes force-
pumps are furnished with air-chambers to cause a con-
tinual flow of water. Fig. 102 shows a model of such a
pump. The water is forced up into the tube which branches
off to the left, and compresses the air there into the upper
h 10*
114
NATURAL PHILOSOPHY.
part. This presses upon the surface of the water and drives
it in a constant stream through
the small tube.
195. Rotary Pump. To
supply cities with water, to
empty mines, and wherever
large quantities of water must
\B be raised, rotary pumps are
often used. They are made
in many ways, one being
shown in Fig. 103. It is a
round iron box, in which four
paddles turn. These suck the
water up the lower tube and
drive it up the upper one.
196. Fire-Engine. Fig. 104
represents a common hand
fire-engine. It has two force-pumps, which drive the water
Fia. 103. ROTARY PUMP.
FIG. 104. HAND FIRE-ENGINE.
into an air-chamber between them, whence it is forced out
through the hose by the pressure of the compressed air.
GASES.
115
The water is usually supplied by being carried in buckets,
and the pumps are worked by several men. The steam
fire-engine is a powerful steam-pump, generally rotary,
which draws its water through a hose from some artificial
or natural reservoir, and drives it out with great force
through another hose.
197. The Siphon. If a tube open at both ends be bent,
as in Fig. 105, having one arm longer than the other, we
have a siphon. If this be filled with water, and then be
placed, as in the figure, with the short arm in a vessel of
FIG. 105. A SIPHON.
water, the water in the tube will, of course, tend through
gravity to flow down, and out of, both arms of the tube ;
but this it cannot do, because it would leave a vacuum
above. And as the long column, ef, is heavier than the
short one, dc, the water runs down the long arm, and that
in the vessel flows up the short arm (through the pressure
116
NATURAL PHILOSOPHY.
of the air upon the water in the vessel) to fill the vacuum
there, and in this way the vessel may be emptied of the
water.
198. Starting the Siphon. It is evident that the siphon
will not start itself. It may be filled by putting it under
water, and then both ends must be closed by the fingers
FIG. 106. A SIPHON WITH EXHAUST-TUBE.
until it is in position. Or it may be put in position empty
and filled by sucking at the end of the long arm. Where
this cannot be done, or is undesirable, the siphon can have
a suction-branch, as in Fig. 106.
Why is the end of the siphon kept closed by the finger in starting
it ? Will it be necessary to suck the long arm full before the siphon
will begin to run ?
199. Uses and Limitations of the Siphon. The siphon is often
used to empty vessels of liquids. It may be used to carry the water
from a spring over a low hill to a house or a barn which is below the
level of the spring.
The end of the tube from which the liquid flows must always be
below the surface of the liquid in the vessel. If the surface should
GASES.
117
be lowered until it is on the same level with the outlet, the flow
will stop. As atmospheric pressure will not raise water more than
FIG. 107.
FIG. 108. TANTALUS'S
CUP.
34 feet, if water is to be siphoned, the top
of the curve must not be more than 34
feet higher than the surface of the water.
200. Experiments with the Siphon.
Experiment 51. Fig. 107 represents
a vessel with a closely-fitting lid which
has two openings in it. Through a cork
fitting one of these openings runs a
siphon-tube. After being started, the
water in the vessel will flow, but will
stop when the other opening in the lid
is stopped by the finger : why ?
Experiment 52. Fig. 108 represents
the "cup of Tantalus." It will be noticed
that the handle is a siphon, the short arm
of which opens into the bottom of the
cup. When the cup is filled full, or
when it is tilted so as to bring the water
up to the highest part of the handle, the
water will begin to run, and will empty
the cup.
Fig. 109 shows how a self-acting foun-
tain can be made of the bottom of a
glass bottle, a cork, and two glass tubes.
A dandelion-stem will make a good
siphon. Try it.
FIG. 109. SELF-ACTING FOUNTAIN.
201. Intermittent Springs. These are springs which flow
only at intervals. They have been explained on the prin-
ciple of the siphon. Fig. 110 shows how this may be. If
a reservoir in the earth had such a siphon-shaped outlet as
is there shown, when it filled up to the bend of the outlet^
118
NATURAL PHILOSOPHY.
the water would run until the reservoir was emptied, and
then would cease running until filled up to the bend again.
% ~. ~ "91
FIG. 110. THE INTERMITTENT SPRING.
Exercises. 1. In Fig. 82 the mercury stands 90 inches higher in
the long tube than in the short one. If ab equals 6 inches, how
many inches of air are there below bl Ans. 1^ inches.
2. How many inches of mercury have been poured in to condense
this ? Ans. 99 inches.
3. If one column is 20 inches higher than the other, what is the
length of the air-column in the short arm ? Since the pressure is If,
or f as great as before, the air will occupy f as much space, or 3f
inches.
4. If one column is 10 inches higher than the other, what is the
length of the air-column in the short arm ? Ans. 4^ inches. What
if it is 45 inches higher ?
5. The specific gravity of mercury is 13.6, that of alcohol is .8 : how
high a column of alcohol will the atmosphere support? Ans. 42 feet
6 inches.
6. How high a column of sulphuric acid, whose specific gravity is
1.8, will the atmosphere support ?
7. A tumbler whose sides are vertical is inverted and pushed down,
into water until the air is condensed into the upper half of the
GASES. H9
tumbler : how deep is the tumbler ? Ans. 34 feet. Is it the bottom,
the middle, or the top of the tumbler that is 34 feet deep?
8. How deep must the tumbler be if the air is compressed into the
upper third of it ? Ans. 68 feet. How deep if it is compressed into
the upper fifth of the tumbler ?
9. How high will the barometer stand at a place 1800 feet above
the sea ?
10. Barometers are often marked FAIR opposite 30J inches, CHANGE
opposite 29J inches, RAIN opposite 28J inches, etc. If a person were
to buy such a barometer and take it to a place 900 feet above sea-
level, what would be the result? what if he lived in a place 1800 or
2700 feet above the sea ?
11. Explain how you fill your lungs with air.
12. How do you suck water through a tube?
13. Why will a liquid flow out of the spigot of a barrel so much
faster when the bung at the top is out ?
14. Why does water gurgle and flow so irregularly when poured
out of a bottle ?
15. Why will water flow through a funnel so much better when
the funnel is raised a little in the mouth of the bottle which you are
filling with water?
16. What part of the air is left in the receiver of an air-pump
when the mercury in the gauge is 3 inches higher on one side than on
the other ? Ans. T V When inch higher ?
17. What is the difference of heights in the gauge when j^^ of
the air is left in the receiver ?
18. A pair of Magdeburg hemispheres have a diameter of 3
inches. If the air were perfectly exhausted, what force would it
take to pull them apart ? Ans. 106 pounds.
19. Otto Guericke's hemispheres are said to have been 2 feet in di-
ameter. Had he been able to exhaust all the air, what force would
have been needed to pull them apart? It is sometimes said that
30 horses, 15 on each side, were unable to pull them apart. Can that
be true ?
20. If the inside diameter of a weight-lifter is 6 inches, what
weight will it lift, provided a perfect vacuum be produced ?
21. How heavy a stone will a perfect u sucker," 4 inches in diame-
ter, lift ?
22. What is the difference in the heights of the columns of the
air-pump gauge when, by using Sprengel's pump, only T.-jnrV.oinr of
the air is left in the receiver ? Ans. .00003 inch.
23. Bunsen's air-pump uses falling water as Sprengel's does falling
mercury : how long must the tube below x be ?
24. Denver, Col., is about 1 mile above sea-level : how high would a
perfect pump raise water there? Ans. 28 feet. (See foot-note, p. 98.)
25. If a certain pump will raise fresh water 25 feet, how high will
it raise salt water ?
26. The diameter of the piston of a pump is 2 inches, and the
height of the top of the water in the pump above the piston is 18
feet : what is the pressure upon the piston ?
27. What will be the pressure upon the piston in the last problem if
the diameter of the upper 10 feet of the column of water is 3 inches ?
120 NATURAL PHILOSOPHY.
CHAPTEE T.
SOUND.
SECTION I. THE CAUSE AND PHENOMENA OF SOUND.
202. Sound is a Vibration. All sound is caused by the
vibration of some body. When a violin-string is sounded,
the vibrations can be seen. If a tuning-fork be sounded,
and the fork be touched to the lips or teeth, the vibrations
can be felt.
Experiment 53. Fasten, with wax, a short bit of fine wire, or a
bristle, to the end of one prong of a tuning-fork. Sound it by striking
it against the table, and draw the end of "the wire gently over a piece
of smoked glass. The vibrations of the fork will trace a beautiful
wavy line on the glass.
FIG. 111. TUNING-FORK RECORDING ITS VIBRATIONS.
The word sound is used in two senses. It is sometimes used to de-
note the vibration of the sounding body, but is often er used to denote
the effect of this vibration upon an organ of hearing. Accordingly,
when the old question, "If a tree were to fall in a forest fifty miles
from any living being, would there be any sound?" is asked, the
answer depends upon which definition of sound is taken.
203. Sound usually brought to the Ear by Vibrations of
the Air. As sound is always caused by the vibrations of
some body at a distance from the ear, there must be some
way by which it is carried to the ear. This is almost
SOUND.
121
always done by vibrations of the air, as may be shown by
the following experiment.
Experiment 54. Set a small
clock, or a music-box, under the re-
ceiver of an air-pump, taking care
to put under the clock a number of
thicknesses of flannel. Exhaust the
air, and the ticking of the clock, or
the sound of the music-box, will
grow fainter and fainter, until it can
no longer be heard.
Fig. 112 shows a bell which can
be kept ringing by clock-work, and
is hung by cords in the receiver of
an air-pump, which is often used to
prove this fact. Here, as also above,
the experiment is more satisfactory
if, after the air is exhausted as far
as possible, the receiver be filled with
hydrogen and again pumped out.
Fig. 113 is a simpler piece of appa-
ratus to illustrate the same thing.
On the tops of high mountains
sounds are considerably fainter than
upon the surface of the earth : why ?
I
FIG. 112. BELL IN A VACUUM.
204. How Air conveys Sound. Suppose a tuning-fork be
sounded and held at one end of a tube,
as shown in Fig. 114. As the prong of
the fork flies out, it will drive the air that
is in front of it forward a little way and
compress it. This air will condense and
drive forward the air in front of it, and
so the condensation will be driven through
the tube. Any one particle of air moves
forward only a very little way, when it gives
its motion to the particle ahead of it, but the
condensation, or the wave, moves through the whole tube. Sound-
waves are just like water-waves, as described in Art. 158,
except that in sound-waves the particles of air move
F 11
FIG. 113. BELL IN A
VACUUM.
122
NATURAL PHILOSOPHY.
lengthwise, but in water-waves the particles of water move
up and down.
FIG. 114. SOUND-WAVES IN A TUBE.
The sound-wave is not a puff or blast of air, such as you blow
from your mouth. Tyndall 1 has shown this very neatly by the fol-
lowing experiment.
Experiment 55. Fill the long tube shown in the figure with smoke
from burning paper, set a lighted candle at one end, and make a loud
noise, by clapping two blocks together, or otherwise, at the other end.
The flame will be put out, yet no blast of air rushes through the
tube, for the smoke has not been driven out.
FIG 115.
In the open air these condensations move in all direc-
tions. Each one must therefore be a spherical shell, grow-
ing larger as it moves farther in every direction from where
the sound was made. Following every condensation there
must of course be a rarefaction. And so these successive
waves of condensation and rarefaction are constantly given
out in all directions as long as the sounding body vibrates.
1 John Tyndall (1820-), an English natural philosopher, and one
of the greatest of living scientists. " Tyndall on Sound" is the best
book on this subject in the English language for most readers and
students.
SOUND. 123
205. Velocity of Sound in the Air. Every one who uses
this book has probably noticed that when a whistle, some
distance off, is blown, the escaping steam can be seen a
little time before the sound can be heard, and that the
sound keeps coming just as long after the steam can be seen
to have stopped. And when a wood-chopper is working at
a considerable distance, you hear the blow after you see
it. As we shall presently learn, light travels so exceedingly
fast that we see the steam immediately after it escapes, so
that the difference between the times of seeing it and hear-
ing the whistle is the time that it has taken the sound to
travel from the whistle to us.
The velocity of sound through the air has been very
carefully measured. It is found to vary according to the
temperature. When the temperature of air is at the
freezing-point of water, 32 degrees in our common ther-
mometers (Fahrenheit's), sound travels through it 1090
feet per second. And its speed is about 1 foot more per
second for every degree that the thermometer is above 32.
How fast does sound travel through the air when the temperature
is 70 ?
206. Solids and Liquids may also convey Sound.
Experiment 56. Get a companion to scratch one end of a long
piece of wood (a board in the floor or a sound fence-rail will do)
lightly with a pin. By putting your ear to the other end
you can hear the scratch distinctly, although you cannot
hear it through the air when you lift your ear from the
wood. Try the same thing with a long bar of iron.
Experiment 57. Get a companion to strike two stones
together 10 feet from you, and notice how loud it sounds.
Hold your head, or one ear, under water while he strikes
the stones together under the water, at the same distance,
and notice how much louder it sounds.
Sound travels faster and farther through solids and liquids
than through the air. Through iron it travels about 16,000 FIG. 116.
feet per second, through most kinds of wood almost as fast, scope! "
and through water about 5000 feet per second. The stetho-
scope is a small tube of wood or metal widening out at one end, whic'n
is much used by physicians. The physician places the wide end upon
124 NATURAL PHILOSOPHY.
his patient's chest, and puts his ear to the other end. The faint sounds
made by the organs in the chest are distinctly carried to his ear
through the stethoscope, and he can judge of their condition. The
Indians are said to put their ears to the ground and thus hear the ap-
proach of their enemies long before it could be heard through the air.
The ordinary string telephone which boys make by knocking the
bottoms out of two fruit-cans, stretching parchment tightly over one
end of each, and joining these parchments with a stretched string,
will convey sound quite a distance. A whisper in one can easily be
heard in the other across the street. And when carefully made and
very fine copper wire is used instead of string, conversation can be
carried on through them for a quarter of a mile or farther.
Experiment 58. Suspend a poker by two strings, and thrust the
fingers holding the poker into your ears. Then swing the poker
against a piece of wood, and you will be surprised at the sound.
207. Loudness of Sound, Tap a table gently, and a faint
sound is produced ; strike it hard, and a loud sound is pro-
duced ; or, better, pull a violin-string a very little to one
side, and it sounds faintly ; pull it strongly to one side, and
it sounds loud. Short vibrations of the sounding body pro-
duce faint sounds, long vibrations produce loud ones. Short
vibrations of the sounding body make short vibrations of
the particles of air, and longer vibrations of the body make
longer vibrations of the particles of air. Hence although
each particle of air in a sound-wave moves only a very short
distance forward and backward, yet it makes a longer
swing when conveying a loud sound than when conveying
a faint one.
208. Loudness of Sound affected by Distance. Common
experience teaches us that all sounds grow fainter as they
get farther from the sounding body, and finally become too
faint to be heard. But if, instead of being allowed to
spread in every direction, the sound be confined to a narrow
tube, it is carried much farther. Hence speaking-tubes are
often found in large buildings so arranged that a whisper
into one end of the tube can be heard at the other end in the
farthest corner of the building. Speaking-trumpets are much
used at sea to enable the voice of the officer in command
SOUND. 125
to be heard better and farther in any one direction. They
seem to guide the sound of the voice in one direction, so
FIG. 117. SPEAKING-TRUMPET.
that it is louder and goes farther than if allowed to spread.
Ear-trumpets are funnel-shaped instruments that
collect all the sound that enters the mouth of the
funnel and concentrate it into a small opening at
the other end of the ear-trumpet. By putting
the small end to the ear, partially deaf persons
can hear better.
If sound moves through the air unobstructed in all di-
rections, and if the air is uniform, or homogeneous, the
loudness must vary inversely as the square of the distance
from the sounding body. Twice as far off the sound would
be .one-fourth as loud, tbree times as far off one-ninth as
loud, etc. This is because at twice the distance from the
sounding body the air in a hollow shell or surface of a sphere of twice
the former radius is vibrating. But surfaces of spheres increase ac-
cording to the squares of the radii ; therefore the sound is spread out
over four times as much surface, and must be one-fourth as loud at
any one place.
209. Conditions of the Atmosphere as affecting Sound.
Although sound travels many times faster than the
strongest wind, yet it can often be heard three or four
times as far with the wind as against it. The cause is not
certainly known.
It was formerly thought that rain, snow, fog, etc., ob-
structed sound ; but Tyndall has recently shown that they
have no effect whatever upon the transmission of sound.
The same observer has shown the existence of acoustic
clouds in the atmosphere. These are masses of air differing
from the surrounding air in temperature, or in the amount of
11*
126 NATURAL PHILOSOPHY.
moisture they contain. . They have no connection with or-
dinary clouds, they are entirely invisible, and the air may
be full of them upon the clearest day. Yet they obstruct
and reflect sound very much. It is to the reflections from
these acoustic clouds that the rolling of thunder seems to
be mainly due. And probably the fact that noises are heard
farther and more distinctly by night than by day is partly
due to there being fewer acoustic clouds formed by night
than by day, and partly also to the stillness of the night. 1
210. Reflection of Sound. When sound-waves strike a
wall or other obstruction, they rebound or are reflected,
and the angle of reflection is equal to the angle of inci-
dence.
Fig. 119 illustrates an experiment in the reflection of sound. Two
concave metal mirrors are placed facing each other and so far apart
that the ticking of a watch could not be heard from one to the other.
Then, as shown in the figure, a watch is hung in front of one so that
the sound-vibrations are reflected out from the mirror in a straight
line to the other one, which concentrates them so that if the ear is
placed there, or if a short speaking-tube runs from there to the ear,
the ticking of the watch can be distinctly heard.
211. Whispering-Galleries. In some large circular build-
ings it is found that low whispers spoken near the wall on
one side of the building can be heard distinctly at the op-
posite side. The sound seems to be reflected repeatedly
until it reaches the opposite side, when it is so concen-
trated from all directions that it is distinctly heard. The
gallery in the dome of St. Paul's Cathedral in London is a
famous whispering-gallery. The dome in the Capitol at
Washington is another.
212. Echoes. When the reflecting surface is near the
source of the sound, as the walls of an ordinary room in
1 The writer's own observations leave no doubt in his mind that
the popular notion that distant sounds can be heard more distinctly
before a storm is correct. Probably at such a time the air is homo-
geneous and free from these acoustic clouds ; but some instances are
not easily explained in this way.
SOUND.
127
which a sound is made, the reflection follows the sound
itself so closely that it cannot be distinguished from it. It
FIG. 119. CONCENTRATION OF REFLECTED SOUND.
may, however, modify one's voice in some way and give a
peculiar resonance to the room. But when the reflecting
FIG. 120. REFRACTION OF SOUND.
surface is fifty feet or more away, the reflection can be heard
after the sound ceases, and is called an echo.
128 NATURAL PHILOSOPHY.
Between two walls, or between cliffs, and in like places, echoes are
often repeated many times by being reflected from side to side. Large
halls sometimes have an echo that is very annoying to both the speaker
and his hearers. In such cases the echo is generally less when the
hall is filled with people, and especially so if the seats rise towards
the back of the hall, or if there is a gallery there.
213. Refraction of Sound. Fig. 120 shows how a faint
sound may be concentrated so as to be heard farther oif
than it could otherwise be heard. B is a small balloon filled
with some gas heavier than air, as carbonic acid. The waves
of sound are bent around, or refracted, by the heavy gas
and concentrated at one point. If the ear is placed there,
or if a funnel is placed there to convey the sound to the
ear, the ticking of the watch may be distinctly heard. This
refraction of sound is like the concentration of the sun's
heat with a burning-glass. In light it is a very important
subject, and will be fully taken up there.
FIG. 121. EDISON'S PHONOGRAPH.
214. The Phonograph. Fig. 121 represents a phonograph, a re-
markable talking-machine recently invented by Mr. Edison. 1 4 is a
brass cylinder into which is cut a continuous groove, winding around
it from one end to the other. When the handle 1 is turned, the screw-
thread, seen under 7, moves the cylinder slowly along to the left
1 Thomas A. Edison (1847-), a famous American inventor, who
lives at Menlo Park, New Jersey.
SOUND. 129
while it is revolving. Above 4 is the mouth-piece, the bottom of
which is covered with a thin elastic metal plate. From the under
side of this plate a short needle runs down. To use the phonograph,
a piece of tin-foil is wrapped tightly around the brass cylinder, and the
handle 6 is pushed down upon the screw-head 5 and held there. This
presses the needle down upon the tin-foil. If the handle is turned as
the cylinder ^revolves and moves to the left at the same time, the
needle pushes the tin-foil down into the groove beneath it, and thus
makes a shallow spiral groove in the tin-foil. But if you talk into
the mouth-piece the sound-waves will make the elastic plate vibrate,
and the needle, being attached to it, will also vibrate up and down,
and will make successive dots and dashes in the bottom of the groove
in the tin-foil. If we were to take the tin-foil off the cylinder and
examine the bottom of the groove with a microscope, we should find
a peculiar indentation for every pulse of the sound-wave. But, in-
stead of taking the foil off the cylinder, let us raise 6 and run the
cylinder back to the starting-place. If the needle be now pressed
down into the groove and the handle be turned as it was when we
were talking to it, the indentations there will cause the needle to
vibrate up and down, precisely as it vibrated when it caused these
indentations, and the needle will vibrate the plate, just as the plate at
first vibrated the needle, and hence cause it to send out into the air
the same vibrations or sounds as were driven against it when you
talked to it. In this way the phonograph repeats the words said to it,
as well as laughter, crying, and sounds of any kind. But, as its voice
is feebler than yours, it needs for a speaking-trumpet a cone of paper,
in order that it may be heard over a large room.
SECTION II.-MUSICAL SOUND.
215. Noise and Musical Sound. When the sound-vibra-
tions are irregular, no two at the same distance apart, we
hear a noise, such as would be made by the crash of a pane
of glass. But if the waves of sound follow one another at
regular intervals, we hear a musical sound, such as is made
by the prong of a tuning-fork or a violin-string, which vi-
brates regularly, and produces sound-waves all at the same
distance apart. No matter how the vibrations are caused,
if they are at regular intervals and rapid enough, they will
produce a musical sound. Taps on a table, the striking of
a stick upon the pales of a fence or the teeth of a wheel,
130 NATURAL PHILOSOPHY.
the puffs of a locomotive, if regular and rapid enough to
blend together, .produce a sound as truly musical as the
voice of the best singer, or a note of a flute, though it
may not be as pleasant.
If a number of boys should run across a room all keeping step, the
noise of their steps would be heard at regular intervals ; and if they
could run so fast that the sounds from their steps would blend into
one continuous sound, they would make a musical note. But if the
same boys were to run back just as fast without keeping step, their
steps would make a noise.
216. Pitch of Sounds. Experiment 59. Kun the back of a
knife over the milled edge 1 of a coin. You will produce a musical
sound. Eun the knife over the edge faster, and your sound will be
higher ; run it still faster, and the pitch will be still higher.
Experiment 60. Wind a string around the axis of the wheel (Fig.
122), and pull it so as to revolve the wheel rapidly.
Hold a card to the teeth, and a musical sound is pro-
duced. Revolve the wheel faster and faster, the pitch
becomes higher and higher.
These experiments show that the pitch of
sounds depends upon the rapidity of the vibra-
tions. Their loudness depends, as has been
said, upon the extent of the vibration of the
sounding body, and, therefore, of the parti-
cles of air; their character, such as distin-
guishes the sound of a violin from that of a piano or a
human voice, is due to other causes ; but the pitch of
sounds is due solely to the number of vibrations per
second.
217. The Siren. The number of vibrations which pro-
duce any given pitch of sound is best found by means of a
piece of apparatus called a siren, which makes a musical
sound by a succession of puffs of air following one another
1 If you notice, you will see that all the gold and silver coins now
made in the United States have their edges finely notched. They are
said to be milled. Perhaps you can think or find out why they are
so made.
SOUND.
131
very quickly. Fig. 124 shows a siren cut open, so that its
mechanism may be understood. Air is forced up through
the tube below from a pair of bellows (not shown in the
figure) into the air-chamber seen open. Leading up from
this is a small opening, and above is a wheel made to re-
volve, and having a circle of holes in it. When one of the
holes in the wheel comes over the hole in the top of the
air-chamber, the air forced in by the bellows can puff out;
FIG. 123. THE SIREN.
FIG. 124. THE SIREN, INSIDE VIEW.
when the solid part of the wheel is there, it cannot. So, as
the wheel turns, a succession of puffs is heard as the holes
in the wheel pass, one after another, over the hole leading
up from the air-chamber. If the wheel turns fast enough,
the separate puffs cannot be distinguished from one another,
but are blended into one sound, rising higher in pitch as
the wheel goes faster and therefore produces more puffs
per second. By means of the cog-wheels seen at the top
of the figure the wheel registers its revolutions, and the
132 NATURAL PHILOSOPHY
hands on the dials (Fig. 123) show how many revolutions
the wheel makes per second. This multiplied by the num-
ber of holes in the wheel gives the number of puffs, and
therefore the number of sound-waves or vibrations, per
second. It will be noticed in Fig. 124 that the opening 1
leading upward from the air-chamber slants. This forces
the air obliquely against the wheel and causes it to revolve.
This ingenious little instrument will produce a note of
any pitch, from the lowest to the highest, and tell us the
number of vibrations it makes to produce it. And if a note
be sounded on any musical instrument, the pitch of the
siren may be raised (by working the bellows harder) until
our ears tell us that its pitch is the same as that of the
musical instrument; then the number of vibrations per
second of the siren is the number that the instrument is
making. In this way we can count the vibrations which
the human voice, or any other musical sound of any pitch,
is producing.
218. The Limits of Human Hearing, It is found that
when the puifs of the siren are fewer than 16 per second
they are heard as separate puifs, but when they reach
about that number they cannot be separately heard, and
make a continuous and very low note. The lower limit
of sounds, then, is about 16 vibrations per second, which
make a sound of the lowest possible pitch. When the
puifs reach about 38,000 per second their exceedingly
shrill piercing note suddenly ceases, and though the wheel
can be seen to be revolving, and, as the hands show, faster
than ever, nothing can be heard. We have reached the
upper limit of human hearing. The ear can hear nothing
when the vibrations are more than about 38,000 per second.
1 There is really a circle of holes in the top of the air-chamber, cor-
responding exactly with the holes in the wheel, and when the air
puifs through one hole it puffs through all. Only one puff is heard,
but it is stronger, and the wheel can be driven around much faster,
than if there were but one upward opening.
SOUND. 133
The pitch of the keys of our ordinary pianos ranges from 27 to 3482
vibrations 1 per second, while the middle C-string vibrates 1 272 times
per second. Human voices from the deepest bass of men to the high-
est treble of women lie between 80 and 1000 vibrations per second.
The upper limit of hearing varies in different persons, and very
curious results often follow from this. u Nothing can be more sur-
prising," says Sir John Herschel, 2 " than to see two persons, neither
of them deaf, the one complaining of the penetrating shrillness of a
sound, while the other maintains there is no sound at all." And
Tyndall notes that in crossing the Alps with a friend, "the grass at
each side.of the path swarmed with insects, which to me rent the air
with their shrill chirruping. My friend heard nothing of this, the
insect-music lying beyond his limit of audition."
219. Lengths of Sound-Waves. If the temperature of
the air is 62, sound travels through it about 1120 feet per
second. And if a tuning-fork that vibrates 256 times per
second is sounded, at the end of 1 second the first wave of
sound must be 1120 feet from the fork, and the 256th has
just left the fork, and so scattered through the 1120 feet
there are 256 waves. As the tuning-fork gives out a musi-
cal sound, the waves must be at equal distances from one
another, and, therefore, dividing 1120 feet by 256 gives us
the distance between any two successive condensations, or
the length of a wave. It is 4 feet 4J inches.
When the temperature of the air is 82, a man is speaking in a
pitch that produces 120 vibrations per second : what is the length of
one of the sound-waves? Ans. 9 feet.
At the same temperature a woman's voice is producing 300 vibra-
tions per second : what is the length of one of the sound-waves that
she produces?
SECTION III. MUSICAL INSTRUMENTS.
220. The Sonometer. The piece of apparatus most com-
monly used in experimenting with musical sounds is the
1 The vibrations meant here and elsewhere are from one side of the
swing across to the other, and back again, sometimes called double
vibrations.
2 A famous English astronomer and scientist, born 1792, died 1871,
son of the great astronomer Sir William Herschel.
12
134 NATURAL PHILOSOPHY.
sonometer. It is a long wooden box, over which one or
more wires are stretched by weights. The wire rests on
wooden bridges at the ends of the box, and between them
is a bridge which can be moved anywhere along the scale
FIG. 125. SONOMETER.
of inches which is marked off under the wire. If the
stretched wire be pulled aside 'with the thumb and finger,
or if it be bowed with a violin-bow, a clear musical sound
will be produced that lasts a short time.
221. The Laws of Vibrating Strings. If the wire be
shortened, by moving the movable bridge, so that half of it
vibrates, it is found to make twice as many vibrations per
second as the whole wire. If one-third of it is vibrated,
it will vibrate three times as fast as the whole ; if one-fourth,
four times as fast, 1 etc. Hence,
222. The First Law. The number of vibrations of a string
is inversely proportional to its length.
Without using the movable bridge, put more weights on
the string until they are four times as heavy as at first,
the string will vibrate twice as fast as at first ; with nine
times as much weight it will vibrate three times as fast, etc.
Hence,
1 The number of vibrations can be counted by bringing the siren
to the same pitch and counting its vibrations ; or any one even slightly
acquainted with music can tell the relative number of vibrations by
the pitch, as will be explained in the next section.
SOUND. 135
223. The Second Law. The number of vibrations of a
string is directly proportional to the square root of its tension.
If a second wire of the same material, but weighing four
times as much to the yard, be stretched beside the first one,
and the stretching-weights and the lengths are the same, it
will vibrate one-half as fast ; one nine times as heavy will
vibrate one-third as fast, etc. Hence,
224. The Third Law. The number of vibrations of a string
is inversely proportional to the square root of its weight.
The Pitch of Vibrating Strings. As the pitch of musical
sound depends solely upon the number of vibrations per
second, the laws of vibration are also the laws of pitch.
Experiment 61. Vary the length of the wire, the stretching-
weight, and the weight of the wire on the sonometer, and notice the
changes in pitch.
Experiment 62. Lift the lid of a piano, sound the highest key,
and notice that the shortest wire 1 is struck. Strike the lowest key,
the longest wire is struck : which law ? Repeat the law to yourself.
Notice also that the wires struck by the higher keys are very thin and
light, while those struck by the lower keys are much heavier and
have extra wire wrapped around them to make them heavier still :
why ? Repeat the law.
If you cannot play the violin yourself, watch some one tuning and
playing one. Why are some of the strings heavier than others?
Which have the highest pitch ? What is peculiar about the one that
has the lowest pitch ?
What eifect does it have upon the pitch to tighten up the strings in
tuning the instrument? Repeat the law.
Why does the player touch the strings in diiferent places while
playing? Explain this fully by referring to the law.
225. Sympathetic Vibrations. Experiment 64. Sound a
tuning-fork, and set the end of the handle on a table or against the
panel of a door. It sounds very much louder than in the air. The
vibrations of the fork have set the wood to vibrating too, and it sounds
out louder than the fork.
The vibrations of the wood thus caused are called sym-
pathetic vibrations. They are very commonly produced,
and are of great importance in music and sounds generally.
1 In most pianos there are two wires for each key, both, of course,
of the same length. In some of the better modern pianos there are
three for each key.
136 NATURAL PHILOSOPHY.
For experimentation, tuning-forks are very frequently
mounted upon sounding-boxes (Fig. 126), which strengthen
the sound as the table did. It is
not necessary that the sounding
body actually touch another to set
it to vibrating. It may be done by
the sound-waves in the air.
Experiment 64. Kaise the lid of a
piano, lift the dampers from the wires
by putting your foot on the right pedal,
and make a sound over the strings with
the voice. The sound-waves set in mo-
tion by your voice cause the sounding
parts of the piano to vibrate, and when
your voice stops you hear the piano
sounding in exactly the same pitch as
FIQ. 126. TUNING-FORK ON your voice had.
Experiment 65. If two tuning-forks
of the same pitch, mounted on sounding-
boxes, be placed side by side, and one of them be sounded, the other
will take up the sound, and may be heard after the first is silenced.
But if the pitch of one of them be lowered by sticking a small lump
of wax upon one of its prongs, the sounding of the other will not set
this one to vibrating.
The strings of a violin would give out very feeble sounds
if they were not reinforced by the sympathetic vibrations
of the wooden shell below them. Underneath the strings
of a piano you may see a thin board, the sounding-board.
Without that the sound of the piano would be insignificant.
Experiment 66. Touch the handle of a vibrating tuning-fork to
the body of a violin or to the sounding-board of a piano, and notice
how it sounds out. It will keep on sounding after you have taken
away and silenced your fork. Do not fail to notice that it gives out
the same pitch as the fork.
Experiment 67. Stretch your sonometer wire, or one like it, across
an open door- way, and notice the comparative feebleness of the sound.
You see why you have a wooden box under your wire.
Professor Tyndall illustrated this, as well as the conduction of
sound by solids, very beautifully in his lectures in London. On the
second floor below his lecture-room he placed a piano. A pine rod
rested on the sounding-board of the piano and came up through the
floors in front of his desk. When the piano was played, the rod was
of course set in vibration, but too feebly to be heard. When, how-
SOUND. 137
ever, Professor Tyndall laid a violin on the end of the rod, the vibra-
tions of the rod set the wood of the violin to vibrating, and it repro-
duced the music of the piano so that it could be heard all over the
room. A guitar, a harp, and even a thin flat board, when put in the
place of the violin, reproduced every note of the piano.
226. Resonance. This capability of being set to vibrating
by sound-waves and of giving forth sound of the same
pitch is called resonance. Different bodies possess it in
various degrees according to their material and their shape.
Experiment 68. Sound the tuning-fork and touch the end of the
handle against your slate ; a window-pane ; a book, open and shut ; a
stone or brick wall ; a lath-and-plaster partition ; iron ; stone ; the
blackboard-pointer ; your hand, etc. Notice the differences in inten-
sity, and whether they are due to the material or the shape of the body.
Eesonance may also be caused by sympathetic vibrations
of a body of air, and it is to such vibrations that the term
is usually applied.
Experiment 69. Fix the mouth as if about to say e, and bring a
sounding tuning-fork close before it. Quickly change the mouth as
if to say o, and notice that the sound is strengthened. The latter
shape gave a more resonant body of air, hence the stronger sound.
Experiment 70. (Fig. 127.) Take a deep glass jar and hold the
sounding tuning-fork over its mouth. The sound of the fork will
probably be only slightly strengthened. Pour water into the jar
quietly ; the resonance increases as the air-column shortens, until
presently it becomes very strong. "We have found the length of air-
column which is best vibrated by the waves from our fork. If more
water be poured in, the resonance decreases again.
Let us see if we cannot learn why one particular length of the air-
column makes the resonance greatest. Fig. 128 represents the fork
vibrating over the jar. As the prong moves from its position of rest
down to 5, the air is condensed below it, and the condensation moves
down to the bottom of the jar (or to the surface of the water) and is
reflected back again. In order that the vibrations of the air should
fit those of the fork, the column of air ought to be long enough to
allow this condensation (after reflection) to reach the prong again
just as the prong reaches the middle of the vibration ; or while the
prong is making an excursion to one side and back to the middle
again, which is half a vibration, the condensation must travel twice
the length of the air-column. In swinging up from its middle posi-
tion the prong produces a rarefaction, which must also travel to the
bottom of the column and back again while the prong is making the
12*
138
NATURAL PHILOSOPHY.
upper half of its vibration. It is clear that if the vibrations of the
air-column did not thus fit those of the fork, they would interfere
with one another or with the fork, and thus be weakened. When the
vibrations of two bodies fit together, as do those of the fork and the
column of air when the resonance is greatest, they are said to be
synchronous. 1 Since a pulse must pass along the air-column four
times during one complete vibration of the fork, the tube ought to be
one-fourth the length of a sound-wave of that pitch. If the depth
of the air-column which sounds loudest for a fork vibrating 256 times
per second be measured, it will be found to be about 13 inches deep,
* FIG. 127.
and we have found in Art. 219 that a fork making 256 vibrations per
second sends out waves 52 inches long, which very accurately con-
firms our reasoning.
Fig. 129 represents a piece of apparatus often used to illustrate
resonance. It consists of a bell, best sounded by drawing a violin-
bow across its edge, and beside it a tube with a movable bottom that
has been adjusted to the right depth for the bell. While the tube is
1 Pronounced sink'ro-nus ; derived from the Greek, and meaning
happening at the same time, or simultaneous.
SOUND. 139
at some distance from the bell the latter sounds feeble, but when we
slide the tube up close to it the bell sounds surprisingly strong.
Move the tube back and forth,
and notice the changes.
The murmuring sound heard
in a hollow shell when placed
close to the ear is due to reso-
nance. Tyndall says, " Chil-
dren think they hear in it the
sound of the sea. The noise
is really due to the reinforce-
ment of the feeble sounds with
which even the stillest air is Fia. 129.
pervaded, and also in part to
the noise produced by the pressure of the shell against the ear itself."
Questions. When the air has a temperature of 62, what is the
length of the tube that will resound best to a fork vibrating 480
times per second? Ans. 7 inches. What to one vibrating 280 times
per second ?
Sound travels nearly four times as fast in hydrogen as in air.
Would a column of hydrogen have to be longer or shorter than a
column of air to be synchronous with a certain tuning-fork ?
227. The Two Classes of Musical Instruments. Most of
the musical instruments are either stringed instruments or
wind instruments. The piano and violin are the most
common stringed instruments. The music of all of this
class of instruments is made by the vibrations of strings,
generally reinforced by the sympathetic vibrations of sound-
ing-boards. In wind instruments tubes full of air are in
some way set to vibrating, and these bodies of air give out
the sounds. Pipe- and cabinet-organs, flutes, horns of all
kinds, are wind instruments.
228. Interference of Sound. We have learned (Art. 159)
that in water-waves, when the highest part of one wave
meets the lowest part of another of the same size, the
two waves neutralize each other and produce smooth
water. In the same way, when the condensed part of one
sound-wave meets the rarefied part of another, silence is
produced.
140
NATURAL PHILOSOPHY.
\
Experiment 71. Sound a tuning-fork, hold it upright a short dis-
tance from the ear, and roll it slowly around between the thumb and
the finger. Its sound will grow fainter, almost or entirely die out,
then grow strong again, and so on as it continues sounding.
Fig. 130, which rep-
resents the ends of the
fork, will help to make
the cause of this clear.
When the prongs are
moving outward, there
are condensations at a
and b. But, as the air
will rush in from the
sides to fill the partial
vacuum caused by the
prongs, there will be
rarefactions at c and d.
Along the dotted lines
the condensations and
rarefactions meet and
destroy one another-
These are the lines of silence. When the prongs move back again,
they will drive the air out at the sides and cause condensations at c
and d, while at a and b there will be rarefactions, and there will be
the same interference along the dotted lines as before.
In the experiment
just described, the fork
must be held close to
the ear ; but by rein-
forcing the sound of
the fork with a reso-
nating -jar it may be
heard all over a room.
If the vibrating fork
be slowly rotated as it
is held over the jar, the
alternations of loud
sounds and silence will
be very striking. If the
fork be held in the po-
Fio. 130. INTERFERENCE OF SOUND, SHOWN WITH
A TUNING-FORK.
Fio. 131.
sition of silence, and a
pasteboard tube be slipped over one prong, as shown in Fig. 131, the
SOUND.
141
sound will swell out as loud as ever. The vibrations of the un-
covered prong are protected from the vibrations of the other, and are
no longer quenched.
229. How the Vibrations of the Air-Columns are excited
in Wind-instruments. Fig. 132 shows a complete and a
sectional view of an organ-pipe from
a pipe-organ or large church-organ.
The air is forced up from below by
a bellows, and, rushing against the
sharp edge of an opening in the pipe,
is thrown into vibrations, which com-
municate themselves to the column
of air in the pipe. It is much like
an ordinary willow whistle. In a
cabinet-organ the air is set in motion
by the vibration of reeds. A reed is
a strip of brass, fastened only at one
end, and arranged so as to vibrate
in an opening which it almost fills.
There is a reed of a different pitch
for every key, and pressing down
that key opens the way for the air
to pass from the bellows to its reed.
The reed is made to vibrate by
forcing air from a bellows through
the opening around the reed. The
vibration of the reed sets the air
about it in motion. The melodeon.
which has been almost superseded
by the cabinet-organ, also produces its music by reeds of
this kind, and in a very similar way. (Fig. 133.) The
accordion is almost literally a hand cabinet-organ, with
bellows and reeds. The common mouth-organ is a reed
instrument, and its reeds can easily be seen.
Experiment 72. Take a piece of wheat- or rye-straw, and slit a
tongue in it down to a joint, as shown in Fig. 134. This tongue is a
reed, and the whole is a simple reed instrument. Blow into the open
FIG. 132. ORGAN-PIPES.
142
NATURAL PHILOSOPHY.
end, and note the pitch. Cut an inch or two off the open end and
blow again ; the pitch is higher. Cut off another piece ; the pitch is
FIG. 133. CABINET-ORGAN KEEDS.
still higher. Careful experiments show that, so far as length is con-
cerned, the law of the sound-vibrations of a column of air is the same
as those of a string : the number of vibrations of a column of air is
inversely proportional to its length.
FIG. 134. REED MADE or WHEAT-STRAW.
The clarionet has a wooden reed in the mouth-piece.
The flute and the fife are played by blowing against the
sharp edge of an opening in the side
of the tube. The vibrations are
caused very much in the same way
as in the pipe-organ, and in the same
way as when one whistles in a key.
In a cornet or a horn the lips
of the player, pressed against the
mouth-piece, act as reeds.
230. The Human Voice, The
voice is produced in the upper part
of the windpipe: the "Adam's
FIG. 135.-THE VOCAL CORDS, apple" marks the place. Fig. 135
shows the vocal apparatus as looked
down upon by means of a laryngoscope. 1 o is a slit through
1 Pronounced la-ring'go-skop. A pair of mirrors so arranged as to
show this part of the throat.
SOUND. 143
which the air passes to and from the lungs. On either side
of this is a membrane, v, v, projecting from the sides of the
windpipe. These membranes are called the vocal cords, al-
though they are not cords at all. In ordinary breathing
these cords are loose and close to the sides of the windpipe,
leaving a wide opening between them. But when we wish
to make sounds, they are, by muscular action, stretched
tight and brought close together, so as to leave only a
narrow slit between them. The air from the lungs passing
between them sets them in vibration, and their vibrations
produce the sounds of the voice, just as the reeds of a
cabinet-organ produce sound. The human voice is a reed
wind-instrument.
The vocal cords can only make sounds of different pitch
and loudness. The resonance of the cavity of the mouth
and nose, varying with its shape, "changes the sounds of the
vocal cords into the distinct vowels and consonants. The
pitch of one's voice depends upon the length and thickness
of the vocal cords. The ordinary tones of women's voices
produce more than twice as many vibrations per second as
those of men's voices (Art. 218).
Experiment 73. Notice that women or girls, and boys whose voices
have not changed, show no Adam's apple in the neck, but that it is
prominent in men , and especially in men with bass voices : why is this ?
Experiment 74. Get from a butcher the upper part of the wind-
pipe of a hog or other slaughtered animal, cut it open from front to
back, and examine the vocal cords. They are very much like yours.
You will see what will look like two pairs of cords. The lower ones
are the true vocal cords ; the upper ones perhaps serve to modify the
sounds which the lower ones alone produce.
231. Vibrations of Strings in Parts. Experiment 75. Touch
the middle of the sonometer wire with your finger, or with a feather,
and draw the bow across the middle of one half. The middle point
which was held by the feather is stationary, but each half of the
wire is vibrating. Set a rider, made by folding a bit of paper into
the shape of a V, upon the middle of either half, it is thrown off.
Set it upon the middle of the wire, it stays there : why ?
Experiment 76. Again, touch the wire at one-third the distance
from one end, and draw the bow across the middle of one third. The
wire will vibrate in thirds. Test the points of greatest vibration and
of no vibration with the riders. In the same way the wire may be
made to vibrate in fourths, fifths, etc.
144
NATURAL PHILOSOPHY.
The parts of the wire which we have made to vibrate
are called segments. The points between the segments,
where there was no motion, are the nodes. When a string
is thus vibrating in parts only, its pitch is higher than if
Fio. 136. STRING VIBRATING IN HALVES.
it were vibrating as a whole, for, according to the first law
of vibrating strings, when it vibrates in halves each seg-
ment vibrates twice as fast as the whole string would ; when
in thirds, each segment vibrates three times as fast, etc.
When a string vibrates in parts, the segments are always
FIG. 137. STRING VIBRATING IN THIRDS.
equal; each is an exact division of the whole string. And
again, when a string vibrates in parts, any two consecutive
parts are always moving in opposite directions. Thus, in Fig.
136 ; while one half moves up the other half is coming down ;
SOUND. 145
and in Fig. 137 the two end segments are swinging in one
direction while the middle one swings in the other.
232. A String may vibrate in Parts and as a Whole at
the Same Time, If the wire of the sonometer be plucked
near one end, it will vibrate in parts and as a whole at the
same time. Fig. 138 shows a string thus vibrating as a
FIG. 138. STRING VIBRATING AS A WHOLE AND IN HALVES.
whole and in halves. The middle arrows show the direc-
tion of the whole string, the others show the smaller and
quicker vibrations of the halves. In the same way it may,
while vibrating as a whole, be also vibrating in thirds,
fourths, etc. And it may even be vibrating as a whole, in
halves, thirds, fourths, etc., all at the same time.
233. Vibrations of Air-Columns in Parts. The air in an
organ or other pipe may vibrate as a whole or in parts, or
as a whole and in parts at the same time, just as a string
may.
Experiment 77. Take a tube of glass or other material, about 18
inches long and from a quarter to half an inch in diameter, close one
end with the finger, and blow rather gently across the other, and you
hear a low note, the lowest or the fundamental note of your tube : the
air-column is vibrating as a whole. Blow again and strongly, and
you make a much higher note. The air-column is vibrating in seg-
ments. Try the same experiments with the lower end of the tube
open : the results are like the others.
In trying the above experiment you must have noticed that the
lowest note of the open pipe was much higher than the lowest note
of the closed pipe. This is because the air in a pipe open at both
ends can never vibrate as a whole : there is no bottom to the pipe to
a k 13
146 NATURAL PHILOSOPHY.
send the wave back again. The lowest note that such a pipe can
give is when it is- vibrating in halves ; then the two waves meet each
other at the middle and turn each other back. Just at the middle
there is no motion of the particles : there is a node there. A pipe
open at both ends gives the same pitch as one of half its length which
is closed at one end. In fact, it is just the same as two closed pipes
with the closed ends together. The keys in horns and the finger-holes
in flutes, etc., enable the player to change the nodes and the lengths
of the vibrating columns of air, and therefore to vary the pitch of
his tones.
234. Overtones. When a whole string, or a column of air,
and its various parts are vibrating together, the vibrating
parts also produce tones, higher in pitch, of course, than
that of the whole string. These are called overtones. The
overtones cannot usually be distinguished from the funda-
mental tone by ordinary ears, and so they do not affect the
pitch of the sound, which is that of the string as a whole ;
but they do change the character of the tone, as we shall
see hereafter.
Helmholtz 1 has invented an instrument to enable us to detect the
overtones in a compound sound. It is called a resonator, and is
shown in Fig. 139. This is
made of just the size to be
resonant to the sound made
by halves of a certain string.
When the string is sounding
as a whole, and also in halves,
the small end of the resonator
is put into the ear, and by its
resonance it so strengthens the
sound of the halves that they
can be distinctly heard. An-
other resonator of different
FIG. 139. HELMHOLTZ'S EESONATOE. size will strengthen the sound
of the thirds enough to be
heard, another the fourths, and so on. By having a whole set of
these resonators, all the overtones in a compound sound can be dis-
1 H. L. F. Helmholtz, 1821-, Professor of Physics in the University
of Berlin, and one of the greatest scientists of this or any other age.
SOUND.
147
Fio. 140.
tinguished. These instruments show that the sounds of almost all
our musical instruments are very complex. The strings of pianos
and violins, the reeds of organs, etc., besides sounding as wholes, are
also vibrating in halves, thirds, fourths, fifths, and often many more
parts. The human voice has many overtones.
235. Manometric Flames. Koenig, an instrument-maker of
Paris, has devised an apparatus
which shows the effects of the over-
tones very beautifully. It consists
of two parts, one of which is shown
in Fig. 140. m is the mouth-piece of
a tube, across the other end of which
is stretched a piece of india-rubber,
r, f is a gas-burner, fed by the tube g. The gas-tube is separated from
the other only by the thin sheet of rubber. The
vibrations of the voice sounding at tn set the rub-
ber partition to vibrating, and drive out the gas
in puffs. These cause changes in the height of
the flame, but they are too rapid to be noticed,
and the gas-flame looks to the eye to be steady.
But when a square box having its four sides
covered with mirrors (Fig. 141) is rapidly ro-
tated in front of the flame, its changes can be
seen.
Fig. 142 shows the various forms that may be
produced. 1 shows the reflection of the gas-
flame when the mirror is stationary. 2 is the
reflection when the mirror revolves without any
sound being made in the tube. 3 is a low, simple sound, with no over-
tones. 4 is a higher simple sound, but with no overtones. In 5 the
first overtone (in halves) is sounding with the fundamental, only
every other vibration of the overtone being seen, the others are united
with the fundamental. In 6 the second overtones (in thirds) are
vibrating with the fundamental. 1
Almost any sound can be analyzed with this instrument, making
very interesting and curious experiments.
236. Character of Sound. Besides pitch and loudness,
1 3 and 4 can be produced by singing into the tube oo as in pool ; 5,
by singing a in B[j (second space below the treble clef) ; 6, by singing
a in the note F. (From Mayer's Sound, p. 160.)
FJQ 141<
148
NATURAL PHILOSOPHY.
sound has another quality. A piano, a violin, and a human
voice may all sound with the same pitch and the same
loudness, and yet they sound very unlike ; any one can tell
them apart. This quality which distinguishes different
'3 ' '
4-
FIG. 142. VIBRATIONS SHOWN BY MANOMETRIC FLAME APPARATUS.
kinds of sounds from one another is called character, or
timbre. The character of sounds has been found to be wholly
due to the overtones. If a sounding body is vibrating only
as a whole, and not in parts, or if while vibrating as a
SOUND. 149
whole only the halves, and perhaps the thirds, are also
vibrating, its sound is pure or simple. This is the case
with a tuning-fork or an organ-pipe. But if a sounding
body while vibrating as a whole is also vibrating in many
different divisions at the same time, its sound, though of
the same pitch as the other, has a very different character :
it is more " brilliant." The sounds of the violin, horn, and
cymbals are good examples.
237. The Three dualities of Sound. The pitch of sound
depends wholly upon the rapidity of the vibrations. The
loudness of sound depends wholly upon the amplitude, or
length of swing, of the vibrations. The character of sound
depends upon the number of overtones, or vibrations of
parts, that are mingled with the fundamental sound. All
the difference between musical sounds of any kind is made
by one or more of these three qualities.
238. Vibration of Plates in Parts. Experiment 78. Get a
piece of good window-glass about six inches square, rub its sharp
edges smooth with a grindstone. Clamp it
in the middle with a vise like that shown
in Fig. 143, which has been fastened to the
edge of a table by the lower screw. Scatter
writing-sand over the glass, and draw a
well-resined heavy bow across the edge
near one corner, while touching the middle
of another edge with the finger. The sand FIG. 143.
will arrange itself in lines as in Fig. 144.
Again, touch the glass at one corner, and draw the bow across the
middle of one edge, Fig. 145 will be produced.
These are called Chladni's l Figures. The finger holds the
glass still where it touches it, and starts a node there. The
glass vibrates in parts, and shakes the sand gradually to the
nodal lines between the vibrating parts where there is no
vibration. As with strings and columns of air, any two
consecutive segments are always vibrating in opposite di-
rections. Fig. 146 shows some of the many sand-figures
1 E. F. F. Chladni (klad'ne), 1756-1827, a German natural phi-
losopher.
13*
150
NATURAL PHILOSOPHY.
that have been thus produced by touching and bowing the
plate in different ways.
Bells, gongs, cymbals, etc., vibrate in parts as these plates
FIG. 144.
FIG. 145.
do, and both their fundamental tones and their overtones
are due to such vibrations.
SECTION IV.-MUSIC.
239. The Scale. There is a regular succession of eight
sounds of increasing pitch used by all persons in singing
or playing any musical instrument, called the scale. The
names of these sounds as they are used in singing are do,
re, mi, fa, sol, la, si, do. 1 In instrumental music the sounds
of the scale are denoted by the following letters : C, D, B,
F, G, A, B, C. The first or lower do, or C, is called the key-
note, or fundamental note, of the scale.
Almost all who study this book are familiar with the scale, and
can sing it for themselves. If any cannot, they may hear it by
striking eight successive white keys of a piano or organ, beginning
with C.
240. The Derivation of the Scale, To derive the scale, let
us use our sonometer again. It will be convenient to have
the wire 30 inches long to start with. If it is longer than
that, we may use that much of it by putting a bridge under
it, 30 inches from one end.
To produce do, sound the whole string.
1 Pronounced do, ra, me, fah, sol, lah, se, do.
SOUND.
151
Fio. 146. SAND-FIGURES.
152 NATURAL PHILOSOPHY.
To produce re, move the bridge so as to make the wire
| as long as at first (26f inches), and sound it.
To produce mi, move the bridge so as to make the wire
| as long as at first (24 inches), and sound it.
To produce fa, move the bridge so as to make the wire
| as long as at first (22J inches), and sound it.
To produce sol, move the bridge so as to make the wire
f as long as at first (20 inches), and sound it.
To produce la, move the bridge so as to make the wire
f as long as at first (18 inches), and sound it.
To produce si, move the bridge so as to make the wire
-^ as long as at first (16 inches), and sound it.
To produce upper do, move the bridge so as to make the
wire ^ as long as at first (15 inches), and sound it.
1> f > f > t> f> f > -fsi i> are tne proportionate lengths which
a string (whose tension is unchanged) must invariably
have to produce the common scale. The eight sounds are
called an octave. 1
241. The Number of Vibrations of the Notes of the Scale.
According to the first law of vibrating strings, the num-
ber of vibrations of a string is inversely proportional to its
length. Therefore, if we invert the fractions given above,
we have the relative numbers of vibrations per second
which are produced when the successive notes of the scale
are sounded. They are as follows : 1, f , f, f , f , f, l -/, 2.
It will be noticed that the upper do, or C, is produced by
exactly twice as many vibrations as the lower one. This
note is called the octave of the one below, and this use of
the word octave is rather more common than the use given
in the preceding paragraph. When the octave of a note is
sounded with the voice or with any instrument, twice as
many vibrations are invariably produced.
If lower do is produced by 24 vibrations per second, how many
vibrations will produce the succeeding notes of the scale ?
1 From the Latin octavus, meaning eighth.
SOUND. 153
242. The Repetition of the Scale. In any scale the upper
do is the lower do, or key-note, of the next octave. The
sounds of this octave are denoted by the same names or
letters as those of the octave below. The notes of this oc-
tave are produced by strings having the same proportion
to the length of the string sounding its key-note as the
notes of the octave below had to theirs. And the ratios
of the numbers of vibrations are just the same as before. In
the same way the scale is repeated in every seven notes
above or below the one we have started with to the upper
and lower limits of audibility (Art. 218). Every note, no
matter how made, is produced by twice as many vibrations
as the note of the same name in the octave below, four
times as many as the one in the second octave below, etc.
Questions. The upper do produced according to the directions
given in Art. 240 was made by the vibrations of a wire 15 inches long :
what must be the successive lengths of the wire to produce the notes
of the octave above, of the second octave above, of the octave below?
If the key-note of a scale is produced by 24 vibrations per second,
how many vibrations will be necessary to produce the notes of the
octave above ? of the second octave above ? How many of the notes
of the octave below can be produced ? Why can they not all be pro-
duced ?
243. The Fixing of the Pitch of the Key-Note. Any
pitch whatever may be taken for the key-note, and the
different notes will range above or below this, according
to the laws just given.
One person may sing a piece of music using a key-note of a certain
pitch. A second person may take for his key-note the pitch which
the first gave to re and sing the same piece through. Each of his
sounds will of course be one note higher than those of the other singer.
A third singer may take the pitch of the sol of the first for his key-
note ; and so on. This is very noticeable when different persons start
tunes without the aid of instruments. The natural limits of the
human voice, however, confine us in our choice of the pitch of the
key-note to rather narrow limits, varying according to the compass
of the singer's voice and the range of the piece of music sung.
Leaders of vocal music often use tuning-forks in order to get the
most suitable pitch.
Piano-tuners use tuning-forks or whistles, which always make a
154 NATURAL PHILOSOPHY.
certain known number of vibrations per second, and tune pianos by
them. In the best American pianos middle makes 268 vibrations
per second.
244. Intervals between the Notes of the Scale vary.
The following numbers are the answers to the problem
given in Art. 241, and are the relative numbers of the
do re mi fa sol
vibrations of the notes of any scale, viz.: 24, 27, 30, 32, 36,
la si do
40, 45, 48. Ee is produced by % or -| more vibrations than
do, mi by -1- more than re, fa by j 1 ^ more than mi ; from fa
to sol and from la to si the increase is again -J-, from sol to
la 1, and from si to do y 1 - again. Thus we see that in three
of the intervals there is an increase of -J. in the number of
vibrations, in two of the others an increase of , and in the
remaining two an increase of only -fa. The five longer
intervals are called whole tones, although they are not all
of the same length, as we have seen. The two shorter
ones are called half tones, although they are really longer
than half of any of the whole tones, as you may see by
comparing -Jg. with the halves of -J- and -J-. In every common
scale the intervals between the notes are in exactly these
proportions, and their order never varies.
A scale is sometimes used which is made by inserting an extra note
in the middle of each whole tone: this gives us thirteen notes in the
scale, all about the same distance apart. This is called the chromatic l
scale. But it is not natural to sing the scale with half tones any-
where else than between the third and fourth and the seventh and
eighth notes, so that few people can sing the chromatic scale. When
any other than the natural half tones are wanted in a piece of music,
the composer usually transposes the scale; that is, he starts with his
key-note a little higher or lower than the do of the ordinary or
natural scale, and thus brings the regular half tones just where he
wants a half interval between two of his notes to come.
245. Temperament, If a piano or an organ is tuned according
to the natural scale, from C to D there is an increase of J in the number
1 From the Greek word meaning color, because these inserted tones
used to be represented in colors.
SOUND. 155
of vibrations, from D to E of , from E to F of ^, etc. If, then,
one should play upon such an instrument a piece of music in which
the key-note is D, the interval between that and the next key would
be only ^ instead of , so that it would not give correctly the second
note of the scale. The next key, T ^ higher, would not be a correct
half note between the second and third notes of our scale, as it should
be, and so on through the scale. Not one interval in our scale would
be correct. The same would be true of every other scale ; none but
the one in which the instrument was tuned could be played upon it
correctly. This is partly corrected by the tuner distributing these
errors equally over all the scales. This distribution of these errors is
called temperament. The result is that no scale on a piano or an
organ is absolutely correct, but the errors in any are so slight that
most persons cannot notice them. If the instrument were tuned cor-
rectly for any one scale it would sound very badly when played in any
of the others. The piano and the organ, therefore, are not perfect
instruments, and can never make perfect music. But in the violin
and the flute the pitch is controlled by the player, and they may in
the hands of a skilful player produce perfect music.
246. Beats. Experiment 79. On a piano, or, better still, on a
cabinet-organ, sound together the lowest key and the black key next
to it. Mingled with the sounds of the two keys you will notice a
peculiar quivering sound. These quivers, or bursts, of sound, which
on the organ or piano are entirely too rapid to be counted, are called
beats.
To understand the cause of these beats, we must go back
to the interference of sound-waves, about which we learned
in Art. 228. Let us suppose that two sound-waves, one
vibrating 100 times per second and the other 101 times per
second, start out together. At the start their condensa-
tions will coincide; they will strengthen each other and
make a louder sound than either would alone. After half
a second one is at the end of exactly fifty vibrations, and
is, we may suppose, at its greatest condensation, but the
other is at the end of fifty and a half vibrations, so that it
must be at its greatest rarefaction. There the two sounds
would destroy each other. At the end of the second the
100th condensation of one coincides with the 101st con-
densation of the other, and they strengthen each other
156 NATURAL PHILOSOPHY.
again. These will be repeated as long as the sounds can
be heard. These alternate strengthenings and quenchings
of the sound cause the beats.
It is clear that in the illustration just taken there would be one beat
each second ; and the same would be true with any two sounds, one
of which vibrates once oftener than the other in a second. If one
has 100 and the other 102 vibrations per second, at the middle one
wave is at the 50th and the other at the 51st condensation. These
strengthen each other twice in each second. Again, if one vibrated
100 and another 105 times per second, the 20th condensation of one
would strengthen the 21st of the other ; the 40th of the one, the 42d
of the other ; the condensations coincide five times, or there are five
beats, each second. The number of beats in a second is equal to the
difference in the number of vibrations which the two sounds make
per second.
Beats can be made much better than on a piano or an organ by
using two large tuning-forks of the same pitch, mounted on sound-
ing-boxes, and loading one of them with a little wax. By increasing
the wax the beats are made more frequent.
Beats are always produced when two notes of different
pitch are sounded together. Generally they cannot be
noticed, but nevertheless they have a most important effect
upon the sound, as we shall see in the next paragraph.
247. Harmony and Discord. " If, towards sunset, you
walk on the shady side of a picket-fence, flashes of light
will enter your eye every time you come to an opening
between the pales. These flashes, coming slowly one after
the other, cause a very disagreeable sensation in the eye.
Similarly, if flashes or pulses of sound enter the ear, they
cause a disagreeable sensation." 1 When two notes of
different pitch are sounded together, beats are always pro-
duced. If these are very slow, the effect is not particularly
disagreeable, but if they are numerous, as when any two
contiguous keys of a piano or an organ are sounded, they
produce a harsh sound, which we all recognize as a discord.
" But if the flashes of light or beats of sound succeed
1 Mayer's Sound, pp. 174, 175.
SOUND. 157
one another so rapidly that the sensation of one flash or
beat remains till the next arrives, you will have continuous
sensations that are not unpleasant. In other words, con-
tinuous sensations are pleasant, but discontinuous or broken
sensations are disagreeable." 1 If, therefore, the beats are
very numerous, we have harmony.
For instance, when a note and its octave are sounded together, every
other vibration of the upper note and every vibration of the lower
coincide : we have the greatest possible number of coincidences or
beats that two sounds of different pitch can have, and we have what
is universally recognized as the most perfect harmony. When men
and women sing together the same part of a piece of music, the
women's voices are just an octave above the men's. Again, when do
and sol are sounded together, every third vibration of sol coincides
with every second vibration of do ; the next most numerous coinci-
dences that are possible produce what is well known to be the next
best harmony. For the same reason the first and fourth notes, and
the first and third, make pleasing sounds. But do and re only coin-
cide at every eighth vibration of do, and si and do at every fifteenth
of si. Here the beats are not rapid enough to be pleasant, and these
make discords.
Why very many beats are agreeable and produce harmony, while
a less number are disagreeable and produce discord, may be illustrated
by remembering that a single cobweb, or even a considerable number
of cobwebs, if brushed across one's face, tickle it very disagreeably ;
yet if these cobwebs could be woven into a piece of velvet, it would
produce the same pleasant sensation that a piece of ordinary velvet
does when rubbed over one's face.
248. Harmonics. We have learned (Art. 232) that when a string,
a reed, a column of air, or any other sound-producing body, is vi-
brating as a whole and thus producing its fundamental sound, it is at
the same time generally vibrating in parts also, which produce the
overtones. If only the larger parts are vibrating, as the halves, thirds,
or fourths, or if the sounds of these predominate, we can now see
that these would harmonize with the fundamental sound and with one
another, and blending all together they would produce a pleasing
sound. These lower overtones are therefore called harmonics. It is
to them that we owe the pleasing effect of a sweet voice, of a lower
or middle key of a good piano, or of any other single note that we
1 Mayer's Sound, pp. 174, 175.
14
158
NATURAL PHILOSOPHY.
recognize as pleasant. But if the overtones are wholly or mainly
the vibrations of the sevenths, eighths, ninths, etc., they will not
harmonize with the fundamental note or with one another, and the
result is a harsh sound. It is these that make a harsh voice, scraping
on a violin, and other unpleasant musical sounds so disagreeable.
Experiment 80. Strike middle C of a pjano two or three times, so
that you can recognize its sound when you hear it again, then press
it down gently so as to make no sound, "and hold it there, thus keep-
ing the damper oif the wire. Now strike the C, one octave below,
vigorously, and, after holding that key down for three or four seconds,
let it rise again. Its damper stops its sound at once, but you now
hear a faint sound, which you recognize as that of middle C, which
you are holding down. When you struck lower C it vibrated in
halves, besides its vibration as a whole. And the vibrations of these
halves set the wire of middle C to vibrating. In the same way you
may hear the sympathetic vibrations of Gr above middle C produced
by the thirds of the lower C. And possibly its fourths may set C,
two octaves above it, in vibration.
Their overtones also have an effect upon the harmony or discord of
two notes. To make them harmonious these two must make very
rapid beats with each other and with the fundamental notes.
249. The Human Ear. This organ is shown in Fig. 147.
The end of the tube
leading in from the
outer ear is entirely
closed by a thin
membrane called the
tym'panum. Behind
this is a small cavity
called the drum of
the ear. This cavity
is connected with
the back part of the
mouth by the Eusta-
chian (yu-sta'ke-an)
tube. A chain of four
FIG. H7. HUMAN EAR. very small bones
stretches across the
drum from the tympanum to another smaller membrane
that covers an opening into the labyrinth. This labyrinth
is a small, curiously-shaped cavity in the solid bone of the
SOUND. 159
skull, and is filled with a watery fluid. The nerve of hear-
ing runs from the brain to the labyrinth, and there divides
up into thousands of microscopic branches, which stick out
like bristles from the sides of the labyrinth into the liquid
which fills it.
250. How we Hear. The sound-vibrations enter the ear,
strike the tympanum, and set it in vibration. Its vibra-
tions are carried across the drum of the ear by the chain
of little bones, and also by the air there, and set the mem-
brane covering the openings into the labyrinth into vibra-
tion ; and this communicates its vibrations to the liquid
within. The tiny bristles which project into the liquid
are of different lengths and thicknesses, and it is supposed
that these are tuned each to a different pitch, and, in all,
to all the pitches that are audible. It is likely, then,
that the waves in the liquid which are produced by sound
of a certain pitch set to vibrating the bristle which is
tuned to the same pitch, and that the nerve-thread at-
tached to this bristle conveys this impression to the brain
and to the mind. When the sound contains overtones as
well as the fundamental, each element of the sound must
set in motion the bristle tuned to its pitch, and the com-
bined impressions of these give us the true impression of
the sound.
Exercises. 1. Why does touching a call-bell with your finger
silence it?
2. There is helieved to be no atmosphere of any kind on the moon :
would this have any effect on sounds there ?
3. Your pulse probably beats about 80 times per minute. Suppose
that on a day when the temperature is at the freezing-point you count
five beats of your pulse after you see the escaping steam of an engine-
whistle, and before you hear its sound : how far off is the engine ?
Ans. 4087 feet.
4. Suppose that on a summer day, when the thermometer stands
at 80, you count four beats of your pulse between a flash of light-
ning and the first sound of the thunder : how far off is the lightning ?
5. A leader of a room full of singers is at one end of the room,
which is 60 feet long. If the temperature of the room is 68 (which
is about what it ought to be), how much will the words of the singers
on the back seat seem to the leader to be behind his own ? Ans.
seconds.
160 NATURAL PHILOSOPHY.
6. What is the temperature of the air when the velocity of sound
is 1150 feet per second ? Ans. 92.
7. Until recently the velocity of sound was always given as 1142
feet per second : what must have been the temperature when that
result was obtained ?
8. How far off is a barn when the echo of your voice comes back to
you after you have counted three beats of your pulse, the tempera-
ture being at 60 ?
9. The bell in the clock-tower at Westminster Abbey, London, is
300 feet above the ground : find the time sound takes to pass from
the bell to a point on the ground 400 feet from the foot of the tower,
the temperature being the same as in the last problem ? Ans. f f $
seconds.
10. Could you set your watch to the second by the striking of a
tower-clock some distance off? Why will a large company of singers
keep better time if their leader beats time instead of leading them
with his voice? How will it affect the drill of a long line of soldiers if
the officer gives his commands while standing at one end of the line?
11. How much louder is a sound 50 yards from its origin than at a
point 70 yards distant ? Ans. As ^^ : ^, or as 4900 : 2500.
Therefore ff- as loud.
12. How much louder will a sound be 40 yards than 90 yards
away?
13. What is the length of each wave of the lowest sound that we
can hear ? of the highest ?
14. Give the difference between musical and non-musical sounds.
15. Explain the meaning and causes of loudness, pitch, and char-
acter.
16. Give an example of two musical sounds that agree in one of
these characteristics only ; of two others agreeing in two of them.
17. A certain string vibrates 100 times per second : find the number
of vibrations of another string which is twice as long and weighs
four times as much per foot and is stretched by the same force.
Ans. 25.
18. A musical string vibrates 400 times per second : what takes
place when the string is lengthened or shortened without altering the
tension ? when the tension is made greater or less without altering
the length?
19. A tuning-fork vibrates over a jar 15 inches deep, and a strong
resonance is produced : what is the rate of the fork's vibrations if the
temperature is such that sound travels 1120 feet per second?
20. If do vibrates 264 times per second, how many vibrations in
mi above it ? in sol ? in the upper do ?
21. If do vibrates 264 times per second, how many vibrations pro-
duce re, si, and fa in the octave below ?
22. Draw on the blackboard a line 30 inches long, and above it
draw lines of the right proportions to represent strings which would
give the notes of the octave above.
23. Middle C of a piano vibrates 272 times per second. In a seven-
octave piano the lowest key is the fourth A below middle C, and the
highest is the fourth A above it : what are the rates of vibrations of
these two keys ?
SOUND.
24. In a seven-and-one-third-octave piano the lowest key is the
same as before, but the highest is the fourth C (four octaves) above
middle C : how many more vibrations per second will the highest key
of this piano make than the highest one of the "other ?
25. If re is produced by 216 vibrations per second, how many will
produce do below ? re below ? la above ?
26. Over how many octaves does the range of human hearing
extend ?
27. How many beats per second will there be when middle C and
G above are sounding together on a piano ? how many when B above
is sounded with middle C ?
28. If corresponding keys towards the upper end of the key-board
be sounded together, will the beats be the same as in last problem ?
How will it be if they are taken in the lower end of the key-board?
162 NATURAL PHILOSOPHY.
CHAPTEE YI.
LIGHT.
I.-THROUGH UNIFORM MEDIA.
251. Sources of Light. Light comes to us from the sun
by day and from the moon and stars by night. It is pro-
duced on the earth by combustion, by friction, by elec-
tricity, and by phosphorescence. Light from combustion
is familiar in all fires. Light from friction may be seen by
rubbing two pieces of white sugar together in the dark.
The light from meteors (shooting-stars) is produced by the
friction of small bodies moving with great velocity through
the atmosphere. Light from electricity is visible when a
cat is stroked vigorously in the dark. The lightning and
the aurora are forms of this. Light from phosphorescence
is often seen in decayed wood, in "luminous paint," a salt
of calcium which glows when taken from a light place to
a dark one, and in a fire-fly.
Astronomy tells us that the sun is one of the stars, and
that the moonlight is only reflected sunlight. Hence we
may say that we have one celestial source of light, the
stars, and four terrestrial sources, combustion, friction,
electricity, and phosphorescence.
252. Cause of Light. In all these cases the light is
produced in the same way. The particles of the body
from which the light comes are put in extremely rapid
vibration. The surrounding ether catches up these vibra-
tions and carries them along like waves in water till they
reach the eye of the observer, and the sensation produced
is light.
LIGHT. 163
253. Light-Waves. Light-waves lie across the direction
in which the light travels. If we suppose
the ray of light to be moving perpendicu-
larly to this page, the particles of ether
vibrate up and down in ab, across in cd t
and diagonally at all angles in ef, etc.
The water-wave moves horizontally, while FIO. us CROSS-SEC-
TION or RAY OF LIGHT.
its particles vibrate up and down only.
The method of vibration of the sound-wave has already
been explained. The light-wave is different from either
of these. Its particles move transversely to the motion of
the wave in all directions. Its vibrations are very minute
and very rapid. When a piece of iron is heated, its par-
ticles are set into vibration. At first this vibration is slow,
and only affects the nerves sensitive to heat. But when
the temperature is raised so that about 400 million million
of them occur in a second, a red glow begins to show itself.
Light is given out. When the temperature is further
raised so that the number of vibrations is nearly doubled,
the iron is white-hot. The intensity of the light is greatly
increased. From 40,000 to 70,000 of these waves are in a
linear inch.
254. Light moves in Straight Lines. These vibrations
are carried forward in straight lines so long as they do not
meet with any change in the substance through which
they pass. We always recognize this. We assume an
object to be in the direction in which we see it, that the
light by which we see it carries the impression to the eye
in a straight line. We can test the same fact by an
experiment.
Experiment 81. Arrange three cards by fastening them to blocks
so that they will stand upright on a table. Pierce a small hole in
each card, and place them so that a stretched string will go straight
through all the holes. Now put a lamp in front of the end hole. It
will shine through all. But if any of the cards be moved so that the
holes are not in a straight line, the light will not shine through.
Experiment 82. Darken a room, and make a small hole in a shut-
ter opposite a white wall. Over this paste a piece of paper in which
164
NATURAL PHILOSOPHY.
a large pin-hole is pierced. The outside landscape will be projected
on the wall inverted, for all the rays will cross at the opening. Kays
from a will move in straight lines to ', and rays from b to b / .
FIG. 149. IMAGE THROUGH A SMALL HOLE.
T"
n l'"
FIG. 150. LIGHT MOVES
IN STRAIGHT LINES.
Experiment 83. Hold a candle in front of a card in which a pin-
hole is pierced. The candle will be seen inverted
on a small screen held beyond the hole.
Experiment 84. Have made in a a temporary
window-shutter a number of small openings of
different shapes, and let the sunshine through into
the room. Keceive the image from them on a
screen placed at a distance from the holes. These
images will all be round, not the shape of the holes.
They are images of the round sun.
The same may be seen in the light patches on the ground under a
tree, formed by the passage of sunlight through the small openings
of the foliage.
255. Opaque, Transparent. When a body allows light to
pass through it, it is said to be transparent ; when it does
'not, it is said to be opaque.
Name several opaque and several transparent substances.
256. Shadows. Shadows are a result of the motion of
LIGHT.
165
light-waves in straight lines. If an opaque body be placed
FIG. 151. IMAGE BY PASSING LIGHT THROUGH A SMALL HOLE.
between a source of light and the wall, a dark place is
shown on the wall,
which is due to the
fact that the light
which would other-
wise fall on it is cut
off by the opaque
body.
Experiment 85.
Stretch a string from the
source of light touching
the edge of the shadow ; FlQ> ^.-SHADOW.
it will touch the edge of
the body.
Experiment 86. Make the body a square, and place it exactly half-
way between the light and the wall. Measure the shadow. Its side
will be twice the side of the square, and hence its area will be four
times that of the square.
166 NATURAL PHILOSOPHY.
257. Law of Light-Variation. This last experiment ex-
plains an important law. The light which would have
been spread over the space occupied by the shadow now
is collected on the square, and therefore covers only one-
fourth the space. Hence it is four times as intense on the
screen as at the wall. The wall is twice as far from the
light as the square is, and the intensity is only one-fourth
as great. Were the wall three times as far away, the in-
tensity of the light would be only one-ninth as great. The
general law is, Light diminishes as the square of the distance
increases.
258. Photometry, We can compare the relative intensi-
ties of two lights by the aid of this law.
Experiment 87. Place an opaque body in front of a wall, and
arrange the lights so that the two shadows shall be side by side.
FIG. 153. PHOTOMETRY.
Move one of the lights backward or forward till the shadows are of
the same intensity of darkness. The shadow from a is still lit up by
&, and the shadow from b by a. If the shadows are equally bright,
the intensities of the light given by the two bodies at the wall are the
LIGHT.
167
same. Now measure the distance of each light from the wall. The
squares of these distances will be the relative intensities of the lights.
259. Umbra and Penumbra, If the source of light, instead
of being small, is of considerable size, we shall find that the
FIG. 154. UMBRA AND PENUMBRA.
shadow is not definite in outline, but gradually shades out.
The cause of this is shown in Fig. 154.
The portion directly behind the intercepting object does
not receive any light from the source, and is called the
umbra. The shaded portion on each side of this receives
light from part of the source only, the part increasing as
we depart from the umbra, and is called the penumbra.
The penumbra gives to the shadows of bodies a softness
of outline which they do not receive when the source of
light is very small. Moreover, as this penumbra increases
in size as the distance from the body increases, this soft-
ness shows itself more conspicuously as we move the body
away from its shadow.
Experiment 88. Throw a shadow on a wall by a body close to it.
Move the body away, and notice the change in distinctness of shadow.
260. Velocity of Light. For a long time it was supposed
that light was propagated instantaneously. Galileo took
a lantern to the top of a mountain, and had an assistant on
the top of another, where there were no intervening objects.
He cut off the light suddenly, and told his assistant to cut
168
NATURAL PHILOSOPHY.
his off as soon as he missed the light from Galileo's. As he
did not notice that it took any time between the extin-
guishment of the two lanterns, he concluded that the light
took no time to travel. He erred only in this, that the
time was too small to be detected by such rude means.
261. Velocity obtained from Jupiter's Moons. The first idea
that light had velocity was gained by examination of Jupiter's satel-
lites. In the figure, TOY
represents the orbit of the
earth around the sun, and
JJ a part of Jupiter's
orbit. Jupiter casts a
shadow on the side away
from the sun, and into this
shadow plunge his little
moons in their revolution
about him. The time of
these eclipses can be cal-
culated in advance, and it
has been found that when
the earth is at T'it appears
to us earlier than when
the earth is at T. The
reason of this is that the
light has to travel the dis-
tance from T' to T, the
diameter of the earth's
orbit, farther in one
case than in the other.
The difference in time
amounts to about 16J
minutes. As we know
that the diameter of the
earth's orbit is about
185,000,000 miles, we can readily calculate the velocity of light.
Thus, 16^ minutes = 990 seconds :
185,000,000 miles -=-990=: 187,000 miles, nearly, per second.
262. A Better Method. A still more accurate determination can
be obtained by the following method : a is a mirror which can re-
volve about a vertical axis, ef. & is a stationary mirror, g is an
opaque body containing a narrow slit. Sunlight is thrown through
FIG. 155,
-VELOCITY OF LIGHT BY ECLIPSES OF JUPI-
TER'S SATELLITES.
LIGHT.
169
this slit so that it falls on the mirror a, and is reflected to 6, and back
again to a. If a has not
moved, the light would be
again reflected directly to the
flit in g. But a may be
made to revolve with great ra-
pidity, and during the minute
time that the light has been
travelling from a to b and
back again, the mirror has
changed its position a little,
so that the light is now thrown
to some other point, as h.
Knowing the velocity of the
mirror and the distance of h
from the slit, it is possible to
calculate the time required in FIG. 156 FOR FINDING THE VELOCITY OF LIGHT.
passing twice between a and
b. Now measuring the distance, the velocity of light is found.
The best results obtained for the velocity of light are
299,940 kilometres, or 186,380 miles, per second.
Exercises. 1. A board 1 foot square is held between a point of
light and a wall, parallel to the wall. If 2 feet from the light and 4
feet from the wall, what is the size of the shadow?
2. A coin casts a shadow on a wail to which it is not parallel : what
is the shape of the shadow ?
3. A lamp 8 feet from a wall throws a shadow which is just as
bright as that thrown by a candle 2 feet from the wall : compare the
light of the two.
4. Light requires about 3 J years to come from the nearest star :
how far is it away ?
5. Does the fact that we see the stars prove that they are in existence
at ae present time ?
i. How long would it take light to go to the moon ? how long
a.ound the earth ?
II. REFLECTION.
263. Reflection. When light falls on a smooth surface
which it cannot penetrate, it is turned back, or reflected.
Experiment 89. Allow sunlight to shine into a dark room through
a small hole. The beam l will be visible by lighting up the particles
1 This is better arranged by means of a heliostat, which reflects the
light into the room. A sample one is described, together with a
H 15
170
NATURAL PHILOSOPHY.
of dust which are always floating in the air. It can be in this and
other cases made still more evident by smoke from heavy brown
paper. Let it fall perpendicularly on a mirror. The beam is turned
directly back on its track. Turn the mirror 45, the light goes off
at right angles to its former course.
Experiment 90. Allow the beam of light from the sun or a lamp
h to shine through a hole in a card
at dj to fall on a mirror at 6, and
J to be reflected on another card at e.
n Make a hole at e at the same height
above c that d is above a. Look
through the hole at e and see the
light reflected from b. Mark the
exact point where the light falls at
b. Now measure ab and be. They
will be equal. We can readily prove
from this by geometry that the angle dbh is equal to the angle ebh.
264. Incident and Reflected Rays. In Fig. 157, db is
said to be the incident ray, and be the reflected ray ; dbh is
the angle of incidence, and ebh the angle of reflection.
265. Law of Reflection. The general law of reflection is
that the angle of incidence is equal to the angle of reflection.
266. Principle of Mirrors. We may understand from
FIG. 157. REFLECTION OF LIGHT.
FIG. 158. PRINCIPLE OF MIRRORS.
this and from Fig. 158 how it is that we see objects in a
looking-glass. Objects are seen in the direction in which
number of interesting experiments to be performed with it, in Light,
by Mayer and Barnard.
LIGHT, 171
the rays of light from them enter the eye. The glass turns
these rays back, making the same angle with the perpen-
dicular that they had before, and we therefore seem to see
them, back of the glass, the same distance from it that
they are in reality in front of it, but inverted right and left.
The image is not real; it is an optical delusion. Such
images are said to be apparent images.
267. Natural Objects. It is by the aid of reflected light
that we see most natural objects. When the object is
smooth, as a mirror, the light is reflected in parallel rays,
and we notice only the glare ; but when its surface is rough,
such as that of a book or wall or landscape, the reflected
light is diffused in all directions, and the object is seen by it.
268. Multiple Images. We sometimes see more than one
image of an object.
Experiment 91. Take a mirror out into the starlight, and see the
reflection of a bright star or planet at an oblique angle. The star
will seem to be attended by a small companion. This is due to the
reflection from the front face of the glass, as shown in Fig. 159. One
FIQ. 159. DOUBLE IMAGE. FIG. 1GO. IMAGES BY Two MIRRORS.
reflection comes to us from the silvered back of the mirror, the other,
the fainter one, comes from the front face.
If two mirrors are inclined to each other, quite a number of images
may be seen. Fig. 160 shows one case of this.
Fig. 161 shows the reason of this. If p is the candle, and e the eye
172
NATURAL PHILOSOPHY.
of the observer, he sees one object at p / by direct reflection from ab,
FIG. 161. IMAGES BY Two MIRRORS.
one at p" by reflection from be, and one at p" r by reflection first from
ab and then from be.
269. The Kaleidoscope. The kaleidoscope is composed of three
mirrors inclined at angles of 60 to one another, and arranged along
the whole length of a tube. At one end the person
puts his eye and sees a number of colored glasses
at the other end, reflected and re-reflected from
mirror to mirror, thus causing the appearance of
symmetrical figures of great beauty. Fig. 162
shows a cross-section. The circle represents a
tube, which may be of pasteboard. The straight
FXG. ^.-CROSS-SECTION lines are stri f of g lass (clear glass will answer)
OF THE KALEIDOSCOPE, placed along it. An eye-hole must be at one end,
and in the other some ground glass or oiled paper,
or some semi-transparent substance. On this a few irregular pieces
of broken colored glasses are scattered. These are kept in the bottom
of the tube by a piece of clear glass.
The ingenious student can make a kaleidoscope for himself.
270. Concave Mirrors. Concave mirrors produce a dif-
ferent effect from plane mirrors. Let ab be an arc of a
circle, and cd the direction of an in-
cident ray of light. The perpendic-
ular to the surface will always pass
through the centre, /, of the arc,
fA and the reflected ray will be in the
direction de, making cdf=edf. Any
FIG. 163.-PRINCIPAL FOCUS, other ray, as gh t parallel to bd, will
be reflected in the line he, which will
meet de in some point e. Hence the effect of a concave
LIGHT,
173
mirror is to converge the rays of light, or to make diver-
gent rays less divergent.
271. Principal Focus. The point to which the parallel
rays converge is called the principal focus, and is midway
between / and k.
272. Parabolic Mirror. If ab is a circle, all parallel rays
will not meet in exactly one point. In order for this, ab
must be a curve called a parabola (see page 43). Also, if
FIG. 164. CONJUGATE Foci.
a light be placed at e, the rays, after reflection, will all be
parallel. This principle is used in making reflections for
lanterns. The light is so placed inside the parabolic mirror
FIG. 165. CONJUGATE Foci.
that all rays which strike it are reflected forward in par-
allel or nearly parallel lines. The principle is also used in
the mirrors of reflecting telescopes, where parallel rays
frqm the heavenly bodies are brought to a focus, near which
the eye is placed. If the rays do not come in parallel, but
diverge from some point as S (Figs. 164, 165), they will
converge to some other point as s. If they diverge from s,
they will converge to S. S and s are called conjugate foci.
273. Images by a Concave Mirror, Let ab be an object
174
NATURAL PHILOSOPHY.
placed farther from the mirror than the centre, c. Now,
whenever any bundle of rays pro-
ceeding from a single point are
brought together at another point,
an image is there formed. All
rays from a will meet in a point
at a'. This point can be most
easily found by drawing the par-
allel ray, ag, and its direction of
reflection through the principal
focus, gfa' ; also the ray, ah, through the centre, which is
reflected directly back towards the centre. The intersection
a' of go! and a'h is tne image of a. Similarly, the light
FIG. 166. IMAGES BY CONCAVE
MIRROR.
FIG. 167. IMAGE BY CONCAVE MIRROR.
from b will be focussed at V, and all points of ab will have
corresponding points in a'b'. We shall then have a real
LIGHT. 1 75
image, inverted and smaller than the object. By holding
a piece of white paper at a'b', we can, if it does not cut
FIG. 168. IMAGE BY CONCAVB MIRRORS.
off too many of the rays which would fall on the mirror
from ab, see the inverted image.
If the object be placed at a'b f , the image will be formed
inverted and enlarged at ab. (Fig. 166.)
Exercises. Show by construction that (a) if the object be at the
centre the image will be at the centre inverted ; (b) if the object be
at the focus there will be no image ; (c) if the object be between the
focus and the mirror there will be an image behind the mirror, ap-
parent, erect, and magnified.
Experiment 92. Take a glass concave mirror, or, if this cannot
be had, a lantern-reflector, and verify the above in all the cases,
1. By looking in the mirror at varying distances ;
2. By placing a candle at different distances from the mirror and
catching the image on a screen.
274. Convex Mirrors. Convex mirrors cause parallel
rays to diverge from a point behind the mirror, which is
the principal focus. The images from a convex mirror are
always behind the mirror, apparent, erect, and smaller than
the object.
Experiment 93. With a convex mirror of glass or " tin" examine
176 NATURAL PHILOSOPHY.
the truth of these statements by looking into it from varying dis-
tances.
275. Diffusion of Light. The sun shines on the air, and
the little particles of dust and vapor which it contains re-
flect the rays in all directions. This is the reason that
sunlight gets into our rooms and under trees. This brings
light to our eyes and enables us to see objects upon which
the sun does not shine directly.
276. Twilight. Twilight is produced by a similar cause.
Even when the sun is be-
low the horizon some of
its rays are reflected to us
by invisible particles in
the atmosphere. As it gets
farther down it shines only
on the upper layers, and
so the day gradually
FIG. 169. DIFFUSION OF LIGHT. changes into night.
Objects are seen by the
light which they diffuse. If the surface is very smooth,
the light is reflected in parallel lines, and a glare is pro-
duced. If not, the light is reflected in all directions, and
the features of the object are brought out.
Exercises. 1. Shall we notice double reflection when we look per-
pendicularly on a mirror ? Draw a figure to show that the two
images will be farther apart the more obliquely we see the object
reflected from the mirror.
< 2. Draw a diagram to show that an
^f 9 object seen between two parallel plane
"~ . mirrors will have its image several times
TIG. 170. multiplied.
3. Draw a diagram to show that a per-
son can see himself in a mirror half as long as himself.
4. If the sun, 93,000,000 miles away, and an electric light, 20 feet
away, cast shadows of the same intensity, how many times brighter
is the sun than the electric light ?
5. If there were no atmosphere surrounding the earth, why would
the stars look like points of light in a black sky ? why would all
shadows be perfectly black ? Do we see any rays of light except such
as enter the eye ? if not, how do we see a beam of light pass through
a dark room ?
LIGHT.
177
III.-REFRACTION.
277. Refraction, When light passes obliquely from one
transparent substance
to another, as from
air to clear water, it is
turned from its course,
or refracted.
278. Law of Refrac-
tion. This refraction
is shown in Fig. 171.
The course of the beam
will be the same
whether it passes from
FIG. 171. RKFRACTION.
the air into the water or from the water into the air.
The rule is, when light passes from a medium into a denser
medium, it is turned towards the perpendicular to its surface ;
when it passes into a rarer medium, it is turned away from the
perpendicular to its surface.
FIG. 172. COIN MADE VISIBLE BY REFRACTION.
Experiment 94. Place a coin on the bottom of a basin so as to be
178
NATURAL PHILOSOPHY.
just hidden by the edge. Pour water into the basin, the coin will
come into sight. The rays which strike the surface of the water as
ab (Fig. 171) are refracted in the direction be, and enter the eye.
Experiment 95. Place a stick obliquely in clear water, it appears
bent : explain this.
279. Angles of Incidence and Refraction, If the ray is
passing from air into water, the angle aid (Fig. 174) is called
the angle of incidence, and eld the angle of refraction.
280. Law of Sines. There is a law of refraction called the " law
of sines." This may be explained by Fig. 174. If a circle be de-
FIG. 173. STICK BENT BY REFRACTION.
FIG. 174. LAW OF SINES.
scribed about the point where the ray strikes the surface, and froni
the points a and c, where the incident ray and the refracted ray cut
this circle, perpendiculars ab and cd be drawn to the vertical bd, then
the u law of sines" is that ab has to cd a constant
ratio, whatever be the angle of incidence. That
is, if ab is 1% times cd, any other line, ef, will also
be 1 J times gh. 1
281. Limiting 1 Angle. In passing into a
rarer medium, the angle of refraction, fbd,
FIG. 175. LIMITING is greater than the angle of incidence, abc.
For a certain angle of incidence, as ebc, the
angle of refraction becomes 90, or fbg. This angle, ebc, is
1 ab is said to be a sine of the angle of incidence, and cd of the
angle of refraction. This is an expression used in Trigonometry ;
hence the name of the law.
LIGHT.
179
called the limiting angle. In the case of air and water it is
FIG. 176. TOTAL REFLECTION.
about 48J. If the angle of incidence is greater than this,
as hbc, the ray will not leave
the water, but will be re-
flected from its surface, and
pass in the direction bk.
Experiment 96. Hold a glass
of water, with spoon, as in Fig.
177, so that we may look ob-
liquely at the surface of the water
from underneath. There will be
total reflection of the part of the
spoon under water.
282. Total Reflection.
This is called total reflection
because all the light is re-
flected. This is not the case
with ordinary reflection.
If a glass prism shaped
FIG. 177. TOTAL REFLECTION.
FIG. 178. TOTAL REFLECTION.
180
NATURAL PHILOSOPHT.
like abc be so placed that the light will fall vertically on
the face ab, it will pass into the glass. It cannot pass
through the surface, ac, into the air, for the angle of in-
cidence, is greater than the limiting angle. The light
will suffer total reflection, and will pass off in a perpen-
dicular, /, to its former course.
283. Refraction through Glass. If light passes through
a piece of glass with
parallel sides, it is
refracted by both
surfaces in differ-
ent directions, and
emerges parallel to
its original course.
284. Refraction
through a Prism.
If the sides are not parallel, the light emerges in a new
direction.
FIG. 179. REFRAC-
TION BY GLASS
WITH PARALLEL
SIDES.
FIG. 180. REFRACTION BY
PRISM.
Experiment 97. Procure a thick piece of clear glass and hold it
so that part of an object shall be seen obliquely through it and part
past the edge. The two parts will not fit together.
FIG. 181. REFRACTION BY PLATE-GLASS.
Experiment 98. Procure a glass prism, and notice the apparent
change of position of objects seen through it. (The colors seen will
be explained farther on.)
285. Explanation of Refraction. The effects of refraction have
LIGHT.
181
been illustrated in the following way. Suppose a combination of two
wheels and an axle to be moved over the floor. It will, if the floor is
FIG. 182. REFRACTION BY TRIANGULAR PRISM.
smooth, roll in a straight line. But if it comes obliquely against a
square piece of velvet, the wheel that strikes first will be delayed, and
FIG. 183. EXPLANATION OF REFRACTION.
FIG. 184. REFRACTION BY CONVEX LENS.
the path will be bent towards the perpendicular to the surface. When
it gets to the other side, the same wheel will reach the smooth floor
first and be accelerated, and so the path will be parallel to its origi-
nal direction.
16
182
NATURAL PHILOSOPHY.
If the piece of velvet is convex, the effect will be to bend the path
in the same direction at each surface ; if triangular, as a prism does.
286. Lenses. A lens is a circular piece of glass to refract
the rays of light. At least one of its surfaces must be
FIG. 185. LENSES.
curved. It may be of any of the following shapes: a,
double-convex ; b, plano-convex ; c, concavo-convex ; d,
double-concave ; e, plano-concave ; /, convexo-concave.
FIG 186. CONVEX LENS.
287. Effect of a Convex Lens. The effect of a convex lens
is to cause rays of light to converge.
LIGHT.
183
Fia. 187. EFFECT OP A CONVEX LENS.
288. Effect of a Concave Lens. The effect of a concave
lens is to cause rays of light to diverge.
FIG. 188. EFFECT OF A CONCAVE LENS.
Experiment 99. Verify the first of these statements by means of
glasses from spectacles, or " magnifying-glasses." Light is concen-
trated to a point.
To illustrate the properties of lenses we will study the cases of
double-convex and double-concave lenses of the same curvature on
both sides. This, with a knowledge of the principles of refraction,
will enable anv one to understand the effects of other lenses.
FIG. 189. PRINCIPAL Focus.
289. Double-Convex Lens. A double-convex lens will
184
NATURAL PHILOSOPHY.
bring parallel rays to a point called the principal focus. The
distance from the centre of the lens, A, to the principal
focus, F, is called the focal length of a lens.
FIG. 190. CONJUGATE Foci.
If the rays diverge from a point, as A, they will con-
verge to another point, as B, farther from the lens than the
FIG. 191. CONJUGATE Foci.
principal focus. If they diverge from B, they will converge
at A. The line joining A and B will always pass through
the centre, D, of the lens.
FIG. 192. MAGNIFYING EFFECT OF A CONVEX LENS.
A and B are called conjugate foci. If the eye be placed
at F, the converging of the rays from any object beyond
LIGHT.
185
the lens, as AB, will cause an enlarged image of the object,
as A' B'. The rays from A appear to come from A', and the
rays from B appear to come from B', and so for interme-
diate points.
The eye and the object must be in the conjugate foci of
the lens for distinct vision.
FIG. 194.- IMAGE BY CONVEX LENS.
Experiment 100. Hold a magnifying-glass so as to see an object
distinctly. Now move the object from the lens. The eye must be
placed closer to the lens to secure distinct vision. As one focus recedes
from the lens, the other approaches.
Experiment 101. Hold a lens in front of a wall or a piece of paper
16*
186
NATURAL PHILOSOPHY.
so that the light of a candle will shine through the lens. By moving
the lens to and from the wall, the position is found where an image
of the candle will be cast on the wall or paper, inverted.
Experiment 102. Try the same in the daytime in such a way as to
throw an image of the window on the wall.
Experiment 103. When a distinct image of a distant window or
candle is thrown on the wall, measure the distance of the lens from
the wall. This will give approximately its focal length ; for the rays
are nearly parallel.
Experiment 104. Hold the lens in the direct rays of the sun; ad-
just it so as to make the circle of light on the screen the least possi-
ble. Measure again from the screen to the lens. This should agree
with the last measure. The circle of light is the image of the sun.
Fig. 195 shows why the object is inverted. All rays from
a are brought to a focus in a line through o at #', from b at
&', from c at c f , etc. When
the object is nearer
lens than the image
FIG. 195. IMAGE BY CONVEX LENS.
the
the
image will be enlarged,
and vice versa.
Experiment 105. In the ar-
rangement of Fig. 195 move
the candle nearer the lens ; the
image will recede and get larger.
Experiment 106. Having
found the focal length by exper-
iment 104 or 105, place a candle at just twice the focal length from
the lens ; the image will be the same size as the object.
Experiment 107. Place the candle at the principal focus. There
will be no image, for all the rays move out parallel.
Experiment 108. Place the image still nearer the lens. The rays
will diverge, and will form no real image.
290. Construction of the Image. The position and size
of the real image can be con-
structed in the various cases
as follows.
Draw the parallel ray ad.
It will be refracted through
the principal focus /. Also
draw the line ao through the
centre. Where these meet will be the position of the image
of the point a. The same may be done from other points.
291. Concave Lens. Since a bundle of rays from a point
FIG. 196. CONSTRUCTION OF THE IMAGE.
LIGHT.
187
are made to diverge still more by concave lenses, they do
not form real images. The images are smaller than the
objects, and are erect.
The principal focus is the point from which parallel rays
appear to diverge.
292. Spherical Aberration. A spherical convex lens will
not bring all rays to exactly the same point. The rays
near the edge are refracted more than those near the
centre. Thus, while rays like db
are brought to a focus at c, those
like ed are refracted to g, and hence
a perfectly distinct image is -not
formed. This is called "spheri-
cal aberration," and has to be cor-
rected for by deviations in the lenses
from the spherical form.
293. Atmospheric Refraction, When a ray of light en-
ters the atmosphere from the sun or a star, it is refracted j
as it enters each denser layer, it is more and more refracted,
being always bent towards the perpendicular to the sur-
face, so that it finally enters the eye as if it came from a
point higher up in the sky than it really does. The effects
of this are principally important to astronomers.
294. Mirage. In hot and sandy deserts the surface layers
Fia. 197. SPHERICAL ABERRA-
TION.
FIG. 198. MIRAGE.
of air are sometimes so expanded by the heat as to be rarer
than those above. Rays from a distant object are then bent
188
NATURAL PHILOSOPHY.
in the other direction, until finally, reaching the lowest
angle, they suffer total reflection. These strata from which
the objects and sky are reflected appear as a glassy pool.
The illusion is called mirage.
IV. DISPERSION.
295. Dispersion. When light passes from one medium
into another of different density, the light is not only re-
FIG. 199. DISPERSION OF LIGHT.
fracted, but the image of the object is seen to be surrounded
by a fringe of color.
Experiment 109. Look through a prism of glass, and notice the
colored fringes surrounding objects. Allow the direct rays of the sun
to shine through the prism, and notice the rainbow-colors thrown on
the wall or on any object in the room.
LIGHT. 189
Instead of a glass prism it is much better to use a triangular bottle
filled with carbon bisulphide.
Experiment no. With such a prism, allow a beam of light to
pass into a room through a narrow slit. Or obtain a beam from a
projecting lantern, and pass it through the slit. Place in front of the
slit a prism of glass, which may often be obtained from off a lamp.
Or, better, directly in front of the slit place a
double-convex lens in such a position as to
throw a well-defined image of the slit on a
wall or a screen. In the path of the light, after
passing through the lens, set a carbon bisul-
phide prism. A beautiful band of colors will *r
now be seen on the wall, not, however, di-
rectly in front of the slit.
296. Spectrum.-This band of colors FIQ 200 ._ DISPERSION .
is called a spectrum, and the separation
of the beam of light into tbe various colors is called dis-
persion.
297. Order of Colors. By an examination of the spectrum
it will be seen that the colors are arranged in this order,
violet, indigo, blue, green, yellow, orange, and red ; that
the violet is refracted from its straight course the most, and
the red the least.
298. Cause of Spectrum. We may now see the cause
of the spectrum. All these colors existed in the beam of
light as it came through the slit. But the prism refracted
them differently, turning the violet aside the farthest, tben
the indigo, and so on, and projecting them at different
places on the screen. If they are all united, the original
white light will be produced.
Experiment in. Hold a mirror in front of the prism so as to
throw the spectrum on the ceiling. Kapidly rotate the mirror, so that
the colors shall blend together on the ceiling. The image will now be
white.
299. Color-Disk. A color-disk is a circular piece of paste-
board, on which are pasted sectors of colored paper contain-
ing the rainbow-colors. When this is rapidly revolved, the
colors all blend together in the eye and make white or gray.
If the colors were perfectly pure and well lighted up,
190
NATURAL PHILOSOPHY.
the disk would be entirely white. The gray tint is pro-
duced by the impurity of the colors.
FIG. 201. COLOR-DISK.
300. Waves of Different Lengths. It has been said that
light is propagated in waves. All waves of light are not,
however, of the same length, nor do all have the same quick-
ness of vibration. Experiment has shown that the vibra-
tions of the violet rays are shorter and more rapid than
those of other colors, the indigo next, and then in the order
of arrangement in the spectrum. When light made up of
all these waves strikes the prism, the short, quick vibrations
of violet are turned aside the most, and the larger and
slower vibrations of red the least. This is the cause of
dispersion.
Experiment 112. Stand with the eye in the spectrum looking
towards the prism. The different colors will be seen in order as the
eye changes from side to side.
301. The Spectroscope. This explains the spectroscope.
In the end of the right-hand telescope is a narrow slit,
LIGHT.
191
through which the light enters. The eye looks towards
the prism through another telescope, which magnifies ob-
IlIlKalllli
FIG. 202. THE SPECTROSCOPE.
jects, and sees the spectrum directly. The third telescope
is for the purpose of throwing a scale into view, so as to
determine the positions of the various colors.
When used for celestial objects, this is attached to the
eye-end of a telescope, so that the light from the object after
going through the telescope will pass into the slit.
302. Effect of a Train of Prisms. If the light, after pass-
ing through one prism, falls on another, the spectrum will
be further dispersed. By using more prisms the spectrum
may be made of any required length, though each disper-
sion causes a loss of some light, due to reflection from the
faces of the prism.
303. Different Spectra from Solids and Gases. Light
coming from glowing lime, or from the heated carbon
particles in the flame of a lamp or candle, will give similar
192 NATURAL PHILOSOPHY.
spectra, differing only in brightness. If, however, the
spectrum of glowing vapor of sodium, made by sprinkling
a little common salt in an alcohol, or Bunsen burner, flame,
be examined with a spectroscope, it will be seen to consist
of one or two 1 yellow bands only. There will be no red,
green, or any of the other colors. If a vapor of strontium
be formed in the same way, there will be bands or lines of
red, yellow, and blue, and not of the others. In this way
every substance has its own peculiar lines when reduced to
the state of a glowing gas and examined with a spectro-
scope. We may thus judge of the composition of a sub-
stance by the character of its spectrum, Glowing solids and
liquids give continuous spectra, the colors running into one an-
other, and all are alike. But gases give spectra of bright lines,
and each gas has its peculiar spectrum. Several are shown in
the frontispiece.
304. Dark-Line Spectra. If the light passes from a glow-
ing solid through a gas, the spectrum shows all the colors ;
but it is crossed by dark lines, and the most careful measure-
ments, as well as theory, show that these lines are in the
exact position of the bright lines which the gas gives out
by itself. Thus, if the light passes through sodium vapor
there are seen in the yellow of the spectrum two dark lines
side by side. If in examining a heavenly body we found
such a spectrum as this, it would therefore indicate the
composition of the vapor through which the light passed,
but not the composition of the substance giving the light ;
the position of the dark lines would tell of the vapor which
made them, while the continuous spectrum would not tell
the character of the substance giving the light, except that
it was not a gas under ordinary pressure.
305. Solar Spectrum. The solar spectrum is seen in the
frontispiece. We infer from this that the sun is a glowing
1 There are two, but so close together that often they are not sepa-
rated.
LIGHT. 193
solid or liquid substance, and has an atmosphere of gas,
which produces the dark lines.
306. Cause of the Dark Lines. The cause of these dark
lines is as follows. A gas has power to take from light the same
vibrations which it gives out when glowing. When light from
glowing lime shines through sodium vapor, the vapor ab-
stracts from the light the particular vibrations that make
up yellow light. The dark lines therefore indicate the
absence of the spectrum in those positions. It is true that
the vapor gives its own bright yellow lines, but they are
faint compared with the spectrum from the solid, and hence
look dark by comparison.
307. Convergence of Spectra. As a glowing gas becomes
cooled down, the bright lines which it shows in the spec-
trum broaden into bands, till finally, when it cools down to
the state of a glowing liquid or solid, the bands run together,
and a continuous spectrum is formed. This shows that the
two kinds of spectra are not so distinct as would at first
be supposed.
308. Heat-Rays. The rays which convey the impression
of heat from a glowing solid are also refracted and dis-
persed by a prism. They are the same rays as the light-
rays, and extend also on both sides of the visible spectrum,
more especially on the red side. The rays by which photo-
graphing is done lie principally about the violet end of the
spectrum.
309. The Sun Blue. Prof. Langley has recently shown
that the atmosphere quenches much more of the rays near
the violet end than of those near the red end of the spec-
trum, and that if we could see the sun outside our atmos-
phere it would appear blue rather than yellow, as it does.
310. The Rainbow. The rainbow is a spectrum. Kain-
drops are the prisms. Whenever a ray of light enters one
of these drops there is refraction, and wherever there is
refraction there is dispersion.
The red is on the outside of the arc, and the violet on
i n 17
194
NATURAL PHILOSOPHY.
the inside. When there is a fainter secondary bow the
order of colors is reversed. The radius of the arc is about
41 , 1 and its centre is always exactly opposite the sun.
"When the sun is just setting, how much of a circle is seen ? how
near to the horizon must the sun be to make a bow ?
The path of the rays through a drop is seen in Fig. 203.
From S the rays come, are refracted at I, reflected at A, and
FIG. 203. PATH OF RAYS TO FORM PRIMARY Bow.
again refracted at I', and pass out dispersed towards M. The
lines SI and I'M make
an angle of about
41 with each other.
Hence a person
standing so that he
would receive these
rays. I'M, would have
them colored. But
the air is full of drops.
Those in such a posi-
FIG.204.-PATH OF BAYS TO FORM SECONDARY Bow. ^ ^ anyinstant
as to send the ray to the observer would always be 41 (for
1 A little less than half the distance from the horizon to the zenith.
LIGHT. 195
the red 42, and for the violet 40 J) distant from the point
opposite the sun, and hence would lie in an arc of a circle.
Other rays which enter the drop are also refracted, but
only those which pass as in the figure are kept together so
as to make an impression. The remainder are scattered.
The secondary bow is produced by two refractions and
two reflections, as in Fig. 204.
Fig. 205 shows the formation of both bows, a and a'
indicate the position of the drops which form the violet
rays, and b and b' that of the drops which form the red rays.
> Z
FIG. 205. FORMATION OF PRIMARY AND SECONDARY Bows.
311. Halos. Halos are circles of light around the sun
or moon, formed by refraction from crystals of ice floating
in the air. They are seen in summer as well as in winter,
for the cold of the upper regions makes ice-crystals at
any time of the year. When formed by the sun, there is
often sufficient light to show the colors of the rainbow.
196
NATURAL PHILOSOPHY.
A section of an ice-crystal is often of the shape of a six-
sided figure. When rays enter one face they are sometimes
refracted so that they emerge from the next face but one.
This forms the smallest and most common halo, with a
radius of about 22. Sometimes the rays enter a side and
come out at the base. This makes a larger and fainter
halo.
FIG. 206. HALOS AND PARHELIA.
312. Parhelia. There is often also a circle of white light
parallel to the horizon, formed by reflection from crystals of
ice suspended vertically in the atmosphere. This cuts the
halos in two points. In these points the light is concen-
trated, some coming from the halo and some from the circle
of reflection, and parhelia (otherwise called " mock suns," or
" sun-dogs") are formed.
LIGHT.
197
In Fig. 206, the bright spots are parhelia. The various
curves are produced by varied refractions and reflections.
Fig. 207 shows circles seen in the United States in Janu-
ary, 1883. In this
case parhelia were
noticed at C, D,
C', and D', even
though no halos
were seen from C
and C' and D and
D'. Distinct ones
were noticed at
A, B, A', and B',
and two colored
halos.
313. Colors of
Opaque Objects. " ^ - - - - ^ "'
It has been Said Fia 207. HALOS AND PARHELIA OF JANUARY, 1883.
that the light
which opaque objects diffuse is that by which they are seen.
But the light which they diffuse after it has entered slightly
within their surfaces is generally different from that which
falls upon them. Their surfaces have the power of choosing
out certain rays from the white light which is incident to
them, and of destroying them. The remainder is diffused,
and gives the objects their colors. If the colors of the red
end of the spectrum are absorbed, the object will appear of
some shade of blue. If the red and blue are both absorbed,
the remaining colors will mix, and the general effect will
be green. If nothing is absorbed, the color is white ; and
if all is absorbed, the object will appear black.
314. Colors of Transparent Objects. If the object is trans-
parent, it may be seen by the color which it transmits.
Blue glass transmits the blue rays, and quenches or reflects
the rest. Sometimes a piece of glass is seen to be of one color
by transmitted light and of another color by diffused light.
17*
198 NATURAL PHILOSOPHY.
Experiment 113. Place a piece of blue glass in the path of the
light which passes through the prism. The red end of the spectrum
will be quenched, the blue end will be undisturbed. Try the same
with glass of different colors.
315. Cause of Blue Sky. The little particles of aqueous
vapor and other things which exist in the air are so minute
as to reflect only the short blue vibrations. Hence the sky
appears blue by reflected light. When near sunset, the sun
is shining through a great stretch of air. 1 The blue is
largely taken out of his rays by this process of reflection,
and the red is transmitted to the eye. The blue rays make
the blue sky of places west of us. The clouds being lit up
by this red light which remains, seem to be of a ruddy
color. If there are no clouds, the strata of air nearest the
horizon are of a reddish hue, which hue imperceptibly shades
into the blue of the zenith through the intermediate shades
of the spectrum, orange, yellow, green, more and more
of reflected blue light being mingled with the transmitted
red as we recede from the horizon.
316. Primary Colors. All the colors seen on the earth
are composed of one of the colors of the spectrum or of
several of them blended together. Furthermore, all the
colors of the spectrum are composed of one or more of
the three primary colors, red, green, and violet. Eed and
green mixed in varying proportions produce the colors
which lie between them, and green and violet the rest.
Red and violet produce shades of purple. Therefore, also,
red, green, and violet produce white.
Experiment 114. Collect together a number of objects of different
colors in a dark room, and light them up by the light of a sodium
taper, made by holding metallic sodium or common salt 2 in the flame
of a Bunsen burner or an alcohol lamp. If the flame is bright enough,
the effect is very striking. Yellow colors are brought out plainly.
All others appear dark or of some shade of gray.
317. Only Yellow in Sodium Flame. It has been shown
1 Show this by a diagram.
8 A pine stick soaked in a solution of salt will answer well.
LIGHT. 199
that when the sodium flame is analyzed by a spectroscope
nothing is found in it but yellow light. Hence, when it
falls on objects, only those which can diffuse yellow light
are colored. The others quench it and appear dark. An
object cannot appear red or green, because no light con-
taining these colors falls on it.
Experiment 115. Place a strip of red paper in the red part of the
spectrum. It will appear of its natural color. Place it in the blue. It
will appear black. Ked paper quenches blue rays and diffuses red. Try
the same with paper of other colors. Most colored objects are colored
by a mixture of the spectrum colors : hence they may reflect more
than one.
318. Complementary Colors. We have said that red,
green, and violet produce white. Hence a mixture of
green and violet, as bluish green, will produce white when
combined with red. Also, since purple is a combination of
red and violet, purple and green colors will produce white.
Two colors which, when mixed together, produce white are
called complementary colors. The mixture of any two of
the primary colors is complementary to the third. We
can obtain complementary colors by combining violet with
bluish green for one shade, and red with yellowish green
for the other. The whole spectrum must be included in the
two colors. The names of some of the prominent comple-
mentary colors are as follows :
Red and bluish green.
Orange and turquoise-blue.
Yellow and ultramarine.
Yellowish green and violet.
Green and purple.
Two colors which are complementary show in contrast
to better advantage than two others.
319. Blue and Yellow. If solutions of aniline-yellow
and ammoniacal sulphate of copper be placed in tanks with
parallel sides, and light be passed through them so as to
be thrown on the screen in the same place, the mixture of
the blue and yellow colors will produce white.
200 NATURAL PHILOSOPHY.
Experiment 116. Make two solutions of blue and yellow liquids,
and pour them together ; the resulting liquid will be green.
The green is produced because the blue liquid allowed
the colors from green to violet to pass, and the yellow
those from green to red. Green is the only color which
both allow to pass, hence the mixture as seen by trans-
mitted light is green.
320. Effects of Complementary Colors. After the eye has
seen one color for a time, it gives to other objects the com-
plementary color.
Experiment 117. Make a broad black ink-mark on green paper,
and cover it with white tissue-paper. The mark will appear red.
This is an optical illusion. The eye is filled with green
rays, and the tendency is to see other objects of the comple-
mentary color. The white tissue-paper tones down the
intense blackness of the mark, which would otherwise, by
its distinctness, prevent the illusion.
321. Interference Of Rays. Color is sometimes produced by
interference of waves of light. This means that two waves so meet
each other that the depression of one corresponds to the elevation of
the other, so that they neutralize each other, as we have seen in the
case of water-waves (page 87). If in white light the colors of the red
end of the spectrum are thus neutralized, the resulting effect is blue.
If the blue and the red are neutralized, the color may be green.
322. Colors of Soap-Bubbles. This effect is seen in soap-
bubbles.
Experiment 118. Make a liquid out of good Castile soap and a
little glycerine and water, and blow some soap-bubbles. Notice how
beautifully the colors chase one another over the film.
The light is reflected to us from the outer and also from the inner
surface of the film. If the thickness of the film is just a quarter
of a wave-length, the light that comes from the inner surface, having
to pass twice through the film, is just one-half a wave-length behind
that which is reflected by the outer. If the film were three-quarters of
a wave-length thick, it would be one and a half wave-lengths behind;
and so on. In all these cases there would be destruction of light-
waves. As the film is continually changing its thickness, and as the
LIGHT. 201
wave-lengths of the different colors vary, there is a continually
changing view of colors seen on the bubble.
323. Diffraction. Another effect of interference is shown in what
is commonly called diffraction. If light passes through a very nar-
row opening, fringes of color are seen along its sides. These are due
to the fact that the waves of light radiating in all directions from the
opening come in contact, and certain vibrations destroy one another,
leaving the resulting colors.
324. Gratings. Another form of diffraction is produced by sub-
stances whose surfaces are covered with parallel lines very close
together. This is shown in mother-of-pearl shells, where the edges
of the layers constitute the lines. This is caused by interference of
the rays reflected from the'different surfaces. Glass or any metallic
surface ruled by fine lines affords an excellent substitute for a prism in
a spectroscope. The diffraction spectra are not so bright as the pris-
matic from the same source, as not nearly all the light is reflected, but
the colors are purer. The finer and closer the lines, the better will
be the spectrum.
Exercises. 1. What difference is there between the causes of the
color of a red book and of red glass ?
2. Why are some objects of different colors by candle-light from
what they are by daylight?
3. If the sun were composed of glowing sodium vapors only, what
colors should we have on the earth ?
4. What difference in color is there between the electric light and
gas-light, and what would be the effect of this difference on the colors
of objects lit up by them ?
5. Why will a strip of red glass cast a shadow on the blue of the
spectrum and not on the red ?
6. Will there be any difference in the effect on the spectrum if a
piece of colored glass is held in the path of the ray after and before
it passes through the prism ?
7. If held as in the former case, which part of the spectrum will be
seen on a piece of red glass ?
8. A star gives a spectrum crossed by bright lines : what is its
general constitution ?
9. Certain parts of a comet give a spectrum of bright lines only :
what does this indicate ?
UNIVERSITY OF CALIFQRf
DEPARTMENT OF PHYSICS
202
NATURAL PHILOSOPHY.
V. POLARIZATION.
325. Polarization. In water, while the wave moves hori-
zontally, every particle vibrates vertically.
In light the motion is also perpendicular to
the direction of propagation of the ray, but
at all angles to the vertical. Thus, if a
beam be supposed to move in a direction
FIG. 208. TRANSVERSE perpendicular to this page, the vibrations
SSE* OF BAY OF of the ether are not nl y in tne line ab > but
also in all other lines, as cd, 6/, etc. When
all the vibrations are quenched except such as move in one
direction, as ab, the light is said to be polarized.
326. Polarization by Crystals. This can be produced in
various ways. Plates cut from
crystals of tourmaline * parallel to
the axis have the power to de-
stroy all vibrations except such
as are parallel to the axis, li we
could suppose the crystal to be
made up of bars which cut off
all vibrations across them, we
should have the effect. Hence
a beam of light passing through
such a plate is polarized. While
there is no change in it visible
to the eye, the polarization can
be detected by means of another
similar plate. If this is held so that its axis is parallel to
that of the first, so that the " bars" of the two run in the
same direction, the light will still pass through. If it is held
at right angles, so that one destroys the rays which have
passed through the other, no light will pass through. By
FIG. 209. CRYSTAL OF TOURMA-
LINE.
1 Tourmaline is a semi-transparent mineral, crystallizing in long
prisms. The axis runs parallel to its greatest length.
LIGHT.
203
gradually revolving it from this latter position, more and
more light can be seen. This is most readily experimented
with by a pair of " tourmaline tongs," in one fork of which
FIG. 210. TOURMALINE TONGS.
the crystal can revolve. The first plate is called the polar-
izer, the second the analyzer.
327. Polarization by Reflection. Light can also be po-
larized by reflection. If
a ray be allowed to fall
on a plate of glass at an
angle of incidence which
is about 57, it will be
polarized in the plane of
reflection. That is, the
vibrations will now be in
lines parallel to the re-
flector, and others will
be destroyed. If the re-
flected ray fall on a second
plate at the same angle,
it may be revolved so as
to destroy the rays which the other keeps, or to keep them,
and the polarization will be made evident. When placed in
a position to reflect the light, as in Fig. 211, there will be
no apparent change in brightness, but when the analyzer
is revolved 90 the whole ray will be quenched. Such an
instrument as this is one form of polariscope.
328. Polarization by Refraction. There is still another
FIG. 211. POLARISCOPE.
204
NATURAL PHILOSOPHY.
method of polarizing. If a crystal of Iceland spar be
placed over a mark, the mark will appear double. The
Fia. 212. CBYSTAL OF ICELAND SPAR.
FIG. 213. DOUBLE REFRACTION.
FIG. 214.
FIG. 215.
crystal has the power not only of separating the two vibra-
tions, but of polarizing the parts, so that while one ray is
polarized in one plane the other
is in a plane perpendicular to
this. If the direction of vibra-
tion of one ray be in the line
of Fig. 214, the direction of the
other will be shown in Fig. 215.
329. Colors by Polarization. If a plate of selenium l or a
piece of glass under compression be placed between the two
plates of tourmaline of Fig. 210, a beautiful series of col-
ored rings will be seen. If the analyzer be rotated through
90, the colors will change to complementary. These
colors are due to interference.
330. Uses of the Polariscope. The polariscope is used in
testing sugar, to determine the strength of a solution. An
analyzer is also used to determine whether the light from
comets, the solar atmosphere, and other heavenly appear-
ances is polarized or not, thus determining whether it is
light radiated directly by the body or sunlight reflected
from it.
1 An impure form of this is gypsum, or land-plaster.
LIGHT.
205
VI. OPTICAL INSTRUMENTS,
331. Microscope. The simplest form of microscope is
FIG. 216. SIMPLE MICROSCOPE.
a double-convex lens, or magnifying-glass. Here we see
an image of an object placed
within its focal length magni-
fied, because the rays are re-
fracted so as to enter the eye as
if they came from a larger ob-
ject. The more convex the lens,
the greater is the magnifying
power. When very great power
is required, it is, however, better
for clearness of view to use two
or more lenses of less curvature.
The one next the object is the
object-glass^ or objective ; the one
next the eye is the eye-piece, or
ocular.
The object-glass makes a real
and inverted image of the object.
This image is viewed by the eye-
piece as if it were an object. It
does not reinvert the image;
18
Fia. 217. THE MICROSCOPE.
206 NATURAL PHILOSOPHY.
hence, with respect to the original object, the final image
is inverted. Fig. 217 gives the course of rays through a
microscope.
332. Telescope. In a telescope the principle is the same.
FIG. 218. PRINCIPLE OF THE REFRACTING TELESCOPE.
An image of a distant object is formed at the focal length
of the objective, and is magnified by the eye-piece.
In the microscope the image of the object is greater than
the object, and in the telescope it is less. In the former
the image increases as the focal length of the objective de-
creases ; that is, as the curvature becomes greater. In the
latter, for distant objects, the image increases as the focal
length increases ; that is, as the lens is made flatter.
333. Object-Glass. To make a good objective, it has to
be corrected not only for spherical aberration (page 187),
but also for the dispersion produced by the glass. This
would have the effect of producing spectra and surround-
ing all objects with fringes of color. This is chromatic aber-
ration. The method of making the correction is as follows.
A double-convex lens of crown glass is combined with a
plano-concave lens of flint glass. These glasses, being differ-
ently made, have different internal structure. The tendency
of the flint glass is to neutralize the dispersive effects of the
crown glass, but not its refractive effects, except in part.
Hence the rays are brought to a focus, and the colors are
not much seen ; though it is impossible to make the correc-
tion complete.
334. Refracting and Reflecting Telescopes, Such tele-
scopes as the above are called refracting telescopes. Some-
times the first image is made by a concave mirror, and is
LIGHT.
207
then viewed by an eye-piece, as in the case of the other.
These are reflecting telescopes. One form of them is seen in
Fig. 219.
Here also the first image is inverted. In case it is de-
sired to see things erect, as in a terrestrial telescope or a
FIG. 219. PRINCIPLE OF THE REFLECTING TELESCOPE.
spy-glass, another lens is added, to reinvert the image.
Two lenses are found to answer better than one for the
eye-piece. Also in a terrestrial glass four lenses are used
instead of two.
335. Opera-Glasses. The first telescope ever made Gali-
leo's was a combination of a convex objective with a con-
FIG. 220. PRINCIPLE OF THE OPERA-GLASS.
cave eye-piece. The latter was placed so as to intercept
the rays before they reached the focus, so that no image
was formed by the objective. An apparent image was
208
NATURAL PHILOSOPHY.
formed by the eye-piece, which was erect. This telescope
has a large field of view, but small magnifying power, and
is used in opera-glasses. Each tube is such a telescope.
336. Cause of Solidity. Bodies appear solid to us because
we see them with both eyes. With one eye we see a little
around one side, and with the other a
little around the other. These two
pictures give the appearance of solidity.
Experiment 119. Look with one eye at ob-
jects of which you do not know the shape, and
notice how flat they appear. Notice, also, how
difficult it is to judge of distance with one eye
shut, by attempting to place the finger on the
object. With one eye shut, endeavor to place
against each other two pencil-points at arms'-
length.
337. Stereoscope. The stereoscope
is constructed on this principle. Two
pictures of an object are taken from
slightly-different positions. These are
placed so that the light from them
after passing through glasses appears to throw them into
the same position. The points of difference in the two
Fm - ^
FIG. 222. PRINCIPLE OF THE PROJECTING LANTERN.
pictures are brought out and blended together, giving the
effect of solidity.
338. Projecting Lantern. A projecting lantern is often
used for lecture and educational purposes for throwing pic-
tures on a screen in front of the audience. A light, usually
LIGHT. 209
composed of a burning stream of house-gas and oxygen
playing upon a piece of quick-lime, is contained in an
opaque box. In the front part of this box are one or two
double-convex lenses, which bring the rays to a focus. In
front of this lens is placed the picture to be exhibited. An
image of this, real and inverted, is then thrown on the
screen by another combination of lenses. The size of the
image depends on the distance of the screen from the
lantern.
339. The Camera. The camera used by photographers
is a dark chamber with a convex lens in front and a screen
at the back. The lens produces on the screen an image
of the objects in front of it. The screen is ground glass,
semi-transparent, so that the image can be seen from
behind. When this image is made clear by careful focus-
ing, the lens is covered, the sensitive plate is put in, and
exposed by uncovering the lens.
340. The Eye. The eye is an instrument in optical prin-
ciples nearly the same as the camera. It consists of a ball
surrounded with a strong, firm coat, the sclerotic coat, the
" white of the eye," except a little space in front, where
there is a transparent coat, the cornea. Inside the sclerotic is
the choroid coat, of dark color, to quench the scattering rays ;
this is seen through the pupil of the eye. Inside of this,
again, is the retina. Back of the cornea is a chamber filled
with a transparent liquid, the aqueous humor. Behind this,
again, is the iris, a mass of radiating fibres, which by their
expansion and contraction change the size of the hole in
the centre, the pupil, and also give the color to the eye.
Back of this is the .crystalline lens, a double-convex lens of
cartilage, held in place by muscles. Back of the crystalline
lens, and filling the main body of the eye, is the vitreous
humor. The rays of light from external objects are made
slightly more convergent by the cornea, and are brought to
a focus on the retina by the crystalline lens, forming a real
and inverted image there. The impression of this image
210
NATURAL PHILOSOPHY.
conveyed to the brain by the optic nerve gives the sensa-
tion of sight. Each eye forms its own image, as in the
N
FIG. 223. THE HUMAN EYE.
FIG. 223. THE HUMAN EYE. A, cornea; B, aqueous humor; C, pupil : D, iris; E, crys-
talline lens; H, sclerotic coat; I, choroid coat; K, retina; L, vitreous humor;
M, optic nerve ; N, 0, P, muscles.
stereoscope : these images are slightly different, and their
blending gives the idea of solidity.
341. Defects in the Eye. When the image is clear and
distinct on the retina, the impression is clear and distinct.
If, through any error of curvature of the cornea or crys-
talline lens, the image is not made exactly on the retina,
sight is not perfect. If the image is formed in front of the
retina, the person is short-sighted; if it is intercepted by
the retina before reaching a focus, the person is long-sighted.
It is the case of a camera out of focus. The unconscious
endeavor to focus the eye in such cases produces straining
of the muscles, pain, and disease. This is corrected by the
use of glasses, either concave or convex. If the person is
long-sighted, a convex lens is put in the spectacles, to assist
LIGHT. 211
the crystalline lens in bringing the object to a focus on the
retina; if short-sighted, a concave lens, to overcome the
effect of the too great convexity of the crystalline.
342. Focus of the Eye. As rays from a near object do not
come in so nearly parallel as if the object were distant, the
muscles have the power to change the curvature of the
crystalline lens to suit the differing distances. This is done
without effort on our part, and, unless continued so long as
to tire the muscles, without any inconvenience. The eye
can immediately turn from reading a book to look at the
distant horizon without effort or pain, though it involves
considerable changes in the curvature of the lens.
Experiment 120. Procure an eye of an ox or other animal, freeze
it, and cut it into two from front to back with a razor. Notice the
various parts described above.
343. Persistence of Impressions. An impression on the
retina is not immediately effaced, but after the object
creating it is removed, it will still remain a few seconds.
If a stick with a glowing coal on it be whirled around, a
whole circle of light can be seen. Experiment 111 is also
explained by this. The different colors are mixed in the
eye, and white is produced.
344. Inversion of the Image. The image is inverted on
the retina by the convex crystalline lens, but the impres-
sion is rearranged in the optic nerve or in the brain. An
image is seen in both eyes, but these are combined into
one, except in the case of an object too close for distinct
vision, or in other abnormal cases.
345. Blind Spot, The part of the retina immediately
over the end of the optic nerve does not transmit its im-
pressions to the brain. This is the " blind spot" of the eye.
Its presence may be shown as follows.
Experiment 121. Make three heavy circles, as below. Close the
left eye, and hold the left spot in front of the right eye ; look at it
212 NATURAL PHILOSOPHY.
intently. By moving the paper slightly right and left a place can be
found where the left spot will be visible and not the centre one. Its
image falls on tlie blind spot.
General Exercises. 1. Suppose a coin an inch in diameter to be
held up before a wall parallel to it ; let the distance of the coin from
the source of light be 15 inches, and that of the wall from the source
5 feet: show that the area of the shadow is 1G times that of the coin.
2. Show that if light takes three years to pass trom a star to the
earth, that star is nearly 200,000 times more distant from the earth
than the sun is.
3. If the weight of a molecule of light amounted to but one grain,
show that its momentum would be about equal to that of a cannon-
ball weighing 150 pounds and moving with the velocity of 1000 feet
in a second.
4. Show at what angle a ray must be incident on a plane reflecting
surface in order that the reflected ray may make a right angle with
the incident ray. Ans. 45.
5. Find the angle between two plane reflectors so that a ray origi-
nally parallel to one of them may, after two reflections, be parallel
to the other. Ans. 60.
6. A man stands upright before a plane vertical reflector, and
observes that he cannot see the image of his head or of his feet :
show that if he goes nearer to the reflector or farther from it he can
still see only the same portion of his image as before.
7. A man stands before a looking-glass of his own height : show
that he can see his whole image, and determine how much of the
looking-glass is concerned in the formation of the image.
8. The sun is 30 degrees above the horizon, and his image is seen
in a tranquil pool : determine in this case the angle of incidence and
reflection.
9. A man stands before a looking-glass with one eye shut, and
covers its place on the glass with a wafer : show that the same wafer
will hide the other eye as soon as it is shut and the first is opened.
10. A small object is placed half-way between the centre and the
principal focus of a concave reflector : draw the image, and show in
what proportion it is to the object.
11. State what would be the appearance of a man standing on the
brink of a lake to an eye under the water.
12. The rays of the sun are received on a large converging lens,
the focus being rendered visible by the dust floating in the air ; a
screen placed a little in front of the focus shows a white circle sur-
rounded by a red fringe, and placed a little behind the focus shows a
white circle surrounded by a blue fringe : explain this.
13. A window-bar is viewed through a prism, the edge of which is
parallel to the bar : show that the side of the bar which is nearer to
the edge of the prism is fringed with red and orange, and the other
side with violet and blue.
HEAT. 213
CHAPTEE VII.
HEAT.
346. What is Heat ? Heat, like light, consists of waves
of ether. The waves of heat cannot be seen by the eye ;
they can be felt by the nerves of sensation, which are
scattered over the whole surface of the body.
Heat is, then, a mode of motion. 1 When a body is heated
its particles are set in vibration. This vibration is then
communicated to the ether which is in contact with them,
and so is conveyed to the senses. As the temperature is
raised, the vibrations become more and more rapid, till after
a while they have such rapidity that they are capable of
being perceived by the eye, and the body is seen to glow.
347. Theories of Heat. There was an old theory that
heat was caused by the passage of particles of matter from
the heated body. But this seems to be now disproved.
The present theory of heat is called the undulatory theory.
348. Sources of Heat. The sources of heat are in general
the same as the sources of light. The great reservoir is
the sun. It is constantly giving it out to the earth : the
earth uses some of it up, and some it radiates again into
space. An immense amount of heat is received even in
the frigid regions from the sun. Were it not for this, the
temperature of the whole earth would be far below zero
continually.
1 Prof. Tyndall has written a book called "Heat a Mode of Motion."
This is an excellent treatise on the subject, and will give to students a
valuable lesson in the careful habits which are necessary to a scientific
investigator.
214 NATURAL PHILOSOPHY.
349. Chemical Action a Source of Heat. Chemical action
is another source of heat.
Experiment 122. Mix some strong sulphuric acid and water slowly
together, stirring the mixture. They combine, and the vessel is
heated. A thermometer will show the rise in temperature. 1
The heat from combustion is from this source. There is
a chemical union between the oxygen of the air and the
carbon and hydrogen of the combustible. A certain amount
of heat is necessary to start this action, but when started
it keeps itself going by the heat which it generates.
Experiment 123. Put some "quick-lime" in water; apply the
thermometer to the water before and after. There is here chemical
union between the lime and the water, and " slaked lime" is formed.
350. Stoppage of Motion a Source of Heat, The stoppage
of motion is a great source of heat.
Experiment 124. Lay a nail on an anvil, and strike it two or three
sharp blows with a hammer. Then quickly touch the nail to a little
piece of phosphorus, or, if this is not to be had, give it more strokes
and touch it to the head of a match. The phosphorus or the match
will take fire.
We say the motion is converted into heat. This means that
the motion of the hammer is changed into the vibratory
motion of the particles of the nail, which in turn commu-
nicates itself to the particles of the phosphorus. It is an
illustration of the correlation of forces.
351. Illustrations of the Conversion of Motion into Heat.
There are many illustrations of the conversion of motion
into heat. Meteors, or "shooting-stars," are little stones
which enter our atmosphere with great velocity. They
strike so many particles of air, and so much of their motion
is stopped, that they become intensely hot, and finally burn
up, giving out the light by which we see them. All fric-
tion is accompanied by heat, for a similar reason. It is
the stoppage of motion. Friction-matches, the heating of
1 For this and similar experiments a thermometer should be pro-
cured without a frame, and with the markings on the tube.
HEAT. 215
axles, the Indian habit of rubbing two sticks together or
of striking flints to light a fire, rubbing the hands to warm
them, are illustrations.
352. It is believed that the heat of the sun is partly
supported by the fall of bodies into it and the conversion
of their motion into heat. As we know that the sun is
continually expending its energies in all directions into
space, we must explain in some way its sustenance, and
the heat generated by the fall of bodies from some dis-
tance away would be many times greater than that which
would be produced by their combustion were they com-
posed of solid coal. 1
353. Mechanical Equivalent of Heat. A given amount
of motion stopped will always produce the same amount
of heat. The amount of motion in a body depends on two
things, the mass and the velocity, and is measured in
foot-pounds. To raise one pound of water through one
degree Fahrenheit requires 772 foot-pounds of motion
stopped. If a pound-weight could fall into a pound of
water from a height of 772 feet, and all the heat resulting
could be collected in the water, its temperature would be
raised one degree Fahrenheit.
This number 772 is called the mechanical equivalent of
heat, and was determined by Joule x in a number of ways,
one of which was the following. He had a box of water in
which were a number of paddles which churned the water.
These paddles were turned by a weight falling. The
weight being known, and the space through which it fell,
also the difference of temperature of the water at the be-
ginning and at the end of the fall, the amount of fall neces-
sary to produce an increase of 1 was easily calculated.
Thus, a 100-pound weight falling through 20 feet would
perform 2000 units of work. If this raised the temperature
1 See Sharpless and Philips 's " Astronomy," Art. 47.
3 James P. Joule (jool), an English physicist, 1818-.
216
NATURAL PHILOSOPHY.
of one pound of water 2.59, then to raise it 1 there
would be 2000 -f- 2.59 = 772.2 units of work expended.
FIG. 224. JOULE'S MACHINE.
354. Conservation of Energy. If now this heat
could all be utilized in an engine, it could just
lift the weight to the point from which it fell.
We have another illustration of the " conserva-
tion of energy." The mechanical motion is de-
stroyed, but an equivalent in molecular motion
(heat) is produced. A certain amount of me-
chanical motion always produces the same
amount of heat, and if this could all be collected
it would in turn reproduce the mechanical
motion. The energy is not lost, but is converted
into another form. Heat is converted into me-
chanical motion in locomotives. This goes again
into heat in the friction of the bearings of the
different axles of the train, of the wheels against
the track, and of the train against the air.
355. Thermometers. Temperature is measured
by thermometers. The most common thermometer is the
FIG. 225.
THERMOME-
TER.
HEAT.
217
mercury thermometer, and it depends upon the principle
that heat expands the mercury in a tube and cold causes it
to contract. It consists of a bulb with a tube attached.
The bulb and part of the tube are filled with mercury, and
the remainder contains no air, but only a little vapor of
mercury. To construct a thermometer the mercury is
heated in the bulb, and when the tube is full of vapor it is
sealed up at the upper end. Then in cooling most of the
vapor condenses and leaves nearly a vacuum in the upper
part of the tube.
FIG. 226. To FIND THE
FREEZING-POINT OF A
THERMOMETER.
FIG. 227. To FIND THE BOILING-POINT OF A THER-
MOMETER.
356. Freezing-Point and Boiling-Point. There are several
ways of graduating thermometers, but in all there are
19
218 NATURAL PHILOSOPHY.
two points which must be determined. These are the
freezing-point of water and the boiling-point of water.
To determine the first, the bulb is kept in a mass of
chopped ice or snow till the mercury settles at a definite
place. This place is then marked.
To determine the boiling-point, the bulb is placed in
boiling water, from which the steam is allowed to pass
freely and to envelop the tube. The point at which the
mercury settles is then also marked.
357. Graduation. We have now two marks, and it is
necessary to graduate the thermometer between them.
There are two common methods of doing this.
358. Centigrade Thermometers. The first is the Centi-
grade method, used in France, and by scien-
100 - -212 tific people everywhere. The freezing-point
is marked 0, and the boiling-point 100, and
the space between is divided into 100 equal
divisions. Divisions of the same size are
then continued above 100 and below as
^ ar as necessar y-
359. Fahrenheit Thermometers. The other
is the Fahrenheit method, used by people in
general in England and the United States.
FIG. 228.-CENTI- The freezing-point is marked 32, and the
G BADE AN D ol '
FAHRENHEIT boiling-point 212, and the space between is
THERMOMETERS.
divided into 180 equal divisions, which are
continued up and down. Both methods will be used in
this treatise, the addition of the letter C. or F. stating
which.
As 100 C. are equivalent to 180 F., 5 C. are equivalent
to 9 F. ; hence any number of degrees of one scale can be
reduced to its corresponding number of the other.
Exercises. 1. To what marking on F. scale does 40 C. corre-
spond ?
Since 5 C.=9 F.,
1 C. r=f F.,
and 40 C. = 72 F.
17 s - -
HEAT. 219
This gives the number of F. degrees above freezing-point, which
is 32 above zero. Then the reading of the F. scale would be 104.
2. To what marking on C. scale does 122 F. correspond ? Ans.
50.
3. To what marking on F. scale does 10 C. correspond ? Ans.
+50.
4. To what marking on C. scale does 40 F. correspond ? Ans.
40.
5. How many units of work are required to raise 1 pound of water
through 1 C. ? Ans. About 1390.
360. Unit of Heat. It is convenient to have some unit
by which to measure the amount of sensible heat in a body.
The unit adopted is the amount of heat required to raise the
temperature of one pound of water at 32 through one degree.
361. Specific Heat. If instead of taking a pound of
water we take a pound of mercury and expose it to the
same heat, its temperature will rise more than that of water.
More of the heat given to the water is employed in keep-
ing the molecules in vibration than in the case of the mer-
cury, so that it does not show itself by a thermometer. All
known substances except hydrogen will rise in tempera-
ture farther than water by the application of the same
amount of heat. The specific heat of a substance is the
amount of heat necessary to raise one pound of it through one
degree, the specific heat of water being 1.
One way of determining the specific heat of a substance
is by the method of mixtures.
Experiment 125. Mix together one pound of water at 80 and
one pound at 50. The mixture will be at 65. The former loses as
much as the latter gains.
Experiment 126. Mix one pound of water at 80 with one pound
of mercury at 50. The mixture will be at 79. The water has lost
1, and that has raised the mercury through 29. The specific heat
of mercury is therefore ^.
362. Heat produces Expansion. The general effect of
heat is to expand bodies. An iron ball that will just pass
through a ring when cold, is too large when hot. An iron
rod will measure a little longer when heated. The rails
of a track laid in summer will be separated in winter.
The expansion is accomplished by the separation of the
220
NATURAL PHILOSOPHY.
molecules, and the separation is caused by their rapid vi-
bration. This requires more room, and overcomes to some
extent the force of cohesion. The force of separation is so
FIG. 229. EXPANSION OF SOLIDS BY HEAT. FIG. 230. EXPANSION BY HEAT. GBIDIBON
PENDULUM.
great that it is generally useless to try to counteract it.
In iron buildings and bridges arrangements are made so
that the pieces can be allowed to expand without injury.
363. Melting and Evaporation by Heat. As the heat is
increased, the particles are more and more agitated and dis-
persed, and the force of cohesion becomes less and less, until
finally the body changes from a solid to a liquid. If heat
is still applied to it, the molecules are farther separated,
until they reach such a distance apart that no cohesive
force acts between them, and the liquid becomes a gas.
HEAT.
221
Melting and evaporation, then, must be considered as the
shaking apart of the molecules by the vibratory motion
communicated to them, which vibratory motion is heat.
FIG. 231. EXPANSION OF LIQUIDS BY HEAT.
FIG. 232. EXPANSION OF AIR.
364. Expansion of Liquids. The expansion of liquids can
be readily seen by
Experiment 127. Partly fill with colored liquid a glass tube with
a bulb. Immerse the bulb in water, and apply heat gently. The
colored liquid will rise in the tube. Thermometers are based on
the principle of the expansion of liquids by heat.
19*
222 NATURAL PHILOSOPHY.
365. Expansion of Gases. The expansion of gases can be
seen by the following :
Experiment 128. Heat a flask filled with air, and conduct a tube
into a vessel of water. The expanded air will be driven out of the
tube, and will bubble up through the water.
Experiment 129. Tie up a bladder or a toy balloon partly filled
with air. Heat it, and the balloon will expand.
In Experiment 128 it is evident that the air remaining
in the flask will weigh less after being heated than did the
original, for there are fewer particles.
366. Law of Expansion of Gases. There does not seem
to be any general law which can be said to govern the
cases of expansion of solids and liquids, since they are so
diverse in their qualities. But a true gas (not a vapor) will
expand according to a certain law, whatever its composi-
tion. If kept under a constant pressure as it expands, it will
increase -%fo of its volume at for every Centigrade degree of
heat given it.
To illustrate this, suppose p to be a piston fitting closely
in a tube ab, but moving up and down without fric-
tion, and suppose the portion pb below the piston to be
filled with gas at a temperature of C. If the tem-
perature be raised to 1, the gas will expand ^^ of
its volume, and will lift the piston ; if raised to 2, it
will expand yfg- of its original volume ; and so on. If
raised to 273, it will have just double its original
volume.
We can also carry the process the other way. If
1 of heat be taken from the gas, the resulting volume
23?; will be |^| of the original ; if 2, |^J ; and so on down.
In theory, when the gas is cooled to 273 it would
have no volume at all. But practically it becomes a solid
long before it reaches this temperature, and the law does not
apply to solids. This number, 273 Centigrade, is called
the absolute zero of temperature.
What would be the absolute zero on F. scale ?
HEAT. 223
367. Relation between Heat and Volume. When a body
is heated, some of the heat goes to expand it, so that the
temperature is not so great as it would otherwise be. If
the piston in Fig. 233 were held down so that the gas could
not expand, the same amount of heat applied to it would
raise its temperature higher. In expanding, part of the
heat is used up in doing the work of separating the mole-
cules. This heat is consumed continuously in keeping the
molecules apart, and any abstraction of heat will allow
them to come together again. Hence cold produces con-
traction. Cooling is the loss of vibratory motion, and as
the motion ceases, the molecules approach one another.
.N~ow, if the expansion is produced by a force, without
the application of any external heat, cold is produced. For
part of the heat previously in the body is now consumed in
maintaining the separation of the molecules. The sudden
stretching of a wire lowers its temperature. 1
368. Heat and Fusion, When heat is applied to a solid
body so as to raise its temperature to the point of fusion
or melting, the addition of more heat will not further raise
the temperature till the body is completely melted. The
heat does the work of driving the molecules apart, and so
changing it from solid to liquid. A certain amount of heat
is consumed in maintaining the liquid form.
Experiment 130. Place a piece of ice in a vessel over a slow fire.
As the ice melts, keep it well stirred, and frequently apply a thermom-
eter. It will indicate the freezing-point until all the ice is melted.
Although much heat has gone into the ice, it has been
destroyed as sensible heat, and is employed in keeping the
molecules at such a distance from one another as to make a
liquid. This energy, which does not show itself by a ther-
mometer, is called latent heat It requires 80 units of heat
to melt ice, or as much as would raise the same weight of
1 India-rubber seems to be an exception to both laws. "When
stretched, heat is produced, and the application of heat contracts in-
stead of expanding it.
224 NATURAL PHILOSOPHY.
water through about 80 C. of temperature. When the ice
freezes, the same amount of heat is given out.
Melting, then, implies the using up of heat. As this heat
comes from external sources, its effect is to reduce their
temperature. Freezing, on the contrary, liberates heat
and raises the temperature of surrounding objects. Melting
causes cold, and freezing causes heat.
Experiment 131. Mix some chopped ice with salt, and stir well
together, and keep a thermometer in the mixture. It will indicate a
temperature much below the freezing-point. The salt makes the ice
melt, and so causes cold. This is the common freezing mixture used
by ice-cream-makers.
Experiment 132. Pulverize some nitrate of ammonium in a thin
glass vessel, add water, and stir. As the salt dissolves, insert the bulb
of a thermometer. The mercury will rapidly fall. Place the vessel
on a wet board. It will freeze to it.
Here the rapid solution of the salt in water abstracted
heat from the vessel, from the thermometer, and from the
board. Hence not only fusion, but solution, causes cold.
Define fusion and solution.
369. Heat and Evaporation. Similar effects are seen in
the passage from the liquid to the gaseous state. Heat is
required to keep up the gaseous condition of a body : hence
evaporation takes heat from surrounding objects and causes
cold, and condensation liberates it and raises temperature.
Experiment 133. Pour a little ether in the palm of the hand. As
it rapidly evaporates, considerable cold is felt. Dip a thermometer in
ether and quickly remove it. The ether which adheres will evaporate
and take heat from the mercury in the bulb.
370. Freezing in Red-Hot Vessels. Sulphurous acid
the gas formed when sulphur is burned in air is capable
of being made liquid by passing it through a tube immersed
in a freezing mixture of ice and salt. If a crucible be heated
red-hot, a little water put in it, and immediately the liquid
sulphurous acid poured on it, so great a degree of cold will
be produced by the sudden vaporization of the acid that
the water will be frozen in the red-hot crucible.
371. Solidification of Gases. If a gas be condensed by
HEAT. 225
great cold and pressure, and then suddenly be allowed to
expand by passing out through a fine tube, the great expan-
sion and evaporation will cause such cold that the gas will
be liquefied, and in some cases solidified. Hydrogen, the
lightest of all gases, has been made solid by this method,
and been heard to rattle on the floor like minute hailstones.
372. Cryophorus. A cryophorus is an instrument con-
sisting of two glass bulbs connected as in Fig. 234.
One of these is partly filled
with water, and the rest
of the apparatus is made
as nearly as possible a
vacuum. This is soon filled
with vapor of water, which FIG. 234. CEYOPHORUS.
passes oif under the low
pressure. If the other bulb is placed in a freezing mixture
of ice and salt, the vapor is condensed, and evaporation
goes on so rapidly from the water that it finally freezes.
373. Artificial Ice. In India, ice is made by putting
water into pots of porous earthenware. The water evap-
orates from the outside of these so as to freeze the water
on the inside. Artificial ice is produced in warm coun-
tries on a large scale by passing liquid ammonia through
pipes which line the bottom and sides of a vessel of water.
The liquid is quickly converted into a gas, and this takes
so much heat from the water that it is frozen.
Experiment 134. Heat some water, having the bulb of a ther-
mometer in it during the operation. The mercury will gradually
rise till it reaches the boiling-point ; after which, if the steam is not
confined, it will not indicate any higher temperature till the water is
boiled away.
374. Heat and Evaporation. In this experiment the heat
applied after the water commenced to boil is all expended
in changing the liquid to a gaseous form, and becomes latent
in the gas. To change water into vapor requires about
537 times as much heat as would raise the same amount
through one degree of temperature, in other words, 537
P
226 NATURAL PHILOSOPHY.
units of heat. This number 537 is called the latent heat
of steam, as 80 (see Par. 368) is the latent heat of water.
They represent the number of degrees of heat stored up
and kept in constant use in maintaining the condition of
the body, and which will not show itself by a thermometer.
375. Heat expended in Fusion and Evaporation. To
show the meaning of these figures, let us suppose a mass
of ice at a temperature of 10 C., and let it be heated
from a source which gives it 1 a minute. In 10 minutes
it will be brought to 0. In 80 minutes more it will be
all melted, but it will still be at 0. In 100 minutes more
it will be raised to a temperature of 100, and will begin
to boil. In 537 minutes more it will all be converted into
vapor at a temperature of 100. This vapor can then be
increased in temperature by the application of heat.
Exercises. 1. Why does moist clay contract when heated?
2. Why do telegraph-wires hang down more in summer than in
winter ?
3. Why does a wheelwright put the tire on the wheel hot?
4. Will sugar placed in coffee cool it more than the same amount
of sand at the same temperature ? why ?
376. Expansion by Freezing 1 . The general effect of cold
is to contract. There are exceptions to this in the case
of water under certain circumstances, and of a few other
substances. When water is reduced in temperature it con-
tracts in volume till it reaches the temperature of 39
F. or 4 C., after which it begins to expand. This expan-
sion amounts to about T ^ of its original bulk, and shows
itself in bursting vessels in which it is contained. Heavy
iron shells can be thus burst. Fig. 235 represents the
effects of this expansion. A large shell was filled with
water and the hole tightly stopped by a wooden plug.
When it froze, the plug was forced out with great velocity
and a cylinder of ice eight inches long issued from the
hole. At another time the shell split in two, and a sheet
of ice was forced out.
This lightness of ice causes it to float on water. If it
SEAT. 227
continued to contract as it cooled, it would sink, and all of
it would be at the bottom of the ponds.
FIG. 235. EFFECTS OF FREEZING.
377. Freezing. Freezing is the formation of crystals.
They begin to form around the edge of the pond or around
some object floating in the water, and add one to another
till the whole surface is frozen. The process can be watched
by the following method.
Experiment 135. Wet a clear piece of glass with a solution of
sulphate of copper or chloride of ammonium, and hold it between
you and the light. In a little while, as the water dries, the crystals
will begin to shoot out in various directions over the glass. The
effect is much improved if the plate is placed in a projecting lantern
and the formation of crystals shown on the screen.
378. Melting, Melting is the reverse process from freez-
ing. When the temperature is raised above the freezing-
point the crystals gradually dissolve into water. This
goes on all through the mass, and the ice becomes rotten
before it disappears.
379. Evaporation and Boiling. Evaporation goes on at
all temperatures. Ice is converted into vapor without
passing through the intermediate stage of liquids. Clothes
hung out in cold weather will become dry while the tern-
228
NATURAL PHILOSOPHY.
perature is all the time below the freezing-point. But the
process goes on the more rapidly the higher the tempera-
ture. As water is slowly heated, steam passes away from
its surface with greater rapidity until, when a certain tem-
perature is reached, steam begins to form all through its
mass. This, being lighter than water, is forced up through
it to the top. This is boiling. The heat being applied at
the bottom, that portion is most heated, and steam is there
formed most vigorously. JSTot only the steam but also the
heated water, being expanded, rises, and the other water
takes its place, to be in turn heated. Thus there is a con-
stant circulation.
Experiment 136. Add a little chalk-dust from the blackboard to
water in a glass flask, and heat it ; watch the circulation of the water
by the aid of the particles of dust.
In such experiments
wipe the flask dry on the
outside, and apply the
heat gradually at first.
380. Relation of
Boiling-Point and
Pressure. The boil-
ing-point varies with
the pressure. By ex-
hausting the air over
water it can be made
to boil at a much
lower temperature.
Whenever the ten-
sion of the vapor
equals the outside
pressure, boiling be-
gins.
Experiment I37-
Boil some water in a
flask, and remove the
lamp. "When the boiling has ceased, cork the flask, invert it, and
pour some cold water on its base. The boiling will begin again.
The cold water condensed the vapor and reduced the pressure.
FIG. 236. BOILING AS AN EFFECT OF REDUCED
PRESSURE.
HEAT. 229
This principle is used in the manufacture of certain dye-
stuffs, and in sugar-refining, where it is desirable to evapo-
rate the water at a low temperature. A partial vacuum is
formed in the boiler, and the steam, as fast as it passes off,
is condensed by a falling spray of water.
As we ascend a mountain the boiling-point lowers. An
approximation to the height may be formed in this way :
Eoughly, the height in feet will be found by multiplying
600 by the number of degrees below 212 F. at which
water boils.
Questions. 1. On a certain elevation water is found to boil at
200 F. : what is its height ? 12 X 600 = 7200 feet, nearly.
2. A mass of gas at 60 C. arid under a pressure of 30 inches
measures 100 cubic inches : what will be its volume at 40 C. and
under a pressure of 28 inches?
Solution. At 60 its volume will be -ffe greater than at ; at
40, Ys greater. Now, 100 cubic inches l^-, or fff, its volume
at 0. Hence
Volume at = ||f X 100 = 81.9.
Volume at 40 = f }f of 81.9 == 93.8.
This is the volume under 30 inches pressure. Under 28 inches, by
Mariotte's law, the whole will be f| of 93.8 = 100.5 cubic inches.
3. A mass of gas at C. occupies a litre : what will be its volume
at 546 C. under the same pressure? Ans. 3 litres.
381. Steam. Steam occupies about 1700 times as much
space as the water which produces it. In other words, a
cubic inch of water will make about a cubic foot of steam.
382. Distillation. Condensation is the reverse of evapo-
ration. It takes place whenever the vapor is reduced in
temperature below the boiling-point of the liquid. This is
what causes the formation of dew, clouds, and rain. 1 Dis-
tillation is the condensation of certain portions of a liquid
which separate from contained solids, or pass off at a lower
temperature than the remainder. In this way water can
be separated from the impurities which it contains, and
alcohol from the water with which it is mixed.
The instrument by which this is effected is a still. A
1 This subject will be found more fully treated in the chapter on
meteorology.
20
230
NATURAL PHILOSOPHY.
retort containing the liquid is heated and the vapor passed
over into a " worm," which is kept cool by being immersed
FIG. 237. STILL.
in cold water. Here the vapor is condensed and runs out
at the lower end, while the solid impurities or the less
volatile liquids remain in the retort.
Experiment 138. Drop a little water on a piece of iron heated to
about 150 C. It will form into a drop and dance about the surface,
and not evaporate very rapidly. Allow the plate to cool. At a cer-
tain temperature the drop will break, spread over the iron, and
almost immediately change to vapor.
In this case the great heat of the plate causes such a
down-rush of steam that the drop rests on a cushion of steam,
and not on the plate. This fact can be readily seen by
Experiment 139. Place a candle in the right position, and you
can see light between the drop and the plate.
TRANSMISSION OF HEAT.
383. Transmission of Heat. Heat travels through ether
just as light does. The vibrations of the heated body are
communicated to the particles of ether in contact with
them, these act on the next, and so the motion is extended.
The heat- and the light-rays are, partly at least, exactly
the same rays. Some rays give us sensations of both light
HEAT.
231
and heat, some of heat only ; hence heat- and light-rays,
being largely the same, follow the same laws. Heat, like
light, decreases as the square of the distance increases
FIG. 238. REFRACTION OF HEAT BY A BURNING-GLASS.
(see Par. 257) ; it is refracted in accordance with the " law
of sines" (see Par. 280), and it is reflected, making the angle
of incidence equal to the angle of reflection.
384. Luminous and Dark Heat. The laws are the same
whether the heat comes from a glowing body, like a candle
or the sun, or from a dark body, as a vessel filled with hot
water. In the one case we have luminous heat, and in the
other we have dark heat.
385. Radiation and Radiant Heat. The passage of heat
from a heated body is
called radiation, and
heat on its passage is
radiant heat.
386. Reflection of
Heat. To prove that FIG. 239. REFLECTION OF HEAT.
dark heat undergoes reflection, we can place a vessel of
boiling water at the principal focus (see Par. 270) of a con-
232 NATURAL PHILOSOPHY.
cave mirror, when the heat-rays will be reflected ; and if
collected by another concave mirror, a thermometer placed
at its principal focus will show a decided increase of tem-
perature.
If a piece of ice is used instead of the vessel of hot
water, the mercury falls. This would seem to indicate
that cold is also reflected. Such is not the case. The
cause of the fall is that the thermometer parts with its
heat faster than the ice does, and it goes to the ice to raise
its temperature, or to melt it.
To prove the refraction of heat we have the ordinary
" burning-glass."
387. Heat Reflected, Diffused, Absorbed, and Transmitted,
Like light, all the heat which falls on a body is not re-
flected. Some of it is diffused (scattered in all directions),
some of it goes into the body, and is either used up in
doing work among the molecules or is transmitted.
388. Different Bodies have Different Effects. Different
bodies differ greatly in their power of radiating, of trans-
mitting, of reflecting, and of absorbing heat.
389. Difference in Radiation. If there be three vessels
of equal size filled with hot water, one made of polished
tin, one coated with isinglass and one with lamp-black, then
in the same time there will be eight times as much heat
radiated by the lamp-black as by the tin, and seven times as
much from the isinglass as from the tin. As a general
rule, metallic bodies are poor radiators, and the brighter
and smoother the surface the poorer radiators they become.
Good reflectors are commonly poor radiators, and the re-
verse. A body that radiates well will absorb well and re-
flect badly.
390. Difference in Transmission. As regards transmis-
sion of heat, certain substances which are opaque to light
allow heat to pass freely, and some transparent to light
entirely cut off the heat. In the chapter on light we
learned that blue glass allowed blue rays to pass through
HEAT. 233
and cut off the red : in the same way thin metallic foil
will allow luminous rays to pass and cut off almost all the
dark heat. Bad radiators are bad transmitters, for the
bad radiators, like polished tin, reflect much of the heat
that falls on them, and so transmit but little.
391. Special Substances. Lamp-black (the soot from
lamps) is an excellent absorber ; it transmits no heat and
reflects but little. Polished silver is a good reflector; it
transmits nothing and absorbs very little. Eock-salt in
transparent crystals transmits nearly everything; it ab-
sorbs none and reflects but little. Crystals of alum, equally
transparent, will absorb nearly all the heat and transmit
almost none. Ice is also a very poor transmitter.
392. Dr. Franklin's Experiment. Dr. Franklin made the
experiment of putting pieces of cloth of different colors on
snow when the sun was shining. He found that the dark
colors melted themselves into the snow farther than the
light, from which he inferred that they were in general
better absorbers. This is true in so far as it relates to
luminous heat, but in the case of dark heat, such as we get
from a stove, color does not seem to make any difference.
393. Effect of Screens. A screen placed in front of a
fire protects from heat. But, as it receives heat itself, it
becomes in time a source of radiation. We do not feel the
radiation so strongly, because the heat which it intercepts
it sends out in all directions, and hence not so strongly in
any one.
Exercises. 1. Should stoves be kept bright if we desire to have
the most heat from them? Should teapots be of polished metal?
cylinders of steam-engines?
2. Which is cooler in the direct rays of the sun, light clothing or
dark ? in a house by a hot stove ?
3. If we had a convex lens of alum and one of rock-salt exposed
to the sun, in the focus of which would be the higher temperature ?
4. How much is the heat diminished by moving twice as far from
its source ?
5. The dark heat-rays are found near the red end of the spectrum :
which have the more rapid vibration, the dark or the luminous waves ?
6. Is a glass screen as effective in front of an open fire as in front
of a stove ?
20*
234
NATURAL PHILOSOPHY.
CONDUCTION OF HEAT.
394. Conduction of Heat. When heat travels along by
communicating motion from one particle of a body to an-
other, the movement is called conduction of heat. Eadiation
is movement through ether, and radiant heat has the same
velocity as light. Conduction is a comparatively slow
process.
Experiment 140. Heat one end of an iron rod to which nails
are stuck by little pieces of wax. The nails will drop off one by one
as sufficient heat reaches them to melt the wax.
FIG. 240. CONDUCTION OF HEAT.
395. Different Conducting Power. Diiferent bodies diifer
in their power to conduct heat.
Experiment 141. Hold an iron rod in the fire till it begins to feel
hot. Hold a glass rod the same time, no perceptible increase of
heat is felt.
Experiment 142. Coat bars of various substances with wax, and
place them all with one end in hot water. Notice how far on each
the wax melts.
FIG. 241 .DIFFERENT CONDUCTING POWER.
396. Conducting Power of Metals. The following table
gives the relative conducting power of certain metals :
HEAT.
235
Silver 100
Copper 74
Gold 53
Tin.... 15
Iron 12
Lead 9
Bismuth 2
397. Conducting Power of Liquids and Gases. Liquids
and gases are poor con-
ductors of heat.
Experiment 143. Pack
snow in a test-tube, and
apply heat near the top.
The water may be made to
boil at the top while the
snow is still unmelted at
the bottom.
398. Conducting
Power of Air. Dry
air is a poor con-
ductor of dark heat, a
better one of luminous
heat, but moist air is
a worse conductor of
both dark and luminous
heat. The sun's heat
comes to us through
the air and heats up
the earth. This then
radiates dark heat, part
of which is retained by the moist air surrounding it.
On high mountains the sun's luminous heat penetrates
the rare air without warming it, and heats the mountain-
tops. But the radiated heat from the.m is not retained, but
quickly passes off, leaving the air cold. A cloud or fog
over the mountain would change all this.
The glass of a hot-house produces the same effect as the
moisture of the atmosphere.
An open fire gives out luminous heat, which penetrates
the air of a room readily and warms up the surfaces of
solid bodies. The heat from a stove or a furnace, on the
Fia. 242. POOR CONDUCTING POWER OP WATER.
236 NATURAL PHILOSOPHY.
contrary, is more retained in the air. In the one case we
keep warm by direct radiation, in the other by living in a
warm atmosphere.
Clothing is especially useful in retaining a layer of warm
air next the body. This by its poor conducting power
prevents the passage of heat outward.
399. Sensation of Heat. Our sensation of heat depends
largely on the conducting power of the substance with
which we are in contact. A carpet and an oil-cloth lying
side by side may actually contain the same amount of heat.
But if we touch both at the same time, the best conductor,
the oil-cloth, conducts away from us the most heat, and so
seems colder. It would produce the same effect in a ther-
mometer, carrying away heat from the mercury.
Exercises. 1. Why is a glass tumbler more readily cracked by
hot water than a vessel of better conducting power?
2. Why are the handles of teapots often made of glass or porcelain ?
3. Why is woollen clothing warmer than cotton ?
4. Why can a man plunge his hand into molten iron without being
burned ?
5. A brass cylinder covered with thin paper may be held in a
flame for some time without having the paper scorched ; not so when
the cylinder is made of wood : why is this difference ?
6. Why do hollow walls and double windows keep a house warm?
7. Would a hot-house be effective if heated by a stove from above
instead of by the sun?
8. Why does the coming of clouds frequently make it warmer ?
9. Are our sensations safe judges of temperature ? Having had
one hand in ice and the other in hot water, what will be the effect if
we plunge both into tepid water ?
CONVECTION OF HEAT.
400. Convection of Heat. When a liquid or a gas is heated
from below, the warm particles rise and are replaced by
colder heavier ones. This makes constant circulation,
which carries the heat about. This method of conveying
heat by actual transmission of the particles of water is
called convection of heat.
This can be well observed in the boiling of water, as
seen in Experiment 136.
HEAT. 237
The diffusion of heat by currents is shown on a large
scale in the Gulf Stream. This great body of warm water,
which is a result of the heating of the earth at the equator,
conveys this heat to the coasts of England and Norway.
THE STEAM-ENGINE.
401. History of the Steam-Engine, About the year 1700
a machine to pump water out of mines by the aid of steam
was invented and used in England, but about 1775 James
Watt, 1 a Scotch mathematical instrument-maker, invented,
and soon after brought almost to its present perfection, the
stationary engine. The first locomotive-engine was built
and run in 1804 or 1805 in England. But it was not until
1829 that the first really efficient locomotive was built by
George Stephenson, 1 an Englishman.
402. The Stationary Engine. Fig. 243 shows the essential
features of the stationary engine. M is the boiler, where
the steam is generated. At first we will suppose the valve
b to be shut and a to be open. The steam will pass from
the boiler through a and drive the piston, p, to the bottom
of the cylinder, a is now closed and b and d are opened.
While the steam is now passing through b to the under
side of the piston and pushing it up, that steam which was
above the piston is rushing through d down to the con-
denser, I, where it is condensed by the cold water there,
leaving a vacuum above the piston, so that there is no
obstacle to its ascent. When it reaches the top of the cyl-
inder again, b and d are closed and a and c opened, and so
on constantly. The figure shows how the up-and-down
motion of the piston turns the fly-wheel, E, and thence by
a belt or otherwise the machinery is set in motion.
1 Watt and Stephenson were two of the greatest benefactors to
mankind that ever lived. Samuel Smiles has written lives of both
these men that would be exceedingly interesting and valuable to
every one who studies this book.
238
NATURAL PHILOSOPHY.
403. The High-Pressure Engine. The condenser adds
much machinery to the engine, and requires a constant
supply of cold water. Many engines, therefore, have no
condenser; d and c open directly into the air. The air
condenses the steam and itself fills up the vacuum, so that
the piston in returning has to drive the air out of the
cylinder ahead of it. With a condenser the piston is driven
back through a vacuum, so that there is no resistance ;
without it the piston must be driven against the pressure
of the atmosphere, nearly 15 pounds per square inch.
FIG. 243. STATIONARY ENGINE (LOW-PRESSURE).
When there is no condenser, the pressure of the steam must
be about 15 pounds per square inch greater or higher to
do the same work : hence an engine without a condenser is
called a high-pressure engine, while one having a condenser
is called a low-pressure engine. Almost all small stationary
engines are high-pressure. This is especially true of por-
table engines, such as steam fire-engines, engines for work-
HEAT.
ing thrashing-machines, portable saw-mills, and the like.
A high-pressure engine of course takes more fuel to do the
same work. In a high-pressure engine the steam escapes
from the cylinder in puffs, and this puffing is characteristic
of this kind of engine.
404. How the Valves are worked. In Fig. 243, for the
sake of simplicity, it is supposed that the four valves are
worked by hand. Fig. 244 shows how one valve does the
work of all four. In the right-hand figure the valve is
raised, which allows the steam coming in by the pipe on the
left to flow into the lower part of the cylinder, while the
peculiarly-shaped valve, called a D-valve, connects the pipe
from the other end of the cylinder with the opening 0, which
leads into the condenser. When the piston reaches the
upper end of the cylinder, an arm, worked by the engine
itself, pushes the D-valve down, as seen on the left, and the
upper part of the cylinder is connected with the boiler,
while the lower part is connected with the condenser.
405. Three Important Attachments to the Engine. An
opening is made in the top of the boiler, which is closed by a close-
Fia. 244. D-VALVE AND CYLINDER.
FIG. 245. THE GOVERNOR.
fitting plug of iron. This plug is held down by a lever-arm, at the
end of which is a certain weight. When the pressure of the steam
240 NATURAL PHILOSOPHY.
becomes so great that there is danger of its bursting the boiler, it
lifts this plug and escapes. This is called the safety-valve. A gauge
is usually attached to boilers, which shows how great the pressure
upon each square inch is at any time.
Fig. 245 shows a very ingenious invention of Watt's, which auto-
matically controls or governs the speed of the engine ; hence it is
called the governor. This is so attached to the engine that it re-
volves. If the engine runs too fast, the governor will revolve faster,
and the two large balls will be thrown outward by centrifugal force.
This raises R, which works a valve and shuts off a part of the supply
of steam from the cylinder. If the engine runs too slow, there is less
centrifugal force, and the balls fall, which lets more steam into the
cylinder.
The large wheel seen in Fig. 243 is the fly-wheel. It is a heavy
iron wheel, and, besides running the belt which drives the machinery,
it is of great use in equalizing the motions of the engine and in
storing up power so as to overcome by its inertia sudden resistances
to the machinery.
406. The Locomotive. Fig. 246 is a section of a loco-
motive, showing its essential parts. In order to reach the
smoke-stack the heated air and flames of the fire must
pass through metal tubes. These tubes run directly
through the boiler, and are very numerous, thus giving a
very large heating surface. They are surrounded by the
water in the boiler, and without these tubes it would be
impossible to make steam fast enough to drive the loco-
motive at high speed. The cylinder is seen in front, and
right above it is the D-valve, worked by the small rod
which may be seen connecting it with the other machinery.
The locomotive has no condenser, and is therefore a high-
pressure engine. The steam escapes from the cylinder
through the D-valve into the blast-pipe v, and thence up the
smoke-stack. This greatly increases the draught of the fire,
and causes the puffs of sound that we hear, and the puffs
of smoke that we see. Increasing the draught by letting the
waste steam escape through the chimney, like the tubes in
the boiler, was a very important invention, as it keeps up
a hotter fire and thus generates steam faster.
HEAT.
241
Every one who uses this book is strongly urged to examine thor-
oughly engines of both sorts. Engineers will generally be willing to
explain all their details.
FIG. 246. THE LOCOMOTIVE ENGINE (HIGH-PRESSURE).
407. How the Power of the Steam-Engine is estimated.
The power of an engine is usually estimated in horse-power.
Watt estimated that a horse could raise 1000 tons one foot
high in an hour. 1 An engine that can do that much work
is a one horse-power engine ; one that can lift 5000 tons one
foot in an hour, or its equivalent, is a five horse-power en-
gine. It is found that the steam produced from one cubic
1 The raising of one ton 1000 feet in an hour, of half a ton 2000
feet in the same time, or any other equivalent, would be one horse-
power.
L 21
242 NATURAL PHILOSOPHY.
foot of water will just about raise 1000 tons one foot per
hour, so that an engine which can change five cubic feet of
water into steam each hour is a five horse-power engine.
The student will not fail to notice that the steam-engine
is a notable example of the conversion of energy. Heat is
changed to mechanical force by the agency of steam and
the machinery of the engine. Neither the steam nor the
engine produces the power, and in the most efficient engine
they really waste a great deal of it. But they are the
best means yet found of converting the molecular motion
or force of the heat into mechanical motion. Nor will
it be forgotten that the power to produce heat is in the
coal, and was stored away by the sun's light and heat ages
ago in the forests which produced our coal-beds. So it is
really the sun's light and heat shed upon the earth many
thousands of years ago that are drawing all our railway-
trains, driving all our steamships, and moving all our steam
machinery to-day.
General Exercises. 1. Find the degree in the Centigrade scale
which corresponds to 113 F., and that 'which corresponds to 140 F.
2. Find the degree in Fahrenheit's scale which corresponds to 15
C., and that which corresponds to 35 C.
3. A piano which has been tuned in a drawing-room in a morning
may produce discords in the evening, when the room is heated by the
pressure of a large evening party : explain this.
4. A flask with a long neck contains alcohol, which fills the flask
and rises to some height in the neck ; the flask is placed in hot water,
and the liquid at first falls in the neck as if it were contracting : ex-
plain this.
5. Show that 30 cubic inches of air would expand to about 41 in
passing from C. to 100 C.
6. A gas measures 98 cubic inches at 185 F. : find what it will
measure at 10 C. under the same pressure. Ans. 77, about.
7. If 50 cubic inches of air at 5 C. below C. are raised to 15
C. under the same pressure, find the volume. Ans. 53.8, about.
8. Air which is known to have a volume of 100 cubic inches at
C. is found to have expanded to 120 cubic inches without any change
of pressure : determine the temperature. Ans. 54.6.
9. Find what weight of ice at C. will be melted if put in a
pound of water at 50 C. Ans. 10 ounces.
10. A mixture is made of 3 pounds of water at 12 C. with 3
pounds of water at 16 C. : find the temperature of the mixture.
Ans. 14.
HEAT. 243
11. A mixture is made of 4 pounds of water at 7 C. with 6 pounds
of water at 12 C. : find the temperature of the mixture. Ans. 10.
12. Unglazed pottery is sometimes used to hold water and to keep
it cool : explain this.
13. Carbonic acid may be reduced to the liquid form by strong
pressure ; when the pressure is removed, the liquid returns to the state
of gas, but some of it becomes solid carbonic acid : explain this.
14. A pound of iron at 99 C. is immersed in a pound of water at
C. : find how many degrees the temperature of the water will be
raised, taking the specific heat of iron at .1. Ans. 9.
15. The air on a high mountain may be intensely cold although
the sun is shining and no clouds exist: explain this.
16. The bulb of a mercurial thermometer is exposed to heat: will
any difference be produced in the rate of rising of the mercury if the
bulb is covered with silver foil ?
17. Suppose we are provided with bars of copper, silver, gold, and
platinum : explain how we must proceed to determine the conductive
power of these metals.
18. A piece of platinum may be held in the hand while one end is
red-hot, but a piece of copper of the same length under such circum-
stances will speedily burn the fingers : explain this.
19. A kettle which has been in use for some time often becomes
coated by a deposit on the inside, and then water takes a long time
to boil in it : explain this.
20. A weight of a ton is lifted by a steam-engine to the height of
386 feet : find how many units of heat are required for this work.
Ans. 1000.
21. A 68-pound cannon-ball strikes a target with a velocity of
1544 feet per second : supposing all the heat generated by the collision
to be communicated to 68 pounds of water, how many degrees would
the temperature of the water be raised ? Ans. 2.
22. Show that to raise the temperature of a pound of iron from
C. to 100 C. an amount of heat is required which would lift about
3| tons of iron a foot high.
244 NATURAL PHILOSOPHY.
CHAPTEE VIIL
MAGNETISM.
408. Magnets. A certain ore of iron, 1 frequently called
loadstone, possesses the property of attracting metallic iron
and steel quite strongly, and of attracting many other sub-
stances very slightly. A piece of iron, while near or in
contact with a loadstone, possesses the same property, and
a piece of steel placed in contact with the loadstone not
only acquires this property, but retains it after having been
withdrawn. The mountains surrounding the ancient city
of Magnesia, in Asia Minor, were formerly famous for the
production of loadstone, and from this city the name mag-
net has come to be applied to a piece of loadstone, or to any
piece of iron or steel exhibiting the same power of attrac-
tion. When we have finished this chapter and the next, we
shall have learned that there are many ways of imparting
this interesting property to bars of iron and steel. At pres-
ent we will consider magnetism, or this power of attraction,
as a property communicated by the loadstone or " natural
magnet." Good loadstones are small, inconvenient, and ex-
pensive, and bars of steel which have been stroked from end
to end with the loadstone become magnets themselves, and
are capable of transmitting the power to others. We shall,
therefore, use steel magnets for our present experiments,
and learn how to make them as we progress. A pair of
such magnets, from three to six inches long, may be had
1 An oxide of iron, usually of the composition Fe 3 4 . A large
proportion of this ore of iron does not exhibit magnetic properties.
MAGNETISM.
245
for a small sum, and will answer well for many of the fol-
lowing experiments.
409. Poles Of Magnets. Experiment "144. Lay a magnet
down on a bed of iron-filings, or in a box-lid containing a quantity
of carpet-tacks or finishing-nails or " card-teeth." Be sure they are
evenly distributed, so that all parts of the magnet may have equal
access to them. Pick up the magnet, holding it horizontally by the
middle. Notice that the small particles of iron are clustered at the
ends, and that very few are to be found near the middle.
The attractive power of magnets resides at or very near
the ends. These are termed the poles of the magnet.
Every ordinary magnet has two poles.
410. The Two Poles of a Magnet different in Kind. Ex-
periment 145. Touch two
magnets together, end to end,
and reverse one of them and
then the other several times.
Unless they are very different
in size or strength, it will b
found that in two positions
they attract and adhere to
each other, and in the remain-
ing two positions they do not.
Put temporary marks on the
poles (if not already marked),
so that they may be dis-
tinguished.
Experiment 146. B a 1 -
ance one of the magnets on
the edge of a ruler. Bring
each end of the other magnet
from above quite near to each
end of the balanced magnet.
If the balancing is delicate
enough, it will be found that
the ends which in the pre-
vious experiment refused to attract each other, actually repel each
other.
From these experiments it is evident that the two poles
of a magnet, although capable of producing the same ap-
parent effect in the iron-filings or tacks, are in some way
different.
411. Action of Similar and Dissimilar Poles. Experiment
147. Hold two magnets of the same size and strength perpendicu-
larly, one in each hand, and dip the lower end of each into a pile of
21*
FIG. 247. ACTION OF SIMILAR AND DISSIMILAR
POLES.
246
NATURAL PHILOSOPHY.
little nails, or something similar. Now bring the loaded magnets
together, side by side. Keverse one of the magnets, and repeat the
experiment. In one case the loads will remain adhering to the mag-
nets after they are brought together, in the other case the loads will
drop as soon as the magnets touch each other. Notice that the poles
which are together when loads are sustained are those which were
marked as repelling each other in Experiment 146, while those which
are together when the loads are dropped are those which were marked
as attracting each other.
It is evident that when the two poles unitedly sustain
the double load, they must be acting together, i.e., they must
be similar, and that when the two poles which were
strong separately refuse to hold any load unitedly, they
must be acting differently or 'oppositely, i.e., they must be
dissimilar. We are now ready to mark the poles of our
magnets again, but not permanently yet. Put similar
marks upon the poles that act together in sustaining the
double load. From these experiments we derive the
Law of Action between Magnets :
Similar magnetic poles repel each other; dissimilar magnetic
poles attract each other.
412. Iron magnetized by Induction, Experiment 148.
With either pole of a magnet pick up a nail not too large to adhere
firmly to the magnet and to stand out from it in any position. Touch
the free end of this nail to another nail of the same size or smaller.
It will be attracted. If the
magnet is strong enough,
the second nail will support
(suspend) a third, this a
fourth, and so on.
Experiment 149. Touch
the lower end of the chain
of nails of the last experi-
ment with that pole of the
other magnet which is dis-
similar to the pole from
which the nails are hang-
ing. It will adhere firmly.
Form a chain again on a
pole of one magnet, and ap-
proach its lower extremity
with the similar pole of the
other magnet. The nails
will either be repelled or else they will let go their hold on one another
and drop. If there are several nails in the chain they will probably all
FIG. 248. NAILS MAGNETIZED BY INDUCTION,
MAGNETISM. 247
drop, one by one, till the last one is reached, and it will be strongly
repelled. Vary the experiment as follows : Kest the upper magnet
on a table top, so that one pole will project beyond the edge of the
table. Attach a chain of nails to this pole, and, when the magnet is
nearly loaded, carefully pull the top nail downward a short distance
from the magnet to which it adheres. If this is done carefully the nails
will still adhere to one another, and exhibit the same properties of at-
traction and repulsion that they did while the upper nail was in con-
tact with the magnet.
This experiment shows that there are two dissimilar poles
in each nail while it is near to, or in contact with, the mag-
net ; in fact, that each nail is then a magnet in itself. It
is the steel magnet which, by its presence, induces the nails
thus to act as magnets, and they are accordingly said to be
magnetized by induction. Remember this word and the
reason for its use, as it will be found frequently in this and
the following chapter.
413. Magnetization of Steel. Steel is magnetized by in-
duction, as iron is, but it is very much slower in yielding to
the magnet's influence. If one end of a needle be placed
against a pole of a magnet it will exhibit very little at-
traction at its farther end. It requires repeated strokes
across the end of a magnet fully to magnetize it, but when
once magnetized, the steel, if good, retains its magnetism.
Experiment 150. Lay an ordinary needle on one pole of a magnet,
and, taking it by either end, draw it slowly across the magnet until
it is torn loose from it. Lay it on the other pole of the magnet, take
it by the other end, and draw it across as before. Kepeat this a few
times, being careful that the same end of the needle shall in each
case be pulled from the same end of the magnet. The needle will be
found to be permanently magnetic.
414. Large Magnets. Large steel magnets may be made
in a similar manner, except that the bar to be magnetized
is generally laid on a flat table and one or two good mag-
nets are drawn along it several times. The magnets which
are thus used do not lose any of their own strength, though
they impart the same amount to any number of bars. As
a matter of fact, large steel magnets are generally made by
contact with powerful electro-magnets. Further reference
248 NATURAL PHILOSOPHY.
to the subject must therefore be left till we reach electro-
magnetism.
415. Poles in the Particles of a Magnet, Experiment 151.
Magnetize two sewing-needles so that corresponding ends shall be
similar poles, and test the strength of one with very small tacks. Cut
it in half, and lay the pieces in a bed of the tacks. Each half will be
a complete magnet with two poles. Compare the poles with the uncut
needle. They will be found to correspond in kind with the poles to
which they were nearest in the whole needle. Cut either half again
and again, until the pieces are very small. In each case each piece
will exhibit two poles, and each pole will be found as strong as the
original poles of the whole needle.
We may make any number of short magnets by cutting
up a longer one, the limit being reached only when the
pieces become so small that we can no longer divide them
with our cutting-tools. As we know the pieces of steel to
be composed of infinitely smaller pieces than we can thus
make, we may fairly conclude that each particle of a mag-
net possesses the poles and other. essential properties of the
whole magnet. This is also the case with the particles of
a bar of iron which is rendered magnetic by the inductive
influence of a magnet near it.
416. Why a Bar is magnetized, We are now ready to
state a little more clearly the theory of magnetism as ex-
hibited in iron and steel bars. For the purpose of illustra-
tion, we will consider a bar to be a line of single particles
placed end to end. When such a bar is brought sufficiently
near the pole of a magnet, the particle nearest the magnet
is polarized by induction ; that is, it has two poles formed
in it, one of which is attracted by the pole of the magnet,
and the other repelled. The attracted pole is, of course,
unlike the contiguous pole of the magnet, and the repelled
pole is like it. This particle then acts by induction on the
second particle, thus polarizing it; this acts on the third,
the third on the fourth, and so on until all the particles are
polarized, each one by the influence of the one next to it.
When the particles are all thus polarized, each pole is en-
gaged in attracting the pole next to it, except those at the
MAGNETISM. 249
two extremities of the bar. These two, accordingly, are free
to polarize and attract other pieces of iron, and they are
therefore the poles of the magnet.
417. Poles may be neutralized. If the two poles of a
magnet be allowed to exert their attraction fully on each
other, the magnet loses its power of attracting other bodies.
This may be beautifully shown by the following :
Experiment 152. Procure a piece of watch-spring about six
inches long (your jeweller will willingly contribute it), and magnetize
it by drawing it several times by alternate ends between the thumb
and the respective poles of a magnet. Dip the poles of the magnet
thus formed into small tacks. Carefully lift the load, and bring the
poles together so as to make a circle of the spring. The load will
drop, and any attempt to make it adhere to any part of the circle
will be in vain if the spring has been evenly magnetized. In Ex-
periment 147 the same effect was exhibited with the unlike poles of
two magnets.
418. The Attracted Body polarized. Every particle of
iron or steel attracted by a magnet is first polarized by the at-
tracting magnet, unless previously polarized by some other
means. Fig. 249 suggests an experiment for verifying
FIG. 249. MAGNETIC INDUCTION.
this law. The smaller piece is soft iron. (" Soft iron" is
the technical name for good wrought iron, and is used in
distinction from steel.) If the piece of soft iron in the
above figure were of the same size in cross-section as the
magnet, and the two were placed in contact, end to end,
there would no longer be any poles at the junction, but
there would be one at each end of the compound bar.
250
-
DEI *T OF PHYSICS
NATURAL PHILOSOPHY.
419. Compound and Horseshoe Magnets. As the at-
tracted piece of iron is polarized, it is evi-
dent that the magnet would attract each end
equally if it could reach them both at once.
To accomplish this end, magnets are fre-
quently bent into the form of a capital U.
Such magnets are called " horseshoe" mag-
nets. The action of a horseshoe magnet on
a piece of soft iron is indicated in Fig. 250.
The soft iron is called the keeper. When so
constructed as to move pieces of machinery,
it is called an armature. To obtain the best
results from a large magnet of any shape, it
must be made by fastening several smaller
bars together, parallel with one another.
FIG. 250. COMPOUND This makes a compound magnet. Fig. 250
HORSESHOE MAG- .
NET AND KEEPER, is a compound horseshoe magnet.
420. Lines of Force. Experiment 153. Cut a
groove in the face of a smooth board, so that a flat bar magnet may lie
FIG. 251. LINES OF MAGNETIC FORCE.
in it and have its upper side flush with the board. Place the magnet
in the groove, cover it over with a smooth sheet of writing-paper, and
MAGNETISM. 251
sift iron-filings l well over the paper. The position of the magnet is
plainly indicated by the filings. Tap the board gently, and the
filings will arrange themselves in a series of curves as shown in Fig.
251.
These curves are called the lines of force of the magnet.
They show the direction which any other magnet, placed
in the plane of the paper, and influenced by the covered
magnet, tends to assume. The following beautiful experi-
ment shows that these lines of force exist in all planes
other than that which happens to be occupied by the
paper.
Experiment 154. Take an ordinary whalebone, or a similar piece
of elastic wood, a few inches long, and string it as a bent bow, with
a silk thread which has been unspun or combed out so that it will
have no tendency of its own to twist. Tie a knot, or stick a piece of
wax, in the middle of the string. Thrust a sharp needle, which has
been magnetized, half-way through the knot or bunch of wax.
Taking hold of the bow for a handle, approach a magnet with the
needle. Whether the needle be held above, below, on either side, or
in any oblique position with reference to the magnet, it will always
assume a position corresponding to the direction of the lines of
filings in the preceding experiment.
421. Intensity of Magnetic Attraction. "We notice in Ex-
periment 153 that the filings near the pole are much more
powerfully affected than those farther off. The needle of
Experiment 154 was agitated most violently when near
either pole of the magnet. When we approach the pole
of a magnet with a piece of iron, we notice how the attrac-
tion seems to strengthen as the distance between them be-
comes less. With delicate appliances for measuring the
pull or push exerted by magnets on other bodies, or on
each other, we learn the
Law of Magnetic Attraction :
Magnetic attraction or repulsion varies inversely as the square
of the distance through which it acts.
Notice that the laws of gravitation, sound, light, heat, etc., acting
through different distances, are similar to this.
422. Directive Tendency of the Magnet. Experiment 155.
Make a stirrup of paper, and hang it to a convenient support by a
1 Iron-filings may be bought of a dealer in chemicals.
252'
NATURAL PHILOSOPHY.
string that has no tendency to twist. Balance in the stirrup, one at
a time, the two magnets which have been used in many of the previ-
ous experiments. After swinging backward and forward a few times,
the magnets will each come to rest, pointing nearly north and south.
It will be found that the ends of the two magnets which point in
either of these directions are those which were marked as similar to
each other after we had tried Experiment 147. "We are now ready to
mark the poles of our magnets permanently. Mark the pole which
points northward "N," for north, or, rather, north-pointing, and mark
the other end "6'," for south-pointing.
All magnets tend to arrange themselves in nearly a north-
and-south direction. This is because of magnetic property
in the earth itself. Indeed, the whole earth may be con-
sidered as a vast magnet, having its magnetic poles near
the geographical poles. How the magnetism of the earth
is supposed to originate will be referred to in a subsequent
chapter.
423. The Magnetic Needle. A thin magnet, nicely bal-
anced on a hard point, so that it may have great freedom
of motion, is called a magnetic needle. Fig. 252 shows a
common form.
FIG. 252. MAGNETIC NEEDLE.
FIG. 253. HOME-MADE
NEEDLE.
Experiment 156. To make a very good magnetic needle, take a
piece of watch-spring six or eight inches long. Straighten it between
MAGNETISM. 253
the thumb and finger. Then, holding the middle of it in the flame
of a lamp, bend it as nearly "double" as possible without breaking.
Bend the ends back into a line with each other, as shown in Fig. 253.
Magnetize each end separately. Wind a waxed thread around the
short bend that is left, and balance on a needle held upright in a flat
cork or a card. A little filing or grinding will be necessary to make
it balance. With a point filed on the north-pointing pole the needle
is finished.
424. The Compass. A magnetic needle, when fixed in a
frame which is graduated in degrees and properly equipped
with sights and levels, forms the surveyor's compass.
When the needle carries a circular card with the " points"
(north, south, east, west, etc.) marked on it, the arrange-
ment is the essential feature of the mariner's compass.
425. Magnetic Declination. Although the compass was
used a thousand years before the Christian era, it has long
been known that in most places the direction of the needle
is not a true north-and-south line. The deviation from the
meridian is called the declination of the compass. Navigators
must know the declination for a given place and allow for
it. If the declination in a given place were constant, the
allowance could easily be made, but it is subject to many
variations, some extending over long periods, some over
shorter periods, some regular and some irregular. As the
greatest amounts of variation occur regularly and take
place slowly, the compass is still a valuable aid to navi-
gators and explorers. The declination at Philadelphia in
1883 is about 5 west. At London it is about 20 west.
426. Magnetic Dip. If a steel bar be exactly balanced
in its centre of gravity so that it may move about its sup-
port in any direction, and then magnetized, it will not re-
main level, but (in the Northern hemisphere) the north-
pointing pole will incline downward, pointing towards a
place considerably below the horizon. This is known as
the dip of the needle, and a needle so balanced and mag-
netized is a dipping needle. The dip is greater the nearer
we approach to the magnetic poles of the earth. In the
Southern hemisphere the south-pointing pole dips down,
22
254
NATURAL PHILOSOPHY.
The dipping needle indicates the direction of the earth's
lines of magnetic force. Therefore, if we know the position
of the magnetic poles
of the earth, latitude
may be roughly deter-
mined by means of a
dipping needle. Hum-
boldt 1 relates that on
one occasion he suc-
cessfully directed his
vessel into the port of
Callao, on the west
coast of South Amer-
ica, by determining his
latitude in this way.
The dip of the needle
at Philadelphia is about
^____ 75 with the horizon.
FIG. 254. NEEDLE INDICATING BOTH DIRECTION The magnetic equator,
AND DtP. ,. f ^
or line of no dip, is
somewhat irregular in shape, but crosses the equator in
two points at an angle of about 12, being that distance
north of the equator in the Indian Ocean and the same
distance south in Brazil. The north magnetic pole is about
10 north of the north shore of Hudson's Bay, and the
south magnetic pole is in a corresponding position south
of Australia.
427. The nature of the influence which magnets exert over bars
of iron and steel to polarize their particles and make magnets of them,
as explained in Art. 416, is little understood. We shall find in a suc-
ceeding chapter, however, that there is a close connection between
magnetic phenomena and the existence of electric currents. A sub-
ject of much interest awaits us.
1 Alexander von Humboldt, German, 1769-1859. An illustrious
traveller, and an eminent scholar in many branches of learning. An
authority on most scientific subjects.
ELECTRICITY. 255
CHAPTEE IX.
ELECTRICITY.
I, FRICTIONAL ELECTRICITY.
428. Electrical Phenomena. It was known to the an-
cients that amber rubbed with some soft material pos-
sessed the power of attracting light bodies. It has since
been discovered that many other substances exhibit the
same property. The Greek name of amber is elektron;
hence the name electricity came to be applied to the force
thus developed, whether in amber or in any other sub-
stance. A gutta-percha comb, after being drawn through
dry hair, in cool, dry weather, will pick up small tufts of
cotton, pieces of paper, scraps of corn-stalk-pith, or any
similar light substance. A sheet of thin paper rubbed with
an eraser adheres tightly to the sheet under it, or to a wall.
The force which holds these bodies together is electricity.
429. Note. Apparatus Needed. The following small articles
will be needed frequently in trying electrical experiments, and should
be kept on hand. Two glass rods, or heavy tubes, about 15 inches
long, and at least f of an inch in diameter ; two smaller rods of
shellac (sealing-wax or gutta-percha may be substituted for shellac) ;
a silk pad, made by quilting together from three to six pieces of silk,
about 8 inches square ; a similar pad of flannel, or a cat's skin tanned
with the fur on (a silk handkerchief and a flannel cloth will do) ; a
lot of pith-balls from } to inch in diameter, made by cutting the
dried pith of corn-stalks into shape with a sharp knife ; a spool of
sewing-silk ; a spool of thread ; a few bottles and other glass vessels ;
a supply of corks, pins, needles, wax.
In addition to these, a class should have a proof-plane and an electro-
scope. They are easily made. The proof-plane is a circular piece of
tin about two inches in diameter, with a piece of glass tube or a gutta-
percha pen-holder stuck to it with sealing-wax, for a handle. A very
good electroscope may be made as follows (see Fig. 257). Procure a
wide-mouthed jar of about a quart capacity ; paste on the inside, on
256 NATURAL PHILOSOPHY.
opposite sides of the jar, two strips of tin-foil 3 inches long and 1 inch
wide. These should extend upward from the bottom of the jar.
Have a cork to fit the jar, and pass through it a stout wire. Make a
stirrup on the lower end of the wire, say two inches from the cork.
If convenient, solder to the upper end of the wire a circular tin
plate of the same size as the proof-plane. Hang in the stirrup by
the middle a piece of thin gold-leaf 4 or 5 inches long and J inch
wide. It may be bought of a dealer in chemicals, or of a dentist, for
a few cents, but, if it is not at hand, take silver-leaf, gilt paper, or
very thin tin-foil instead. Be sure that the bottle is dry. Insert the
cork, and run melted wax over it. The gold-leaves should open
towards the strips of tin-foil.
In trying experiments in electricity all apparatus must be dry, and
it should be warmed by the stove frequently while being used. Much
of the glass of commerce contains metallic impurities, which render
it unfit for electrical experiments. If failures occur, when every-
thing seems right, try new glass. " Bohemian" glass has given the
writer the most satisfaction.
Experiments in frictional electricity succeed best in crisp winter
weather, when the atmosphere contains but little moisture. In sum-
mer weather it is sometimes difficult or impossible to produce electrical
excitement.
430. Electrical Attraction, Experiment 157. Grasp a glass
rod near one end and rub it briskly with the silk pad. A crackling
noise and a sensation as of cobwebs on holding the rod near the face
indicate that it is electrified. Hold it near a light rubber ball placed
on a smooth table. The ball will be attracted, and will follow the rod
around the table several times. A round collar-box or a hoop of any
light material will answer equally well. Rub a rod of shellac with
the flannel and present it to the ball or the hoop. The same result
will follow.
431. Attraction and Repulsion. Experiment 158. Make a
"wire loop" (such as is shown in Fig.
255) of sufficient size to hold the glass
and shellac rods. Suspend it by a silk
thread or narrow ribbon to a convenient
support. Rest in it one of the glass
rods. Rub the other rod with the silk,
and bring it near the suspended rod.
There will be an attraction. Repeat
the experiment, but this time rub the
first rod before placing it in the loop.
On presenting the other glass rod,
freshly rubbed, there will be a re-
pulsion.
Follow the same course with the rods
Fia. 255. WIRE LOOP. of shellac rubbed with flannel. They
will act in the same way. Remove the
electrical excitement from the surface of one of the shellac rods by
drawing it through the hand. Place it in the loop and present a
freshly-rubbed glass rod. There will be attraction. Rub the shellac
rod and again present the rubbed glass. There will still be attraction.
ELECTRICITY. 257
432. Two Kinds of Electricity. The last experiment
shows that the two electrified bodies, though behaving
similarly towards the unelectrified indicator, are different
manifestations of the same force. It recalls the experiment
which proved the difference between the two poles of a
magnet. Here, however, both ends of the electrified body
are similar. It is the electric states of the two bodies, the
glass and the shellac, which are dissimilar. For distinction,
the electric force developed on smooth glass by rubbing it
with silk is called positive electricity, and that developed on
shellac by rubbing it with flannel is called negative electricity.
These are old names, and the theory which gave rise to
them has been abandoned, but, as they have very distinct
applications and are frequently used, they must be remem-
bered and distinguished. The friction of many other sub-
stances produces electricity, but it all proves itself to belong
to one or the other of the above classes.
The sign -f is used in many of the figures which occur in this
chapter to denote positive electricity, and the sign to denote nega-
tive electricity. These are not to be read plus and minus, but positive
and negative.
433. Law of Attraction and Repulsion. Experiment 158
will have suggested the following law : The two kinds of
electricity attract each other, but each is self-repellent.
434. No reason has been discovered why one body should
exhibit positive electricity and another negative. When a
substance whose nature is unknown is electrified, it must
be tested by one whose electricity is known. To test a
body, ascertain whether excited glass or excited shellac
repels it.
435. What is Electricity ? We might further say that no
reason has been discovered why a body should be electrified at all.
Electricity is a state of strain which a body exhibits as an equivalent
of the energy applied to produce it It is a complete example of the
conservation of energy. In the experiments which we have thus far
tried, the energy applied in the rubbing of the rod appears as a force
in the rubbed rod capable of moving light bodies. We shall see,
r 22*
258 NATURAL PHILOSOPHY.
as we proceed, that it is capable of reappearing as energy of other
kinds.
436. To Charge a Body. Experiment 159. To each end of a
silk thread two feet long attach a pith ball,
and suspend the silk by the middle. Hub a
glass rod with silk and touch it to the balls
as they hang together. They will now repel
each other and stand apart for a considerable
time.
This experiment shows that elec-
tricity passes from one body to an-
other. Each ball has taken some
of the positive electricity from the
glass, and the two, being similarly
electrified, repel each other. A body
FIG. 256,-ELECTRicAL RE- w hich has taken some electrical force
from another is said to be charged;
a body which has been electrified by friction is said to be
excited.
437. Neutral and Excited Bodies. If the excited glass
and the excited shellac be rubbed or rolled thoroughly over
each other, each will lose the principal part of its charge,
This leads us to conclude that each is capable of undoing
or neutralizing the electric state of the other. This is ex-
pressed by saying that the two electricities will unite with
each other. If the positive charge of one body and a cor-
respondingly heavy negative charge of another body unite,
neither body manifests electrical excitement after the union.
The bodies may then be said to be neutral. Nearly all
bodies capable of electrical excitement are usually in a
non-excited state. We may express this by saying that
the two electricities neutralize each other in such bodies.
When they are excited by rubbing, the rubbed body exhibits
one kind of electricity and the rubber the other kind. Try
the following :
Experiment 160. Rub a glass rod with the silk pad (holding the
pad in a piece of sheet-rubber, e.g., the top of an old overshoe), and
present the pad to some light pieces of feather or something of the
ELECTRICITY. 259
kind. There will be an attraction, showing that the pad is electrified.
Kub the rod again, and suspend it as in Experiment 158. The pad
and the rod will attract each other, showing that they are differently
electrified. The neutral, inactive electricities of the two bodies were
roused up in some manner by the rubbing, and arrayed themselves
against each other, part of the negative of the glass going to the pad,
and part of the positive of the pad going to the glass.
Experiment 161. To show that the two electricities do exist in the
glass before excitement, rub a glass rod with flannel, or, better, on a
cat's skin. It will repel excited shellac, indicating that it is negatively
electrified. To procure positive electricity on glass, be sure to rub it
with silk. 1
438. Conductors and Insulators. If an excited rod be
touched to one end of a metal bar, an indicator at the
other end shows that the electric force is immediately felt
there. If the same experiment be tried with a glass bar,
the electricity does not manifest itself to any appreciable
extent at the farther end. Substances which readily trans-
mit electricity are called conductors. The metals, charcoal,
wood, water, hemp, and animal bodies are conductors.
Two or more bodies connected by conductors are said to
be in electrical connection.
Substances which transmit electricity feebly, or not at
all, are called insulators, and a body in contact with nothing
but insulators is said to be insulated. Dry air, shellac, rosin,
beeswax, glass, india-rubber, and silk are among the most
common insulators. As the human body is a conductor, it
is evident that we should handle all electrified bodies by
means of insulating handles if we would have them retain
their electrical condition. Particles of dust and moisture
which may collect on insulators have some power of con-
1 When we speak of " two electricities existing in" a body, we are
using language rather loosely, as electricity is not a substance, but a
force. It would be more accurate to say that a body is capable of
exhibiting either phase of the electric force ; but we could not de-
scribe the experiments in the more strict language without making
very tiresome sentences, so philosophers agree to use the simpler
expressions for convenience, and ask their students not to picture to
themselves electricity as a material.
260 NATURAL PHILOSOPHY.
duction : hence the caution to keep all electrical apparatus
while in use clean and warm.
439. Electrical Induction. As a magnet may communi-
cate its power of attraction to a piece of iron at a short
distance from it, so an electrified body may induce electrical
excitement in another body without touching it.
Experiment 162. Bring the excited glass or shellac rod near the
knob or plate of the gold-leaf electro-
scope (Art. 429). As it approaches the
leaves will diverge, and as it recedes the
leaves will come together. Kepeat sev-
eral times in succession.
The gold-leaves in this experi-
ment were similarly electrified by
induction, hence they repelled each
other. For a full understanding
of many of the phenomena which
FIG. 257,-GoLD-LEAF ELEC- we are aDO ut to study, it is neces-
sary for us to bear constantly in
mind that any excited body tends to excite by induction insulated
bodies near it. It is also essential that we should be able to
tell, in any case, what kind of electricity one body induces in
another, or in different parts of it.
Experiment 163. Touch the proof-plane (Art. 429) to an excited
glass rod, and then to the top of the gold-leaf electroscope. The
leaves become charged, and remain diverging after the proof-plane is
withdrawn. Carry a second charge from the glass to the gold-leaves.
They diverge more widely. While they are still divergent, carry to
them with the proof-plane a charge from excited shellac. The nega-
tive electricity neutralizes some or all of the positive in the leaves,
and they fall towards each other.
440. To Test the Kind of Electricity. This experiment
indicates how we are to test the kind of electricity on any
excited surface. Diverge the gold-leaves with a known
kind. While they are still divergent, the contact of a body
similarly electrified produces more divergence, and the con-
tact of a body oppositely electrified produces less divergence.
ELECTRICITY. 261
441. Body electrified by Induction. Experiment 164. Pro-
cure or make a cylinder whose length is about four times its diame-
ter. Eight and two inches
are very convenient di-
mensions for these experi-
ments, though very much
smaller will do, and very
much larger are better
when we have much elec-
tricity. The ends must
be convex, as shown in
Fig. 258. The outside of
the cylinder, ends and all,
must be of some conduct-
ing material. Turned
wood covered with tin-foil Fl< *. 258. INDUCTION CYLINDER.
answers admirably. A
hollow tin can with round ends would be good. An egg, an apple,
a croquet-ball, would do. This is an induction cylinder. Support it
on glass or wax, or hang it by silk. Hold an excited rod near one
end. While it is held there, touch first one end and then the other of
the induction cylinder with the proof-plane, and test each with the
gold-leaves. The end next to the excited rod will be found in the
electrical state opposite to that of the rod, and the farther end will be
found similar to the rod. Try the middle of the cylinder. It will
be found neutral.
442. Cause of Attraction by an Electrified Body. All
bodies electrified by induction show the above result. The
electrifying body attracts the opposite and repels the simi-
lar electricity, in accordance with Art. 433. This brings
us to an important principle of electrical attraction, viz.,
a body attracted by an electrified surface is first electrified by
induction, and the apparent attraction of the bodies is really
the attraction of the opposite hinds of electricity.
443. Why a Body is charged. The body which electri-
fies another by induction does not thereby lose any of its
charge ; but if a body which is electrified be brought into
contact with one which is not, the electrified body does lose
some of its electricity. Suppose the first body to be posi-
tively electrified. Part of the positive electricity com-
bines with the negative which has accumulated on the
nearest part of the other body. The farther extremity
of the second body remains positively electrified by repul-
262 NATURAL PHILOSOPHY.
sion. When the electrifying body is withdrawn, this posi-
tive electricity disposes itself symmetrically over the
surface of the body, and the body is charged.
444. Insulators easily charged. It will have been no-
ticed by the pupil, before reaching this point, that the sub-
stances upon which we develop electricity are insulators.
This is largely because glass, shellac, etc., are easily ex-
cited, but partly because the very fact of their being insu-
lators enables them to retain the charge which is developed
on their surface. When any point of a charged conductor
is placed in electrical connection with another conductor
of very large size (the earth, for example), the whole charge
passes off, and the body is said to be discharged. In order
to discharge a charged insulator, all parts of its surface must
be placed in electrical connection with a large conductor.
445. Action of Points. Before going into the study of
electrical machines it will be necessary to observe and re-
member the effect of pointed conductors on a charge of
electricity.
Experiment 165. Touch an insulated cylinder (see Fig. 258) with
an electrified body. While the balls are divergent, point a needle
or an open penknife towards it. The balls will fall together, and re-
main so after the point is withdrawn.
446. The Earth is the Great Reservoir of electricity, both
positive and negative. A person standing on an ordinary
floor is in electrical connection with the earth. An elec-
trified body tends to draw towards it the opposite elec-
tricity of any object sufficiently near. (Art. 441.) When
the surfaces are curved, as in the induction-cylinder, the
electricity, though attracted by the inducing body, is kept
back by the insulating air, a large surface of which is op-
posed to the electricity, and thus prevents its passage.
When the surface at the place to which the electricity is
drawn by induction is very small, as the needle-point, the
air can oppose but little resisting surface, and the elec-
tricity flies across the insulating space to the inducing
ELECTRICITY.
263
body. If the point be attached to an insulated conductor,
instead of being held in the hand of a person standing on
the floor, the conductor will be found charged with one
kind of electricity by the escape of the opposite kind from
the point.
447. The Electric Spark. When a charge of electricity
is sufficiently intense, it will pass through an insulator from
one conductor to another though the surfaces be round and
smooth. Such a charge, in passing through the insulating
medium (mostly air), produces the electric spark.
448. Electrical Machines. We have now learned all the prin-
ciples involved in the construction of electrical machines, and, as
many experiments succeed best when an electrical machine is used,
we shall describe a few common forms.
449. The Plate Electrical Machine. The circular glass plate
G (Fig. 259) is clamped to the axle and turned by the handle. The
Fia. 259. PLATE ELECTRICAL MACHINE.
arrow shows the direction of rotation. Two rubbers at K are pressed
by springs agairst opposite sides of the plate. These springs are con-
nected with the ball N, which is insulated on glass and forms the
264 NATURAL PHILOSOPHY.
negative conductor. On the opposite side of the plate is the positive
or prime conductor P, also on an insulating support. The combs C
are the points over which the negative electricity is to flow to the
glass plate. They are of brass. The rubbers may be chamois-skin
coated with " electrical amalgam." (This is a compound similar to
the coating on a looking-glass. The rubbers have tallow spread over
the face, and the amalgam is spread evenly over this.)
When the handle is turned, the friction of the rubbers develops
positive electricity on the surface of the glass and negative on the
rubbers. The negative conductor thus becomes charged. As the
rubbers are expected to take an unlimited quantity of negative elec-
tricity, it must be constantly carried away to the earth, or neutralized
by positive from the earth, or from the prime conductor. As we
generally wish to use the positive electricity, we connect the negative
conductor with the ground by a chain dropped on the floor, or, better,
attached to a stove- foot or a gas- or water-pipe.
When the plate with its positive electricity has turned half-way
round, it acts by induction on the prime conductor, drawing the nega-
tive towards it and repelling the positive to the other extremity. At
C the negative electricity finds the points of the " comb" and rapidly
escapes to the glass, neutralizing the positive on its surface. The
positive electricity on the prime conductor finds rounded surfaces, and
remains till it becomes of considerable intensity. This action is con-
tinuous as long as the handle is turned. The lower half of the plate
is always positively electrified. The upper half is neutral. Positive
electricity may be drawn from any part of the prime conductor while
the machine is worked, but it is more intense towards the outer end
(the small ball in the machine here shown). The excellence of a
machine, or of atmospheric conditions, is determined by the distance
the charge will pass through the air, as a spark, from the end of the
prime conductor to the knuckle of the operator or some other convex
conductor. This distance is called the length of the electric spark.
If we wish to use the negative electricity from the machine, the
ground-connection is made with the prime conductor. The negative
spark is much shorter and less intense than the positive. Connection
may be made between the two conductors. In this case the two
kinds of electricity will neutralize each other, and the earth-supply
will not be needed.
450. The Cylinder Machine. Fig. 260 represents a cylinder
machine, which is much less expensive than a plate machine. Any
school-boy may make one. A large bottle (one that would hold from
ELECTRICITY.
265
one to four quarts) will answer for the cylinder. A glass rod, G,
supports the prime conductor, C. This may be of wood, covered
with tin-foil. Let the tin-foil extend so far as to the pin-points, P.
FIG. 260. CYLINDER ELECTRICAL MACHINE.
R is the rubber, made of leather, or chamois, or silk, stuffed with
wool. A silk apron, S, attached to the rubber and extending over
the cylinder, adds to the certainty of its working. The rest of the
machine is of dry wood.
451. Other Electrical Machines. For explanations of many
other interesting forms of electrical machines the reader is referred
to more extended works on Natural Philosophy. The Holtz induc-
tion machine, and the Armstrong hydro-electric or steam electrical
machine, are both capable of developing electricity in prodigious
quantities.
Note. "With either of the devices explained above, most of the fol-
lowing experiments may be made to succeed in good weather. If the
machine is home-made, be sure there are no sharp corners or loose
edges of tin-foil where they would allow the charge to escape. Grind
off edges of thick metal, and carefully press down with the finger-nail
all edges of tin-foil. A coat of varnish helps insulators to keep dry.
452. Experiments in Attraction and Repulsion. Experi-
ment 166. To the top of a stem of wood hinge a slender wooden
toothpick, so that it will move in an arc of 90. Stick the free end of
the toothpick into a pith ball. A paper scale may be attached, as
shown in Fig. 261. This is a quadrant electrometer. Stand it up in
a gimlet-hoie carefully bored in the top of the prime conductor. It
M 23
266
NATURAL PHILOSOPHY.
indicates, by the rising of the pith ball, the presence of electricity in
the conductor.
Experiment 167. Hang from the end of the prime conductor a
round metal plate by the centre. Hold under it a similar plate on
which are placed a few paper or pith images. When the machine is
operated, the images will dance vigorously between the plates. Vary
this experiment by supporting the lower plate on glass. Explain
both phenomena.
FIG. 261. QUADRANT ELECTROMETER.
FIG. 262. ELECTRICAL CHIMB.
Experiment 168. Suspend three bells, as shown in Fig. 262. Any
bells will do. Suspend those at the end by conductors, and the middle
one by silk. Suspend two little metal clappers by silk. Let a chain
or wire drop from the middle bell to the floor. Operate the machine
and hear the result.
Experiment 169. Suspend a light figure of a boy in a silk swing
a foot long. Arrange the swing so that the figure will hang midway
between the prime conductor and a metal knob, or a knuckle held a
few inches distant. Let the machine be turned. Devise a see-saw, a
pump-handle, or a man sawing wood to be operated by electricity.
Experiment 170. Grind to a point a stout wire six inches long.
Bend the wire at right angles near the point. Insert the other end
into the hole in the prime conductor. When the machine is worked,
hold a lighted candle at the point of the wire. The flame is blown
from the point. This is because the molecules of the air are succes-
sively charged by the electricity of the point, and are repelled from it.
Experiment 171. Stick four or six of these sharpened and bent
wires into a cork, so that they will all be in the same plane and bal-
ance horizontally. Insert a thimble or a lamp-extinguisher in the
cork, and push the wires in against it. Balance on a straight sharp
wire which stands in the hole in the prime conductor. The points
and the molecules of air repel each other, causing the " flyer" to re-
volve (Fig. 263).
Experiment 172. -Cut a large number of very narrow strips of
thin paper. Bind them together at one end by a wire, and hang on
the prime conductor. Turn the machine.
ELECTRICITY.
267
Experiment 173. Make a very small hole in the bottom of a
tomato-can. Partly fill the can with water, and hang on the prime
conductor by a wire. If the water drops
slowly from the hole before the machine is
operated, it will be forced out in a diverg-
ing spray on the turning of the handle.
453. The Electrophorus, Fig. 264, is
a very simple and at the same time a very
instructive instrument sometimes used for
the development of electricity. Any boy
or girl may make one. The lower disk,
OT plate, is of resin, which has been melted
and poured into a tin vessel a half-inch
deep, and a foot, more or less, in diameter.
A tinsmith will furnish both the vessel and
the resin (rosin). The lid is of metal, or
of wood covered with tin-foil. It must be
rather smaller than the plate. The handle is of glass or sealing-wax.
FIG. 263. ELECTRICAL FLYER.
Experiment 174. Stroke the plate of the electrophorus with a cat's
skin or a piece of flannel. It will be negatively electrified. Holding
the lid by the insulating han-
dle, place it flat on the plate.
After a moment's contact, re-
move it, and test with the elec-
troscope. It is not appreciably
electrified. Place the lid on
the plate again, and touch it
with the finger before remov-
ing it by the insulating han-
dle. After it is lifted from
the plate, touch it with a
knuckle of the other hand.
A spark will pass, showing
that it is charged. Charge
the lid again, and try it with
the proof-plane and electro-
scope. Its electricity is posi-
tive.
FIG. 264. THE ELECTROPHORUS.
Be sure to understand
the action of the electro-
phorus before going further. It opens the way for easily
understanding the Leyden (ll'den) jar and other condensers
of electricity. When the lid was placed on the excited plate
by the insulating handle, the neutral condition of the lid
268 NATURAL PHILOSOPHY.
was undone by the inductive action of the plate. Its posi-
tive was drawn to the surface next to the plate, and its
negative repelled to the upper surface. When the lid was
lifted by the insulating handle without having been touched
by the finger, the two kinds of electricity reunited and
neutralized each other as soon as the lid was out of reach
of the inductive influence of the plate. In the other case,
when the lid was touched by the finger, the repelled nega-
tive electricity found a way to the earth and escaped.
Then, when the lid was lifted by the handle, the positive,
having no negative to unite with, diffused itself over the
surface as a charge. The important principle which the
electrophorus illustrates is that when a body is electrified
by induction, the attracted electricity is bound, and the re-
pelled electricity is free. To render this more apparent,
touch the proof-plane to the lid as it lies on the plate, both
before and after it has been touched by the finger. The
electroscope detects negative electricity in the first case,
and no charge in the second case.
In the electrophorus we are to consider a thin layer
of air between the lid and the plate, except at the com-
paratively few points of contact. The resin being a non-
conductor, the positive electricity of the lid cannot pass
to the surface of the plate by way of these points, so
it is simply held as near the plate as possible. The lid
may be repeatedly charged from the plate after it has
been once excited, which would be impossible if the lid,
touched by the finger, came in contact with the whole
plate. Although air is an insulator, a very thin layer
of it offers but feeble resistance, so that no considerable
charge can thus be obtained. A thin layer of glass offers
much more resistance to the passage of electricity than
the same amount of air does, but it does not interfere with
induction. Two conductors separated by glass, may there-
fore be heavily charged with the two kinds of electricity,
each holding the other bound, and neither showing its
ELECTRICITY.
269
presence when tested by a neutral body. Such an arrange-
ment is called a condenser.
454. The Leyden Jar. The most common form of condenser is
the Leyden jar, so called because the discovery which led to its con-
struction was made at Leyden about the middle of last century. As
bought of an instrument-maker, it consists of a glass jar (see Fig.
265) with coatings of tin-foil inside and out, covering the bottom, and
FIG. 265. DISCHARGING LEYDEN JAR.
the sides about two-thirds of the way to the top. A rod, piercing the
cork, ends above in a ball or ring, and below in a chain or wire
reaching to the bottom of the jar. To charge the jar, take it in one
hand by the outside coating. Present the knob to the prime con-
ductor. Sparks of positive electricity pass from the conductor to
the ball, and so to the inside coating. Each spark of positive thus
conveyed to the inside surface of the jar holds bound against the out-
side surface a corresponding amount of negative, and repels its own
amount of positive through the arm and body of the operator. A
large number of sparks may thus be passed into the jar, each one
increasing the amount of positive on the inside and the amount of
negative on the outside, till the tension approaches its limit, when
23*
270 NATURAL PHILOSOPHY.
the sparks become noticeably less vigorous. The jar is now charged,
and if a conductor is made to reach from any point of the outside
coating to the knob, the two kinds of electricity unite with great
energy. This is discharging the jar. An experimenter uses for this
purpose a bent or jointed rod with an insulating handle. Fig. 265
shows an ordinary Leyden jar and a jointed discharger. A heavy
bent wire, with rings formed on the ends, will do. The discharge in
this way is instantaneous. If a body capable of taking a small
charge of electricity is suspended by a silk thread between two con-
ductors which are in electrical connection with the two coats of the
jar, it will carry successive charges of positive to the outside coat,
and of negative to the inside coat, until the two are neutralized in
both. The little clapper shown in Fig. 266 will swing between the
bells and keep up a chime for an hour,. under favorable conditions.
FIG. 266. SLOW DISCHARGE.
455. The Shock. When the discharge of a Leyden jar
takes place through a conductor which is not very good,
the human body, for instance, it produces a " shock" of
more or less severity.
An accidental shock led to the invention of the Leyden jar. A
pupil of an experimenter in Leyden was u storing" electricity in a
bottle of water, by passing a rod into it from the prime conductor of a
machine. The bottle was held in one hand, and after the machine
ELECTRICITY. 271
had been in operation a short time he attempted to remove the rod
from the water with the other hand, when he was surprised and
alarmed by receiving a shock. The news of this shock spread with
great rapidity, and various modifications of the bottle of water were
soon devised. The water served as the inside coat or conductor, and
the hand of the operator as the outside coat. Let the pupil construct
any or all of the following devices and take shocks from them.
456. Various Devices for giving Shocks. Experiment 175.
Fill a small round bottle about two-thirds full of water. Put a piece
of wire or a nail through a cork, and insert the cork in the bottle.
The lower end of the wire must reach into the water, and the upper
end must terminate in a ball or ring. Holding the jar in one hand,
present the ball to a prime conductor, electrophorus, excited rod, or
even a gutta-percha comb drawn through the hair. After the ball
has taken several sparks, touch it with a knuckle of the free hand.
If it is at hand, paste tin-foil as a coating over the outside of the
jar. A much larger condensing surface is thus obtained. Or, in-
stead of the hand or tin-foil, set the jar in a vessel partly full of
water, and dip a finger into the water while charging and discharging.
Experiment 176. Paste a sheet of tin-foil on each side of a pane
of glass. The foil should be smaller than the glass. Support the
pane thus coated horizontally by one hand placed under the middle
of it. Lay a coin on it. Bring the top coat, with the coin on it,
near a prime conductor. After several sparks have passed, try to
pick up the coin with one hand while the other is still in contact with
the lower coat.
Experiment 177. Let one pupil hold a pane of glass on the palm
of one hand. Let a second pupil, who is standing on a stool with
glass or rubber feet (see Exp. 180), rest his open hand flat on the glass,
over the hand of the other, and bring a knuckle of the free hand
near the prime conductor. After a few seconds, let them bring their
free hands near together.
A class of inventive boys or girls will vary these experiments in-
definitely. The shocks given by either of these devices, or by a
regular Leyden jar, may be felt by several at once. To accomplish
this, let all form a circle by clasping hands. When the circle is com-
plete, break it in one place, and let the two persons thus separated
touch, one the outside and the other the ball of the charged Leyden
jar, or the corresponding parts of any other device.
A Leyden jar of a capacity of one quart will furnish a shock suffi-
ciently severe for one person, though two or three times the amount
of surface which it contains might be discharged through the human
body without producing permanent injury. A large number of per-
sons may take the discharge of a larger jar without injury.
457. The Discharge Instantaneous, Experiment 178. To
prove that the discharge of the Leyden jar by a conducting rod (and
272 NATURAL PHILOSOPHY.
therefore presumably through the human system also) is instantane-
ous, set a wheel to rotating so rapidly that the spokes cannot be dis-
tinguished. Darken the room, and discharge a Leyden jar near the
wheel. The separate spokes will not only be seen, but the wheel will
appear to be stationary.
What is thus true of the spark of the Leyden jar is
true of the electric spark under any circumstances. A
rapidly-rotating carriage- wheel, or even a moving cannon-
ball, illuminated at night by lightning, appears stationary.
458. Heat and Light from Electricity. In previous chap-
ters we have learned that resistance to motion causes the
molecular vibrations which produce heat and light. The
same effect is produced by resistance to the free passage of
electricity. Passing over a good conductor, electricity pro-
duces no visible effects. The particles of bad conductors
are so shaken up by their unsuccessful attempts to stop the
flow of the electric charge through them that they fre-
quently develop, first, heat, then light. The ordinary elec-
tric spark is caused by the heating of the molecules of air
and " dust" in the path of the discharge. When the elec-
tric spark is produced in any other gas, the color of the
spark is characteristic of that gas in a state of incan-
descence.
It is a well-known fact that barns and other buildings
are burned by lightning. Lightning is ordinarily due to a
discharge between two clouds differently electrified, but in
cases in which objects on the earth are " struck" it is a
discharge between a cloud and the earth. Should it strike
a poor conductor of comparatively small size in its line
of connection with the earth, it develops heat, sometimes
enough to fire the object.
The following experiments exhibit the heating power of the elec-
tric spark on a smaller scale.
Experiment 179. Present a very shallow metal cup containing a
spoonful of ether or carbon bisulphide to the prime conductor of a
machine. The spark will ignite the liquid.
Experiment 180. Support a dry board about one by two feet on
three or four stout tumblers, bottles, pieces of wax, or on feet shod
ELECTRICITY.
273
with india-rubber. This is an insulating stool. Stand on this stool,
and take in one hand a chain or wire leading from the prime con-
ductor. Take in the other a cold, dry icicle.
Presented quickly to a vessel of carbon bisul-
phide, or to an ordinary gas-burner, the bisul-
phide or the gas may be ignited. This is pretty
sure to succeed best if the gas-burner is used,
and turned upside down, the icicle being pre-
sented from below (Fig. 267). Any water that
may chance to form will then run back on the
icicle instead of collecting on the end in a drop,
which tends to dissipate the charge and prevent
a spark.
Mixtures of oxygen and hydrogen, gun-
powder, gun-cotton, and other explosives
may be ignited by the electric spark. To
fire gunpowder, the discharge must pass
through a poor conductor, e.g., a wet
string, before reaching the metal ball
suspended over the powder. Otherwise,
by the suddenness of the discharge, the
powder is blown away and not ignited.
459. The Insulating Stool, The insulating stool affords a
means of endless instruction and entertainment. A person standing on
such a stool may be charged by connection with the prime conductor of
a machine, or, standing near a conductor, he may be electrified by in-
duction, or by presenting a knife-point or a row of pins to a prime con-
ductor, or a revolving plate or cylinder, or excited rod, he may make
a prime conductor of himself. In either case a few energetic school-
mates will think of a dozen expedients for testing his electric condition.
460. Mechanical Effects of Electric Discharge. The
electric shock is sufficient evidence that the passage of
electricity through a poor conductor produces a shaking
of the body, rather different from the molecular vibrations
which produce heat. A loose block of wood is shaken by
having a Leyden jar discharged through it. A piece of
paper placed between the knob of a Leyden jar and the
knob of the discharger is pierced by the discharge of the
jar. A large jar, or several jars, will pierce thick card-
board, leather, and even glass.
274 NATURAL PHILOSOPHY.
461. The Charge on the Surface. Delicate experiments
have shown that the charge of an electrified body lies wholly
on the surface. A hollow sphere of the thinnest metal will
contain as heavy a charge as a solid ball of the same size,
and so with a conductor of any external shape.
This may be experimentally proved by trying the inside and out-
side of a hollow charged conductor with the proof-plane and electro-
scope. Faraday l tried the experiment on a much larger scale. He
built a box of wood twelve feet in each dimension, and covered it over
with copper wires and tin-foil. This was connected with a powerful
machine; and then (in his own words) U I went into the cube and
lived in it, using lighted candles, electrometers, and all other tests of
electrical states. I could not find the least influence upon them, or
indication of anything particular given by them, though all the time
the outside of the cube was powerfully charged, and large sparks and
brushes were darting off from every part of its outer surface."
So persistently does the charge keep to the outside that
if a charged conductor be turned inside out any number
of times without discharging it, the electricity shifts from
one surface to the other, and is always found on that sur-
face which for the time being is outside. Faraday devised
for this experiment a linen bag, kept open by a ring at the
mouth and turned either way by silk strings made fast to
the bottom.
462. Electrical Tension on Different Parts of a Surface.
As has been intimated before, the amount of electricity on
a given area of the surface of a charged conductor, or the
electrical tension, varies unless the surface is a sphere. On
a sphere the tension is equal at all points of the surface ; on
a cylinder with round ends it is greatest at the extremities ;
on an egg-shaped body it is greatest at the smaller end ;
1 Michael Faraday, English, 1791-1867, one of the most noted
philosophers of this century. His researches, abundant and striking
in many branches of chemistry and physics, were especially so in
electricity and magnetism. He was the discoverer of the present
method of producing the current for electric lights, and of many
other facts and methods of interest.
ELECTRICITY. 275
on a round disk it is greatest at the circumference ; on a
square disk it is greatest at the corners ; and, in general,
on symmetrical surfaces it is greatest at the parts farthest
removed from the centre of gravity of the surface. Points
or sharp edges connected with a surface, wherever situated,
show the greatest tension, hence electricity escapes easily
from them (Art. 446).
463. Thunder-Storms, Every one now knows that light-
ning and thunder are due to electricity. The discovery was
made by Dr. Franklin but little more than one hundred
years ago. How the electricity is produced in the air we
are not prepared to say with certainty, but the friction of
masses of air over one another, and between the air and
particles of moisture and snow, and the evaporation and
condensation constantly going on, are capable of develop-
ing a large quantity of free electricity. But, however
developed, the free electricity is there at all times, though
we are sensible of its presence mainly at the time of thun-
der-showers. The phenomena attending these storms may
be explained by the principles which we have just learned.
When a large number of molecules of atmospheric moist-
ure condense and coalesce to form a cloud, the body of the
cloud becomes a conductor, and all the electricity which
may previously have been in the space now occupied by
the cloud comes to the surface and there acquires consider-
able tension. Different conditions give one cloud a charge
of positive and another a charge of negative. It is plain
that a discharge would take place between these clouds
when they come sufficiently near to each other. Or a
cloud heavily charged with either kind of electricity, on
coming near a neutral cloud, would electrify it by induc-
tion, and a discharge might take place between the sides
next to each other, which would be oppositely electrified
(Art. 441). These are discharges between clouds. When
a cloud heavily charged with electricity comes near the
earth, it attracts the opposite kind of electricity by indue-
276 NATURAL PHILOSOPHY.
tion, and, as the earth has a large store to draw upon, or a
large surface to distribute the repelled electricity over, the
charge becomes very intense. In fact, we have a vast
Leyden jar, the air acting as insulator. When the layer
of air between the two becomes too thin to resist the ten-
sion of the opposing kinds of electricity, they combine, and
we say the lightning came to the earth. High objects are
most likely to be thus " struck," partly because the electric
tension on such would be greatest, and partly because the
insulating air between the two charges is thinnest over
such places. The sudden motion of the air along the line
of the lightning discharge, caused by its displacement, and
also by its expansion and contraction on account of the
intense heat, is the probable cause of thunder.
464. Lightning-Rods. We are now ready to understand
the eifect of the lightning-rod. If the charge excited in
the earth by the electrified cloud finds a pointed conductor
extending towards the cloud, it tends to flow from the point
to the cloud, and thus the electricity of the cloud becomes
neutralized by the quiet discharge from the point, and the
flash of lightning and the " striking" are avoided. The
most efficient lightning-rods are those furnished with
several points. Even then there should be several on a
large building to render it comparatively safe against the
intense charges which clouds sometimes carry.
Lightning-rods should be of ample size and good metal. Wrought-
iron rods should be nearly an inch in diameter. Copper rods may be
somewhat smaller. They should run several feet into the ground, and
be connected with buried water-pipes (if they are large), or else they
should terminate in several branches and be packed in coke, which is
a good conductor.
465. Electricity in Rarefied Air. Though the air in its
ordinary state is a non-conductor of electricity, highly-
rarefied air carries a charge with but little resistance. The
aurora borealis, which is sometimes seen in our latitude,
and more frequently in the far north, is probably due to
ELECTRICITY. 277
electric currents in the higher and rarer regions of the
atmosphere.
A philosophical-instrument-maker will furnish an "aurora tube,"
with which a beautiful experiment may be performed. The tube has
a pointed metal rod sealed into the upper end, and the lower end fits
the air-pump. On exhausting the air and connecting the rod at the
top with the prime conductor of a machine, the tube is filled with
beautiful rosy streams of light, visible in a dark room. The electri-
fied particles of air remaining in the tube, and which produce the
light, are attracted like other electrified bodies, and the streams may
be diverted towards the hand placed against the outside of the tube.
In a succeeding section the subject of electric currents in rarefied
gases will be more fully treated (Art. 514).
Exercises. 1. Two boys stand on different insulating stools, and
one strokes the other a few times with a cat's skin : what will be the
difference in their condition, and how may it be shown ?
2. A girl on an insulating stool presents a row of pins to the prime
conductor of an electrical machine in operation : what is her electri-
cal condition ?
3. If the induction-cylinder of Experiment 164 be touched to the
prime conductor of a machine, what will be its condition after being
removed ?
4. Let the pupil draw a diagram representing three insulated con-
ductors in a row, but not touching, that at one'end connected by wire
with the prime conductor and that at the other end with the negative
conductor : indicate by the signs -f- and the condition of each
end of the middle cylinder.
5. If an excited rod be held over some very small pith balls lying
on a table and then over some others lying on a pane of glass, what
difference in their behavior should be noticed ?
II. CURRENT ELECTRICITY.
466. Definition. Electricity in the condition in which it
was treated in the last section has generally been called
frictional electricity, from the fact that it is most readily
developed by friction. But, whether developed by friction,
by induction, or by any other method, it always possesses
great intensity. On this account it is frequently called high
tension electricity. But one of its most striking character-
istics is shown by its remaining for a long time on an in-
sulated body as a charge after the source of excitement has
been withdrawn. On this account it is called static elec-
tricity, the word static meaning standing or resting.
24
278 NATURAL PHILOSOPHY.
In strong contrast with this kind of electrical excitement
is the electricity produced by a battery such as may be seen
in any telegraph-office. Electricity thus developed " flows"
constantly over a conductor (generally a wire) so long as
it is properly connected with the battery, but as soon as
this connection is broken all sensible evidence of electrical
excitement in the wire, or in anything which may have
been connected with it, ceases. 1 The electricity produces
its effect while flowing as a current through the wire. On
this account it is called current electricity. The word cur-
rent means running. In honor of two early experimenters
with it, current electricity is frequently called galvanism?
or voltaic* electricity, or the voltaic current. " Galvanic bat-
tery" and " voltaic battery" are general terms applied to all
forms of battery producing current electricity.
467. Principle of the Voltaic Battery. The origin of the
electric current produced by a battery is chemical action
between two substances, generally an acid fluid and a
metal.
Experiment 181. Put into any convenient small glass vessel a
mixture of 1 part of sulphuric acid to 10 or 20 parts of water. Dip into
this a strip of zinc and a strip of copper. A copper cent, fastened to a
wire, answers very well for the copper strip. Set the vessel in a light
place and examine the liquid near each metal strip. Minute bubbles
may be seen rising from the sides of the zinc, but none from the cop-
per. Touch the zinc and copper together above the surface of the
liquid, the lower parts remaining immersed. Bubbles will begin to
1 This is not strictly correct when applied to conductors of enor-
mous size, such as an ocean telegraph-cable several thousand miles
long, or when the current is made by a very powerful battery.
2 Aloisio Galvani, Italian, 1737-1798, Professor of Physiology at
Bologna, discovered that a piece of copper and a piece of zinc in
contact with the nerves and muscles of a dead frog, and with each
other, give rise to a current of electricity.
3 Alessandro Volta, Italian, 1745-1827, discovered that any two
metals in contact, and in situation to be chemically acted on, give
currents of electricity. He was the inventor of Volta's pile, and of
the simple voltaic or galvanic battery.
ELECTRICITY.
279
rise rapidly from the copper plate, and a few will probably continue
to rise from the zinc. Separate the metals, and the bubbles stop
rising from the copper plate.
These bubbles are hydrogen gas, liberated from the water
(which is composed of oxygen and hydrogen) by the chem-
ical union of the zinc with the other elements of the acid
fluid. This chemical action is accompanied by the develop-
ment of electricity, which, when the metals are in contact,
or connected by a wire, takes the form of a " current"
through the wire, from the copper to the zinc. This chem-
ical action and electrical excitement are inseparable, one
undoubtedly dependent on the other. If the chemical action
is stopped, the current ceases; and if the current is stopped, the
chemical action ceases.
468. Pure Zinc needed, The continuous rise of bubbles from
the zinc is due to slight traces of some other metals as impurity.
The particles of such metals being in contact with the zinc, a num-
ber of small " local" currents are established. This action uses up
the zinc without giving any compensation in the way of a current
over the wire, where, only, we can make use of it. A pure metal by
itself is not dissolved in the dilute acid. The surface of the zinc is
rendered practically pure by
coating it with mercury. Zinc
so coated is said to be amalga-
mated.
Experiment 182. To amal-
gamate zinc, dip it into dilute
sulphuric acid for an instant,
and then rub it or slap it with
a little muslin bag containing
an ounce or two of mercury.
Make it shine all over, and
repeat Experiment 181, using
the amalgamated zinc.
469. The Simple Voltaic
Cell. The apparatus em-
ployed in the last experi-
ment is essentially a vol-
taic cell. Fig. 268 shows a form of nicely-made cell. The
arrows show the direction of the current along the wire
Fiu. 268. VOLTAIC CELL.
280
NATURAL PHILOSOPHY
M. The upper extremities of the plates, or of the wires
attached to them, are the poles, or electrodes. The positive
and negative are indicated respectively by the signs -|-
and . We may conceive of electricity being propagated
along the wire from the negative as well as from the posi-
tive electrode, but the direction on the wire from the positive
to the negative is spoken of as the direction of the current.
The wire, the plates, and the liquid between the plates
constitute the circuit. If all parts of the circuit are con-
ductors of electricity, the circuit is said to be closed. When
any break exists in the circuit, as would be the case if the
wire were disconnected from one plate, or if either plate
were taken out of the liquid, the circuit is said to be open.
Many combinations are used in the construction of different kinds
of batteries. Instead of dilute sul-
phuric acid, a saturated solution of
sulphate of copper i.e., blue vitriol, or
"blue-stone" may be used. This is
the gravity, or Callaud (kal-lo') cell,
shown in Fig. 269. It is the common
" local battery" in way-stations on tele-
graph lines. Gas carbon may be used
instead of copper for the positive elec-
trode. Gas carbon and zinc, in an acid
solution of bichromate of potassium,
forms a very convenient and effective
battery for experimental purposes.
This is called the "one-fluid bichro-
mate battery." A dozen other single-
fluid cells might be mentioned. Zinc
is almost universally used as the positive metal, i.e., the metal acted
on by the acid.
470. Two-Fluid Cells. In most single-fluid cells the
hydrogen retards the action. With two fluids this may be
obviated. The most powerful of the two-fluid batteries is
Grove's. The zinc plate, in the form of a hollow cylinder, or
something equivalent, is immersed in dilute sulphuric acid
contained in a glass vessel. A vessel of porous earthen-
FIG. 269. GRAVITY, OR CALLAUD
CELL.
ELECTRICITY. 28l
ware, filled with strong nitric acid, is set in the hollow
zinc, and is, of course, surrounded by the dilute sulphuric
acid. A strip of platinum, immersed in the nitric acid,
completes the cell. The nitric acid supplies oxygen, which
unites with and removes the hydrogen that would other-
wise surround the platinum. Platinum is used because it
is not dissolved by nitric acid. The porous earthenware
cup becomes soaked with the acids, and thus conducts the
current of electricity, but it does not permit of much mix-
ing of the liquids. Bunsen's battery uses gas carbon in-
stead of platinum. (See Figs. 272 and 273.)
471. Batteries of Several Cells. The term " battery" has
been unavoidably used several times in the last few pages.
The different arrangements which have been described as
producing the voltaic current are properly cells. A cell of
a given construction gives a current of a definite strength,
or, rather, of a definite electro-motive force. In order to ob-
tain more electro-motive force than one cell will give, we
connect several cells together by means of wires. Such an
arrangement is properly a voltaic battery. Fig. 272 shows
a Bunsen's battery of two cells, and Fig. 273 one of four cells.
It will be seen in Fig. 273 that the zinc of the right-hand
cell is connected with the carbon of the second cell, the zinc
of the second with the carbon of the third, and so on through
the battery. When the first zinc and the last carbon are
connected, the circuit is closed and the current flows.
472. Characteristics of Current Electricity. In Art. 466
current electricity is so called because its chief characteristic
is that it does its work and makes itself known only as it
flows through a conductor. This is true of currents from
all ordinary batteries. With an enormous battery of hun-
dreds or thousands of cells a current may be obtained
which has an appreciable amount of tension, or tendency to
escape ; but even this is very low compared with the ten-
sion of the electricity on the prime conductor of a working
electrical machine. The difference between frictional and
24*
282
NATURAL PHILOSOPHY.
voltaic electricity may therefore be considered a difference
in the intensity of the eleclrical excitement, and voltaic
electricity may properly be called electricity of low tension.
The quantity of electricity developed by an ordinary bat-
tery is very much greater than that developed in the same
time by an ordinary, or even a very large, electrical ma-
chine. The constancy and rapidity of the current take a
large quantity through a conducting wire in a given time.
On good conductors the rate of an electric current has been
measured at more than 200,000 miles per second. Electro-
motive force is the force with which a current is urged for-
ward, and is shown by the ability of a current or a charge
to jump through an insulator. The charge of a small
electrophorus lid will jump one-fourth of an inch through
the air. The current from a thousand Bunsen cells will
produce a spark scarcely y^nr of an inch in length. The
electro-motive force of current electricity is very small.
A number of cells connected, as shown in Fig. 273, increase
the electro-motive force in the direct ratio of the number
of cells employed. A battery so connected is said to be
connected for intensity of current, or connected in series.
FIG. 270. BATTERY CONNECTED " SIDE BY SIDE."
When a larger quantity of electricity is wanted than one
cell will produce, several cells are connected side by side,
as shown in Fig. 270, i.e., the zinc plates are all connected
with one wire, and the carbon plates with another.
ELECTRICITY.
283
473. Resistance, The electric current encounters some
resistance in all parts of the circuit. The resistance in the
liquid of the battery is very great compared with that in
the same length of connecting wire. In a wire of given
material the resistance is directly proportional to the length
of the wire, and inversely proportional to the area of its
cross-section. 1 Different conductors offer different amounts
of resistance. When the resistance is considerable, an ap-
preciable amount of heat results. Thin wires of platinum
and thin strips of carbon are readily rendered white-hot
by the passage of the current. If a copper or iron con-
ducting wire from a battery be cut in one or more places,
and pieces of thin platinum wire be stretched across the
breaks thus formed, they become white-hot on the passage
of a moderately-strong current, and will ignite illuminating
gas, gunpowder, or any similar substance in which they
may be placed. Such arrangements are
very extensively used in lighting the gas
in high buildings and in blasting in mines.
Platinum offers much more resistance than
copper, and the thin wire more than a
thicker one would. The thicker tele-
graph-wires are, the better they will per-
form their work.
474. The Edison Lamp. The Edison elec-
tric lamp consists of a small ribbon of paper-char-
coal in the form of a horseshoe, placed between
metal tips in a glass globe from which the air has
been exhausted. Fig. 271 shows the general ap-
pearance of the lamp. A current being passed through from one of
the wire ends to the other, the carbon is intensely heated on account
of its resistance. As no air is present, it cannot burn away, and so
1 For instance, a copper wire 200 feet long offers twice as much
resistance as one of the same diameter 100 feet long. A wire of a
given length and -fa of an inch in diameter offers 4 times as much re-
sistance as a wire of the same length and T J ^ of an inch in diameter,
* (A)*: (A) 1 -
284 NATURAL PHILOSOPHY.
will give a continuous light for many weeks or months. Other
incandescent electric lamps are in use, some of which use platinum
instead of carbon.
475. Division of Current. If two conductors extend be-
tween the plates of a battery, or are so introduced into a
circuit that the current may take either, a part of it takes
each route, and the amounts are in the inverse ratio of the
resistances of the conductors. If, for instance, two copper
wires of equal length and equal thickness extend between
two points in a circuit, half of the current will follow each.
If two points in a circuit be connected by two copper
wires, one of which is ^ o f an inch in diameter and the
other -^ of an inch, and both of the same length, the
larger wire will carry of the circuit, and the smaller J.
In this way currents are frequently divided for purposes of
electric lighting, duplex telegraphing, etc. So a current
may be divided into any number of parts.
476. The Ohm. The unit of resistance is the ohm. This
is used in designating the amount of electricity required
to produce a given effect in electric lamps, telegraph-
" sounders," etc. It is nearly the resistance offered by 666
feet of copper wire ^ of an inch in diameter. The resist-
ance of 1332 feet of copper wire ^ of an inch thick would
be 32 ohms (2 X 4 2 ).
477. Resistance and Work. The amount of work done by
a given current in any part of its circuit is directly proportional
to the resistance of that part of the circuit.
This applies to the amount of light or heat developed in
the conducting wire, the strength of magnetic attraction
caused by electric currents, etc.
478. The law of the conservation of energy is forcibly illustrated
by the heating and lighting eifects of the electric current. The
burning of the zinc before a blow-pipe, or in a furnace, would pro-
duce both heat and light. When it is consumed in a battery the
same amount of energy is given out, but in the form of an electric
current, which in turn is converted into heat and light, and which,
as we shall presently learn, is far more effective than ordinary fric-
tional electricity in producing motion.
ELECTRICITY.
285
479. Electrolysis. In the production of the electric cur-
rent the water of the battery is separated into oxygen and
hydrogen. If the conducting wires be immersed in another
vessel of water, so that it will form part of the circuit, this
water will also be decomposed, oxygen being liberated
from the positive electrode and hydrogen from the nega-
tive. Fig. 272 shows the method of illustrating this. As
FIG. 272. ELECTROLYSIS OP WATER.
water is composed of two volumes of hydrogen to one of
oxygen, one tube will collect gas twice as fast as the other.
Electro-plating. The galvanic battery decomposes not only
water, but solutions of very many salts of the different metals. The
metal of the salt separates in a pure state. The metals are generally
positive with reference to the other ingredients of a salt, and therefore
separate at the negative electrode. If we wish something coated or
" plated" with silver, gold, or nickel, it is made the negative electrode
of a battery by attaching it to the wire from the zinc. It is then dipped
into a proper solution of the metal which we wish to plate with. On
dipping into the same liquid a plate attached to the positive wire of
the battery the circuit will be closed through the solution, the salt will
be decomposed, and the metal deposited on the negative electrode.
Fig. 273 shows a silver-plating tank in operation. The vessels and
other articles which are being plated are all suspended from the rods
which are connected with the zinc electrode of the battery. The large
square plates suspended from the positive electrode are pure silver,
286
NATURAL PHILOSOPHY.
which is dissolved as the process goes on and keeps the solution of a
uniform strength.
Any boy or girl, with very little outlay, may find instructive enter-
tainment in electro-plating. The apparatus here figured may be of
FIG. 273. ELECTRO-PLATING, WITH BATTERY OF FOUR BUNSEN CELLS.
very much smaller dimensions. The battery may be home-made, a
tumbler will hold the plating-solution, and a brass watch-chain or
hook, or a copper cent, may be plated. In fact,
plating may be done in the battery, and that may
be easily constructed.
Experiment 183. Put a small silver coin into a
dish and pour over it a few teaspoonfuls of nitric acid.
(It should be out of doors or in a fireplace, as the
fumes are hurtful.) If the acid is strong, put in as
much, or twice as much, water. Heat the dish mod-
erately. The coin will dissolve rapidly. When the
coin has disappeared, pour the solution into a glass
vessel. Add some weak u muriatic" acid, or a strong
FIG 274 SILVER- solution of salt in water, as long as it continues to
PLATING A COIN, form white " curds" in the liquid. These white
curds are chloride of silver. They will settle to the
bottom of the vessel. Pour off the blue liquid, or most of it. Fill up
the vessel with water, and pour off several times. This is to remove
the copper with which the silver of the coin was alloyed. It is blue
in the solution, and when the blue color disappears the chloride of
silver is washed enough. It will be necessary now to have about an
ounce of cyanide of potassium, a very poisonous salt, used to wash
ELECTRICITY. 287
out stains of indelible ink. Dissolve this in water, and add it to the
chloride of silver, stirring it round till the white curds are all dis-
solved. Make this quite weak by the addition of water. A dime
will make a half-pint of liquid strong enough for our present purpose.
Fill a porous battery cup with this, or, if that is not at hand, a flower-
pot with the hole stopped with plaster or putty, or, for a small quan-
tity, the " bowl" of a tobacco-pipe with a plug in the broken-off stem.
Set this in any convenient glass vessel, and till that with dilute sul-
phuric acid to the level of the silver solution. Put a piece of zinc
in the outer vessel, and suspend from it by a wire a small clean article
to be plated. Take it out and rub it with a cloth after a minute.
Eepeat several times, each time leaving it in longer. In ten minutes
there will be a very good plating, and in an hour or more, depending
on the strength of the current, a really thick plating.
480. Deposit always on the Negative Plate. It will be
noticed that in the above experiment the article to be
plated takes the place of the copper plate, while in the
methods given in which the battery and the plating solu-
tions are separate the article to be plated is fastened to the
wire from the zinc plate. This is because in the battery the
copper is the negative plate. The negative plate is that
towards which the positive current flows. If the circuit be
opened at any place, that end of the break from which the
current flows is the positive, and that towards which it flows
is the negative, electrode. In determining where to place
an article to be plated, remember that the metal is carried
with the current in the plating solution, and that the current
flows around continuously from copper to zinc in the wire,
and from zinc to copper in the battery.
Many interesting variations of the above plating experiment may
be tried. Any ordinary soluble salt is decomposed by the voltaic
current, the metal going with the current to the nearest electrode.
481. Secondary Batteries. We have seen that the cur-
rent from a battery has the power of separating many
compounds into their constituent parts. The reuniting of
substances thus separated will, under proper conditions,
give rise to a voltaic current opposite in direction to the
current which caused the decomposition. This fact is made
use of in the construction of what are now (1883) just
coming into use under the name of secondary batteries.
288 NATURAL PHILOSOPHY.
Probably the most successful of the secondary batteries is Faure's
(for), or some- one of the very numerous modifications of it. The
principle may be understood from a description of the original form,
devised by Faure. It consists of two large plates of very thin sheet-
lead, each coated with a layer of minium (red oxide of lead), and
rolled together into a spiral like a roll of carpet. The sheets are kept
separated by rolling in with them soft paper saturated with weak acid.
One of these sheets is connected with each of the wires from a bat-
tery. Oxygen from the weak acid is liberated on the surface of the
lead plate which forms the positive electrode, and hydrogen on the
surface of that which forms the negative electrode. The oxygen
unites with the coating of red lead on the positive sheet, converting
it into a higher oxide of lead. The hydrogen unites with the oxygen
of the red lead coating on the negative sheet, and forms water, re-
ducing the oxide of lead to pure lead in a very fine state of subdi-
vision. When all the red lead on one sheet has been converted
into the higher oxide, and all that on the other has been reduced to
the condition of metallic lead, the secondary battery is said to be
"charged." If, now, the wires are disconnected from the charging
battery and brought into contact with each other, a current will be
found to pass through them, and, as said before, it flows backward
with reference to the direction of the primary current, or from the
-oxidized to the deoxidized plate.
482. Energy of Secondary Battery. The total amount
of energy given out in the discharging of a secondary bat-
tery is, of course, equal to that consumed in charging it,
and in practice this may nearly all be made available. The
total " quantity" of an electric current, or of the energy of
a given current, is equal to the amount for any unit of
time multiplied by the time during which the current flows.
A secondary battery may be charged by a small battery
working for a considerable length of time, and may be dis-
charged in a powerful current flowing a proportionately
short time. This feature renders it admirably adapted to
electric lighting, or to the driving of electric motors, where
such use is needed for but a small part^of each day. The
secondary battery is also very much lighter than a primary
battery required to give a current of equal intensity. It
is thus adapted to use where the size and weight of a large
ELECTRICITY. 289
battery are an objection. It has already been applied to
driving road-carriages and to lighting steamships and rail-
way-cars.
III. ELECTRO-MAGNETISM.
483. Oersted's Discovery. About the year 1820, Hans
Christian Oersted (ur'sted), Professor of Physics at the
University of Copenhagen, discovered that a wire through
which a voltaic current is flowing has the power of de-
flecting a magnetic needle out of the meridian. This dis-
covery at once established the connection between elec-
tricity and magnetism, and laid the foundation for the
many useful applications of " electro-magnetism" which
we now see all about us. Oersted also discovered that the
conducting wire of a battery is magnetic while the current
is passing.
484. Direction of Deflection. The direction in which a
needle is deflected by ~*^
the voltaic current - < rl|Sl +
may be readily re-
membered by the fol-
lowing rule :
Consider the de-
flecting force to rotate
around the conduct-
ing wire as the thread
Winds around a SCreW, FlG . 275. -SHOWING DIRKCTION OF NEEDLE'S DE-
moving from the head
towards the point of the screw, that is, rotating as the
hands of a watch turn. When the current is passed near
a magnetic needle, and parallel with it, the north-pointing
end of the needle is turned from its position in the direction
of the action of such a force, whether eastward or west-
ward, or upward or downward.
For instance, suppose a current pass on a wire parallel
to a needle, from the north to the south, if it pass above
N t 25
290
NATURAL PHILOSOPHY.
the needle, the north-pointing pole will be turned east-
ward ; if it pass beneath, the same pole will be turned
westward ; if at the same level on the right-hand side, the
north pole will be raised ; if on the left-hand side, it will
be depressed.
In Fig. 275 the arrow-head, as well as the + and
signs, indicates the direction in which the current flows
over a wire, and the arrows on the wheel show the direc-
tion of rotation of the magnetic force. In whatever posi-
tion the wire is held, imagine the circumference of this
wheel to strike the north end of the magnet and carry
it in the direction of its own motion.
485. The Amount of Deflection of a given needle depends
on the total effective strength of the current. A given cur-
rent may multiply its effect on the needle by passing several
times. If one current pass above a needle from north to
south, and another pass beneath it from south to north,
the two currents will tend to deflect the needle in the
same direction, and the effect will be a double deflecting
force. The same result is obtained when the wire is bent
so that the same current may pass in one direction above
the needle, and in the other direction
under it. The result is intensified by so
coiling the wire as to make the current
pass many times around the needle.
This principle is made use of in the con-
struction of the galvanometer, or instru-
ment for detecting and measuring the
galvanic current.
486. Galvanometer. Fig. 276 repre-
sents a common form of galvanometer.
It has a double, or astatic needle, i.e.,
two magnetic needles so arranged that
they neutralize each other's tendency to stand north-and-
south, suspended by a thread of "unspun" silk. The
graduated circle which lies on the coil of wire, and just
FIG. 276. GALVANOME-
TER.
ELECTRICITY. 291
under the uppermost needle, indicates the amount of deflec-
tion.
487. The Electro-Magnet. The galvanometer needle is
never deflected more than 90 degrees, or till it stands at
right angles to the direction of the electric current. A
comparatively feeble current will turn a needle nearly at
right angles to its course, indicating that the natural posi-
tion of magnets is across the direction of electric currents.
Not only do currents tend to turn magnets into this direc-
tion, but they magnetize iron or steel bars near which they
pass. A magnet formed by passing a voltaic current across
a bar of iron is called an electro-magnet. It is magnetic only
while the current passes.
488. The Helix. A current crossing an iron bar only
once makes a very feeble magnet of it. If the conducting
wire be covered with an insulating cover of wax, india-
rubber, silk, or even cotton, it may be wound many times
around a bar, as cotton is wound on a spool. As many
currents multiply the effect of one, there is scarcely a
limit to the power of electro-magnets thus made. Fig.
277 shows a horseshoe electro-magnet. A layer of wire
wound from end to end or over a considerable part of the
length of a bar is called a helix. Several layers, such as
are shown on each arm of the horseshoe in the figure, con-
stitute a coil.
Experiment 184. Procure of a dealer from two to four ounces of
very fine covered copper wire. Wind it neatly around an iron bar
as large as an ordinary lead-pencil, making several layers. Connect
the free ends of the wire with any simple battery, and experiment
with the electro-magnet thus formed. Dip it into nails, and, when
it is loaded, break the circuit. Notice that some of the nails in-
cline to stay on after the current is stopped. This is on account of
the residual magnetism which iron is apt to exhibit after having been
once magnetized. Try the poles of the electro-magnet with a mag-
netic needle, and notice the direction of winding of the coil of wire
as looked at from each end. Refer to rule for deflection of needle
by the electric current, and notice that the same rule holds here.
As electro-magnets are much more powerful than steel magnets,
they are mostly used in magnetizing steel bars. Fig. 278 shows the
292
- NATURAL PHILOSOPHY.
method of operation. Of course, reference to the direction of wind-
ing indicates the respective poles of the electro-magnet.
FIG. 277. ELECTHO-MAGNET.
489. The Helix a Magnet, A helix, or coil carrying a
voltaic current, not only communicates magnetic properties
FIG. 278. MAGNETIZING STEEL BAR.
to the bar of iron in the middle, or " core," but is itself a
magnet. It attracts iron, is attracted and repelled at the
ELECTRICITY. 293
different ends by the poles of a steel magnet, and, if prop-
erly suspended, arranges itself in the magnetic meridian,
the hollow centre taking the north-and-south direction. If
a strong steel magnet be placed directly under a helix sus-
pended horizontally, the helix assumes the direction of the
length of the magnet, the convolutions of the wire being
across its length. This shows a mutual action between
electric currents and magnets, and that they are naturally
at right* angles to each other.
490. Electric Currents in the Earth. The north-and-south
tendency of magnets may be due to electric currents flowing westward
around the earth. In cases of unusual fluctuation of the compass,
electric currents have frequently been detected, in such direction as
they should flow, to account for some of the observed phenomena.
The existence of currents to account for all the ordinary phenomena
of the magnetic needle is not established, but there are strong reasons
for believing that they do exist.
491. Magnetic Storms. Telegraph-operators frequently report
electrical or " magnetic storms," which are sometimes of considerable
extent and cause them much inconvenience. They are not neces-
sarily accompanied by wind, rain, snow, or any other of the phenom-
ena ordinarily included in the term "storm," but are simply dis-
turbances in the electrical or magnetic condition of the earth and the
air. Magnetic needles move backward and forward through several
degrees, telegraph-wires refuse to carry the battery currents with any
regularity, and fine displays of aurora borealis are witnessed. The
aurora may not be seen where the disturbances are felt, but it is sure
to be visible somewhere within a few thousand miles of the centre of
greatest disturbance.
As illustrations of the effect of such storms, we quote from Chicago
dispatches an account of the effect there of one which occurred in the
autumn of 1882 : " The storm seemed to go in successive negative
and positive waves, alternately neutralizing the currents on the tele-
graph lines, or increasing their intensity to such a degree as to burn
things up. The ' switch-board' at Chicago was on fire a dozen times,
and half a dozen keys of instruments were melted. The atmospheric
electricity on one of the country wires had such power as to suffice
to keep an electric lamp burning. Fully two-thirds of the sky is
ablaze to-night with auroral light of many colors, a rare phenomenon
in this region." At Nashville, during the same storm, the telegraph
25*
294 NATURAL PHILOSOPHY.
lines " were worked at intervals solely by the auroral current. The
needle in the galvanometer oscillated in a most eccentric manner,
varying as much as 80 degrees." This storm was wide-spread, ex-
tending over all the northern half of the United States and north
and east as far as telegraph lines extend. A dispatch was sent from
Bangor, Maine, to North Sydney, Cape Breton, a distance of 700
miles, without a battery ! The disturbance to telegraphic communi-
cation was greatest on lines extending east and west, and this was
largely removed by using wires for the whole circuit instead of em-
ploying the earth for the conductor in one direction, as is usually
done. 1
492. Applications of Electro - Magnetism. As electro-
magnets are magnetized and demagnetized by simply clos-
ing and breaking the circuit which carries the current
through the coil, they find many useful applications. En-
gines have been made in which armatures are attracted in
alternate directions by different electro-magnets acting at
alternate moments. Such an armature may be made to
carry with it a rod to turn a crank, or, in some other
manner, to give motion to ordinary machinery. For very
light work an engine of this kind may be used to advan-
tage, but the cost of maintaining a powerful battery is too
great to admit of its economical use where great power is
required and where steam or water can be conveniently
supplied.
493. The Electric Telegraph, The one successful and
useful application to which electro-magnetism has been put
during the past forty years is telegraphing. The word
" telegraphing" means writing at a great distance, and a
"telegraph" is any instrument by which a person at one
place can make signs which may be read at another place
some distance away.
494. History of the Telegraph. Frictional electricity was
known to the ancients before the Christian era, but conduction and
insulation appear not to have been discovered till 1729. Very soon
1 Some connection seems to exist between these storms and the con-
dition of the sun. (See Sharpless and Philips's Astronomy, p. 58.)
ELECTRICITY. 295
after the discovery of conduction, and the classification of bodies as
conductors and insulators, plans were devised for carrying conducting
wires on insulating supports and transmitting through them charges
of frictional electricity, which should be sent in an order agreed upon
to represent letters or words. Systems arranged on this principle
were never very satisfactory. One of the best employed a separate
wire for each letter of the alphabet, each wire being supplied with a
delicate electroscope. The person sending the message touched the
wires to the conductor of an electrical machine in such order as to
spell out the message to be transmitted, and the person receiving it
watched the order of divergence in the electroscopes, and so read the
message. This system was costly and cumbrous, and it could be suc-
cessfully operated only through short distances (20 or 30 miles), so
that it never came into general use.
Voltaic electricity was discovered about 1792. Oersted's discovery
of the deflection of the magnetic needle was made in 1820, and was
soon applied by Wheatstone 1 and others to successful systems of
telegraphing.
495. The Morse Telegraph. The introduction of the electro-
magnet as an essential feature of the telegraph dates back to about
1836, when Samuel F. B. Morse 2 invented the electro-magnetic tele-
graph now in general use in civilized countries. His original device
consisted of a register (Fig. 279) for receiving the message, and a key
(see Fig. 280) for transmitting it. The register is easily understood
from the figure. The current from the line wire passes through the
coils of the electro-magnet, which is thus rendered magnetic, and
draws down the armature. This elevates the point shown on the
opposite end of the lever. The paper is drawn at a uniform rate be-
tween the rollers by the action of the weight under the table. When
the point is pressed against the paper it describes a straight line, whose
length is proportional to the time the point is held there. This is de-
termined by the operator at the distant station, who alternately de-
presses and elevates his key. While he holds the key down the
current passes, the armature is held down, and the point is pressed up.
Long and short dashes (called respectively " dashes" and " dots") and
vacant spaces are thus recorded in succession on the strip of paper,
1 Charles Wheatstone, English, 1802-1875, professor at King's Col-
lege, London.
2 American, 1791-1872. The inventor of the form of telegraph-
receiver in common use.
296 NATURAL PHILOSOPHT.
and, as a definite group of these dots and dashes represents each letter,
figure, and other mark used,, the receiving operator is able to inter-
FIG. 279. TELEGRAPH-REGISTER.
pret them. The accompanying line of dashes and hyphens represents
the appearance of such a message. The letters above them are in-
tended as a translation, for the benefit *of the readers of this book.
"Wil 1 comeattenAM
The striking of the lever against the screws which regulate the dis-
tance of its motion makes an appreciable sound, and a certain differ-
ent combination of these is used to call the attention of each particu-
lar operator on a given line.
Soon after this system came into use, operators discovered that they
could read the messages as well as the office-call by the click of the
lever against the screws, and the paper was dispensed with. A new
form of instrument, known as the sounder, now takes the place of the
register in most telegraph-offices. Its general structure may be under-
stood from Fig. 280. Th lever is drawn down by the electro-magnet,
and strikes against a solid metal piece, making a loud sound. A
spring is so attached to an arm connected with the lever that it in-
stantly raises the lever on the breaking of the current.
"When a telegraph line is long, the resistance of the wire renders
the current feeble, so that the sounder is not operated with sufficient
force to be satisfactory under all circumstances. To remedy this, a
local battery is introduced at each station to operate the sounder at
ELECTRICITY.
297
that station. The circuit of this battery (the "local circuit") is
opened and closed by a relay, which in turn is operated by the feeble
current of the line- wire. The "relay" is a very delicate electro-
magnet, operating a lever whose end is made to strike against a metal
piece and thus close the local circuit.
Pig. 280 represents, in vertical section, a Morse telegraph-station,
such as may be seen in almost any town or at almost any railroad-
station. The student will please trace out the office and action of
each piece of apparatus. The key, the sounder, and the relay may
be supposed on a table, and the local battery under it. The wire of
the main line is seen entering at one side and leaving at the other.
The key must be kept " closed" at all times, except in the particular
office on a line from which a message is, at the time, being sent. The
current in Fig. 280 we will suppose enters at the left, passes through
the key, and by the wire to the relay, around the coils of the electro-
magnet in the relay, and out at the right, going in the same way
through all the offices which are in the main-line circuit. When no
message is traversing the line, the current is continuous, the cores of
all the relays are magnets, and the armatures are all held against the
opposing anvils. This closes the local circuits and holds down the
levers of the sounders. When a message is to be sent from any office
on the line to any other office, the operator in the sending office opens
his key. This breaks the circuit, stops the current, and demagnetizes
the relay, whose spring pulls back the armature. This in turn breaks
the local circuit and demagnetizes the sounder, whose lever is raised
by its spring. This is the condition of things shown in the figure.
Zine Wire
local.
FIG. 280. DIAGRAM OF MORSE TELEGRAPH STATION.
The sender then operates his key by pressing it down and raising it
at certain intervals. The currents thus sent operate on the relay situ-
ated in each office of the line, and its armature vibrates, keeping time
with the motions of the sender's key. This acts as a key for the local
circuit, and a succession of currents is sent through it, operating the
sounder. Thus it will be seen that a message sent from any one
298 NATURAL PHILOSOPHY.
station to any other station may be read at all the stations in the main
circuit. The sending operator even reads his own message.
496. The Earth Used as a Conductor. In all ordinary tele-
graph and telephone lines the earth is used as a conductor in one di-
rection, and but one wire is employed. Most lines of telegraph have
a battery at each end, the positive electrode of one battery and the
negative of the other being connected with the same wire. The other
electrode of each battery is connected with a " ground- wire," which
is attached to a metallic plate buried in moist earth.
497. Duplex and Quadruplex Telegraphy. The simple Morse
system, just described, is very reliable, but a given wire can transmit
only one message at a time. Various arrangements have recently
been devised by which a wire may be made to convey one or two
messages each way at the same time without conflict. The former is
known as the duplex system, and the latter as the quadruplex system.
A complete explanation of them would take us beyond the limit of
this work.
The art of telegraphy is advancing very rapidly. Mechanical ar-
rangements for transmitting are successfully employed, and auto-
matic arrangements for receiving and for retransmitting if desired.
The simple Morse system was a marvel of completeness and rapidity.
A good operator can send or receive 30 or 40 words per minute, as fast
as a rapid penman can write. This was the capacity of a single wire
until recently. With a combination of the latest inventions the feat
has been accomplished of transmitting 1500 words between New
York and Boston over the same wire in one minute.
498. Ocean Cables. On land lines the line-wire, even if very
long, is charged and discharged nearly instantly, and the current is
no appreciable length of time in traversing it. Ocean cables, being
laid under water, must be surrounded by an insulator. Gutta-percha
is used. The arrangement then resembles a Leyden jar, the con-
ducting wire representing the inside coat, and the water the outside
coat, while the gutta-percha acts as the glass. To charge this re-
quires some time, and to discharge it requires as long. In the cable
between Ireland and Newfoundland this amounts to a total of six
seconds. On this account special instruments are required for send-
ing and receiving messages over ocean cables.
499. Electric Clocks. The electric current is frequently used to
propel or regulate clocks. The pendulum of a standard clock is made
to operate a key, which opens and closes a circuit including all the
clocks to be regulated. These may be distributed over a large build-
ELECTRICITY. 299
ing, or a town, or along a railroad line. The interrupted current
passes through an electro-magnet in each clock. The armature,
moving in exact unison with the beats of the standard clock, either
operates on a ratchet-wheel and communicates motion to the clock,
or regulates the swinging of a pendulum. In either case all the
clocks will keep exactly together and with the regulator.
500. Thermal Electricity. If a bar of antimony (A, Fig.
281) and a bar of bismuth, B, be soldered together at one
end, and the junction be moderately heated, and wires at
the other end be connected with the coils of a galvanome-
ter, an electric current is found to exist flowing from the
antimony through the wire to the bismuth, and from the
bismuth across the heated junction to the antimony. If
the junction be cooled instead of being heated, a current is
established in the opposite direction.
If a large number of such bars be joined together in
series, as shown in Fig. 282, a very slight amount of heat-
FIG. 281. THERMO-ELECTRIC PAIR. FIG. 282. PRINCIPLE OF THERMOPILE.
ing or cooling of the junctions at one end makes an appre-
ciable current, the current always flowing at the warmer
junctions from bismuth to antimony, and at the cooler from
antimony to bismuth. The same effect, in a less degree, is
produced by substituting other metals for the antimony
and bismuth. Two metals so arranged are called a thermo-
electric pair, and a combination of several (usually twenty-
five to one hundred) such pairs constitute a thermopile.
When connected with a galvanometer it is known as the
thermo-multiplier, one of the most delicate of thermometers.
501. Induced Currents. If a coil of wire, around which
a battery current is flowing, be introduced into a larger
coil (see Fig. 283), a galvanometer shows that while the first
coil is moving into the second a current flows in the outside
300
DEPARTMENT OF
NATURAL PHILOSOPHY.
coil. On removing the inside coil, a current flows in the
outside coil. This is an induced current, and it lasts only
while one coil moves towards or from the other. The coil con-
nected with the battery is called the primary coil, and the
FIG. 283. PRIMARY AND SECONDARY CURRENTS
other the secondary coil. Every motion of the primary
coil towards or into the secondary coil produces a current
in the secondary coil opposite in direction to that in the
primary ; and every motion of the primary from or out
of the secondary produces a current in the secondary in
the same direction as that in the primary.
If the primary coil be dropped into the secondary and
allowed to remain, no induced current is noticed after the
primary coil is inserted, so long as the primary current is
constant. Any increase in the strength of the primary cur-
rent induces an inverse current (i.e., opposite in direction to
its own) in the secondary coil, and any decrease in the
strength of the primary current induces a direct current in
the secondary. If the primary circuit be alternately closed
and opened while the coil remains in the secondary, it is
found that every time the circuit is closed an inverse mo-
mentary current is induced in the secondary, and whenever
it is opened a direct momentary current is induced. These
ELECTRICITY.
301
iast currents have a great electro-motive force, will jump a
considerable distance through air, and exhibit other prop-
erties of frictional electricity. They will be more fully
treated of in Art. 513.
If, instead of a primary coil, a magnet be used, its ap-
proach induces a current in one direction, and its removal
induces a current in the opposite direction. If an iron
core be placed in the secondary (Fig. 284), opposite cur-
FIG. 284. CURRENT INDUCED BY MAGNET.
rents are induced by the approach and withdrawal of either
pole of the magnet. These currents are stronger than
those induced by the same magnet in the same coil without
the iron core. This is because the magnet acts by induc-
tion on the iron and makes it a magnet (Art. 412). If,
now, the magnet be placed in the coil, and the piece of iron
be suddenly moved towards it and away from it, the same
alternating currents will be induced, the iron acting as a
magnet. If these currents, instead of being passed through
a galvanometer, as shown in Fig. 284, be passed through a
second coil surrounding a magnet, they vary the strength
pf the magnet, the current in one direction adding to its
strength, on the principle of the electro-magnet, and that
in the other direction taking from it.
26
302 NATURAL PHILOSOPHY.
502. The Telephone. The last article explains the principle
of the Bell telephone, which, although first publicly exhibited at the
time of the Centennial Exhibition in 1876, is now in very extensive
FIG. 285. SECTION OF BELL TELEPHONE.
use throughout the civilized world. Fig. 285 shows the instrument
in section. NS is a steel magnet. B is the coil of fine wire, whose
ends are connected by the binding screws with the line-wires CC.
LL is a sheet of very thin iron, called the diaphragm. The whole is
enclosed in a neat rubber tube, M, and supplied with a mouth-piece
(and ear-piece), RR/. To send a message, the operator speaks into the
mouth-piece. The sound throws the air into vibration, and this in
turn communicates its motion to the diaphragm. The diaphragm,
being so near the magnet, is polarized by induction. As it is pushed
towards the magnet by the sound-waves it induces a current in one
direction in the coil of wire, and as it recedes it induces a current in
the opposite direction. These alternating currents, agreeing in fre-
quency with the sound-waves made by the operator's voice, are propa-
gated through the wires to the distant station, and are there received
by an instrument exactly similar to the transmitting instrument. Of
these rapidly alternating currents, those in one direction strengthen
the steel magnet, and those in the other direction weaken it. It thus
exerts a varying amount of attraction on the diaphragm and causes
it to vibrate, the vibrations keeping time with the alternations of the
current, which in turn keep time with the vibrations of the trans-
mitting diaphragm, and as this keeps time with the vibrations of the
operator's voice, the sound of his voice is reproduced at the distant
station. Fig. 286 represents the two terminal stations of a telephone
line, connected. The letters correspond with those in Fig. 285.
There may be any number of telephones on the line, and the cir-
ELECTRICITY. 3Q3
cuit may be completed by using ground-wires, as with the telegraph.
There should be two instruments at each station, one for the operator
to hold to his ear and one to his mouth. A battery current is sent
through to an alarm-bell (Art. 505) to call attention when a message
is to be sent.
Line Wire.
R/L
\
FIG. 286. DIAGRAM OF BELL TELEPHONE LINE.
503. The telephone is a beautiful illustration not only of electro-
magnetic induction, proving the close connection between electricity
and magnetism, but also of the transformation of energy, and of the
correlation of the physical forces (Art. 83). The sound-waves set
the diaphragm into vibration ; the force of its motion, by reaction on
the magnetic pole, appears as the electric force in the wire ; this is
transformed into magnetic force at the other end of the wire, which
is made known to us by the vibration of the second diaphragm, con-
veyed to our ear through the medium of the air, just as it would
have been had our ear been near enough to catch the vibrations in the
air produced by the speaker's voice!
504. The Telephone Current Feeble. The telephone current
is very feeble. It has been estimated that the force represented by
the amount of heat required to raise one gram of water one degree
Centigrade would be sufficient to impress 10,000 words on a Bell
telephone. This would be more than twenty pages of the large type
of this book.
Many wonderful and useful recent inventions are applications of
feeble currents thus induced in what might be termed secondary coils,
or of the slight changes in strength of primary currents.
505. The Alarm-Bell. The attention of the receiving operator
of a telephone message is called by a bell similar to those employed
in burglar- and fire-alarms, and in hotels and other large buildings
as call-bells. The operation of such a bell will be readily understood
from Fig. 287. The current passes in at one of the " binding screws,"
AD, and out at the other, traversing the coils of the electro-magnet.
The core is thus rendered magnetic, and the armature, B, is drawn
forward, causing the hammer, M, to strike the bell. The current
304
NATURAL PHILOSOPHY.
on its way from A to D passes up through the armature, B, and down
through the spring, K. When B is drawn forward, contact with the
spring, R, is broken, and the current ceases. The core is thus de-
FIG. 287. ELECTRIC BELL.
magnetized, and B is released and thrown back by the small spring
at the bottom. This again closes the circuit, and the operation is re-
peated, in most cases several times in a second, as long as the current
is sent.
IV. MAGNETO-ELECTRICITY AND DYNAMO-ELECTRIC MACHINES.
506. Currents produced by Magnetism. Eeferring again
to Art. 501, we find that the approach of a magnetic pole
to a coil, and the withdrawal of it from the coil, induce
currents in the coil. If the pole be stationary, and the coil
(better with an iron core) be moved, the same currents re-
sult. This is Faraday's discovery, made in 1831, and he
showed that such currents result in all conductors which
move in the magnetic field (the space strongly influenced
by the magnet) in any direction other than parallel to the
ELECTRICITY.
305
lines of force (Art. 420). A current so developed possesses
the properties of voltaic electricity. It is now largely em-
ployed for producing the electric light, and for driving
electric motors. A description of the apparatus used for
generating it will, therefore, be in place here.
507. Clarke's Machine, One of the original forms of magneto-
electric machine is shown in Fig. 288. Its operation is plainly indi-
FIG. 288. CLARKE'S MAGNETO-ELECTRIC MACHINE.
cated. The two coils of wire with soft iron cores are made to rotate
rapidly about the horizontal axis, so that each one is brought oppo-
site each of the magnet's poles in each revolution. As each coil ap-
proaches each pole, a current is generated in it in one direction, and
as it recedes, a current is generated in the opposite direction. These
currents are conveyed to the wires, and, on account of their intermit-
tent nature, they produce a peculiar shaking or " shocking" sensation
on passing through the body. The machine here shown is intended
u 26*
306 NATURAL PHILOSOPHY.
for giving such shocks. The currents may either be allowed to flow
through the wires in alternate directions, or, by means of a mechani-
cal device known as a commutator, all the positive currents may be
delivered to one of the wires, and all the negative to the other, thus
making the currents all " flow in the same direction."
508. History of Magneto-Electricity. By employing a
large number of powerful horseshoe magnets and a larger
number of revolving coils, machines on this plan were
made, under the supervision of Faraday and others, which
gave currents of sufficient intensity to be used in electro-
plating, electric lighting, etc. In 1866 it was discovered
by Wilde that the current from a large magneto-electric
machine, conveyed around the coil of an electro-magnet,
endued it with a magnetic strength far greater than that
of the whole series of steel magnets used to generate the
current. A fresh and larger armature 1 was made to re-
volve before the poles of the electro-magnet thus formed,
and from this armature a very powerful current was ob-
tained. This in turn was made to magnetize a second
electro-magnet, and from an armature revolving in front
of its poles a current was obtained far exceeding anything
previously known.
509. Dynamo-Electric Machines. The next step in the
manufacture of magneto-electric machines, or, as they are
now commonly called, dynamo- electric machines, consisted
in raising the power of an electro-magnet by its own induced
currents. When the iron core of an electro-magnet has
been once magnetized, it retains for a long time a slight
amount of residual magnetism. An armature revolving
before the poles of such an electro-magnet has very feeble
currents developed in it. These are carried through the
coil of the electro-magnet, increasing its strength. This
increases the current in the armature, which further
strengthens the power of the electro-magnet, and so the
1 The " armature" in magneto-electric machines is the whole series
of the revolving coils with soft iron cores.
ELECTRICITY. 3Q7
current and the magnet strengthen each other, the limit
being fixed by the power of the machine which gives ro-
tation to the armature. The armature with the current
flowing in it, and the magnetic pole which produce's the
current, repel each other as similar magnetic poles do;
hence the necessity of force to overcome this repulsion.
Of course, the stronger the magnet and the stronger the
current, the more force will be required ; and, as there is
no limit to either, the power of the driving-engine decides
the strength of the current. The current which thus ex-
cites the electro-magnet passes, after leaving it, over con-
ducting wires wherever wanted, and becomes the current
of the machine. If this current is made to flow through
the armature of another similar machine, it rotates the ar-
mature backward, by virtue of the repulsion above alluded
to, and the force with which it rotates is equal to that ap-
plied to the first machine, except that which appears as
heat, caused by the resistance of the conducting wire, fric-
tion of parts, etc.
DYNAMO-ELECTRIC MACHINE.
Fig. 289 represents the Brush dynamo-electric machine, one of the
many patterns constructed on plans essentially as described. It is
selected for illustration here on account of its very extensive use in
this and other countries for electric illumination.
The armature, which is represented between the large electro-
308
NATURAL PHILOSOPHY.
magnets, M, is rotated by the pulley-wheel, P. The currents gener-
ated in the coils, or " bobbins," C, of the armature are made to flow
in the same direction by means of a commutator. They are then col-
lected by the contact-springs, S, and conveyed through the wires sur-
rounding the electro-magnets, M, and extending wherever the current
is wanted.
510. The Electric Arc. As previously stated, current elec-
tricity does not jump a break of any appreciable width in the
conducting wire. Whenever a circuit is broken, however, a
momentary spark is noticed at the break,
unless the current be quite feeble. This
spark is due to a few of the particles of
the conducting wire being carried over
in an attempt to keep up the current.
They are rendered incandescent because
of the increased resistance (Art. 473) of
their small number. If two pieces of
gas carbon, placed end to end, be intro-
c duced into the circuit of a powerful bat-
tery, or of a dynamo machine, and then
gradually separated to the distance of
about a half-inch, particles of incan-
descent carbon travel across the break,
producing the most brilliant of artificial
lights. The light-giving area has the
form of a crescent, and on this account
is called the electric arc. A light so pro-
duced is called an arc light, to distin-
guish it from the incandescent lights, of
which the Edison lamp, previously ex-
plained, is a type.
511. The Brush Electric Lamp.
There are many forms of lamp for producing
the arc light. Fig. 290 represents the Brush lamp. The light is
produced in the space between the two carbons, kk. One of the con-
ducting wires is connected with the lower carbon by the binding
screw shown, and the other wire is so connected that the current
FIG. 290. BRUSH'S ELEC-
TRIC LAMP.
ELECTRICITY. 3Q9
passes through the coil, a, and then to the sliding-rod,/, which holds
the carbon at its lower extremity. When the current is turned into
the lamp, the points, kk, are together. The current passing mag-
netizes the iron core, d, of the coil, a, and draws it into the coil, thus
separating the carbons and producing the light. As the carbons are
drawn farther apart, the resistance increases, the current becomes
more feeble, the coil, a, becomes weaker, and stops raising the core, d.
The strength of the current and the distance of the carbons thus main-
tain a constant balance. When the current is shut off from the lamp
the carbons fall together again. The carbons are gradually con-
sumed. The mechanism below the coil, not well shown in the figure,
is for lowering the sliding-rod,/, through the iron core, d, so that
the carbons may be kept at a uniform distance from each other, no
matter how long or how short they may be.
512. Methods of Electric Illumination, Of course any judi-
cious combination of current-producing machinery aifd lamp will
produce the electric light. For street illumination, railroad depots,
etc., the dynamo machine and the arc lamp seem well adapted. For
houses, the incandescent light is by far the more satisfactory, not
having the flicker of the arc light. In large communities- a dynamo
machine will furnish a current economically. For isolated families,
the hope for a satisfactory electric light seems to rest on the perfecting
of the secondary battery (Art. 481).
513. The Ruhmkorff Induction-Coil As stated in Art.
501, currents of great electro-motive force are generated
in a secondary coil at the instants of starting and stopping
the current in the primary coil. These currents not only
possess the characteristics of frictional electricity, but the
discharges may be obtained from such an induction-coil
with much more uniformity than from an electrical ma-
chine, and the coil is not perceptibly affected by atmos*
pheric conditions. Such being the case, a description of
the Euhmkorff l coil, and of some of the effects which may
be produced by it, is here inserted.
Fig. 291 gives a general view of the coil, mounted. The current
from the battery enters by the binding-posts, AA 7 . C is the com-
mutator for reversing the current so that it may be made to flow
1 German, settled in Paris; has gained distinction from this form
of induction-coil.
310
NATURAL PHILOSOPHY.
either way through the primary coil at pleasure. At r is seen the
iron core of the primary, and a small section of the primary coil
FIG. 291. KUHMKORFF'S INDUCTION-COIL.
may be seen. The secondary coil is much larger than the primary,
and forms the large cylinder. The ends of the wire forming the
secondary are seen at BB'. The primary circuit is automatically
closed and opened hy the " break," n. The current traverses the post
at the left of n, then by way of the spring and screw to the right-
hand post, then by way of the wire, etc. In the figure the circuit is
closed. The iron core, extending entirely through the coil, is thus
magnetized, and attracts the disk on the spring, n, drawing it away
from the end of the screw and breaking the current. As soon as the
current is broken, the spring flies back against the screw, thus starting
the current again. The core again attracts the disk, and so the cur-
rent is made and broken several times in a second.
As previously stated, the breaking of the primary current induces
a direct current in the secondary, and the making of the primary
current an inverse current in the secondary. This may be remem-
bered by supposing the direct current in the secondary to be a mo-
mentary continuation of the force of the primary current after it is
broken, and the inverse current to be a reaction on the secondary
wire by the starting of the primary current, just as a horse in starting
a heavy load tends to slip backward. The direct current has very
ELECTRICITY. 31 1
much more electro-motive force than the inverse current has ; in fact,
with ordinary coils the effect of the inverse current is not noticed ;
it is the direct current, or that produced when the primary current is
stopped, that produces the results which we witness. The positive
electrode of the secondary coil is that from which the direct current
flows, and the negative electrode is that towards which the direct cur-
rent flows. To give the direct current its maximum effect, the break
of the primary circuit must be made instantaneously. Though we
adopt a mechanical device which accomplishes this result, it is found
that an " extra current" : lingers for a sensible length of time in the
primary coil and interferes with the intensity of the secondary cur-
rent. To correct this a condenser (Art. 453) is connected with the
primary circuit. This consists of several sheets of tin-foil, separated
by varnished paper, placed in a drawer in the base of the coil. In
the figure the connections with the condenser are shown at pp. The
sheets are connected alternately with the parts of the conducting wire
towards the respective poles of the battery. "When the current is
broken, the extra current spends itself in charging this condenser,
which immediately discharges itself through the wire in the opposite
direction, and thus assists in exciting the secondary current.
The effectiveness of the Kuhmkorff coil increases with the length
of the wire in the secondary coil. As those layers of wire which are
nearest to the primary are most powerfully affected, it is desirable to
have all as near as possible. For this reason the secondary is of very
fine wire, not more than T 7 of an inch in diameter. The best coils
contain several miles of such wire, from 20 to 50 being a not uncom-
mon quantity. The great coil of William Spottiswoode contains 280
miles in the secondary coil. It forms a cylinder 37 inches long and
20 inches in diameter, and will give a spark 42 inches long. An
induction-coil about 6 by 2 inches, and giving a half-inch spark, is a
very convenient apparatus for administering electric shocks.
514. The Ruhmkorff Discharge. The discharge of the
Ruhmkorff coil may be used in many experiments of the
kind indicated for frictional and Holtz machines and the
Leyden jar, but it gives the most interesting results when
made to pass through glass tubes which have been exhausted
1 This extra current is induced in the successive circles of the pri-
mary coil by the breaking of the current in the contiguous parts.
When the primary circuit is a straight wire, the extra current is not
noticed.
312
NATURAL PHILOSOPHY.
of most of their gaseous contents. In Art. 465 it was
stated that the electrical discharge, though taking place
with difficulty through ordinary air, takes place quite
readily through highly-rare-
fied air. The same is true for
other gases. If a glass tube
be filled with air, hydrogen,
oxygen, nitrogen, carbonic
acid, or any other gas, and
then by means of an air-pump
most of the gas be taken out,
the passage of the Kuhm-
korff discharge through the
remaining rarefied gas fills
the tube with a glow of light.
This light is differently col-
ored for different gases. The
color in each case is that which
is due to the incandescence of
that particular gas (Art. 458).
The contents of such a tube
may thus be accurately de-
termined by discharging an
induction-coil through it and
examining the discharge with
a spectroscope (Art. 302).
515. Geissler Tubes, Many
beautiful designs of such exhausted
tubes, Geissler tubes, are in the
market, and they may generally he
made to operate with quite small
Ruhmkorff coils. Fig. 292 gives
an imperfect idea of the discharge
through a Geissler tuhe in a dark
room. The tuhe is supported by being stood upright in a glass vase.
At the two extremities are platinum wires, sealed into the glass and
connected with the wires leading from the Ruhmkorff coil. The
FIG. 292. GEISSLER TUBE.
ELECTRICITY. 313
glass vase and bulbs inside the tube are colored with oxide of
nium, which possesses in a remarkable degree the power of fluo-
rescence when illuminated by the electric spark. The vase at the
bottom is filled with a solution of sulphate of quinine, which ex-
hibits a similar property. The uranium fluorescence should be a light
green, the quinine a soft blue. The violet light in the rest of the
tube is due to nitrogen or air.
Exercises. 1. Suppose the thread on a common wood-screw to
represent a helix and the middle an iron core. With the current
running from the point towards the head, which pole of the result-
ing magnet would the point of the screw represent ?
2. How many ohms of resistance in a telegraph-sounder containing
888 feet of copper wire fa of an inch thick? Ans. 12.
3. It is desired to divide an electric current passing between two
points into two equal parts which shall pass over two iron wires, a and
b. The wire a is 100 feet long and fa of an inch in diameter. The
wire b is 2500 feet long : what must be its diameter ? Ans % inch.
4. When telephone-wires are carried on the same poles with tele-
graph-wires, and parallel with them, the clicks of the telegraph-appa-
ratus are distinctly audible in the telephones : explain this.
5. A small island on the coast of France contains the terminal
stations of two ocean telegraph cables. The stations are not connected
by wire, but frequently the messages being received or sent by one
station may be read at the other : explain this.
V.-EADIANT MATTER.
516. Striae in Vacuum-Tubes. In the figure of the Geiss-
ler tube it will be noticed that the globular section of violet
light near the lowermost (negative) platinum, and also the
light in the narrow part of the tube encircled by the vase,
exhibit distinct stratifications, or striae, across the direction
of the current. These striae, or alternate light and dark
bands, seem to be occasioned by the motion of the mole-
cules and their impact against one another as they transmit
the electric discharge from one to another throughout the
length of the tube. If this view is correct, the bright
bands are to be considered as caused by the incandescence
of the molecules, due to their impact against one another,
and the dark bands as sections in which the residual mole-
cules are moving, in the main, parallel to one another, with-
out impact. In other words, a number of molecules occu-
o 27
314 NATURAL PHILOSOPHY.
pying a section across the tube (more definite if the tube
be of small diameter) carry the discharge a certain part
of the length of the tube and there make exchange with
the next set, and return to their former position, repeating
the operation with very great rapidity, acting as electrified
bodies. The fact that the stratifications exist, though very
fine, in comparatively dense gases, and increase in width
as the exhaustion of the tube becomes more complete,
seems to favor this view.
517. Discoveries of Dr, Crookes. In 1879, William
Crookes, F.R.S., delivered a lecture before the British As-
sociation, in which he announced a new set of phenomena,
obtained in tubes exhausted far beyond the point at which
the striae and luminous effects are best shown. With this
degree of exhaustion, stratification and all other evidence
of the molecules striking against one another cease, and
the remaining molecules are simply repelled with great
violence from the end of the tube which is connected with
the negative pole, and move in straight lines until stopped
by the glass of the containing vessel or some other solid
placed in their path. Now, as the defined characteristic of
gases is an interaction among the molecules by which they
are constantly repelling one another, and as in these ex-
hausted spaces the remaining molecules seem to move in-
dependently of one another, and thus violate the funda-
mental law of the gaseous condition of matter, Professor
Crookes has proposed for the highly-rarefied residue ob-
tained in his tubes the name radiant matter. In gen-
eral, the exhaustion of the radiant-matter tubes may be
said to be y.-Q--^, jpr -$ of an atmosphere, or till they con-
tain but that fraction of the air or other gas which they
originally contained. Brilliant Geissler-tube phenomena
are shown with tubes containing nearly 3000 times as
much gas, or about 3^ of an atmosphere.
518. Radiant Matter repelled from a Negative Electrode.
The properties of radiant matter are best studied by means of the
ELECTRICITY. 315
discharge of an induction-coil. The molecules are repelled from the
negative pole, indicating that in their natural condition they are in a
negatively electrified state. 1 When the negative pole is made in the
shape of a plate with considerable surface, they are repelled from the
surface at right angles to it, otherwise they take the general direction
indicated by the entrance of the negative wire.
519. Phosphorescence produced by Radiant Matter. The
particles of radiant matter produce a bright phosphorescence where
they strike. Fig. 293 shows the form of a tube with which this is
FIQ. 293. SHELL TUBE.
beautifully illustrated. Before being exhausted, the tube has had a
collection of rubies, shells, etc., placed in it. On passing the dis-
charge by means of the wires shown, the mineral collection exhibits
in the dark a rich glow of mixed colors and no inconsiderable amount
of light.
520. Radiant and Gaseous Matter compared. In Fig. 294
are two bulbs which show in a striking manner the difference be-
tween radiant and gaseous matter. The bulb B contains radiant
matter. The bulb A is an ordinary vacuum-tube containing about
3000 times as many molecules of the original air as B does. In
other respects they are entirely similar. Each has a concave alumi-
num plate, a and a', fastened to the sealed-in platinum wire for the
negative electrode. Each has three other sealed-in platinum wires,
b, c, d, either of which may be made the positive electrode. The
negative pole of the Ruhmkorff being connected with a in the tube
1 It might be remarked that the only substances which can be re-
duced to the condition of radiant matter are those elements which have
long been known as the non-metallic or electro-negative elements.
316
NATURAL PHILOSOPHY.
A, the line of light indicating the path of the current extends in a
tolerably direct course to that platinum wire which, for the time
being, is made the positive pole, whether that be at the opposite side,
FIG. 294. GEISSLER TUBE AND RADIANT MATTER TUBE.
the top, or the bottom of the bulb. When, however, the plate- a f in
the bulb B is made the negative pole, the particles are driven across
the tube, as indicated in the figure, whether the positive pole be at 6,
c, or d, or whether it be detached entirely. The point between c and
6, where the molecules strike the glass, is indicated by a bright phos-
phorescent patch. With a strong coil this spot soon becomes white-
hot, and the glass actually melts. No such result is obtainable with
ordinary vacuum-tubes.
521. The "Shadow Tube." The glass of which most of these
tubes is composed is soft German glass, which yields a bright apple-
ELECTRICITY.
317
green phosphorescence on being bombarded by the particles of radi-
ant matter. Fig. 295 represents a device for showing that the phos-
FIG. 295. THE SHADOW TUBE.
phorescence is due to this impact of the molecules. The negative
pole a is a flat disk, which throws the molecules towards the larger end
of the tube. A piece of metallic aluminum, 6, in the form of a cross,
is so placed that it intercepts some of the molecules, and the part of
the glass thus protected gives no phosphorescence, and remains dark,
resembling a shadow.
522. The "Railway Tube." This impact of particles flying
from the negative pole is capable of setting light machinery in mo-
tion. Fig. 296 represents a light wheel with broad mica paddles, set
FIQ. 296. THE RAILWAY TUBE.
on a smooth railway in a highly-exhausted tube. When the disks at
the ends are made the poles of an induction-coil, the wheel rotates
rapidly, and travels from the negative towards the positive pole. By
reversing the current with the commutator of the Kuhmkorff, the
27*
318 NATURAL PHILOSOPHY.
wheel is driven alternately from end to end of the track as often as
desired.
523. Streams of Radiant Matter self-repellent, Fig. 297 rep-
resents a piece of apparatus for demonstrating that a stream of radi-
ant matter acts as a line of electrified bodies moving in the same
direction, and not as a carrier of an electric current. The disks a
and b, slightly inclined to the vertical, may either be made the nega-
tive pole. The positive pole is at c. The back of the tube contains
a screen of phosphorescent substance, which shows the entire path of
the particles which are driven through the slits d and e of a copper
plate. When b is made the negative pole, the stream extends from e
to/. When a is made the negative pole, the stream extends from d
to/. If a and b are both made negative poles at the same time, by
using two equal wires from the negative pole of the induction-coil,
two streams of radiant matter traverse the tube, but they do not
converge towarcte/, but move in parallel or divergent lines to g and
FJG. 297. Two STREAMS OF BADIANT MATTER.
h. This shows them to be repellent, and indicates that they are
moving charged bodies rather than conductors. Parallel conducting
wires attract each other.
524. Many other instructive and beautiful experiments
may be performed with these highly-exhausted vessels.
Enough are here given to indicate that the very rare state
of matter under examination exhibits properties very dif-
ferent from those of gaseous matter, and that time and
further experiments may fully confirm the conclusion that
matter exists in four states, as mentioned in Chapter I.,
viz., solid, liquid, gaseous, and radiant.
METEOROLOGY. 319
CHAPTER X.
METEOROLOGY.
525. Meteorology treats of the atmosphere and the phe-
nomena there noticeable. 1
526. Climate. Climate means the conditions of the at-
mosphere, particularly its states of heat and moisture that
exist at any place.
527. Causes of Climate. The causes which affect the
climate are principally (1) the distance from the equator,
(2) the height above the sea, (3) the distance from the sea,
and (4) the prevailing winds.
528. Latitude of Place. It is familiar to all that the
nearer a country is to the equator, as a rule, the hotter it
is. The reason 2 of this is that the sun shines directly down
on the torrid zone, while away from it it shines obliquely
and its rays are spread over a great area.
529. Height above the Sea. As we rise above the sea-
level, it usually becomes colder. Those who have gone up
in balloons speak of the intense cold in the upper regions
of the air. The cause of this is that in the rare air the
body gives off more heat than it receives. Near the sea-
level the dense and moist air serves as a blanket to keep in
the heat which the earth receives from the sun. When the
sun is shining directly on a mountain it may seem quite
1 The word is derived from Greek words signifying " the science
of things above the earth." It has no special reference to meteors or
shooting-stars.
2 For a fuller explanation, see Sharpless and Philips's Astronomy,
p. 92.
320 NATURAL PHILOSOPHY.
warm, for then heat is being taken in j but as soon as a
cloud passes over, or the sun sets, the radiation of heat
begins, and great cold results. An Alpine traveller has
said that the mercury in a black bulb thermometer indi-
cated 132 while in the shade it was only 22.
Why have a black bulb thermometer ?
There is a temporary exception to this rule under certain
conditions. On a cold, still morning the thermometer will
indicate a lower level in the valleys than on the surround-
ing hills. This is because the cold air, being heavier, sinks
to the lowest level.
530. Proximity to the Ocean, The temperature of a
country near the sea varies much less in a year than that
of one farther inland.
The cause of this is largely the same as that explained
in the preceding paragraph. When the sun's heat-rays
fall on land they do not penetrate to any great depth.
When the sun sets, or gets low down in winter, the slight
amount of heat stored up on the surface of the soil is
quickly lost by radiation, and cold weather sets in.
The heat-rays penetrate much more deeply into the
water. In clear water it is believed that they affect its
temperature to a depth of nearly 600 feet. Water has also
great capacity for retaining heat. Hence it stores up large
quantities during daytime and in the summer season, and
parts with it slowly at night and during the winter. It
therefore tends to preserve a more uniform temperature
throughout the year, and this affects the climate of the
lands bordering on it.
531. Character of Ground. A sandy or stony country, as
a desert, becomes quickly heated when exposed to direct
rays, and as quickly cools off after they are removed,
while a country covered with vegetation retains its heat
much longer. Evaporation from the surface of the leaves
also uses up some heat, so that a fertile and productive
METEOROLOGY. 321
country has a more equable temperature than a sterile
one.
532. Direction of Winds, The direction of the prevail-
ing winds also influences very considerably the character
of the climate. The causes which affect the direction of
the winds will be explained farther on. Since winds bring
the atmosphere of the places which they have traversed,
if the prevailing direction in the Northern hemisphere is
from the south, the weather will be warm, and if from the
north, cold, as compared with that of other countries of
the same latitude. If the wind blows in from the sea, the
air will be moist, and if from off the land, dry.
As the ocean is more uniform in temperature than the
land, winds from off it will be of nearly the same character
the year through, while a country, even if near the sea,
which is frequently subjected to winds from the interior
will vary greatly in climate in the different seasons.
533. Local Causes. There are other causes of climate
more local in their character. If a place has a south
frontage, so that it is exposed to the more direct rays of
the sun, and is shielded from the cold north winds, its aver-
age temperature will be higher, and vice versa.
Two Arctic localities often differ widely in temperature,
from the fact that ice freezes in one and floats away and
thaws in the other. Now, freezing always liberates heat
from the water, while thawing, requiring heat, abstracts it
from the air. The former locality will then be warmer
than the latter.
The exposure to the effects of ocean currents also pro-
duces a great effect on the climate. Water, as we have seen,
has great power to store up heat. If a current of warm
water flows against the shore, the heat is largely given out,
and the temperature of the land is raised. The Gulf Stream
leaves Florida with a temperature of about 80. When it
completes its circulation and again reaches the torrid zone,
its temperature is 40. These forty degrees of heat have
322 NATURAL PHILOSOPHY.
been given to the land, chiefly Western Europe, thus rais-
ing its temperature considerably above that of countries of
the same latitude in America.
534. Interference of Causes. It will thus be seen that a
great many causes go to produce the climate of any place.
It is often impossible to tell how many of them are in
operation. Sometimes they work against one another to
produce opposite results. All countries in the torrid zone
are not hot, and sometimes we find places at high elevation
which are not very cold. But by a careful consideration
of the circumstances it can usually be found out how to
account for any climate.
THE ATMOSPHEKE.
535. Weight of the Atmosphere. The barometer, as we
have seen, indicates the weight of the atmosphere. If it
be watched closely, it will be seen to vary slightly through
the day. By taking the mean of several readings we get
the average height for the day. By taking the mean of
these averages for different days we obtain the average for
the year. This yearly average differs at different places.
536. Variations. The average for one month is not the
same as that for others. It is usually higher in winter
than in summer, and the variation is more marked as we
approach the equator. The highest points for the day
are about 10 A.M. and 10 P.M., and the lowest six hours
from these. The daily fluctuation is also greatest at the
equator.
537. Irregular Changes. But, besides these periodical
changes, which are very small, there are irregular ones,
which are of much greater -consequence and magnitude.
It is by them that we are able in some degree to predict
the weather. As vapor of water is lighter than air, its ad-
mixture with the air causes the mass to become lighter and
to produce a fall of the barometer. A fall of the barometer,
METEOROLOGY. 323
then, usually indicates the increase of the amount of moist-
ure in the air, and, as such, is an indication of rain. The
words "fair," etc., printed on barometers, mean nothing,
because the height of the mercury varies with the locality
and other things, and the barometer pointing to " fair" in
one place would in another, during exactly the same
weather, point to " foul." A sudden descent is generally
an indication of an approaching storm, and a sudden rise,
of clear weather. But it must be borne in mind that the
barometer can indicate a storm only after the moisture is
actually in the atmosphere.
538. Uncertainty of Predictions founded on the Barom-
eter. There are so many other causes affecting the height
of the barometer besides the moisture in the atmosphere,
that meteorologists do not consider that it alone is a safe
guide for the prediction of storms. The direction of the
winds and the appearances of the clouds must also be taken
into account in connection with it, so that, while it is not
useless, its heights are not considered in themselves suffi-
cient grounds for predicting the weather. When properly
combined with other indications they certainly afford some
clue.
539. Isobaric Lines. If the heights of barometers in dif-
ferent parts of the country are observed at exactly the
same time, as is done in the signal stations of the United
States, and if all the stations which have the same baro-
metric readings are connected by lines, it will usually be
found that these are roughly parallel to one another, and
frequently are curves enclosing certain territory where the
barometer is highest or lowest. These lines are called
isobaric lines. They change in position rapidly from time
to time, and their changes are among the facts relied upon
by the head of the Signal Service Bureau to predict the
weather. These lines are shown in Fig. 298.
540. Causes of Changes of Temperature. The air be-
comes heated because (1) it absorbs some of the heat which
324
NATURAL PHILOSOPHY.
passes through it as it comes from the sun ; (2) because it
absorbs heat which the earth is radiating into space ; and
(3) because it comes in contact with bodies on the earth
FIG. 298. ISOBARIC LINES.
which are more or less heated. The second and third of
these causes are not subject to any very sudden variations,
but the first changes with all the positions of the sun with
respect to the observer.
A fourth cause of change of temperature, of less conse-
quence, is the freezing or evaporation of water. When the
air is in such a dry state as to cause much evaporation, the
change abstracts heat from the air, and cold is produced.
When it is already charged with moisture, evaporation
ceases. Every one has experienced how much hotter the
air feels when moist. This is due to the fact that it does
not evaporate the perspiration of the body and so cause
coolness. On the other hand, when freezing or condensa-
tion is going on, heat is, as it were, squeezed out of the
water, and goes into the atmosphere, raising its tempera-
ture. This, probably, explains why the Northern hemi-
sphere is, on the average, about three degrees warmer than
METEOROLOGY. 325
the Southern. The great amount of water in the Southern
hemisphere makes evaporation, which causes cold.
Clouds at a small height above the earth keep it from
losing its heat in space, so that cloudy weather is never the
coldest. In a similar way, a sheet or a newspaper put over
a plant will protect it in frosty weather by retaining its own
warmth and that of the earth.
Our clothing is as much for the purpose of keeping in
the heat of the body as of keeping out the cold of winter.
541. Effect of Clouds." The temperature varies much
less over cloudy than over clear districts ; it varies less in
low than in elevated regions ; it is warmer on one side of
an area of high or low pressure than on the other, and gen-
erally warmer in advance of any storm-centre and colder
in the rear." l
542. Hottest and Coldest Months. The hottest month in
the year is August, and the coldest is January. These do
not coincide with the times when the sun is at his position
of greatest and least power, which are about the 20th of
June and the 20th of December. But for some time after
the 20th of December the earth is still radiating heat more
rapidly than it is taking it in, and hence continues to grow
cooler ; and for some time after the 20th of June the earth
receives more heat than it radiates, and so continues to
grow hotter.
For the same reasons the highest daily temperature
occurs, on the average, at 2 P.M., and the lowest at 4 A.M.
543. Position of Thermometer. By the temperature of
the atmosphere we mean the temperature in the shade. A
thermometer to record this should, therefore, be protected
from the direct rays of the sun, and from radiation from
walls and other bodies liable to become heated.
544. Isothermal Lines. If all the places on the earth
having the same mean annual temperature be joined, these
1 Circular of the Signal Bureau, U.S.A.
28
326
NATURAL PHILOSOPHY.
METEOROLOGY. 327
lines are called isothermal lines. Roughly speaking, they
are parallel with the equator, and agree with parallels of
latitude. But local circumstances affect this considerably.
Fig. 299 shows the isothermal lines. The figures on them
give the mean temperature for the year of all the points
through which they pass. It will be observed how the
Gulf Stream deflects the lines to the north by raising the
temperature of the Atlantic Ocean, and how the warm air
from the Pacific raises the temperature of the Western
United States.
545. Moisture in the Atmosphere. The air is porous, and
particles of vapor of water occupy these pores. When
heated, the air expands, and the pores are enlarged, so that
more room exists for vapor. When the pores are full of
moisture, the air is said to be saturated. If the temperature
is raised, the same air is not saturated ; if it is lowered,
some of the moisture is squeezed out, and shows itself as
mist, dew. frost, rain, hail, snow, or clouds.
546. Relative Humidity. The capacity of the air to hold
water, then, depends on its temperature. The absolute
amount of moisture is not measured by meteorologists,
only the percentage of full saturation. This is called the
relative humidity. If the air is just half full of moisture, the
relative humidity is 50 ; if full, 100 ; if absolutely dry, ;
but if, while the amount of moisture remains the same, the
temperature is raised, the relative humidity is lowered.
547. Dew-Point. If a certain amount of moisture exists
in the atmosphere, the air can be cooled down to such a
temperature that it will be saturated. This temperature is
the dew-point. It is not uniform, but varies with the hu-
midity and temperature of the air. The air is usually not
fully saturated with moisture at the temperature which
exists. The dew-point in ordinary clear weather is about
10 below the actual temperature, and in exceptionally dry
times it is as much as 30 below in this climate. By this
we mean that ordinary air must be diminished in temper-
328
NATURAL PHILOSOPHY.
ature 10 before it will be saturated and dew or clouds
will begin to form.
548. Hygrometer. The relative humidity of the air is
determined by an instrument called the hygrometer.
Experiment 185. Buy two thermometers and place them side by
/i jSijjj, K side. Wrap the bulb of one in a can-
dle-wick, which passes down into a
vessel of water so close that the wick
around the bulb will always be wet.
The " wet-bulb thermometer" will show
a lower temperature than the u dry-bulb
thermometer," for evaporation from the
wick cools the bulb and the mercury in
the tube. The amount of this evapora-
tion will depend on the dryness of the
air. If it is saturated, there will be no
evaporation, and the two thermometers
will register the same. If the air is
very dry, much evaporation will result,
and there will be a great difference.
From the readings of the two thermom-
eters it is possible to calculate the ab-
solute amount of moisture in the air,
the relative humidity, and the dew-
point.
549. Variation of Moisture.
The amount of vapor in the at-
mosphere varies with the time of
day, being greatest during the
latter part of the afternoon, and
least during the latter part of the
night. This is due to the evap-
oration which goes on while the
sun is shining, which adds to the
moisture in the air through the
day, and to the condensation of moisture which results from
the lowering of temperature during the night. For similar
reasons the amount is greater in summer than in winter.
It is also greater near the earth than in the higher regions
of the air, though no air has been found entirely free
from moisture. Up to a height of from 2000 to 3000 feet
there is, however, little, if any, decrease in the humidity.
FIG. 300. HYGROMETER.
METEOROLOGY. 329
" There is an increase of moisture near bodies of warm
water, fields of snow, extensive forests and meadows, etc.,
as compared with dry plains and rocky mountains. The
humidity will be found large in advance of storm-centres,
and small in their rear. It will be greater over warm
cloudy districts than where cold and clear weather prevails.
Certain winds will be found to be moister than others. The
west and northwest are generally the driest in the Missis-
sippi Valley. Dryness will be found attending clearing-
up weather. Dampness or a large increase of relative
humidity accompanies threatening weather as an almost
invariable premonition." 1
550. Indian Summer. The haziness which is noticed in
the atmosphere at certain times, more particularly during
" Indian summer," is largely the result of particles of dust
or charcoal which come from forest fires, and which possess
the property of attracting moisture and thus producing
dry weather. A heavy rain will wash this out and leave
the air clear.
551. Dew. The foliage of plants, the grass, and all
things exposed to the air at night quickly lose their heat.
They cool the air in immediate contact with them below
the dew-point, and, it being no longer able to hold the
vapor, this is deposited on the cold bodies. This is dew.
A pitcher of ice-water will collect dew on its surface from
a similar cause.
A clear night favors the deposition of dew, for when
clouds are above the earth they retain the heat, so that the
grass is not cooled below the dew-point. A comparatively
still night favors it, because in a strong breeze no portion
of the atmosphere is long enough in contact with the
bodies to be sufficiently cooled. Great relative humidity
favors it, for then the dew-point is not much below the
ordinary temperature, and but little cooling suffices.
1 Circular of Signal Bureau, U.S.A.
28*
330 NATURAL PHILOSOPHY.
552. Frost. Frost is frozen vapor or frozen dew. The
vapor freezes in the air, and then settles to the ground in
the form of little crystals. Hence it is necessary for the
temperature to be as low as 32 at the place of freezing in
order for frost to be formed. It is often cold enough to
make frost in the valleys when the thermometer a little
higher up indicates a higher temperature.
553. Fog 1 . When a large mass of air is cooled below the
dew-point, all the vapor which it cannot contain becomes
visible. When this is near the earth it is called a fog or
mist. This cooling may be the result of a cold wind blow-
ing in from the north on air nearly saturated, or of the
presence of a bog or lake, which keeps the air cool at a
certain spot. In the latter case the fog is permanent, while
its particles may be rapidly changing. As soon as a mass
of air blows into this position it is cooled down so as to
make its vapor visible, and when it goes out at the other
side the temperature is raised so that it hides it again.
A fog usually hangs over the banks of Newfoundland,
because there the cold and warm currents meet, and the
warm air is cooled below the dew-point. It is also seen
over rivers, on account of their cooling effect on the air.
554. Fog, Particles of Liquid. Particles of vapor are
transparent, and when they lie between the particles of air
they do not obstruct the view. When, however, they are
not thus placed, they collect in little drops, which float in
the air and obstruct the view, because the light-rays are
lost by their numerous reflections from one to the other.
In the same way glass is transparent, but a vessel filled
with broken glass is opaque. In the condensation which
occurs when fog is formed, the vapor changes from a gase-
ous body to a liquid body. The change may be seen at the
spout of a tea-kettle. Close to the orifice nothing is seen,
for the steam is a transparent gas. When it goes out a
little space it is cooled below the dew-point, and liquid
vapor of water becomes visible.
METEOROLOGY. 331
555. Cloud. When this condensation goes on in the
upper regions of the atmosphere, a cloud is formed. A cloud
is simply a fog or mist at some elevation above the earth.
When we ascend a mountain we often enter a cloud, and no
distinction from a mist is noticed. Clouds are apt to hang
around mountain-tops, for the cold peaks lower the temper-
ature of the air, and as fast as it rises to pass over them it
is cooled below the dew-point. When it descends the op-
posite side it becomes warm again, and the cloud disappears
from view. While the cloud apparently remains fixed in
position, its particles are constantly changing.
556. Causes of Clouds. A cloud may also be formed by
a cold wind blowing on warmer air, or by warmer air
blowing into a colder region, or by an ascending current
of air expanding and so causing cold (Art. 367). The
latter cause is probably the most common. The vapor
formed by the action of the sun upon the waters of the
earth tends by its own expansive force to rise above the
earth ; as it rises it reaches rarer strata of air, and so ex-
pands more rapidly. This expansion causes cold, and, be-
sides this, the air itself is colder as we rise higher. The
vapor is then changed from invisible vapor to the little
particles of water which constitute cloud.
" 557. Forms of Clouds. As the cloud-particles are heavier
than the air, they gradually sink. They would fall to the
ground did they not come into warmer air, by which they
are again converted into invisible vapor. As soon as they
get down to a stratum which raises their temperature
above the dew-point, they disappear from view. This ex-
plains why certain clouds have flat bases while their tops
are heaped up in masses like mountains. This form of
cloud has often great thickness. The bottom may not
be over a half-mile from the earth, but the top sometimes
reaches the height of four miles. In general, the thickness
of clouds is not more than a half-mile, and they vary from
a half-mile to five miles above the surface of the earth.
332 NATURAL PHILOSOPHY.
There is frequently just as much vapor below the cloud
as in them, but the warmer temperature prevents it from
being seen.
Questions. When you build a fire in a damp room, do you de-
crease the amount of moisture in the room? Why is the room
drier ? Is it the visible or the invisible vapor that gives the idea of
dampness ?
558. Classes of Clouds. Clouds are usually divided into
four main classes, cirrus, cumulus, stratus, and nimbus.
559. Cirrus. The cirrus clouds are the light, feathery
masses which float in the air, scarcely screening the sun.
They are believed to be composed of small particles of ice
or snow floating at a great height. They sometimes be-
token the coming of a storm, though usually nothing ever
falls from them.
560. Cumulus. The cumulus or " heap" clouds are clouds
which are common in summer-time in fair weather. They
are the clouds with flat bases and hemispherical tops, men-
tioned in Paragraph 557. They are the tops of columns of
vapor reaching down to the earth which become visible at
a height where the temperature falls below the dew-point.
The shapes of these clouds are best seen through a piece
of blue glass, which diminishes some of the glare of their
light.
561. Stratus. The stratus clouds are those which are
seen in lines stretched along parallel to the horizon. When
overhead, they cover the sky with a cloud of uniform dark-
ness. They are near the earth, and of no great thickness.
562. Nimbus. The nimbus are heavy black clouds, from
which rain falls.
563. Mixed Classes. There are often observed clouds
which partake of the character of two or more kinds ;
these are named cirro-stratus, cumulo-stratus, etc.
564. Disappearance of Clouds. Clouds form and disap-
pear in the sky while we are looking at them. The clear-
ing up after a storm is not so much the result of the clouds
METEOROLOGY. 333
blowing away as of their disappearance by being changed
to invisible vapor by a drier atmosphere.
565. Clouds around a Storm. " Two or more layers of
clouds almost invariably coexist wherever extended rain-
storms prevail, the upper layer stretching far in advance
of the lower, but stretching down to it where rain is falling
most abundantly. In the rear of this area cumulus clouds
are abundant. Cumulus and cirrus clouds are not incon-
sistent with the idea of clear or fair weather. Cirro-stratus
almost invariably precede an extensive rain-storm, whether
in winter or summer. The stratus will generally be found
in connection with threatening weather." l
566. Rain. When the air is suddenly cooled below the
dew-point, the little particles collect in drops, and rain
is formed. This sudden cooling is most readily effected by
an upward current, which carries air nearly saturated to a
cooler level. There is a difference of about 35 between
the air at the surface and the air two miles above the sur-
face of the earth. When the air laden with moisture from
the ocean is carried landward and over a mountain-top, we
usually have copious rains. Another cause is the mixing
of two clouds or two masses of air of different tempera-
tures. If you mix a cubic foot of saturated air at 90 and
another at 30 they will have a mean temperature of 60 ;
but air at this temperature will not hold all the moisture .
of both masses, and some must fall as rain.
567. Amount of Rainfall. More rain falls at the equator
than elsewhere, and the decrease is quite uniform to the
poles. About 100 inches of rain fall at the equator an-
nually. By this we mean that if all of it could be collected
it would cover the surface to a depth of 100 inches. In our
latitude the average rainfall is between 30 and 40 inches.
568. Snow. When the vapor of the air is frozen, snow
is formed. Freezing is a form of crystallization, and the
1 Circular of Signal Bureau, U.S.A.
334
NATURAL PHILOSOPHY.
forms of the crystals of snow are very beautiful. To ob-
serve them well, let them fall on cold pieces of colored
glass and examine them with a microscope of low power.
Do not breathe on them.
FIG. 301. FORMS OF SNOW-CRYSTALS.
Prof. Tyndall speaks of the snow-crystals which he saw
on Monte Rosa as " a shower of frozen flowers ; all of them
were six-leaved ; some of the leaves threw out lateral ribs
like ferns ; some were rounded, others arrowy and serrated ;
but there was no deviation from the six-leaved type."
. 569. Hail. Hail is frozen water. It is produced during
thunder-storms by the approach of a
cold current, which forces upward the
warm, saturated air of the lower re-
gions. Snow is first formed, and the
whirling action of the air collects this
into little balls, which, as they move
through the snow and vapor, become
alternately coated with snow and cov-
ered with ice, gradually but rapidly
growing till they reach sometimes the size of turkey-
eggs. When examined, the centre is seen to consist of
FIG. 302. SECTION OF
HAIL-STONE.
METEOROLOGY.
335
snow, and often alternate layers of snow and ice may be
noticed.
570. Wind, Wind is air in motion. Air having mass,
when it strikes any object it presses against it, the pressure
being harder the faster it moves. A wind moving at the
rate of 4 miles an hour is a pleasant breeze, and presses
against every square foot of surface which it strikes verti-
cally with a force of about an ounce. A brisk wind of 25
miles per hour has a force of about 3 pounds per square
foot; a very high wind of 45 miles per hour, of 10 pounds
per square foot ; a hurricane of 80 miles per hour, of 31
pounds "per square foot.
The mean velocity of the wind in the Eastern United
States is about 10 or 12 miles per hour, being more in
winter than in summer, and is greatest at 2 P.M., and least
at night. The daily curve is seen in Fig. 303.
10 noon.2h. * 6 a 1O xat
FIG. 303. DAILY CURVE OF WIND.
571. Cause of Winds. The air at the equator is heated
by the direct rays of the sun, and is pushed up by the
heavier cold winds from the polar regions settling down to
take its place. The heated air moves as an upper current
towards the poles, while the cold air moves as a surface-
current towards the equator. This interchange would go
on regularly and continually were it not for the rotation
of the earth on its axis. A particle at the equator moves
with greater velocity than one near the poles, because it
has so much farther to go in the same time. The air par-
takes of the motion of the earth below it, and when the
slowly-moving air from the higher latitudes sweeps down
towards the equator it is left behind and falls back towards
336
NATURAL PHILOSOPHY.
the west. This produces the trade-winds of the torrid
zone. When the upper currents from the equator reach
the temperate zones they become sufficiently cooled to fall
again to the surface, and, having the rapid equatorial
motion, they sweep ahead of the earth and form the pre-
vailing westerly winds of our latitude.
The extreme cold of the polar regions produces surface-
currents away from the poles and upper currents towards
them.
FIG. 304. WINDS OVER THE GLOBE.
The surface-winds are shown in Fig. 304, and Fig. 305
gives the whole circulation without the effects of the earth's
rotation.
572. Variable Winds. These are the general systems of
winds. But, as every one knows, the changes in direction
and intensity of the wind are almost continuous. There
are numerous local circumstances which determine par-
ticular winds. Wherever there is low pressure, as indi-
cated by the barometer, there are surface-currents sweep-
ing in from all around, for the equilibrium of the atmosphere
is destroyed and a flow sets in to restore it. If any place
METEOROLOGY.
337
becomes greatly heated, the air will tend to flow into it
in all directions, producing surface-currents towards, and
upper currents away from, the
heated place. When the heated
air rises, it becomes cooled,
spreads out, and falls down,
and is returned again to the
place whence it came.
The reverse would take place
around a cold centre.
573. Land and Sea Breezes.
During the day the land heats
up more than the water, so that
along the sea-coast there are
usually breezes blowing in from
the sea during the day. At
night it loses its heat more
quickly and becomes cooler
than the sea, so that the breeze
sets in in the opposite direc-
tion.
574. Monsoons. The same cause produces the monsoons
of the Indian Ocean. The regions of India become heated
in their summer, and the wind sets in strongly from the
Indian Ocean. In the winter the reverse is the case.
575. Moisture a Cause of Winds, Another local cause
of winds is the moisture in the atmosphere. As vapor of
water is lighter than air, the sudden formation of cloud
will tend to produce a low barometer. Winds will set in
towards this centre to restore the equilibrium.
576. Difficulty in ascertaining the Cause of Winds,
Among all these causes it is often impossible to say which
one is producing the wind at a given time and place. Its
fickleness has become proverbial, and many causes doubt-
less operate together in producing the modifications. The
changes are not the result of chance, but every particle of
FIG. 305. CIRCULATION IN THE AIR.
338 NATURAL PHILOSOPHY.
air moves in obedience to the impulses which act upon it.
Winds are great agents for purifying the earth and making
it healthy, and a multitude of ways in which they are
useful to man will suggest themselves to any one.
577. Storm. A storm is a great commotion in the atmos-
phere. Eain, hail, or snow generally accompanies it.
578. Effect of Heat. In case of the heating of a large
tract, the cold air flows in from all around. The hot air
rises and spreads out. This mingling of the currents often
produces clouds and rain, as has been explained. This
is a storm. The. whole system of currents and clouds is
then carried by the prevailing winds over the country. A
barometer near the centre would show low pressure.
579. Effect of Rotation of the Earth. Were there no ro-
tation of the earth, the surface-air would always blow di-
rectly towards the storm-centre, and the upper air away.
In the Northern hemisphere the winds coming in from the
south are, by their more rapid motion with the earth around
its axis, carried towards the east, and those coming in from
the north are in like manner deflected towards the west.
This makes them approach the centre not directly, but in
a spiral curve, and creates a "cyclone." Nearly all our
storms are more or less cyclonic in their character. The
reverse kind of cyclone exists in the Southern hemisphere.
580. Movement of Storms. The prevailing winds in the
torrid zone being easterly, the storm is carried towards the
west. As it recedes from the equator it reaches the region
of westerly winds, by which it is borne eastward. Most
of our large storms come from the west or the southwest.
This may not be the direction of the wind at the time.
The wind at any time is usually directed obliquely towards
the storm-centre, and this is frequently modified by local
causes, so that there are all possible directions inside the
storm-area. In the Atlantic States the winds commonly
blow from some easterly quarter during a storm.
581. Storm-Centre. In the centre of a storm there is a
METEOROLOGY.
339
calm, and sometimes clear weather. After the centre has
passed, the wind shifts to the west, it often rains hard for a
short time, and then clears away. When the wind shifts
FIG. 306. MOTION OF STORM-CENTRE AND OF AIR AROUND IT.
to the west after several days of east wind, clear weather
soon follows.
582. Direction of Wind around a Storm-Centre. To re-
member the direction of the surface-winds around a storm-
centre, the student may notice that in the Northern hemi-
sphere, to a person situated above, the motion is opposite
to that of the hands of a watch.
583. Direction of Storms, The direction of storms
through the United States is towards the east, varying
sometimes to the northeast or the southeast, and their aver-
age hourly rate of motion is 21 miles in summer and 30 in
winter. They sometimes move faster than this, and some-
times remain almost stationary.
584. Thunder-Storms, The storms of wind and rain of
summer, often accompanied by thunder and lightning, do
not move across the continent, but are local in their origin.
340
NATURAL PHILOSOPHY.
The heat of the sun fills the lower regions with vapor over
some point, and causes it to ascend till its cooling produces
cumulus clouds level at base, heaped up on top. This goes
on till condensation into drops ensues and rain falls. The
winds sweep the clouds along, and there is a certain
amount of cyclonic tendency, but the storm does not ex-
tend far, and is soon exhausted. The electric phenomena
accompanying such storms have been explained in the
chapter on electricity.
585. Cyclones. Frequently cyclones or hurricanes are
formed in the Atlantic Ocean, near the equator, and are
swept along westward, as shown in Fig. 307, then turn
FIG. 307. COURSE OF CYCLONES IN THE ATLANTIC OCEAN.
opposite the South Atlantic States, and are usually lost in
the North Atlantic, though they sometimes doubtless reach
Europe. In this case, as the storm-centre sweeps up the
course of the Gulf Stream, we have east and southeast
winds along our eastern coast, accompanied by heavy rain.
METEOROLOGY. 341
The eastern storms which begin at the South are usually
of this class. Occasionally the storm does not turn till it
reaches the Gulf of Mexico, when it moves centrally across
the United States.
In the equatorial regions the cyclones are more violent,
the rain is more extensive, and the wind is stronger than in
the temperate zones. The energy is somewhat diminished
by the distance travelled.
586. Prediction of Storms Signal Bureau. The laws
governing the motions of storms are now so well estab-
lished that it is possible to predict with tolerable certainty
for one or two days in advance what the weather will be.
This is the work of the Signal Service Bureau of the War
Department of the United States Government. There are
scattered over the country about one hundred stations, at
each of which, three times every day, at the same instant
of actual time, observations are taken by the officer in
charge. These are telegraphed immediately to the chief
signal officer at Washington, who in turn telegraphs many
of them to some of the more important stations, from which
bulletins of the prominent features are issued. These bul-
letins tell
Height of the barometer ;
Change since last report ;
Thermometer ;
Change in the last twenty-four hours ;
Relative humidity ;
Direction of the wind ;
Velocity of the wind ;
Force of the wind ;
Amount of cloud;
Rainfall since last report ;
State of the weather.
These bulletins are open to examination at the signal-
offices and other public places in the cities and towns to
which they are transmitted.
29*
342 NATURAL PHILOSOPHY.
Besides the bulletins, a statement of synopses and indi-
cations is prepared at the office of the chief signal officer,
and thence issued thrice daily. The press agents telegraph
it over the country. This statement is given out at 1 A.M.,
10 A.M., and 7 P.M. daily, Washington time.
587. Correctness of the Indications. The indications
nearly always prove correct. The signal officer receives
reports of storms, or cold waves, or clearing weather, from
the West, and their rate of travel, from which he has to
predict where they will be at a given time. It is not always
a simple matter. He has to take into account a variety of
possible modifying circumstances, and great study and ex-
perience are needed to make it right in nine cases out of
ten, which is about the record of our bureau. JSTo other
nation has so complete or well-arranged a system as ours,
and it is well worth all it costs. Many vessels are pro-
tected from wreck by heeding the signals of a coming
storm which are displayed along the coast, and the dwellers
along the Western rivers are often saved from floods by
timely notice of their approach.
588. Weather Chart. The chief signal officer also issues,
thrice daily, a graphic weather chart, which shows at a
glance the weather all over the country at that hour.
Any one, with proper care and knowledge, can forecast
the weather for himself by a study of these charts.
APPENDIX I.
THE METEIC SYSTEM.
THE metric system of weights and measures was devised in France
about the beginning of the present centu^. It is now in general
use in most of the countries of the civilized world, and in the others
is largely used in scientific work.
The unit of length in this system is the metre, which is equivalent
to 39.37 inches. This was taken because it is one ten-millionth of
the distance from the earth's equator to the pole. 1 On account of its
great convenience, the system was made decimal throughout. The
prefixes to denote the fractions of a unit are the Latin numerals, and
are the same for all the tables, while the Greek numerals indicate
the multiples of the unit in all the tables.
TABLE OF MEASUKES OF LENGTH.
SYMBOL.
METRIC VALUE.
U. S. VALUE.
1 millimetre,
mm.
.001 m.
.03937 in.
10 millimetres
= 1 centimetre,
cm.
.01 m.
.3937 in.
10 centimetres
= 1 decimetre,
dm.
.1 m.
3.937 in.
10 decimetres
= 1 metre,
m.
1 m.
39.37 in.
10 metres
= 1 dekametre,
Dm.
10m.
32.81 ft.
10 dekametres
= 1 hectometre,
Hm.
100m.
19.92 rd.
10 hectometres
= 1 kilometre,
Km.
1,000 m.
.6214 mi.
10 kilometres
= 1 myriametre,
Mm.
10,000 m.
6.214 mi.
The unit of capacity is the litre (lee'ter) ; it is the quantity which
a cubical box, 1 decimetre each way inside, will hold. It is equiva-
lent to 1.0567 quarts liquid measure, or .908 quart dry measure, so
that it is between our dry and liquid quarts, and does not differ
* The more accurate measurements of recent years have shown that the standard
metre which the French adopted, and which is still used everywhere, is a trifle (53^3)
shorter than an exact ten-millionth of this distance.
343
344 APPENDIX.
greatly from either. The same measures are used for both liquid and
dry measure. The table of measures of capacity is exactly the same
as the one for length given above, except that metre is changed to
litre. Its symbol is I.
The unit of weight is the gram ; it is the weight of pure water at
39 F. which a cubical box, 1 centimetre each way inside, will hold.
It is equivalent to 15.432 grains ; a five-cent piece weighs 5 grams
and is 2 centimetres in diameter. The table is made in the same way
as before, by changing metre to gram, in the table given above.
Its symbol is g.
In measuring surfaces the square metre, square dekametre, etc.,
are used. The are (air), which is a square dekametre, is also used,
and a table is made by using it with the common prefixes.
Cubic decimetres, cubic metres, etc., are also used in measuring
solids, as well as the stere (stair), which is a cubic metre. Its table
is made in the same way as the others.
APPENDIX II.
A TABLE OF SPECIFIC GEAYITIES.
LIQUIDS.
Pure water, at 39 F 1.000
Sea-water 1.026
Alcohol 791 to .916
Ether 716
Sulphuric Acid 1.841
Milk 1.032
Mercury, at 32 F 13.596
SOLIDS.
Iridium 23
Platinum .. 21 to 22
Gold 19 to 19.6
Lead 11.4
Silver 10.5
Copper 8.6 to 8.9
Brass 7.8 to 8.5
Iron, cast 7 to 7.3
" wrought 7.6 to 7.8
Steel 7.8
Glass ,. 2.5 to 3
Quartz .....' 2.65
Brick 2 to 2.17
Chalk 1.8 to 2.8
Coal, bituminous 1.02 to 1.35
" anthracite 1.36 to 1.85
Limestone 2.4 to 3.
Ice 93
Wood, lignum-vitae 1.34
" hickory 83 to 1.
" oak 85
" pine 42 to .55
" cork 24
GASES.
Air 1. [Hydrogen.
Oxygen 1.11 |
.07
346
INDEX.
[THE NUMBERS REFER TO PAGES.]
Aberration, spherical, 187.
Adhesion, definition of, 14.
Affinity, definition of, 13.
Air-Brake, 111.
Air-Condenser, 110.
experiments with, 111.
Air-Pump, 104.
experiments with, 107.
Alarm-Bell, 303.
Aneroid Barometer, 99.
Artesian Wells, 73.
Atmosphere, 100, 322.
composition of, 100.
height of, 100.
weight of, 100, 322.
buoyancy of, 102.
moisture in, 328.
Atoms, 8.
Attraction, electrical, 261.
definition of, 13.
Balance a lever of the first kind, 49.
Balloons, 102.
Barker's Mill, 92.
Barometer, 97.
and the weather, 98, 323.
Battery, 281.
Beats in sound, 155.
Bellows, 103.
Boiling Point and pressure, 228.
Cabinet-Organ, 141.
Cables, 298.
Camera, 209.
Capillary Attraction, 14, 80.
repulsion, 81.
Centre of gravity, 36.
Centrifugal Force, 28.
Character of sound, 147.
Clarionet, 142.
Clepsydra, 84.
Climate, causes of, 319.
Clocks, use of pendulum in, 46.
Clouds, 331.
classes of, 332.
Cohesion, definition of, 13.
Colors, primary, 199.
complementary, 199.
Compass, 253.
Complementary Colors, 199.
Composition of forces, 26.
Conduction of heat, 234.
Conductors of electricity, 259.
Conservation of energy, 33, 216.
Convection of heat, 236.
Cornet, 142.
Correlation of forces, 34.
Cryophorus, 225.
Cupping, 101.
Cyclones, 340.
D.
Declination of the compass, 253.
Dew, cause, 329.
Dew-Point, 327.
Diamond the hardest of substances, 12.
Dip of the compass, 253.
Discord in sound, 156.
Dispersion of light, 188.
Distillation, 229.
Dynamo-Electric machines, 306.
Dynamometer, 22.
Dyne, the unit of force, 22.
347
348
INDEX.
E.
Ear, 158.
Ear-Trumpets, 125.
Echoes, 126.
Elasticity, cause of, 11.
of liquids, 64.
Electrical Machines, 263.
Electric Light, 283, 308.
Electricity, chapter on, 256.
two kinds of, 257.
frictional, 255.
current or voltaic, 277.
Electrolysis, 285.
Electro-Magnetism, 289.
Electrophorus, 267.
Electro-Plating, 285.
Elements, number known, 9.
Energy, definition of, 32, 34.
potential energy, 32.
actual energy, 32.
conservation of energy, 33.
Erg, a unit of work, 31.
Ether pervades all matter and space, 16.
probably a form of radiant matter, 17.
Evaporation, 220, 225, 227.
Expansion by heat, 10, 221.
by cold, 10, 226.
Eye, 209.
F.
Falling Bodies, laws of, 40, 41.
Fife, 142.
Fire-Engine, 114.
Floating Bodies, 75, 76.
Flute, 142.
Fog, 330.
Foot-Pound, 31.
Force, kinds of, 19, 20.
represented by lines, 23.
composition and resolution of, 26
correlation of, 34.
Fountains, 72.
Freezing, 227.
expansion by, 226.
Friction, laws of, 57, 58.
friction essential, 58.
Frost, 330.
6.
Galvanometer, 290.
Gases, definition of. 14.
chapter upon, 95.
Gases, compressibility of, 95.
Geissler Tubes, 312.
Governor, 240.
Gravity, 15.
laws of, 35.
centre of gravity, 36.
H,
Hail, 334.
Halo, 195.
Hardness, test of, 12.
Harmonics, 248.
Harmony in sound, 156.
Hearing, limits of, 132.
Heat, chapter on, 213.
cause of, 213.
sources of, 213.
transmission of, 230.
mechanical equivalent of, 215.
conduction of, 234.
Helix, 29.
High- Pressure Engine, 238.
Horse-Power, 31.
Hydraulic Ram, 90.
Hydraulics, 83.
Hydrometers, and how to make them, 79.
Hydrostatics, 63.
Hydrostatic Bellows, 70.
Hydrostatic Press, 65.
Hygrometer, 328.
Images, 173.
Inclined Plane, 55.
Indestructibility of matter, 9.
Indian Summer, 329.
Induced Currents, 299.
Induction, 246, 260.
Inertia, 15.
examples and experiments, 16.
Insulators, electrical, 259, 262.
Interference of waves, water, 87.
of sound, 139.
of light, 200.
Intermittent Springs, 117.
Isothermal Lines, 325.
K,
Kaleidoscope, 172.
Key-Note, 153.
Knee-Joint, 27.
INDEX.
349
Lens, convex, 182.
concave, 183.
Lever, three kinds of, 47.
law of, 48.
Leyden Jar, 269.
Light, chapter on, 162.
velocity of, 167.
reflection of, 169.
refraction of, 177, 180.
dispersion of, 188.
polarization of, 202.
Lightning, 272, 275.
Lightning-Rods, 276.
Liquids, definition of, 14.
chapter upon, 63.
flow of, through pipes, 85.
rise to a level, 72.
incompressibility of, 63.
pressure of, on bottom, 67.
pressure of, on sides, 69.
pressure upward, 70.
Locomotive, 240.
Machines, 47.
create no power, 59.
Magnet, 244.
poles of, 245.
Magnetic Storms, 293.
Magnetism, chapter on, 244.
Magneto-Electricity, 304.
Manometric Flames, 147. .
Mariotte's Law, 95.
Mass, 12.
units of, 13.
Matter, definition of, 7.
properties of, 9-15.
Mechanical Powers, 47.
Melodeon, 141.
Meteorology, 319.
Metric System, 13, 343.
Microscope, 205.
Mirage, 187.
Mirrors, 170.
concave, 172.
convex, 175.
Mobility, 15.
Molecules, 7.
size of, 8.
motions of, 14.
Momentum, 21, 34.
Monsoons, 337.
Motion, kinds of, 19.
Newton's three laws of, 20.
Mouth-Organ, 141.
Music, 150.
Musical Sound, 129.
Needle, magnetic, 252.
Nodes, 144.
Noise, definition of, 129.
0.
Opera-Glasses, 207.
Overtones, 146.
P.
Parallelogram of forces, 24.
Pascal's Vases, 68.
Pendulum, laws of, 44, 45.
for clocks, 46.
Perpetual Motion, 59.
Phonograph, 128.
Photometry, 166.
Piano, 139.
not a perfect instrument, 155.
range of, 133.
Pipe-Organ, 141.
Polarization of light, 202.
Polygon of forces, 25.
Pores found in all matter, 9, 10.
Primary Colors, 198.
Projectile, path of, 42.
Projecting Lantern, 208.
Pulley, 53.
Pump, the common one, 111.
force-pump, 113.
rotary pump, 114.
Radiant Matter, 16, 313.
Radiation of heat, 231.
Rain, 333.
Rainbow, 193.
Reflection of light, 169.
total reflection, 179.
Refraction of light, 177, 180, 187.
law of, 177.
Refraction of sound, 128.
30
350
INDEX.
Resolution of forces, 26.
Resonance, 127, 137.
Resonator, 146.
Resultant of forces, 24, 25.
Rivers, velocity of, 86.
Ruhmkorff Coil, 309.
Scale in music, 150.
Screw, 57.
Secondary Battery, 287.
Shadows, 164.
Signal Bureau, 341.
Siphon, 115.
uses of, 116.
experiments with, 117.
Siren, 130.
Snow, 333.
Solids, definition of, 14.
Sonometer, 133.
Sound, chapter on, 120.
sound a vibration, 120.
velocity of, in the air, 123.
velocity of, in solids and liquids, 123.
loudness of, cause, 124.
affected by conditions of the atmos-
phere, 125.
refraction of, 128.
pitch of, 130.
character of, 147.
Sounding-Boards, 136.
Sound-Waves, length of, 133.
Speaking- Trumpets, 124.
Speaking-Tubes, 124.
Specific Gravity, definitions, 78.
table of, 345.
to find specific gravity of solids, 78.
to find specific gravity of liquids, 79.
to find specific gravity of gases, 80.
Specific Heat, 219.
Spectroscope, 190.
Spectrum of light, 189.
Spherical aberration, 187.
Spirit-Level, 74,
Sprengel's Air-Pump, 109.
Springs, 72.
Stability, 38.
Steam, 229.
Steam-Engine, 237.
Stereoscope, 208.
Storms, 338.
Suspension-Bridges, material of, 12.
Sympathetic Vibrations, 135.
T,
Telegraph, 294.
Telephone, 302.
Telescopes, 206.
Temperament, 154.
Temperature, cause of change, 323.
hottest and coldest mouths, 325.
Tenacity, 11.
Tension of gases, 95.
Thermal Electricity, 299.
Thermometer, 216.
Thunder-Storms, 339.
Timbre of sound, 148.
Triangle of forces, 25.
Twilight, 176.
V.
Vapors, 95.
Vibrating Strings, laws of, 134.
vibrations of, in parts, 143.
Violin, 139.
Voice, human, 142.
number of vibrations in, 133.
Voltaic electricity, 278.
Volume, definition of, 12.
W.
Water-Level, 74.
Waves in water, 86.
of sound, 121.
of light, 163.
of heat, 213.
interference of, 87.
Water- Wheels, 87.
overshot-wheel, 88.
breast-wheel, 88.
undershot, 89.
turbine, 89.
Weather Indications, 342.
Wedge, 56.
Weight caused by gravity, 14.
how it varies, 15.
Wells, 72.
Wheel and Axle, 51.
Whispering-Galleries, 126.
Winds, cause of, 335.
Wind-instruments, 141.
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