(8) 



342 



As we do approacl) the quantity of the component X to zero, 

 we put again : 



Z, = Z\ + RTx^ log X, Z, = Z\ -f RTx^ log .r, . (4) 



etc. In similar way as we have done formerly, now we tind : 



Hi dT — Vi dP + ET.xi + yidl--]+... =—dK . (5) 



t=l,2,....(n+ 1) 

 X, = j[i, .tTj .r, — fi, .r, . . . . ar„^i = /«„^.i .t-, ... (6) 



èZ\ dZ', dZ'„_Li 



d~-^ = d--^ = ....=d~~''-^ = dKy . . . . (7) 



To these equations (7) must be added the corresponding equations 

 for the variables z^ z, . . . Ui u,. The sign d indicates that there 

 must be differentiated with respect to all variables. 



Now we add to one another the n-J-1 equations (5) after having 

 multiplied the first with Aj, the second with A,, etc. Then we obtain : 



2 (W) .dT — 2iXV).dP-^ RT :E (Xx) + ^ {Xy) dKy + 

 + 2 (kz) .dK,-\- = — :E {,).). dK 



Now we put : 



2(X)-=0 of A, + A, + . . . . + K+x '-^ j 



2: {Xx) — of X,x, + X^x^ -h . . . + A„+i ^„+1 = . . (9) 

 :E {Xy) == of A,?/, + A,?/, 4- . . . + A„_|_i 7/„_|_i = » 



etc. but not ^ (A//) and S (XV). 



Then we have ?i equations, so that that the n latio's between 

 A, A, . . . A,i_j_i are defined. The reaction : 



;.,/'\ + >l,F, + .... + A„+iF„+i = .... (10) 



which may occur in the monovariant equilibrium I*J, when the 

 quantity of the component A' is infinetely small, is, therefore, also 

 defined. We shall call this equilibrium, which differs extremely 

 little from E{x = ó) the equilibrium E {Lim x = o) or shortly the 

 equilibrium E{x). With the aid of (9) now (8) passes into: 



rdP\ 2 (XH) 

 _ — — L_^ ....... (11) 



wherein A, A, are defined by (9). 



Consequently the direction of the tangent to curve ^ in its 

 invariant point of begijining or terminating i (x = o) is defined by 

 (11). The relation (7) (XIX) is, therefore, true also when the quan- 

 tity of one of the components approaches to zero. 



