XXIII. Theorems on the attraction of ellipsoids for certain laws of force other than the inverse square
Open Access
- 31 December 1895
- journal article
- Published by The Royal Society in Philosophical Transactions of the Royal Society of London. (A.)
- Vol. 186, 897-950
- https://doi.org/10.1098/rsta.1895.0023
Abstract
1. To find the potential at an internal point P of a thin ellipsoidal shell bounded by similar concentric ellipsoids, the law of force being the inverse k th power of the distance. Let ( x, y, z ) be the coordinates of P; ( l, m, n ) the direction cosines of a radius vector drawn from P to any point Q on the surface; and let PQ = r . Let ( a, b, c ) be the semi-axes of the ellipsoids, and ( α, β, γ ) their squared reciprocals. Then from the equation of the ellipsoid ( αl 2 + βm 2 + γn 2 ) r 2 + 2 ( αlx + βmy + γnz )r - (1 - αx 2 - βy 2 - γz 2 ) = 0.Keywords
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