44 PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 



due to a mass of particles equal to those displaced by the repulsion, 

 and situated in the places from which they have been driven off; we 

 shall get 



dD P (dU _ dV\ 



dx c \ dx dx 



dx 2 c \ dx 2 dx' 



"-)■• 



P id 2 U d 2 V'\ 



V 



f l (TV' &'V d'V'\ 

 dx^ '*"dy T "*" W e \~dx r + ~df + ~dtf~) ; 



d 2 D d 2 D d 2 D P (d 2 V d 2 V d 2 V 



and — r- 5- + — r? + 



, v d 2 V d 2 V d 2 V , _ , 



but -da? + df + dz 2 =-^ P <l> 



d 2 V, d 2 V, d 2 V t : _ 



d 2 (V-V) d 2 {V-V) d*{V-V) A h . k 



•'■ dx 2 + dy 2 + M ; =-^(?-g)> 



d 2 V d 2 V d 2 V' D _ 



or iM + iitf + -dir = -^ PD > 



d 2 D d 2 D dTD 4ttP 2 

 • • rf* 2 + rfy 2 + d% 2 ~ c '"' 



= a 2 D; 

 the solution of which equation is 



Ae« R . 

 R ' 



and, as in the former case, it evidently follows that 



B Ae~ aR \ 4ttP 



\R R J " a 2 



24. By employing a process precisely analogous to that in (13), 

 we obtain the value of V directly, taking into the account the caloric 

 displaced by the material particles ; the expression is 



' ~ a 2 ^1 R R ) + 3 ' ?n i' 



