186 Mr. Ivory's Remarks on the 56th Article of the 



account except those in action at the outer surface ; and it is 

 implied that the like forces, expressed by the same functions 

 of the coordinates, and no others but these, act upon every 

 interior particle of the mass. It follows from this view of the 

 matter that the level surfaces depend entirely on the outer 

 surface, and attempts are made to demonstrate this. Vide 

 Mec. Ccl. livre iii. J 22. 



On the other hand I contend that the figure of the fluid 

 will depend upon the forces that actually urge every particle 

 to move from its place : that, in a homogeneous planet in a 

 fluid state, there are forces prevailing in the interior parts, 

 which Clairaut has neglected: and that the equilibrium is 

 impossible, unless such a figure of the fluid can be found as 

 will set free the interior particles from those irregular forces. 

 For this purpose the true figure of equilibrium must possess 

 a property not deducible from Clairaut's theory ; and this new 

 condition, although it relates only to a particular problem, or 

 to similar problems, it is usual to call my new principle of 

 hydrostatics. 



In the 27th volume of the Annales deChimie ctde Physique, 

 p. 231, M. Poisson considers a homogeneous planet AB C, 

 supposed fluid and in equili- 

 brium. The interior surface 

 abc is similar and similarly 

 posited to the outer surface 

 ABC, on which supposition 

 the interior mass abc will be 

 separately in equilibrium if the 

 exterior stratum were taken 

 away. The narrow canal 

 AabB has its ends in the up- 

 per surface ABC, and the 



part between a and b is wholly within the interior mass abc. 

 M. Poisson proves that the equilibrium of the whole canal re- 

 quires this equation, 



8 = q p 9 or p = q 8 ; 



p and q being the weights of the canals A a and BZ>, and 8 the 

 effort of the fluid in the canal a b, acting from a to b and 

 caused by the attraction of the matter between the two sur- 

 faces. Now I observe that M. Poisson, by allowing that the 

 stratum attracts the particles within it, and by calculating the 

 pressure 8 produced by its action, admits the omission made 

 by Clairaut, and in reality proves that the theory of that geo- 

 meter is insufficient for solving the problem. For there is 

 no force at the outer surface A B C, similar to the attraction 



of 



/^\\ /r^\ 



s~^ v 

 / /^ ^b^ \ 



I ( ) 



V ^^-~-^_~^^ J 



>v c . 



^\ ^^^ 



