On the attractions of homogeneous ellipsoids / [Sir James Ivory].

  • Ivory, James, Sir, 1765-1842.
Date:
1809
Catalogue details

Licence: Public Domain Mark

Credit: On the attractions of homogeneous ellipsoids / [Sir James Ivory]. Source: Wellcome Collection.

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    leave no room for perfecting the theory of the attractions of ellipsoids hi both these respects. It consists in shewing that the expressions for the attractions of an ellipsoid, on any ex¬ ternal point, may be resolved into two factors ; of which, one is the mass of the ellipsoid, and the other involves only the excentricities of the solid and the co-ordinates of the attracted point: whence it follows, that two ellipsoids, which have the . same excentricities, and their principal sections in the same planes, will attract the same external point with forces pro¬ portional to the masses of the solids. This theorem includes the extreme case, when the surface of one of the solids passes through the attracted point: and by this means the attraction of an ellipsoid, upon a point placed without it, is made to de¬ pend upon the attraction which another ellipsoid, having the same excentricities as the former, exerts upon a point placed in the surface.* Le Gendre has given a direct demonstra¬ tion of the theorem of La Place, by integrating the fluxional expressions of the attractive forces; a work of no small diffi¬ culty, and which is not accomplished without complicated cal¬ culations.-f In the Mecanique Celeste, the subject of attractions of ellipsoids is treated by La Place after the method first given by himself in the Memoirs of the Academy of Sciences, J founded on the theory of series and partial fluxions. It was in the study of La Place's work, that the method I am about to deliver, was suggested; and it will not be altogether un¬ worthy of the notice of the Royal Society, if it contribute to simplify a branch of physical astronomy of great difficulty, and which has so much engaged the attention of the most eminent mathematicians. * Acad, des Sciences de Paris pour 1783. f Ibid. 1788. % For 1783.