SOME PROPERTIES OF SOLID BODIES—INERTIA—MOTION—FRICTION—THE
PENDULUM—EQUILIBRIUM.
Those who have followed us through the preceding pages have now, we
hope, some ideas upon Gravity and the Forces of Nature. In speaking
of Forces we said “Force was a cause of Motion.” Let us now consider
Inertia, and Motion with its accompanying opponent, Friction.
[Illustration: Fig. 29.—Shock communicated by elasticity.]
INERTIA is the passiveness of Matter. This perfect
indifference to either rest or motion makes the great distinction
between living and lifeless matter. Inertia, or _Vis Inertia_, is this
passiveness. Now, to overcome this indifference we must use force,
and when we have applied force to matter we set it in motion; that
is, we move it. When we move it we find a certain resistance which
is always proportionate to the force applied. In mechanics this is
termed _Action_, and _Reaction_, which are always equal forces acting
in opposite directions. This is Newton’s law, and may be explained by
a “weight” on a table, which presses against the table with the same
force with which the table presses against the “weight”; or when you
strike a ball, it strikes the hand with the same force.
We can communicate motion by elasticity. For instance, if we place a
number of coins upon a table touching each other and in a straight
line, and strike the last coin of the line by pushing another sharply
against it, the piece at the opposite extremity will slip out of its
place from the effect of the shock transmitted by the coin at the other
end (fig. 29).
[Illustration: Fig. 30.—Experiment to illustrate inertia.]
When two forces act upon a body at the same time, it takes a direction
intermediate. This is known as the resultant. The enormous forces
exercised by the heavenly bodies will be treated of later. We will
first consider _Inertia_.
There are several experiments relating to the subject of Inertia which
may be performed. I once witnessed one quite accidentally when taking a
walk.
[Illustration: Fig. 31.—Another experiment on the same subject.]
I was one day passing the Observatory at Paris, when I noticed a number
of people collected round a professor, who after executing several
juggling tricks, proceeded to perform the curious experiment I am about
to describe. He took a broomstick and placed it horizontally, passing
the ends through two paper rings. He then asked two children to hold
the paper rings by means of two razors, so that the rings rested on
the blade. This done, the operator took a stout stick, and, with all
his strength, struck the broomstick in the centre; it was broken into
shivers, but the paper rings were not torn in the least, or even cut
by the razors! One of my friends, M. M——, a painter, showed me how to
perform this experiment as represented in the illustration (fig. 30).
A needle is fixed at each end of the broomstick, and these needles
are made to rest on two glasses, placed on chairs; the needles alone
must be in contact with the glasses. If the broomstick is then struck
violently with another stout stick, the former will be broken, but
the glasses will remain intact. The experiment answers all the better
the more energetic the action. It is explained by the resistance of
inertia in the broomstick. The shock suddenly given, the impulse
has not time to pass on from the particles directly affected to the
adjacent particles; the former separate before the movement can be
transmitted to the glasses serving as supports.[8]
[Illustration: Fig. 32.—Extracting a “man” from a pile of draughts
without overturning the pile.]
The experiment represented in fig. 31 is of the same nature. A wooden
ball is suspended from the ceiling by a rather slender thread, and a
similar thread is attached to the lower end of the ball. If the lower
thread is pulled forcibly it will break, as shown in the illustration;
the movement communicated to it has not time to pass into the ball; if,
on the contrary, it is pulled very gradually and without any shock,
the upper thread instead will break, because in this case it supports
the weight of the ball. Motion is not imparted simultaneously to all
parts of a body, but only to the particles first exposed to a blow, for
instance. One might multiply examples of this. If a bullet be shot from
a gun, it will make a round hole in a piece of wood or glass, whilst
if thrown by the hand,—that is to say, with much less force,— it will
shiver the wood or the pane of glass to pieces. When the celerity of
the motive force is very great, the particles directly affected are
disturbed so quickly that they separate from the adjacent particles
before there is time for the movement to be communicated to the latter.
It is possible, for the same reason, to extract from a pile of money a
piece placed in the middle of the pile without overturning the others.
It suffices to move them forcibly and quickly with a flat wooden ruler.
The experiment succeeds very well also if performed with draughtsmen
piled up on the draught-board (fig. 32).
[Illustration: Fig. 33.—Calling out a sixpence from the glass.]
Fig. 33 represents another experiment which belongs to the laws of
resisting force. A sixpence is placed on a table covered with a cloth
or napkin. It is covered with a glass, turned over so that its brim
rests on two penny pieces. The problem to be solved is how to extract
the sixpence from underneath the glass without touching it, or slipping
anything beneath it. To do this it is necessary to scratch the cloth
with the nail of the forefinger; the elasticity of the material
communicates the movement to the sixpence, which slowly moves in the
direction of the finger, until it finally comes out completely from
beneath the glass.
We may give another experiment concerning Inertia. Take a strip of
paper, and upon it place a coin, on a marble chimney-piece, as in
the illustration. If, holding the paper in the left hand, you strike
it rapidly and forcibly, you will be enabled to draw away the paper
without causing the coin (say a five-shilling-piece) to fall down (fig.
34).
It is not impossible to draw away a napkin laid as a tablecloth
for one person’s dinner, without disturbing the various articles
laid upon it. A quick motion is all that is necessary, keeping the
napkin tightly extended by the hands at the same time. This latter
experiment, however, is not recommended to boys home for the holidays,
as they may unwillingly practise a feat analogous to that executed by
Humpty-Dumpty, and find equal difficulty to match the pieces.
[Illustration: Fig. 34.—Drawing a slip of paper from beneath a coin.]
We will now examine the term _Motion_. A body is said to be in motion
when it changes its position in relation to surrounding objects. To
perceive motion the surrounding objects must be relatively at rest,
for if they all hurried along at the same rate no motion would be
perceptible. This is evident, for when we stand still trees and houses
appear stationary, as do we ourselves, but we know we all are rushing
round with the earth, though our _relative_ positions are unchanged.
Hence there is no _absolute_ rest.
What are the causes of motion?—Gravity is one. The influence of
heat, which is itself caused by the motion of atoms, the effects
of electricity, etc., and finally, the power of force in men or
animals—any of these causes will produce motion. But a body at rest
cannot put itself in motion, nor can a body in motion stop itself, or
change its condition of motion.
But you may say a body will stop itself. Your ball on the ground, or
even upon ice, will eventually come to a stop. We fire a bullet, and it
will stop in time. We reply it does not stop of itself. The resistance
of the Air and Friction tend to bring the body in motion to a state of
rest. In the case of a bullet gravity brings it down.
There is no need to insist upon the resistance offered by the air
even when it is not rushing violently past to fill up a vacuum beyond
us, and called a breeze, or high wind. But we may say something of
_Friction_.
Friction is derived from the Latin _frico_, to rub, and expresses the
resistance to motion which arises from uneven surfaces. It is a passive
resistance, and depends upon the force which keeps the bodies together.
Thus a train running upon a smooth iron rail would never be able to
proceed but for friction, which gives the necessary purchase or grip to
the wheel and rail in contact.
No surface is perfectly smooth, for we must push a body upon the
smoothest surface we possess. Friction tends to resist motion always,
and is the cause of a great loss of power in mechanics, though it is
employed to stop motion by certain appliances, such as “brakes” and
“drags,” for sliding friction is greater than rolling friction. But
without friction most structures would fall to pieces, and all forward
motion would cease. So though it is an inconvenient force to overcome,
we could not do without it.
If a body is set in motion, we see that the tendency of it is to go on
for ever. Such, indeed, is the case with the stars; but so long as we
are within the influence of the earth’s attraction, we cannot expect
such a result. We know now what motion is; we must also, to understand
it perfectly, consider its direction and its velocity.
The line which indicates the way from the starting point to the end
is the _direction_ of the object in motion, and the rate it moves at
its _velocity_. The latter is calculated at so many miles an hour,
as a train; or so many feet in a second if the object be a shot, or
other very rapidly-moving body. In equal velocity the same distance
is traversed in the same time; and so if a train run a mile in a
minute, we know it will travel sixty miles in an hour, and is therefore
during that minute going at _the rate_ of sixty miles an hour. We
have already spoken of the velocity of a stone falling from a cliff
as sixteen feet in a second, and a stone thrown into the air to rise
sixteen feet will be a second in going up, and a second in descending.
But the velocity will be accelerated in the descent after the first
second of time, and retarded in the upward cast by gravity. So we have
two terms—_accelerated_ and _retarded_ velocity—used to express an
increased or decreased force of attraction.
Perpetual motion has often been sought, but never discovered, nor
will it ever be till the elixir of life has been found. It is quite
impossible to construct any machine that will work without friction;
if any work be done energy will be expended and transformed into other
energy, so the total must be diminished by so much as was employed to
transform the remainder. No body can give unlimited work, therefore
the perpetual motion theory is untenable and impossible.
The _pendulum_ is considered the nearest approach to perpetual motion.
This is so well known that no description is needed, but we may say
a few words concerning it. By the diagram, we see that if we lift
the ball to _b_, and let it fall, it will descend to _l_, and pass
it to _a_ opposite, nearly as far from _l_ as _b_ is from it. So the
oscillations will continue, each beat being less and less, till rest is
reached by the action of gravity (page 23). Were it not for friction
and the pressure of the air, the oscillations would continue for ever;
as it is, it declines by shorter swings till it remains in equilibrium.
[Illustration: Fig. 35.—The pendulum.]
The seconds’ pendulum oscillates sixty times an hour, and must be of a
certain length in certain places. In London it is 39·1393 inches, and
furnishes a certain standard of length, and by an Act of Parliament the
yard is divided into 36 parts, and 39·1393 such parts make the seconds’
pendulum in the latitude of London (_in vacuo_) in a temperature of 62°.
[Illustration: Fig. 36.—Centrifugal Force.]
But the same pendulum will not perform the same number of oscillations
in one minute in all parts of the globe. At the equator they will
be less, and at the pole more. Thus it was discovered that, as the
movements of the pendulum are dependent upon the force of gravity,
and as this force decreases the farther we get from the centre of the
earth, the equator must be farther from the earth’s centre than the
poles, and therefore the poles must be depressed. The decline of the
pendulum at the equator is also, in a measure, due to Centrifugal Force.
_Centrifugal Force_, which means “flying from the centre,” is the force
which causes an object to describe a circle with uniform velocity, and
fly away from the centre; the force that counteracts it is called the
_centripetal_ force. A very simple experiment will illustrate it.
[Illustration: Fig. 37.—Another illustration of centrifugal force.]
To represent its action, we shall have recourse to an ordinary glass
tumbler placed on a round piece of cardboard, held firmly in place by
cords. Some water is poured in the glass, and we then show that it can
be swung to and fro and round without the water being spilt, even when
the glass is upside down (fig. 36).
Another experiment on the same subject is as shown in the above
illustration, by which a napkin ring can be kept in revolution around
the forefinger, and by a continued force the ring may be even held
suspended at the tip of the finger, apparently in the air, without
support (fig. 37).
FOOTNOTES:
[8] The experiment we have just described is a very old one. M. V.
Sircoulon has told us that it was described at length in the works of
Rabelais. The following remarks are in “Pantagruel,” book II., chap.
xvii.
“Panuræ then took two glasses of the same size, filled them with water,
and put one on one stool, and the other on another, about five feet
apart, and placed the staff of a javelin about five-and-a-half feet
long across, so that the ends of the staff just touched the brim of
the glasses. That done, he took a stout piece of wood, and said to the
others: “Gentlemen, this is how we shall conquer our enemies; for in
the same way that I shall break this staff between these two glasses,
without the glasses being broken or injured, or spilling a single drop
of water, so shall we break the head of our Dipsodes, without any
injury to ourselves, and without getting wounded. But that you may not
think there is magic in it, you, Eusthenes, strike with this stick as
hard as you can in the centre.” This Eusthenes did, and the staff broke
in two pieces, without a drop of water being spilt.