*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?