Theme E results and an idealized model are presented that yield energy dissipation rates as a function of radius for liquid-filled, precessing, spherical cavities. Experiments were conducted using cavities 11, 16.5, and 22cm in diameter and filled first with water to give turbulent flow conditions, and next with a silicone liquid (v = 1000 cs) to give laminar flow conditions. The objective of the experiments was to determine whether energy dissipation would be minimized, for a given mass of liquid, by using many small cavities rather than one, or a few, large cavities. An affirmative result would indicate that the use of baffles in a large cavity might, in the same manner, reduce energy dissipation.