345 



in one or more of the phases which arise at increase of volume, then 

 ^i^..v)fj is positive and, in accordance wilh (15) therefore also {dP)x. 



When, liowever, the new substance occurs only in one or more 

 of the phases which arise on decrease of volume, then ^(A.};)^/ is nega- 

 tive and therefore, also {dP)x is iiegative. 



Hence we may deduce the following rules: 



When we add a new substance to an invariant equilibrium 

 £{j; = 0) then a monovariaut equilibrium E occurs, which we 

 represent in a P, T-diagram by a curve E; when the new substance 

 occurs only in one or more of the phases, which arise at the iso- 

 volumetrical reaction on addition (withdrawal) of heat, then the 

 temperature is lowered (raised); consequently curve E proceeds 

 starting from its invariant beginning-point towards higher (lower) 

 pressures. 



In some cases we may also deduce something on the direction of 

 curve E in its invariant beginning-point in the following way. We 

 assume that the new substance which is added to the invariant 

 equilibrium: 



Fix = 0) = F, + F, -f . . . . + F, + ^^+1 + .... + ^«+1 



occurs only in the phases Fg^i . . . Fn^i and, therefore, not in 

 F^, F^ . . . Fq. This is surely the case when F^ . . . Fq are phases of 

 constant composition. When we take away from the equilibrium E 

 the phases -^5-1-1 • • . Fn^\, than we keep an plurivariant equilibrium 

 F^ . . . Fq-, this is represented in the P, 7'-diagram by a plurivariant 

 regjpn. As curve E must be situated in this region, hence follows 

 the said-above. In the special case that the new substance occurs 

 in one of the phases only, curve E coincides, therefore, with one 

 of the monovariant equilibria of the equilibrium E{.v = 0). 



Before applying those considerations to some cases, firstly I will 

 draw the attention to some points, which have been already discussed 

 before. When we know of the isovolumetrical and isentropical 

 reaction the ratio of the coefficients ?.^ }, . . . . and also in which 

 direction those reactions proceed on addition of heat or on increase 

 of volume, then we shall say that those reactions are known quan- 

 titatively. When we know, however, only the signs of ^j A, ... . 

 and also in which direction the reactions are proceeding on addition 

 of heat or on increase of volume, then we shall say that the 

 reactions are known qualitatively. Then we only know which phases 

 are at the one side and which at the other side of the reaction-sign. 



