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.

The explosive force must be exerted in all directions equally.  The real explanation is, that the explosive action of nitro-glycerine is so nearly instantaneous, that the resistance of the atmosphere is very nearly equal to that of the rock; at any rate, is sufficient to cause the rock to be broken up.  The rock yields to the force very nearly as readily as the atmosphere does.

Third.  An interesting solution is presented here of what is to many an astronomical puzzle.  When I was younger than I am now, I was greatly troubled to understand how it could be that if the moon was always falling to the earth, as the astronomers assured us it was, it should never reach it, nor have its falling velocity accelerated.  In popular treatises on astronomy, such for example as that of Professor Newcomb, this is explained by a diagram in which the tangential line is carried out as in Fig. 1, and by