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.
HOW THE FORCE OF GRAVITY IS DEFINED.
516. From the formula
Distance = 16t²,
we learn that a body falls through 64' in 2 seconds; and as we know that it falls 16' in the first second, it must fall 48' in the next second. Let us examine this. After falling for one second, the body acquires a certain velocity, and with that velocity it commences the next second. Now, according to what we have just seen, gravity will act during the next second quite independently of whatever velocity the body may have previously had. Hence in the second second gravity pulls the body down 16', but the body moves altogether through 48'; therefore it must move through 32' in consequence of the velocity which has been impressed upon it by gravity during the first second. We learn by this that when gravity acts for a second, it produces a velocity such that, if the body be conceived to move uniformly with the velocity acquired, the body would in one second move over 32'.
517. In three seconds the body falls 144', therefore in the third second it must have fallen
144' - 64' = 80';
but of this 80' only 16' could be due to the action of gravity impressed during that second; the rest,
80' - 16' = 64',