" 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--_centrifugal force_.

This force presents its claims to attention in all bodies which revolve
about fixed centers, and sometimes these claims are presented with a
good deal of urgency. At the same time, there is probably no subject,
about which the ideas of men generally are more vague and confused. This
confusion is directly due to the vague manner in which the subject of
centrifugal force is treated, even by our best writers. As would then
naturally be expected, the definitions of it commonly found in our