1676 
Chemistry. — “/n-, mono- and divariant equilibria.” IX. By Prof. 
F. A. H. SCHREINEMAKERS. 
(Communicated in the meeting of April 28, 1916). 
18. The direction of the curves in the invariant point. 
In the previous communications we have deduced the P, 7-diagram- 
types without knowing the changes in volume and entropy which 
occur at the reactions. When we know those also, however, then 
we may not only find the P,7-diagramtype, but also the diagram 
itself, viz. the direction of the curves in the invariant point. 
We know that all reactions which may occur between the phases 
of an invariant point, are completely defined by two reactions. 
When we know also the changes in volume and entropy, which 
occur at those reactions, then those changes are known also for the 
other reactions. 
Let one of the reaction-equations be: 
LF, +UF, +... LF ne Ene Tes 0D) 
At the proceeding of this reaction a change in volume and a 
change in entropy occur; we represent the first by AV), the second 
by An. 
Where these changes present themselves we write them behind 
the reaction-equations and first the change in volume, afterwards 
the change in entropy. Consequently we write for (1): 
Liat lb 30) AVS she Ang cae nen 
Herein we may express AV, and Ay by: 
AVi = lv, + lv, +... + bm delen - . « (8) 
An =n, +4n,+..-+thnpt---trtemnte . . « (4) 
Herein v, and y, represent the volume and the entropy of the 
unity of quantity of a phase F,. We take as second reaction- 
equation: 
mF, +... + mpte Fra = 0 Sn (Mie or ve (B) 
When we deduce from (2) and (5) an arbitrary other reaction: 
(Kl,+m,)F,+(Kl,+m,)\F,+...=0 KAV AV; KAn+ Ann. (6) 
then the change in volume is AAV;+ AV, and the change in 
entropy KAn, Ayn. 
When we give to A such a value, that Al, + m, = 0, then (6) 
represents the reaction, which may occur between the phases of 
the equilibrium (/,) and the change in volume and entropy belonging 
to this reaction. Hence follows: 
