46 PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 



4nrl 3 



27. The value of the second force is also 2 .qMP, calling the 

 exterior or mean density q. 



28. To obtain the third force, we must divide the displaced caloric, 

 or rather a portion equal to it placed in a position directly opposite, 

 into two portions; the one containing all that is included in a sphere 

 whose centre is the centre of A, and radius the distance to that point 

 of B which is nearest to A ; the other, the portion arising from the 

 spherical shell included between two surfaces to radii equal to the 

 distances of the nearest and most distant point of B, from the centre 

 of A. 



The former of these is easily found as in (16), equal to 



4* MP A , (1 + ^ _ e _ a(a _ t) I3| + a {a _ l ^ 



a 2 a L ' " 



To obtain the latter, we will first omit the consideration of the 

 portion which would occupy the place of B, supposing that particle 

 removed, and consequently take no notice of the quantity which ought 

 to be displaced there; by this means, it is obvious that we shall estimate 

 the attraction a little too highly; and we shall see that the portion, 

 taken as we have supposed, is actually less than would be obtained by 

 conceiving the mass of B collected at its centre ; consequently the whole 

 attraction is considerably less than that given in (20). Now we saw 

 that the resultant action even on that calculation was essentially nega- 

 tive, it appears then that a more rigorous analysis increases rather than 

 diminishes the difficulty attendant on an attractive atmosphere of caloric. 



29. Let us then proceed to the calculation. 



The action of a mass of caloric in a spherical shell of thickness 8B, 

 whose radius is R on a similar portion of a shell of the body B at 

 radius p, is easily seen to be* 



AMP 4nrR*$Be- aR , rfa . , . .. ''?< 

 v . ^ • UJ 2 f sin d P d( t> cos 0) ; 



* For the construction of the figure, &c. see the Note (a) at the end. 



