Proceedings of the Edinburgh Mathematical Society

Research Article

On the Attractions of Spherical and Ellipsoidal Shells

Professor A. Gray

So far as I am aware, the methods, described below, of finding the attraction of a uniform shell of matter on a particle placed at external or an internal point, are new. They are particular applications of a method of finding the attraction of a thin shell uniform volume density bounded by similar and similarly situated ellipsoidal surfaces (what some have called a homothetic shell, and Thomson and Tait an elliptic homceoidœ) which I explained a paper, on the attraction of ellipsoidal shells and of solid ellipsoids, which was published in the Philosophical Magazine for April 1907. I give here also a short account of the more general problem with some additional notes and remarks. The solution depends on a geometrical theorem of some interest which occurred me in thinking over the problem of the ellipsoidal shell, and its solution by Poisson by a laborious and somewhat difficult process integration (Me'moires de I'Institut, t. xv., 1835).

(Received June 01 1913)

(Revised June 13 1913)