The refined theory of the motion of the outer layer of balls in a ball mill takes into account the relative motion of an upper ball with respect to a lower ball that is at relative rest with respect to the drum. To determine this relative motion, the refined theory provides two differential equations (see the article). This work is devoted to a quantitative assessment of the new theory. The author of the article studies the motion of the outer layer of balls in a ball mill by observing the motion of the upper ball relative to the motion of the lower ball. Each specific numerical example represents the moment when the upper ball separates from the lower ball.