in reply to M. Poisson. 245 



are entirely arbitrary, it manifestly follows that 8 can have no 

 other value but zero. In reality the reasoning of M. Poisson, 

 when pushed to the proper conclusion, turns out to be a de- 

 monstration of my third proposition. 



But it is unnecessary to consider particularly the manner 

 in which the stratum acts upon the interior fluid body ab c. 

 For the exterior matter can produce no action on the interior 

 fluid, except through the intervention of pressures on the sur- 

 face, and the continuance of the equilibrium requires that these 

 pressures be equal. 



I have already sufficiently replied to what is contained in 

 pp. 234, 235, of M. Poisson's article in a note, p. 165, of the 

 last Number of this Journal. 



It does not appear that M. Poisson has refuted my theory 

 of the equilibrium of a homogeneous planet; and he never will 

 be able to refute it. 



There is still one point relating to this subject that seems 

 to require some elucidation. It is the case of a planet very 

 little different from a sphere. This case is the more deserving 

 of attention, because the solution of it seems to be deduced 

 solely from the equation of the outer surface of the fluid. The 

 discussion of this matter would make too great an addition to 

 what I have written ; but I will enter upon it at a future occa- 

 sion, and I will show that the equilibrium can no more be in- 

 ferred from the equation of the surface in this case than in 

 any other, and that in reality there are other principles, be- 

 sides that equation, concerned in the investigation. 



I shall conclude at present, with noticing the postscript to 

 M. Poisson's observations inserted in this Journal for July last. 

 It relates to the heat absorbed or extricated, or, which is the 

 same thing, to the variation of temperature, when a given 

 mass of air changes its volume and at the same time retains 

 the whole of its heat. It is not, however, to the formula (6) 

 of his Memoir in the Conn, des Terns 1826, that I object, but 

 to the use that is made of it, and to the integrals (7) and (8) 

 derived from it. 



In order to elucidate this matter, I shall take the formula 

 (6), Conn, des Terns, 1826, p. 263, viz. 



cu = (/:- 1)(1 + «fl). -^: 



here 9 is the original temperature of the given mass of air; 

 a is the (hhitation of gas for one degree; w is the increase of 

 temperature, or the heat extricated, when the air suffers the 

 small condensation y ; and k — I is a number deduced from 

 the experiment of MM. Clement and Desornies. Let f denote 



the 



