PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 33 



10. The solution of this equation will be found in various Memoirs 

 of M. Poisson and others: it is 



4g-aV(i,-i)»+(j r ,)« + (j,-0» 



Z> = 2 



the symbol 2 having reference to points whose co-ordinates are x t , y t , % r 



With respect to the points in question there can be no difficulty, 

 for, from the form of the solution, it is evident that the medium is 

 influenced symmetrically with respect to any such points, and moreover, 

 the solution of (2) will give V a function of the same quantities, 

 whence equation (1) will determine U to be a function of the same; 



M 



but the value of U being 2 -=* it is obvious that all the quantities 



are functions only of R, or of \/{X— x) 2 + (Y—yf + (Z — %f, 

 hence the value of D becomes 



^ e -a\/(X-x)* + (r-y)*+(Z-z)> 



Z> = 2 



= 2 



Vrx-xf + (r- y y + <z- %y 



Ae- aR 

 B ' 



11. It may be remarked, that in this solution, as in the corres- 

 ponding one in my treatise on Heat, I have departed slightly from 

 M. Mossotti's Memoir, by considering the attraction or repulsion of 

 a particle on another, to be proportional to the product of their masses, 

 so that P 2 , MP, M 2 are respectively the forces exerted at the distance 

 unity, by P acting on P, P acting on M, and M acting on M. The 

 reasoning of M. Laplace, to which M. Mossotti refers for the proof 

 of the theorem that the pressure varies as the square of the density, 

 I have not retained, as I conceive it does not take notice of the real 

 point of difficulty ; namely, that the force which constitutes the right- 

 hand side of the equation, is not the force on any individual particle, 

 unless the sums are so expressed as to indicate the small variations due 

 to the rapid change of action of those particles immediately surround- 

 ing that acted on. Indeed, were they the real actions, their sum would 

 Vol. VII. Part I. E 



