32 



PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 



which form one end of the prism in their places. Now the surround- 

 ing particles will produce this effect, and it is obvious that the 

 action on any individual particle will vary as the number of particles 

 which act on it, supposing the positions left out of consideration. Thus, 

 suppose («) particles occupying certain positions to exert a force F, then 

 if two particles could be supposed to occupy the place of each one, 

 the force would become %F, and so on. Under these circumstances, 

 then, the repulsion on an individual particle would vary as the density, 

 and whatever be the mode of arrangement, the same law appears the 

 most simple and probable. Similar reasoning applies to the density of 

 the particles acted on, and we conclude that p oc Lf, 



Let p = \ elf ; 



dp r.dD 



dx dx ' 



t , dD P (dU dV\ 



and then -j— = — -j j— , 



dx c \dx dx J 



d*D P idU d 2 V 



dx' 



~ ~c \d& ~ ~d¥ 1 ' 



d 2 D P id*U 

 dtf c \ dtf 



d*D P [d*U 



dz 2 



-f( ! 



dz" 



d 2 V \ 

 dtf) 



drr 



dz 2 



(i); 



but 



d 2 V d"V d*V . __ 



-d¥ + dy* + ~d*=~^ Pn 



d 2 U d 2 U d 2 U 



+ S-T + —r^r = 



dx 2 



dtf 



dz 2 



(2). 

 (3). 



. d'D d 2 D d 2 B 



hence -j^- + -x-* + 



dx 2 



dtf 



dz 2 



= -f( 



P id 2 V d 2 V d'V 



dx 1 



dtf dz 



r) 



4ttP 2 



if we designate 



c 



4ttP 2 



D 



(4). 

 by « 2 



