in reply to M. Poisson. 



243 



M. Poisson's first objection to my investigation, is one of 

 his own imagining. In a homogeneous planet the surfaces 

 that possess the new property are all similar to the outer sur- 

 face, and similarly posited about the centre of gravity; and 

 therefore they cannot cross one another as M. Poisson sup- 

 poses. And in that part of my paper, where I have spoken 

 of the equilibrium of a homogeneous mass of fluid consisting 

 of particles that attract according to any law, the indefinitely 

 thin strata are constructed in succession by the principle in 

 § xxi. prem. part, of Clairaut's work on the Theory of the 

 Earth, that is, so that the thickness of a stratum, at any point, 

 is reciprocally proportional to the gravitation at the surface 

 on which the stratum is laid. The surfaces in question have 

 no reference to any points given in space ; but their relative 

 situation with respect to one another is determined ; they are 

 necessarily contained, one within another, which exempts them 

 from M. Poisson's argument. 



M. Poisson next (pp. 230, 231, 232) undertakes to examine 

 in what manner the equilibrium of a mass of fluid consisting 

 of attracting particles may remain undisturbed by the addition 

 of a stratum of the like attracting particles. Plis intention 

 is to prove that there may be an equilibrium in both cases, at 

 the same time that the stratum exerts unequal pressures upon 

 the surface on which it is laid. This would be directly con- 

 trary to my third proposition, and would destroy the whole of 

 my theory. It is ihei-efore necessary to consider this part of 

 M. Poisson's article with particular attention. 



Let ab c be a homogeneous mass of fluid in equilihrio by 

 the attraction of its particles 

 and a centrifugal force ; and 

 suppose that the equilibrium 

 still continues to take place 

 in the larger body ABC, 

 formed by laying a stratum 

 of the fluid upou the first. 

 Let A a i B be a canal of 

 which the branch ab is with- 

 in the interior body, and lies 

 along its surface ; and the 

 other two branches A a and ' 



BZi, perpendicular to the same 



surface, traverse the exterior stratum and end in the outer 

 surface. Because the whole body ABC is in cquilibrio, the 

 fluid in the canal will be so too, and will liave no tendency to 

 run out at cither of the orifices A, B. We must next esti- 

 mate the forces that urge the particles in tlic canal. Resolve 

 2 1 2 ail 



