s, and have
observed the increasing angular velocity, the two obviously increasing
in the same ratio. That is the operation or action which the fourth law
of centrifugal force expresses. An examination of this same figure (Fig.
2) will show you at once the reason for it in the increasing deflection
which the body suffers, as its circle of revolution is contracted. If we
take the velocity A' B', double the velocity A B, and transfer it to the
smaller circle, we have the velocity A C. But the deflection has been
increasing as we have reduced the circle, and now with one half the
radius it is twice as great. It has increased in the same ratio in which
the angular velocity has increased. Thus we see the simple and necessary
nature of these laws. They merely express the different rates of
deflection of a revolving body in these different cases.

THIRD.--We have a coefficient of centrifugal force, by which we are
enabled to compute the amount of this resistance of a revolving body to
deflection from a direct line of motion in all cases. This is that
coefficient. The centrifugal force of a body making _one_ revolution per
minute, in a circle of _one_ foot radius, is 0.000341 of the weight of
the body.

According to the above laws, we have only to multiply this coefficient
by the square of the number of revolutions made by the body per minute,
and this product by the radius of the circle in feet, or in decimals of
a foot, and we have the centrifugal force, in terms of the weight of the
body. Multiplying this by the weight of the body in pounds, we have the
centrifugal force in pounds.

Of course you want to know how this coefficient has been found out, and
how you can be sure it is correct. I will tell you a very simple way.
There are also mathematical methods of ascertaining this coefficient,
which your professors, if you ask them, will let you dig out for
yourselves. The way I am going to tell you I found out for myself, and
that, I assure you, is the only way to learn anything, so that it will
stick; and the more trouble the search gives you, the darker the way
seems, and the greater the degree of perseverance that is demanded, the
more you will appreciate the truth when you have found it, and the more
complete and permanent your possession of it will be.

The explanation of this method may be a little more abstruse than the
explanations already given, but it is very simple and elegant when you
see it, and I fancy I can