663 



direction of this tangent is defined by a : a^ or by (9). Consequently 

 curve Er has a form as uSv in figs. 1 or 2. In tig. 1 it forms a 

 turning-point in S, in fig. 2 a cusp. It follows, however, from (13) 



ZAT 



and (14) that LP: L.T is larger in the one case and smaller in the 

 other case than dP : (IT = a : n^; consequently curve Er has a 

 turning-point as in fig. 1. 



In our considerations on the region E in fig. 7 [XVI] we 

 have already used this result; we have viz. drawn there the 

 turning- line M Sm in the point S with a turningpoint. 



In the previous communication we have deduced for an equili- 

 brium of n components in n phases under constant pressure: 



When ^(kH) and 2{?.(l'Z) have the same sign, then 7Ms maximum; 



When 2{)^H) „ 2{Xd'^Z) have opposite sign, then T is minimum ; 



When 2!{ld^Z) = then T is neither maximum nor minimum. 



Similar properties are valid for equilibria of 7i components in n 

 phases at constant temperature. 



Let us assume now, for fixing the ideas, that 2{).H) is positive 

 on the turning-line MSni in fig. 7 [XVIJ. Then it follows from the 

 rules mentioned above, that 2{hl^Z) must be positive in each point 

 of the branch mS and negative in each point of branch MS. In 

 accordance with (12), however, ^\).d^Z) = in the point S. When 

 we draw in the figure a horizontal or vertical line through the point 

 *S', then we see that this line does not trace the three-leafed-region; 

 under the pressure Ps, therefore, the temperature is neither maximum 

 nor minimum and at the temperature Ts the pressure is neither 

 maximum nor minimum. 



Equilibria of n compo7ients in n phases in the concentration- 

 diagram. 



Until now we have considered the equilibria £■ in the PjJ'-diagram ; 

 now we shall briefly discuss their representation in the concentration- 

 diagram. The composition of a phase, which contains n components, 



48* 



