But I read further that the centrifugal force of a body revolving in any given circle varies as the square of the speed. “Thus a body making 10 revolutions per minute will exert four times as much centrifugal force as will be exerted by the same body making 5 revolutions per minute.” The governor on my engine was making 50 revolutions per minute, and in thinking the matter over it occurred to me that if the governor could be run as fast as my machine, namely, at 300 revolutions per minute, the centrifugal force of one pound would be as great as that exerted by 36 pounds at 50 revolutions per minute. I cried, “Eureka! I have found it.” One-pound balls in place of 36-pound balls would be easily driven. I told my experts of the great find that I had made, and they laughed at me. They told me I ought to know that the momentum of the balls increased in the same ratio with their centrifugal force, _MV²_ being the expression common to both, so, in the same circle, while the centrifugal force of the balls at 300 revolutions per minute would be 36 times greater than at 50 revolutions, it would require also 36 times the force to drive them, and that I would gain nothing by my proposed change, but instead I would have to rotate also the weight that I would need to use to hold the small balls down, and the last case would be worse than the first. This staggered me, and I pondered awhile what I should do. I had a friend living near by on Fourteenth Street, west of Seventh Avenue--a Mr. Thompson, a mathematician and the author of a series of mathematical books then largely used. So I called upon him and stated my trouble and asked his advice. He illuminated the subject to me as follows: “You seem to be a persevering young man; keep hard at it and you will solve the difficulty by and by.” In my despair I just had before me this one thought: The friction must be cured at any rate. After a time I thought that if I made a long joint at the top embracing the center of gyration of the counterpoise, so that the pressure required to drive the balls and counterpoise would be applied at some distance from the axis of the spindle and for that reason would be much lighter, and also would be normal to the surface of the joint-pin instead of being a pinch between opposite faces, the difficulty would be cured, as the force to overcome the friction would be exerted at the ends of levers 50 or 100 times the radius of the pin. I felt so sure of this that I risked making a governor with a single joint at the apex of the cone, as originally employed by Watt, thus making the governor more sensitive, as the height of the cone would not be changed at both ends, still fortunately holding to my little balls and high speed, though I cannot tell why. The joint at the top I made 6 inches in length.