hatever the
nature of the path in which it is moving, and always in the direction of
its motion. The latter force is exerted only by bodies whose path is a
circle, or a curve of some form, about a central body or point, to which
it is held, and this force is always at right angles with the direction
of motion of the body.

Respecting momentum, I wish only to call your attention to a single
fact, which will become of importance in the course of our discussion.
Experiments on falling bodies, as well as all experience, show that the
velocity of every moving body is the product of two factors, which must
combine to produce it. Those factors are force and distance. In order to
impart motion to the body, force must act through distance. These two
factors may be combined in any proportions whatever. The velocity
imparted to the body will vary as the square root of their product.
Thus, in the case of any given body,

Let force 1, acting through distance 1, impart velocity 1.
Then " 1, " " " 4, will " " 2, or
" 2, " " " 2, " " " 2, or
" 4, " " " 1, " " " 2;
And " 1, " " " 9, " " " 3, or
" 3, " " " 3, " " " 3, or
" 9, " " " 1, " " " 3.

This table might be continued indefinitely. The product of the force
into the distance will always vary as the square of the final velocity
imparted. To arrest a given velocity, the same force, acting through the
same distance, or the same product of force into distance, is required
that was required to impart the velocity.

The fundamental truth which I now wish to impress upon your minds is
that in order to impart velocity to a body, to develop the energy which
is possessed by a body in motion, force must act through distance.
Distance is a factor as essential as force. Infinite force could not
impart to a body the least velocity, could not develop the least energy,
without acting through distance.

This exposition of the nature of momentum is sufficient for my present
purpose. I shall have occasion to apply it later on, and to describe the
methods of balancing this force, in those cases in which it becomes
necessary or desirable to do so. At present I will proceed to consider
the second of the forces, or manifestations of force, which are
developed in moving bodies--_