ISDEXED c , 



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THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES.] 

 % 1>\ 



APRIL 1907. -n 



XXXI. The Attraction of Ellipsoidal SI tells and^of 



Ellipsoids at External and Internal Points, with some 

 Historical Notes. By Andrew Gray, LE7T^F.R.S., 

 Professor of Natural Philosophy in the University of 

 Glasgow*. 



1. WROTE out the greater part of the following paper 

 A while on a holiday this summer, and was not aware 

 until my return home that the method given below 

 (§§ 24, 28 to 30) for the determination of the potential 

 of a nomothetic ellipsoidal shell had been anticipated by 

 a passage in Thomson and Tait's c Natural Philosophy ' 

 (Part ii., § 525). That also, I have since found, had been 

 anticipated in § 24 of the beautiful memoir by Chasles, 

 " Sur ^attraction d'une couche ellipso'idale," in the Journal 

 de VEcole Polytechnique (t. xv., 1835). The investigation 

 contained in §§ 14 to 18 below is, however, quite distinct, 

 and I think new. It gives a complete solution of the 

 problem of the shell and the ellipsoid, and leads naturally to 

 the other discussion already referred to, which differs in some 

 respects from the solution of Chasles. I have, moreover, 

 worked out in detail some particular problems. With all 

 due acknowledgment, therefore, I venture to allow my notes 

 to stand. I am aware of course of the recent discussions of 

 the problem, for various laws of density, by Ferrers, Dyson 



* From the 'Proceedings of the Royal Philosophical Society of Glasgow/ 

 1906. Communicated by the Author. 



Phil. Mag. S. 6. Vol. 13. No. 76. April 1907. 2 E 



