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On the Attractions of Spherical and Ellipsoidal Shells


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).

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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