508. We have already learned that the effect of gravity does not depend
upon the actual chemical composition of the body. We have now to learn
that its effect is uninfluenced by any motion which the body may
possess. Gravity pulls a body down 16' per second, if the body starts
from rest. But suppose a stone be thrown upwards with a velocity of 20
feet, where will it be at the end of a second? Did gravity not act upon
the stone, it would be at a height of 20 feet. The principle we have
stated tells us that gravity will draw this stone towards the earth
through a distance of 16', just as it would have done if the stone had
started from rest. Since the stone ascends 20' in consequence of its
own velocity, and is pulled back 16' by gravity, it will, at the end
of a second, be found at the height of 4'. If, instead of being shot
up vertically, the body had been projected in any other direction, the
result would have been the same; gravity would have brought the body
at the end of one second 16' nearer the earth than it would have been
had gravity not acted. For example, if a body had been shot vertically
downwards with a velocity of 20', it would in one second have moved
through a space of 36'.
509. We shall illustrate this remarkable property by an experiment.
The principle of doing so is as follows:—Suppose we take two bodies, A
and B. If these be held at the same height, and released together, of
course they reach the ground at the same instant; but if A, instead of
being merely dropped, be projected with a horizontal velocity at the
same moment that B is released, it is still found that a and B strike
the floor simultaneously.
510. You may very simply try this without special apparatus. In your
left hand hold a marble, and drop it at the same instant that your
right hand throws another marble horizontally. It will be seen that the
two marbles reach the ground together.
511. A more accurate mode of making the experiment is shown by the
contrivance of Fig. 68.
[Illustration: FIG. 68.]
In this we have an arrangement by which we ensure that one ball shall
be released just as the other is projected. At A B is shown a piece
of wood about 2" thick; the circular portion (2' radius) on which the
ball rests is grooved, so that the ball only touches the two edges
and not the bottom of the groove. Each edge of the groove is covered
with tinfoil C, but the pieces of tinfoil on the two sides must not
communicate. One edge is connected with one pole of the battery K,
and the other edge with the other pole, but the current is unable to
pass until a communication by a conductor is opened between the two
edges. The ball G supplies the bridge; it is covered with tinfoil, and
therefore, as long as it rests upon the edges, the circuit is complete;
the groove is so placed that the tangent to it at the lowest point B is
horizontal, and therefore, when the ball rolls down the curve, it is
projected from the bottom in a horizontal direction. An india-rubber
spring is used to propel the ball; and by drawing it back when embraced
by the spring, I can communicate to the missile a velocity which can
be varied at pleasure. At H we have an electro-magnet, the wire around
which forms part of the circuit we have been considering. This magnet
is so placed that a ball suspended from it is precisely at the same
height above the floor as the tinned ball is at the moment when it
leaves the groove.
512. We now understand the mode of experimenting. So long as the tinned
ball G remains on the curve the bridge is complete, the current passes,
and the electro-magnet will sustain H, but the moment G leaves the
curve, H is allowed to fall. We invariably find that whatever be the
velocity with which G is projected, it reaches the ground at the same
instant as H arrives there. Various dotted lines in the figure show the
different paths which G may traverse; but whether it fall at D, at E,
or at F, the time of descent is the same as that taken by H. Of course,
if G were not projected horizontally, we should not have arrived at
this result; all we assert is that whatever be the motion of a body,
it will (when possible) be at the end of a second, sixteen feet nearer
the earth than it would have been if gravity had not acted. If the body
be projected horizontally, its descent is due to gravity alone, and is
neither accelerated nor retarded by the horizontal velocity. What this
experiment proves is, that the mere fact of a body having velocity does
not affect the action of gravity thereon.
513. Though we have only shown that a horizontal velocity does not
affect the action of gravity, yet neither does a velocity in any
direction. This is verified, like the first law of motion, by the
accordance between the consequences deduced from it and the facts of
observation.
514. We may summarize these results by saying that no matter what be
the material of which a particle is composed, whether it be heavy or
light, moving or at rest, if no force but gravity act upon the particle
for _t_ seconds, it will then be 16_t_² feet nearer the earth than it
would have been had gravity not acted.
[Illustration: FIG. 69.]
515. A proposition which is of some importance may be introduced here.
Let us suppose a certain velocity and a certain force. Let the velocity
be such that a point starting from A, Fig. 69, would in one second move
uniformly to B. Let the force be such that if it acted on a particle
originally at rest at A, it would in one second draw the particle to D;
if then the force act on a particle having this velocity where will it
be at the end of the second? Complete the parallelogram A B C D, and
the particle will be found at C. By what we have stated the force will
equally discharge its duty whatever be the initial velocity. The force
will therefore make the particle move to a distance equal and parallel
to A D from whatever position the particle would have assumed, had the
force not acted; but had the force not acted, the particle would have
been found at B: hence, when the force does act, the particle must be
found at C, since B C is equal and parallel to A D.