that it was represented by point 4, then the equilibrium (3) would 
not be converted into the phase 4, but into the equilibrium 125. 
The above considerations can also be applied to systems with 
more components; for this we have only to draw the different 
regions in the P, 7-diagrams or in their symbolical representations. 
Hence it appears at onee which bivariant equilibria may occur. 
It depends on the composition \ of the monovariant equilibrium, 
which of those bivariant equilibria shall be formed from a definite 
complex YX. When we represent the compositions of the phases in 
a concentration-diagram, then, as we have seen above, this question 
may be solved at once. As this represention requires, however, a 
space with more than three dimensions for systems with more than 
four components, we shall follow another way for those systems. 
Let us take as an example the monovariant equilibrium : 
(R=P+Q484+ 74+ 04 V 
of a system with five components, in the invariant point of which 
occur the seven phases: P, Q, RS, 7) U and V. We assume 
that the reactions between those phases are defined by the reaction- 
equations : 
OERS Ty RAV, Om a de 
and 
As those are the same reaction-equations as (18) and (14) in 
communication IV, the diagram is represented by the symbolical 
diagram 21 (IV). Consequently we find for the conversion of the 
monovariant equilibrium (/) ; 
Metast. (R) = P+ Q+84+ 74+ U+ V—Stab. (QV), (PU), 
(SV); (LU) or (GV). 
It depends on the composition of the equilibrium (/) which of 
those five bivariant equilibria shall occur in a definite case: we 
take as an example a complex \ of the composition: 
AP NS TT (9) 
When we bring in (7) and (8) all phases in the first term of the 
equations and when we add them to (9) after having multiplied (7) 
by A and (8) by u, then we find: 
X= (44 2u)P4 (1 +4) Q + (24 + w R44 (24+ 32—aS 
+(1—a+ua)7+(1—a4— 2u) U+(2—44—nu)V . (10) 
We have expressed in (10) the complex Y in the seven phases 
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