_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 showing that in falling from the point A to the
earth as a center, through distances increasing as the square of the
time, the moon, having the tangential velocity that it has, could never
get nearer to the earth than the circle in which it revolves around it.
This is all very true, and very unsatisfactory. We know that this long
tangential line has nothing to do with the motion of the moon, and while
we are compelled to assent to the demonstration, we want something
better. To my mind the better and more satisfactory explanation is found
in the fact that the moon is forever commencing to fall, and is
continually beginning to fall in a new direction. A revolving body, as
we have seen, never gets past that point, which is entirely beyond our
sight and our comprehension, of beginning to fall, before the direction
of its fall is changed. So, under the attraction of the earth, the moon
is forever leaving a new tangential direction of motion at the same
rate, without acceleration.
(_To be continued_.)
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