| Number of seconds | 1 | 2 | 3 | 4 | 5 | 6 | |
| Units of space passed through | 1 | 4 | 9 | 16 | 25 | 36 |
&c. |
so that it appears that the spaces passed through by a falling body are as the squares of the times of falling.
17. Q.--Is not the urging force which causes bodies to fall the force of gravity?
A.--Yes; the force of gravity or the attraction of the earth.
18. Q.--And is not that a uniform force, or a force acting with a uniform pressure?
A.--It is.
19. Q.--Therefore during the first second of falling as much impelling power will be given by the force of gravity as during every succeeding second?
A.--Undoubtedly.
20. Q.--How comes it, then, that while the body falls 64-4/12 feet in two seconds, it falls only 16-1/12 feet in one second; or why, since it falls only 16-1/12 feet in one second, should it fall more than twice 16-1/12 feet in two?
A.--Because 16-1/12 feet is the average and not the maximum velocity during the first second. The velocity acquired at the end of the 1st second is not 16-1/12, but 32-1/6 feet per second, and at the end of the 2d second a velocity of 32-1/6 feet has to be added; so that the total velocity at the end of the 2d second becomes 64-2/6 feet; at the end of the 3d, the velocity becomes 96-3/6 feet, at the end of the 4th, 128-4/6 feet, and so on. These numbers proceed in the progression 1, 2, 3, 4, &c., so that it appears that the velocities acquired by a falling body at different points, are simply as the times of falling. But if the velocities be as the times, and the total space passed through be as the squares of the times, then the total space passed through must be as the squares of the velocity; and as the vis viva or mechanical power inherent in a falling body, of any given weight, is measurable by the height through which it descends, it follows that the vis viva is proportionate to the square of the velocity. Of two balls therefore, of equal weight, but one moving twice as fast as the other, the faster ball has four times the energy or mechanical force accumulated in it that the slower ball has. If the speed of a fly-wheel be doubled, it has four times the vis viva it possessed before--vis viva being measurable by a reference to the height through which a body must have fallen, to acquire the velocity given.