24-4 Mr. Ivory on the Figure of' the Planets^ 



all the forces which act upon the molecules in the branch A a, 

 and multiply every molecule by all the resolved forces which 

 urge it in the direction of the canal from A to a, and call the 

 sum of the products jj. Let q denote the like sum of all the 

 molecules in the canal B b respectively multiplied by the forces 

 which urge them in the direction of the canal from B to C. 

 With respect to the branch ab, M. Poisson observes that we 

 may neglect the centrifugal foixe of the particles contained 

 in it, and the attraction of the interior body a b c upon them ; 

 because these forces acting perpendicularly to the surface a ic, 

 which is in eqicilibrio separately, have no tendency to produce 

 motion in the canal. The attraction of the exterior stratum 

 is the only remaining force that acts upon the fluid in the ca- 

 nal ab, and we shall put I for the sum of the products of all 

 the molecules multiphed respectively by the attraction of the 

 stratum resolved in the direction of the canal from a to b. We 

 now obtain this equation, 



p + — q = 



which expresses that the fluid has no tendency to run out at 

 the orifice B. This equation coincides with what M. Poisson 

 has obtained, p. 232*, and of which he remarks p. 233, " C'est 

 de cette maniere que I'equilibre de la masse interieure n'est 

 pas trouble par les pressions inegales exercees sur la surface 

 aba par la couche fluide qui I'enveloppe de toutes parts." 

 Now this supposes that S stands for some determinate value in 

 the foregoing equation. But innumerable canals may be made 

 to pass from a to b along the surface of the interior body ; and, 

 as the same reasoning will apply to all, S will stand for the 

 sum of the products of the molecules in any one respectively 

 multiplied by the attraction of the exterior stratum reduced in 

 the direction of the canal. Not only so, but 5 will stand for 

 the sum of the like products in innumerable other canals 

 passing from a to b through the fluid mass abc; for the rea- 

 soning requires nothing more than that the canal have its ends 

 at a and b in the surface of abc, and that it be wholly con- 

 tained within that surface. It is plain therefore that 8 can 

 have no determinate value, and that the foregoing equation 

 cannot be true, unless 8 = 0, and ]) = q. Thus the pressures 

 of the exterior stratum upon the surface on which it lies, are 

 equal, and not unequal as M. Poisson alleges. We may 

 arrive at the same conclusion more readily by continuing the 

 canal ab all round the surface of abc, so as to return into 

 tself : ior then 8 must have the same value in the two parts 

 of the canal going from a to b either way; and as these parts 



* Ann. de Chimie ct dc Physique, toiii. xxvii. 



