1385 
each region angle is smaller than 180°; 
each region, which extends itself over the metastable or stable 
part of a curve (/,), contains the phase /,. 
Now we shall discuss still some other properties and for this we 
introduce the idea “coneentration-region’”’. 
In a system of n-components in the invariant point » + 2 phases, 
in the monovariant equilibria » + L and in the divariant equilibria 
n phases occur; the concentration-diagram is situated in a space 
with  — 1 dimensions. 
We take from the divariant equilibrium : 
Ree Rea VA 0) 
a complex X of the composition : 
X—a,F,+4,F,-+...+ Mton oa Se 82) 
wherein 
ee Cet me et yet ee) 
We represent this complex X by a point \ of the concentration- 
diagram. When we give to a,, a, etc. all possible values (of course 
only positive ones), which satisfy 3, then the complex \ gets all 
possible compositions, which are obtainable with the aid of the phases 
Py... Fy42. As with each complex X a definite point X in the 
concentration-diagram corresponds, we obtain in this diagram, therefore, 
an assemblage of points adjoining one another which occupies a 
definite part of the diagram. We call this part the concentration- 
region of the bivariant equilibrium (/’, F,). 
In a binary system [fig. 2 (1)| the concentration-region of the equi- 
librium (PF) =F, + Hs, is, therefore the straight line F,/,; in a 
ternary system [fig. 1 (ID, 3 (ID) and 5 (11)] the concentration-region 
of the equilibrium (1.2) —=3+44-+5 is the triangle 345; in a 
quaternary system [fig. 1 (III), 3 (III), 5 (III) and 7 (IID)] the con- 
centration-region of the equilibrium (4. M= A+ B+ C+ D is 
the tetrahedron ABCD. In a system with more than four compo- 
nents this region is situated in a space with more than three 
dimensions. 
Now we take from the monovariant equilibrium 
(FS Fp Ae FAL ee eat en oe ep) 
a complex A of the composition : 
” NG ee a Haren rly ere | gh eN (6) 
When we give again to this complex Y all possible compositions 
which may be obtained with the aid of the phases #,F,..., then 
the point Y follows again a definite part of the concentration- 
