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 make it quite clear.  I shall have to preface it by the explanation of two simple laws.  The first of these is, that a body acted on by a constant force, so as to have its motion uniformly accelerated, suppose in a straight line, moves through distances which increase as the square of the time that the accelerating force continues to be exerted.

The necessary nature of this law, or rather the action of which this law is the expression, is shown in Fig. 3.

[Illustration:  Fig. 3]

Let the distances A B, B C, C D, and D E in this figure represent four successive seconds of time.  They may just as well be conceived to represent any other equal units, however small.  Seconds are taken only for convenience.  At the commencement of the first second, let a body start from a state of rest at A, under the action of a constant force, sufficient to move it in one second through a distance of one foot.  This distance also is taken only for convenience.  At the end of this second, the body will have acquired a velocity of two feet per second.  This is obvious because, in order to move through one foot in this second, the body must have had during the second an average velocity of one foot per second.  But at the commencement of the second it had no velocity.  Its motion increased uniformly.  Therefore, at