THERMODYNAMIC AL SYSTEM OF GIBBS 99 



We may eliminate ZSnii and 25w2 from this equation, by means 

 of the equations of condition (75) and (76), so that it becomes 



-aMiXdniz - hMi^Lbrm + (a + b)M3X8mz ^ 0, (79) [28] 



so that, as XSms may be either positive or negative, 



-aMi - hMi + (a + 6)^3 = 0, 

 or 



aAfi + 6M2 = (a + h)Mz. (80) [29] 



The relation between the values of the potentials, each of which 

 is determined in a part of the system of which the substance 

 concerned is an actual component, is thus: 



am + &M2 = (a + h)iiz. (81) 



In a more general case, suppose that the system may be 

 considered as having n components Si, 82,- ■ ■ Sn, of which 

 Sk, Si, etc. can be formed out of the components Sa, Sb, etc., 

 according to the equation: 



a<Ba + /3®6 + etc. = /c®,. + X©i + etc., (82) [30] 



where <Sa, @6, ©a, ®z, etc., denote the units of mass of the sub- 

 stances Sa, Sb, Sk, Si, etc., and a, jS, k, X, etc., the numbers of 

 these units which enter into the relation. Then, as before, 

 (73) will reduce to 



M„26ma + Mb^bMb + etc + Mk'Ednik 



+ MiZSmi + etc. ^ 0. (83) [31] 



It is evidently possible to give 25Wa, S5m6, ^8mk, ^dnii, etc., 

 values proportional to a, 13, —k, —X, etc., and also to the same 



this reduces to 



MiS5mi + M22dm2 + MsSSjms ^ 0. (78) 



The limitation of values of 5m to zero, whenever they refer to parts of 

 which the component in question is not an actual component, does not 

 aflfect the range of possible values of SStoi, SSmj and S5wj and may be 

 disregarded. 



