A.—With the velocity which a body would acquire by falling from the height of a homogeneous atmosphere, which is an atmosphere of the same density throughout as at the earth’s surface; and although such an atmosphere does not exist in nature, its existence is supposed, in order to facilitate the computation. It is well known that the velocity with which water issues from a cistern is the same that would be acquired by a body falling from the level of the head to the level of the issuing point; which indeed is an obvious law, since every particle of water descends and issues by virtue of its gravity, and is in its descent subject to the ordinary laws of falling bodies. Air rushing into a vacuum is only another example of the same general principle: the velocity of each particle will be that due to the height of the column of air which would produce the pressure sustained; and the weight of air being known, as well as the pressure it exerts on the earth’s surface, it becomes easy to tell what height a column of air, an inch square, and of the atmospheric density, would require to be, to weigh 15 lbs. The height would be 27,818 feet, and the velocity which the fall of a body from such a height produces would be 1,338 feet per second.
VELOCITY OF FALLING BODIES AND MOMENTUM OF MOVING BODIES.
15. Q.—How do you determine the velocity of falling bodies of different kinds?
A.—All bodies fall with the same velocity, when there is no resistance from the atmosphere, as is shown by the experiment of letting fall, from the top of a tall exhausted receiver, a feather and a guinea, which reach the bottom at the same time. The velocity of falling bodies is one that is accelerated uniformly, according to a known law. When the height from which a body falls is given, the velocity acquired at the end of the descent can be easily computed. It has been found by experiment that the square root of the height in feet multiplied by 8.021 will give the velocity.
16. Q.—But the velocity in what terms?
A.—In feet per second. The distance through which a body falls by gravity in one second is 16-1/12 feet; in two seconds, 64-4/12 feet; in three seconds, 144-9/12 feet; in four seconds, 257-4/12 feet, and so on. If the number of feet fallen through in one second be taken as unity, then the relation of the times to the spaces will be as follows:—
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?