XX. On the attractions of homogeneous ellipsoids

Abstract

1. The theory of the figures of the planets involves in it two distinct researches. In the first of these, it is required to determine the force with which a body, of a given figure and density, would attract a particle of matter, occupying any proposed situation: in the second, the subject of investigation is the figure itself, which a mass of matter, wholly or partly fluid, would assume, by the joint effect of the mutual attraction of its particles, and a centrifugal force arising from a rotatory motion about an axis. To render the second of these inquiries more exactly conformable to what actually takes place in nature, the influence of the attractions of the several bodies, that compose the planetary system, ought to be super-added to the forces already mentioned. It is the first of these two researches, of which we propose to treat at present; and we shall even confine our attention to homogeneous bodies, bounded by finite surfaces of the second order.