Abstract
The bob of a spherical pendulum (or particle on a smooth sphere under gravity) oscillates between two levels, and the change of azimuth in passing from the lower to the higher level, or vice versa, is the same for all such passages during a single motion. Using the language of orbit theory, we shall refer to this change of azimuth as the apsidal angle. It is a function of the two constants of the motion, total energy and angular momentum, but the remarkable fact is that the apsidal angle a always satisfies the inequalities
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