Chemistry. — ‘“J/n-, mono- and divariant equilibria’. XX. By 
Prof. ScHREINEMAKERS. 
(Communicated at the meeting of November 29, 1919). 
Equilibria of n components in n phases, in which the quantity of 
one of the components approaches to zero; the influence of a 
new substance on an invariant (P or T) equilibrium. 
In the communications XVI, XVII and XVIII we have seen 
that a region is two-leafed in the vicinity of a turning-line and 
one-leafed in the vicinity of a limit-line [e.g. curve ab or ed in 
fig. 1 (XVI)]. We shall consider the latter case more in detail. 
We take the equilibrium H=— #, + F,...+ HK of n components 
in 2 phases under constant pressure. This equilibrium is (Comm. 
XVII) monovariant (P); viz. it has one freedom under constant pressure. 
The equations (2) and (3) (XVII) are true for this equilibrium; 
on change of one of the variables e.g. of x, this equilibrium traces 
in the P,7-diagram a straight line parallel to the Z-axis. 
In the vicinity of a limit-line of a region e.g. in the vicinity of 
curve ab or cd in fig. 1 (XVI), the quantity of one of the com- 
ponents approaches to zero. When this is the case with the 
component X, viz. with that component, the quantities of which 
are indicated in the different phases by w,a,...a,, then in (2) and 
(3) (XVII): 
: OZ, OZ, OZ n 
Ox, , On, ; ay Òzn 
become infinitely large, viz in Z, the term 2, /og x, is found, in Z, 
the term w, log a, ete. 
Now we write: 
Z,=Z, + RY x, log x, D= IRI le « o (Ì) 
Herein Z,’ Z,’... and their differential quotients remain always 
finite also for z, — 0, 2,0... It follows from (4): 
Oy VE care 
= + RT (1 + loge) 
Ou, Ow, ; 
Wipe (2) 
07, 07," ry 
== + RTL + log «,) 
Oz, Oa, 
ete. The m equations (2) (XVII) now pass into: 
