THERMODYNAMICAL SYSTEM OF GIBBS 173 



These conditions may be expressed in terms of other sets of 

 variables. Thus using the variables of (252), we have 



P„ = 0, and Qn = 0, (265) 



where Q„ is the determinant formed by substituting the coeffi- 

 cients 



-—, -—,... ~ (266) 



dv ami dnin-i 



in any line of (254). For a system of one component, these 

 equations become 



\dv^/t,m ' \dv^)t,m 



Again, using the variables in (256), we have as the equations of 

 critical phases, 



Un-i = 0, and Vn-x = 0, (268) [208] 



where Fn_i is the determinant formed by substituting the 

 coefficients 



d^ dE^ MJ^ 12071 



drrii drrii dm n-i 



in any line of (258). For two components, these equations 

 become 



m =0, if-) =0. (270) 



Instead of making W2 constant, we may use as the variable 

 expressing the composition, a; = mi/(wi + W2). Then we have 

 as the equations of a critical phase 



\dx^/t.p ' \dxyt,p 



As an illustration of these relations we will return to a con- 

 sideration of the ^-composition diagram of a two component 



