The possible motions of a sphere suspended on a string are found to consist of combinations of (1) a pendulum type of motion and (2) a rolling motion, in which the ball rolls in angular harmonic motion about an axis very near its center. For (1) it is shown (a) the usual formula for the length of the equivalent simple pendulum should be replaced byL(1+2r2/5L2+4r3/25L3+···), whereris the radius of the ball andLthe distance of point of suspension to center of the sphere, and (b) the best way of starting this motion is to pull the ball aside by a horizontal force through its center. For (2) it is shown that the period of oscillation is very close to2π(2r/5g).Photographs are given showing experimental verifications of these effects.