“To find the load which a single hardened steel ball will safely carry in any ball-bearing, either when running between two flat surfaces or between two equally grooved surfaces of hardened steel, in each case the following formula may be applied,—viz.: Load in _d_ pounds = 190 _d_² √(1 + —————————), where _d_ equals the diameter _d′_ − _d_ of the ball in inches and _d′_ equals the diameter of the groove in which the ball runs, either top or bottom. For flat surfaces, _d_ for top and bottom bearing of ball _d′_ = ∞ and ————————— = 0, so _d′_ − _d_ that, for a ball between hardened flat plates, Load = 190 _d_². For _n_ balls in a nest, all in equally fair bearings, the load equals _d_ _n_ 190 _d_² √(1 + ——————————); for example, a one-inch ball between _d′_ − _d_ flat surfaces will carry one hundred and ninety pounds safely. 190 “Again a one-half-inch ball will carry ——— = 47.5 pounds; and again 4 a one-inch ball in a groove of one and one-eighth-inch diameter top 1 and bottom will carry 190 √(1 + —————————) = 570 pounds. So that 1′ (8 − 1) there is great advantage in supplying grooves for the balls to run in. Again, suppose the ball be one inch and the grooves one and one-eightieth inches in diameter; then the load equals seventeen hundred and ten pounds. Again, if the ball is one-half-inch diameter, and the groove nine-sixteenths-inch diameter, the load equals 142.5 pounds, etc. “Hundreds of experiments in all were made on this subject, and the above formula deduced by theory was found to agree almost exactly with the experimental results for hardened steel for balls and track for same. When a much greater load than the above is attempted to be carried, the balls will indent a groove of their own until the necessary bearing surface is obtained. “I am not aware that the coefficient of friction for ball-bearings is definitely known. Experiments made with the Lick telescope, in which the weights of some parts had to be guessed at, gives .00175 for the value of friction coefficient for one-inch balls; but this, though the best I have, is not a reliable figure. It is for hardened steel on hardened steel.” Mr. Robinson here shows an advantage in the groove so far as capacity for resisting strain is concerned, but he would hardly construct a ball-bearing with grooves fitting the balls after a careful perusal of our section on grooves and friction.