1056 
Let us take e.g. the reaction-equation : 
aA + 6B=cC + dD. 
Hence it is only apparent that the four phases form the 
anglepoints of a convex quadrangle, the point of intersection of the 
diagonals divides the diagonal AB into parts, which bear to one 
another the relation «:5 and the diagonal CD into parts which 
bear to one another the relation as c:d. Hence it is not only 
apparent that infinitely many quadrangles exist, but also that the 
place of those quadrangles in the flat plane is still quite arbitrary. 
Consequently we are allowed to conclude from the previous 
considerations : 
the P,7-diagramtypes, deduced above, can all exist; with each 
of the P,7-diagramtypes corresponds a definite type of the concen- 
tration-diagram, which may be deduced in the way indicated above. 
Herewith, of course, the question is not solved whether in the ex- 
perimental examination of all systems e.g. with 5 components, all 
eight P,7-diagramtypes possible (fig. 1 and 2) will occur. For this 
it is necessary that the phases really occurring, lead to the eight 
possible types of the concentration-diagram and only the experiment 
can decide that. 
Now we shall apply the previous considerations, in order to find 
with some P,7-diagramtypes a corresponding concentrationdiagram- 
type. The types of concentrationdiagrams, belonging to the P,7- 
diagramtypes of the binary, ternary and quaternary systems have 
already been discussed before (I, IL and III). As these concentration- 
diagramtypes were represented graphically, we have followed there 
the reverse way, viz. we have deduced from these types the corre- 
sponding P, 7-diagramty pes. 
We take for an example a system with 5 components, in the 
invariant point of which the seven phases A, B, C, D, FE, F, and 
G occur; we assume that the P,7-diagram consists of 7 onecurvical 
bundles, as in fig. 1a. We choose the curves (A) and (/) as position- 
curves. The reactions are: 
eHE+ fF +9G=bB+4+cC+dD 
PEAGGHaA=bBHeCHdD 
The reaction-coefficients must satisfy : 
Oa Pe igi= Dae Haid ne loet va (sy sees) 
Pg Be SHO ead oo we) els aw GB) 
and also the conditions (10) and (11). It is evident that (10) dis- 
appears and that (11) passes into: 
Bit of Magis. gai ad, z 
ee te sk 
