Abstract: 1. Though the ball is small, yet, at high speed, the stress produced by the centrifugal force of the ball can not be neglected. In order to decrease the influence of the centrifugal force, more balls with smaller diameter roust be putted in the groove as one can. Referring to Fig. 3 and 4 in this paper, ΨT = 360°-2arc cos 0.4(D-d)/D+d, Ψp -2(Z-1) arc sin 2dul/D+d, in which D=the outside diameter of the outer race, d =the diameter of the shaft, dul=the diameter of the ball, Z=the number of the balls, ΨT=the limitting angle in theory for putting balls in the groove, and Ψp=the practical angle for putting balls in the grove. If Ψp<<ΨT, then one more ball at least may be added by decreasing slightly the value of the ball diameter, so that ;op can be equal approximately toΨT. 2. The longer is the cyclic period of the stress produced in some body, the stronger is the ability of the body to undertake fatigue, and it is, of course, also true for the ball bearing. As the outer race of the single-row radial ball bearing is fixed, the value of the contact stress on any point of the surface of the ball or the inner race varies on occasion. It is interesting to find that the cyclic period of the maximum contact stress on any point of the surface of the ball or the inner race is influenced closely by the dimensions of the ball, and it is also interesting to find that if the number of the effective value is increased, the bearing life no doubt will be longer. For example, if according to the standard of the ball bearing, the ball diameter of some single-row radial ball bearing equals to 15 mm, now let the same ball diameter change to 14.95 mm (naturally all the relative dimensions of the rest must be suitably changed), then the cyclic period of the maximum contact stress produced in the ball or the inner race will be longer and hence the bearing capacity will be stronger.