1586 
diagram ; we call this the concentration-region of the monovariant 
equilibrium (4). 
In a binary system [fig. 2 (D] the region of (1) = EF, +F, + Aj 
is consequently the line /,/’,; that of (F))= F, + F, + F,, therefore 
the line #’,/’,, ete. In a ternary system this concentration-region is 
a triangle or a quadrangle. When we take e.g. the equilibrinm 
(38) =1+4+2+4-+ 5, then this is in fig. 1 (II) the quadrangle 1425, 
in fig. 3 (If) the triangle 125 and in fig. 5 (II) also the triangle 125. 
In a quaternary system this concentration-region is a tetrahedron 
or a hexahedron. When we take e.g. the equilibrium (4) = A + 
+B6+C+D+E; in fig. 1 AID, 3 (III) and 5 (III) it is the 
hexahedron ABCDE, in fig. 7 (III) the tetrahedron ABCD. 
At last we take a complex: 
X=a,F,+a,F,+...+ onee 5 (©) 
of the invariant equilibrium. Wien we give to this complex X all 
possible compositions, which may be obtained with the aid of the 
phases #’... Mps, then the point X traces the concentration-region 
of the invariant equilibrium. 
In a binary system this is the line PF, [fig. 2 (I)]; in a ternary 
system it is either a quintangle [fig. 1 (II)] or a quadrangle 1253 
[fig. 3 ([1)] or a triangle 125 [fig. 5 (II). In a quaternary system it 
is one of the solids, drawn in figs. 1 (III), 3 (III), 5 (IID) and 7 (III); 
in a system with more than four components this region is situated 
in a space with more than three dimensions. 
It appears from the previous that in some cases the concentration- 
regions of an invariant, monovariant and bivariant equilibrium may 
be the same. In fig. 5 (II) e.g. triangle 125 is not only the region 
of the invariant equilibrium, but also that of the monovariant equi- 
libria (8) and (4) and also that of the binary equilibrium (3. 4) = 
=1+42+4+5. 
When we take a point in a P, 7-diagram, then this point represents : 
1. when it is situated between the curves, one or more bivariant 
equilibria. 
2. when it is situated on a curve, a monovariant equilibrium 
with one or more bivariant equilibria or not. 
When we take e.g. in fig. 2 (II) a point between the curves (1) 
and (2), then this represents a P and 7, at which the bivariant 
equilibria 134, 245 en 345 of fig. 1 (ID) can occur. When we take - 
a point on curve (1) then this point represents a Pand 7, at which 
the monovariant equilibrium (1) = 2 438 + 4 + 5 and the bivariant 
equilibrium 134 of fig. 1 (II) may occur. [The region 134 viz. extends 
over curve (1)]. 
