2d. The direction of the deflection, to which the centrifugal force is the resistance, which is straight to the center.
3d. The measure of this deflection; the versed sine of the angle.
4th. The reason of the laws of centrifugal force; that these laws merely express the relative amount of the deflection, and so the amount of the force required to produce the deflection, and of the resistance of the revolving body to it, in all different cases.
5th. That the deflection of a revolving body presents a case analogous to that of uniformly accelerated motion, under the action of a constant force, similar to that which is presented by falling bodies;[1] and finally,
6th. How to find the coefficient, by which the amount of centrifugal force exerted in any case may be computed.
[Footnote 1: A body revolving with a uniform velocity in a horizontal plane would present the only case of uniformly accelerated motion that is possible to be realized under actual conditions.]
I now pass to some other features.
First.--You will observe that, relatively to the center, a revolving body, at any point in its revolution, is at rest. That is, it has no motion, either from or toward the center, except that which is produced by the action of the centripetal force. It has, therefore, this identity also with a falling body, that it starts from a state of rest. This brings us to a far more comprehensive definition of centrifugal force. This is the resistance which a body opposes to being put in motion, at any velocity acquired in any time, from a state of rest. Thus centrifugal force reveals to us the measure of the inertia of matter. This inertia may be demonstrated and exhibited by means of apparatus constructed on this principle quite as accurately as it can be in any other way.
Second.--You will also observe the fact, that motion must be imparted to a body gradually. As distance, through which force can act, is necessary to the impartation of velocity, so also time, during which force can act, is necessary to the same result. We do not know how motion from a state of rest begins, any more than we know how a polygon becomes a circle. But we do know that infinite force cannot impart absolutely instantaneous motion to even the smallest body, or to a body capable of opposing the least resistance. Time being an essential element or factor in the impartation of velocity, if this factor be omitted, the least resistance becomes infinite.
We have a practical illustration of this truth in the explosion of nitro-glycerine. If a small portion of this compound be exploded on the surface of a granite bowlder, in the open air, the bowlder will be rent into fragments. The explanation of this phenomenon common among the laborers who are the most numerous witnesses of it, which you have doubtless often heard, and which is accepted by ignorant minds without further thought, is that the action of nitro-glycerine is downward. We know that such an idea is absurd.