1005 
1. Reactions are possible, in which all phases of the invariant 
point may participate. We write those reactions: 
a, f+ a, Fy +... + anaes Pag mln |). eas 
and 
u, a, 5 zi fe. ds ap a ea = Un+t2An+e2 En +2 —=0.% (2) 
Now we distinguish the following cases. 
A. ty, ",,... are all different. Consequently there are no indifferent 
phases, then we obtain the general P,7-diagramty pes. 
B. vw, =4,=p. Consequently there are two indifferent phases 
viz. FH, and #, and three singular curves viz. (M), (F,) and (F,). 
In the equilibrium (#, #,) may occur the reaction: 
et ie (a a ask, dein 10 ee 18) 
_ This equilibrium (/, /’,) may be mono- or bivariant (not invariant). 
When (f/f, /,) is monovariant, then it is represented in the P,7- 
diagram by a curve, then the singular curves coincide [Figs. 1 (X) 
and 2 (X)]. 
When (/, #,) is bivariant, then it is represented in the P,7- 
diagram by a region, the 3 singular curves touch one another in 
the invariant point [figs. 1--5 (YV)]. 
Cia. == 1, = p, = we Consequently there are three indifferent 
phases viz. f’,, #, and /F, and four singular curves viz. (M), (F), 
(F,) and (#,). In the equilibrium (#, F, PF) may occur the reaction: 
(u—u,) U, lij (u—u,) a, Te ag wen ye (+) 
This equilibrium (Ff, £, F,) is tri-, bi- or monovariant. 
When it is monovariant, then the singular curves coincide. An 
example is discussed in Communication XIV. 
er i whieh <n. Consequently there 
are 7 indifferent phases and r+ 1 singular equilibria. In the equi- 
librium (/, #,...#,) may occur the reaction: 
(u- Ur+1) Ay + VEE ls « ee Oort Ect: er 
This equilibrium may be from r- to monovariant. 
Nr and grid tn ln =D whieh A= 7. 
Consequently there are two groups of indifferent phases. To the 
first group belong A + 1, to the second group m + 1 singular curves. 
For K=J/E passes into D. 
Also three and more groups of indifferent phases may occur. We 
find an example in the system water + a salt A + a salt 5, when 
in the invariant point occur the phases G+ A + B + A, + B, in 
which A, and B, represent hydrates. 
64 
Proceedings Royal Acad. Amsterdam, Vol. XIX. 
