THE 



PHILOSOPHICAL MAGAZINE 



AND 



ANNALS OF PHILOSOPHY. 



[NEW SERIES.] 



OCTOBER 1827. 



XLI. On the Figure of Equilih-ium of a Homogeneous 

 Planet in a Fluid Slate ; in reply to the Observations of 

 M. Poisson, 'published in this Journal for Julij last. By 

 J. Ivory, Esq. M.A. F.R.S. 



[Continued from p. 168.] 



TN the last Number of this .Tournal I have investiffated the 

 ■*- figure of a homogeneous planet entirely fluid. By a pro- 

 cess of analytical reasoning founded on the homogeneity of 

 the fluid, and the nature of the forces urging the particles, I 

 have shown, what is contrary to the usual theory, that two 

 conditions are necessary to the equilibrium of the whole mass. 

 I have next proved that, when both conditions are fulfilled, 

 the planet will have a permanent figure, and that this will not 

 be the case, if either of them be wanting. This solution is not 

 difftirent fiom the usual theory, except in one of the conditions, 

 to which objections have been made; and, as we shall chiefly 

 have occasion to sj^eak of this condition, it may be proper to 

 recall what it consists in to the recollection of the reader. 



Conceive a level surface in the interior of the j^lanet, and 

 let V denote the sinn of all molecules contained within the 

 level surface divided by their respective distances from any 

 point assumed in that surface, and A.V, tlie like sum for all 

 the molecules exterior to the same surface; then the new pro- 

 perty of the equilibrium consists in this, that A.V must have 

 a constant value for all the points in the same level surface. 

 The invariability of A.V leads to some curious consecjuences. 

 In the first place, A.V merely augments the j)ressnre in the 

 ccjuation of the level surface, thereby showing that the action 

 of the exterior stratum upon the interior fluid has no other 

 effect than to cause a pressure that is ecjuable on all parts of 



Nevs Series. Vol.2. No. 10. Oct. 1827. 2 I the 



