1 squared
one foot radius will be ---------- = 0.000341
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 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.]