motion of any body will be accelerated when it is acted on by a constant
force equal to its weight, and encounters no resistance.

It follows that a revolving body, when moving uniformly in any circle at
a speed at which its deflection from a straight line of motion is such
that in one second this would amount to 16.083 feet, requires the
exertion of a centripetal force equal to its weight to produce such
deflection. The deflection varying as the square of the time, in 0.01 of
a second this deflection will be through a distance of 0.0016083 of a
foot.

Now, at what speed must a body revolve, in a circle of one foot radius,
in order that in 0.01 of one second of time its deflection from a
tangential direction shall be 0.0016083 of a foot? This decimal is the
versed sine of the arc of 3°15', or of 3.25°. This angle is so small
that the departure from the law that the deflection is equal to the
versed sine of the angle is too slight to appear in our computation.
Therefore, the arc of 3.25° is the arc of a circle of one foot radius
through which a body must revolve in 0.01 of a second of time, in order
that the centripetal force, and so the centrifugal force, shall be equal
to its weight. At this rate of revolution, in one second the body will
revolve through 325°, which is at the rate of 54.166 revolutions per
minute.

Now there remains only one question more to be answered. If at 54.166
revolutions per minute the centrifugal force of a body is equal to its
weight, what will its centrifugal force be at one revolution per minute
in the same circle?

To answer this question we have to employ the other extremely simple