1. On the Figures of Equilibrium of a Rotating Mass of Fluid

Extract

(a) The oblate ellipsoid of revolution is proved in Thomson and Tait's Natural Philosophy (first edition, § 776, and the Table of § 772) to be stable, if the condition of being an ellipsoid of revolution be imposed. It is obviously not stable for very great eccentricities without this double condition of being both a figure of revolution and ellipsoidal.

(b) If the condition of being a figure of revolution is imposed, without the condition of being an ellipsoid, there is, for large enough moment of momentum, an annular figure of equilibrium which is stable, and an ellipsoidal figure which is unstable. It is probable, that for moment of momentum greater than one definite limit and less than another, there is just one annular figure of equilibrium, consisting of a single ring.