54.166 squared

--the coefficient of centrifugal force.

There is another mode of making this computation, which is rather neater
and more expeditious than the above. A body making one revolution per
minute in a circle of one foot radius will in one second revolve through
an arc of 6 deg.. The versed sine of this arc of 6 deg. is 0.0054781046 of a
foot. This is, therefore, the distance through which a body revolving at
this rate will be deflected in one second. If it were acted on by a
force equal to its weight, it would be deflected through the distance of
16.083 feet in the same time. What is the deflecting force actually
exerted upon it? Of

0.0054781046
course, it is ------------.
16.083

This division gives 0.000341 of its weight as such deflecting force, the
same as before.

In taking the versed sine of 6 deg., a minute error is involved, though not
one large enough to change the last figure in the above quotient. The
law of uniform acceleration does not quite hold when we come to an angle
so large as 6 deg.. If closer accuracy is demanded, we can attain it, by
taking the versed sine for 1 deg., and multiplying this by 6 squared. This gives as
a product 0.0054829728, which is a little larger than the versed sine of
6 deg..

I hope I have now kept my promise, and made it clear how the coefficient
of centrifugal force may be found in this simple way.

We have now learned several things about centrifugal force. Let me
recapitulate. We have learned:

1st. The real nature of centrifugal force. That in the dynamical sense
of the term force, this is not a force at all: that it is not capable of
producing motion, that the force which is really exerted on a revolving
body is the centripetal force, and what we are taught to call
centrifugal force is nothing but the resistance which a revolving body
opposes to this force, precisely like any other resistance.

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 th