246 J. W. Gibbs — Equilibrium of Heterogeneous Substances. 



potentials for those components which it is convenient to regard as 

 the ultimate components of the gas-mixture. 



In the case of a binary gas-mixture with convertible components, 

 the components will have the same potential, which may be denoted 

 by //, and the fundamental equation will be 



Ci+ a, // — -£/, c.2-i-a.2 /U — E2 



p = a^L^t e -\-a.^L^t e ^ , (342) 



where 



From the 'general equation (93) with the preceding eqiiations the 

 following is easily obtained, — 



c^ [i—E^ Cj^ li — Ej 



--L^{c^t^E^)t"" e "'^ ■^L^{c^t^E.^)f' e "-'^ . (346) 



We may obtain the relation between jo, t, v, and ni by eliminating 

 pi from (342) and (345). For this purpose we may proceed as follows- 

 From (342) and (345) we obtain 



Cj -t-a, fJ-—Ei 



C j + Ct2 /^ — -5*2 



a^t p — (a^ - Uo) E^t ' e ' ; (348) 



and from these equations we obtain 



a, log Ip-a^t^-^j-a^log ia,t"^-p] = {a^ - "3) log (a,— aj 



E — 7^ 



+ a,logii-«2log^-'3+(^'2-''2+^«i-«2)log« --r-^' (349) 



