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—­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 handbooks are generally indefinite, or misleading, or even absolutely untrue.

Before we can intelligently consider the principles and methods of balancing this force, we must get a correct conception of the nature of the force itself.  What, then, is centrifugal force?  It is an extremely simple thing; a very ordinary amount of mechanical intelligence is sufficient to enable one to form a correct and clear idea of it.  This fact renders it all the more surprising that such inaccurate and confused language should be employed in its definition.  Respecting writers, also, who use language with precision, and who are profound masters of this subject, it must be said that, if it had been their purpose to shroud centrifugal force in mystery, they could hardly have accomplished this purpose more effectually than they have done, to minds by whom it was not already well understood.