XIII. On figures of equilibrium of rotating masses of fluid

Abstract

In a previous paper I remarked that there might be reason to suppose that the earliest form of a satellite might not be annular. Whether or not the present investigation does actually help us to understand the working of the nebular hypothesis, the idea there alluded to was the existence of a dumb-bell shaped figure of equilibrium, such as is shown in the figures at the end of this paper. These figures were already drawn when a paper by M. Poincaré appeared, in which, amongst other things, a similar conclusion was arrived at. My paper was accordingly kept back in order that an attempt might be made to apply the important principles enounced by him to this mode of treatment of the problem. The results of that attempt are, for reasons explained below, given in the Appendix. The subject of figures of equilibrium of rotating masses of fluid is here considered from a point of view so wholly different from that of M. Poincaré that, not with ­ standing his priority and the greater completeness of his work, it still appears worth while to present this paper.