484. Velocity, in ordinary language, is supposed to convey a notion
of rapid motion. Such is not precisely the meaning of the word
in mechanics. By velocity is merely meant the _rate_ at which a
body moves, whether the rate be fast or be slow. This rate is most
conveniently measured by the number of feet moved over in one second.
Hence when it is said the velocity of a body is 25, it is meant that if
the body continued to move for one second with its velocity unaltered,
it would in that time have moved over 25 feet.
[Illustration: FIG. 66.]
485. The first law of motion may be stated thus. _If no force act upon
a body, it will, if at rest, remain for ever at rest; or if in motion,
it will continue for ever to move with a uniform velocity._ We know
this law to be true, and yet no one has ever seen it to be true for the
simple reason that we cannot realise the condition which it requires.
We cannot place a body in the condition of being unacted upon by any
forces. But we may convince ourselves of the truth of the law by some
such reasoning as the following. If a stone be thrown along the road,
it soon comes to rest. The body leaves the hand with a certain initial
velocity and is not further acted upon by it. Hence, if no other force
acted on the stone, we should expect, if the first law be true, that
it would continue to run on for ever with the original velocity at the
moment of leaving the hand. But other forces do act upon the stone; the
attraction of the earth pulls it down; and, when it begins to bound and
roll upon the ground, friction comes into operation, deprives the stone
of its velocity, and brings it to rest. But let the stone be thrown
upon a surface of smooth ice; when it begins to slide, the force of
gravity is counteracted by the reaction of the ice: there is no other
force acting upon the stone except friction, which is small. Hence
we find that the stone will run on for a considerable distance. It
requires but little effort of the imagination to suppose a lake whose
surface is an infinite plane, perfectly smooth, and that the stone is
perfectly smooth also. In such a case as this the first law of motion
amounts to the assertion that the stone would never stop.
486. We may, in the lecture room, see the truth of this law verified
to a certain extent by Atwood's machine (Fig, 66). This machine has
been devised for the purpose of investigating the laws of motion by
actual experiment. It consists principally of a pulley C, mounted so
that its axle rests upon two pairs of wheels, as shown in the figure;
it being the object of this contrivance to enable the wheel to revolve
with the utmost freedom. A pair of equal weights A, B, are attached by
a silken thread, which passes over the pulley; each of the weights is
counterbalanced by the other: so that when the two are in motion, we
may consider either as a body not acted upon by any forces, and it will
be found that it moves uniformly, as far as the size of the apparatus
will permit.
487. If we try to conceive a body free in space, and not acted upon by
any force, it is more natural to suppose that such a body, when once
started, should go on moving uniformly for ever, than that its velocity
should be altered. The true proof of the first law of motion is, that
all consequences properly deduced from it, in combination with other
principles, are found to be verified. Astronomy presents us with the
best examples. The calculation of the time of an eclipse is based upon
laws which in themselves assume the first law of motion; hence, when
we invariably find that an eclipse occurs precisely at the moment for
which it has been predicted, we have a splendid proof of the sublime
truth which the first law of motion expresses.