713 
Chemistry. — “/n-, mono- and divariant equilibria.” XI. By Prof. F. 
A. H. SCHREINEMAKERS. 
(Communicated in the meeting of Oclober 28, 1916). 
18. Binary systems with two indifferent phases. 
After the general considerations [Communication X | about systems 
with two indifferent phases, we shall apply them now to binary 
systems. 
When in the invariant point of a binary system occurs the equili- 
brium: MH MH Ft F,, then only one type of P,7-diagram 
exists; we find it in fig. 2 (I). 
When in a binary system, however two indifferent phases occur 
and, therefore, also two singular phases, then two types of P,7- 
diagram exist | figs. 1 and 2]. We may deduce them in different ways. 
When in the concentration-diagram of fig. 2 (1) /’, and F, are the 
indifferent phases, then /’, and F’, are the singular ones; /’, and #, 
have then the same composition, so that the points /, and /’, coin- 
cide [fig. 1]. Then we have the singular equilibria: 
(M)=F,+ fF, [Curve (M) in fig. 1] 
F=f, HEE, [Curve (3) in fig. 1] 
(Ff) =Ff,+f,+ 7, [Curve (4) in fig. 1] 
and further the equilibria: 
(F)=f,+f,+ /, [Curve (1) in fig. 1] 
B) HE, HF, [Curve (2) in fig. 1). 
We may deduce the type of P,7-diagram from fig. 2 (I). As (5) 
and (4) are the singular curves, they must, therefore, coincide. It 
follows from our previous considerations that this coincidence may 
take place in fig. 2 (1) only in such a way that curve (3) coincides 
with the prolongation of (4) and therefore also curve (4) with the 
prolongation of (3). Then we obtain a type of P,7-diagram, as in 
fig. 1, in which curve (J) is bidirectionable. This diagram contains 
two bundles of curves; the one bundle consists of the curves (1), 
(4) and (2), the other only of curve (3). Curve (M) is a middlecurve 
of the (M)-bundle. 
We are able to find the bivariant regions in this P,7-diagram in 
the same way as in other diagrams. Between the curves (1) and 
(4) is situated the region (14) = 23, between the curves (1) and (2) 
we find the region (12) = 34, ete. In fig. 1 those regions are indi- 
cated ; they are the same as in fig. 2 (I), with this difference, how- 
