THE 



PHILOSOPHICAL MAGAZINE 



AND 



ANNALS OF PHILOSOPHY. 



[NEW SERIES.] 



APRIL 1830. 



XXXIV. Letter relatmg to the Figure of the Earth. By 

 James Ivory, Esq. M.A. F.R.S. Sfc. 



To the Editors of the Philosophical Magazine and Annals. 

 Gentlemen, 

 T HAVE to request you will insert, in your next publica- 

 ■*- tion, the few lines which follow, relating to the figure of the 

 earth, on which I have formerly written in your Journal. It 

 is not my intention to add any thing new on this subject, but 

 merely to state briefly what 1 have contributed to the theory, 

 and to assert my claim to my own proper notions. 



1st, I have shown the insufficiency of Clairaut's theory, as 

 it is universally taught and applied, for finding the figure of 

 equilibrium of a homogeneous planet supposed fluid. 



The reason of the insufficiency is, that the theory inadver- 

 tently neglects the attraction between certain portions of the 

 fluid, and by this means omits to take into account pressures 

 prevailing in the interior of the mass and vanishing at the sur- 

 face, which cannot but have an influence on the figure of 

 equilibrium*. This remark alone overturns all the arguments 

 that have been urged against me in the foreign journals. 

 But, if the objections brought forward in these works fall to 



* Clairaut demonstrates the equilibrium from the single consideration 

 that the whole force at every point of the outer surface is perpendicular to 

 the surface. Besides the [jcrpendicularity of the whole force to the sur- 

 face, Maclaurin's demonstration essentially requires cert.iin properties pe- 

 culiar to the ellipsoid. How are the two demonstrations to be reconciled ? 

 The answer is, that Clairaut omits the internal pressures I iiavc alluded to ; 

 and when the inadvertence is corrected, the two modes of reasoning will 

 agree, or rather will be iilentical. Yet the pro[)crty of the ellijisoid, which 

 it essentiui to Maclauriu'tt reasoning, has been said to be accidental, and 

 not necessary. 



N. S. Vol. 7. No. 10. Ajiril 1830. 2 I the 



