414 d. W. Glbhs — Equilibrium of Meter ogeneotis Substances. 



all the quantities relating to the system as functions of jv', and the 

 condition of stability may be written 



de ^ , 1 cPe ^ ,^ . 



where € denotes the total energy of the system. Now the conditions 



of equilibrium require that 



ds 



Hence, the general condition of stability is that 



d^£ ^ / V 



,for. > »• (^") 



Now if we write s', e", e^ for the energies of the two masses and of 

 the surface, we have by (86) and (501), since the total entropy and 

 the total quantities of the several components are constant, 



de = de' + dt" + de^ — ~p' dv' —p" dv" + <? ds, 



or, since dv" = — dv', 



*=-/+^" + .*. (542) 



Hence, 



d'^s _ dp' dp" da ds d^s (tiA'i\ 



and the condition of stability may be written 



d^s dp' dp" do' ds 

 ^ d^^ ^d^'~d^^d^' d^'- ^^ ^ 



If we now simplify the problem by supposing, as in the similar case 

 on page 409, that we may disregard the variations of the tempera- 

 ture and of all the potentials except one, the condition will reduce to 



The total quantity of the substance indicated by the suffix j is 

 Making this constant, we have 



{r: - r.' + r. *)<.„■+(.' g + „.|i: + . |:.).,.=o, (mo) 



The condition of equilibrium is thus reduced to the form 



djUi djUj^ d/i^ 



