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XL. Some Remarks on an Article in the " Bulletin des Sci- 

 ences Matheraatiques" ybr June 1829, §269. 5j/ James 

 Ivory, Esq. M.A. F.B.S. ^c* 



A S I am preparing a treatise on the Theory of the Figure 

 ■^^ of the Earth, I had resolved to take no notice of the ob- 

 jections advanced against the physical conditions I had found 

 necessary for the equilibrium of a planet supposed fluid and 

 homogeneous : the observations in the BuUetiri have induced 

 me to depart a little from the resolution I had adopted. 



I shall use the symbols C and A to denote, respectively, the 

 whole mass of the planet, and any interior portion bounded 

 by a continuous surface. We shall succeed best in throwing 

 light on this subject if we begin with estimating the forces that 

 act upon a molecule of the fluid in the surface of A. I shall 

 demonstrate that, when all that is implied in the hypothesis 

 of the problem is taken into account, there are three distinct 

 forces which act upon every such molecule ; whereas, accord- 

 ing to Clairaut's theory, there are only two of the same forces 

 in action, the third being omitted. But, it may be observed, 

 this is not to be ascribed to any imperfection of the theory 

 mentioned ; for the force neglected cannot possibly be in- 

 cluded in any general theory, because it is a consequence of 

 the particular hypothesis of the problem. 



In the surface of A assume a molecule of the fluid which 

 I shall call m. As the author in the Bulletin has estimated 

 the forces acting upon m, which he represents by K, R', R", 

 I shall borrow from him. The first force R is the x-esultant 

 of the centrifugal force and the attraction of A. The second 

 force R' is the action upon m of the stratum C — A, caused by 

 all the forces that urge the particles of the stratum. The third 

 force R" is the action upon m, caused by the attraction of the 

 stratum C — A upon the particles of A. According to the 

 hypothesis of the problem all the matter of C — A will at- 

 tract every particle of A ; and these attractive forces must 

 produce pressures which, being propagated from particle to 

 particle, will urge w, and every molecule in the surface of A, 

 to move from its place. Suppose that the centre of gravity of 

 C — A falls within A, and conduct a canal from that centre to 

 in : then the effect of R" perpendicular to the surface of A 

 is equal to the hydrostatic pressure caused by the attraction of 

 C — A upon the fluid in the canal. The force R" is therefore per- 

 fectly well defined ; and, from what is said, it is easy to find the 

 analytical expressions of the partial forces, pai-allel to the co- 



• Communicated by the Author. 



ordinates, 



