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',
is due to the velocity with which the body commenced the third second.
518. We see therefore that after the lapse of two seconds gravity has communicated to the body a velocity of 64' per second; we should similarly find, that at the end of the third second, the body has a velocity of 96', and in general at the end of t seconds a velocity of 32t. Thus we illustrate the remarkable law that the velocity developed by gravity is proportional to the time.
519. This law points out that the most suitable way of measuring gravity is by the velocity acquired by a falling body at the end of one second. Hence we are accustomed to say that g (as gravity is generally designated) is 32. We shall afterwards show in the lecture on the pendulum (XVIII.) how the value of g can be obtained accurately. From the two equations, v = 32t and s = 16t² it is easy to infer another very well known formula, namely, v² = 64s.