so that this shall be equal to that of the second point of contact.  When we think about the matter a little closely, we see that at the rim of the wheel the oil has perhaps ten times the velocity of revolution which it had on leaving the journal, and that the mystery to be explained really is, How did it get that velocity, moving out on a radial line?  Why was it not left behind at the very first?  Solely by reason of its forward tangential motion.  That is the answer.

When writers who understand the subject talk about the centripetal and centrifugal forces being different names for the same force, and about equal action and reaction, and employ other confusing expressions, just remember that all they really mean is to express the universal relation between force and resistance.  The expression “centrifugal force” is itself so misleading, that it becomes especially important that the real nature of this so-called force, or the sense in which the term “force” is used in this expression, should be fully explained.[1] This force is now seen to be merely the tendency of a revolving body to move in a straight line, and the resistance which it opposes to being drawn aside from that line.  Simple enough!  But when we come to consider this action carefully, it is wonderful how much we find to be contained in what appears so simple.  Let us see.

[Footnote 1:  I was led to study this subject in looking to see what had become of my first permanent investment, a small venture, made about thirty-five years ago, in the “Sawyer and Gwynne static pressure engine.”  This was the high-sounding name of the Keely motor of that day, an imposition made possible by the confused ideas prevalent on this very subject of centrifugal force.]

FIRST.—­I have called your attention to the fact that the direction in which the revolving body is deflected from the tangential line of motion is toward the center, on the radial line, which forms a right angle with the tangent on which the body is moving.  The first question that presents itself is this:  What is the measure or amount of this deflection?  The answer is, this measure or amount is the versed sine of the angle through which the body moves.

Now, I suspect that some of you—­some of those whom I am directly addressing—­may not know what the versed sine of an angle is; so I must tell you.  We will refer again to Fig. 1.  In this figure, O A is one radius of the circle in which the body A is revolving.  O C is another radius of this circle.  These two radii include between them the angle A O C. This angle is subtended by the arc A C. If from the point O we let fall the line C E perpendicular to the radius O A, this line will divide the radius O A into two parts, O E and E A. Now we have the three interior lines, or the three lines within the circle, which are fundamental in trigonometry.  C E is the sine, O E is the cosine, and E A is the versed sine of the angle A O C. Respecting these three lines there are many things to be observed.  I will call your attention to the following only: