1026 
Chemistry. — “/n-, mono- and divariant equilibria”. V. By Prof. 
F. A. H. ScHREINEMAKERS. 
(Communicated in the meeting of December 18, 1915). 
9. Another deduction of the P,7-diagramtypes. 
Up to now we have deduced the P,7-diagramtypes for unary, 
binary, ternary and quaternary systems and we have indicated also 
in what way we can find the P,7-diagramtype for every definite 
system, composed of an arbitrary number of components. We have, 
however, supposed in all these deductions, that either the concen- 
tration-diagramtype or the compositions of the phases, occurring in 
the invariant point, are known. Now we shall deduce, without 
knowing the type of the concentration-diagram or the composition 
of the phases, the different types of the P,7-diagram, which may 
occur in an arbitrary system of 2-components. 
In our previous considerations we have introduced the idea 
“bundle of curves’. A bundle of curves is formed viz. by curves, 
which follow one another in a P,7-diagram, without being separated 
from one another by metastable parts of curves. 
In fig. 2 (1) the curves (1) and (4) form, therefore, a twocurvical 
bundle, the same is the case with the curves (1) and (5) and also 
with the curves (2) and (3) of fig. 4 (II). [We have to bear in mind 
that the figs. 4 (ID) and 6 (II) have to be changed mutually, as is 
already communicated in the previous publication]. In fig. 2 (IID 
we find three twoeurvical bundles, viz. B’ + D’, A’ + F” and 
C’ + EF’, in fig. 4 (UD the twocurvical bundle B’ + D’ and in 
fig. 6 (III) the twocurvical bundle C’ + EL’. 
We find an example of a threecurvical bundle in figs. 6 (II) and 
6 (II, of a fourcurvical bundle in fig. 8 (III) [viz. A’ + D’ + B’ 
+ €"). 
A bundle of curves is consequently limited at the right and at 
the left by one or more metastable parts of curves. As a limit 
we may call one single curve, which is situated between two 
metastable parts of curves, a “onecurvical bundle”. In fig. 1 (I) 
and 2 (IL) each curve forms, therefore, a onecurvical bundle. 
Consequently we find in fig. 4 (II) two twoeurvical — and one 
onecurvical bundle; in fig. 6 (II) one tbreeeurvieal and two one- 
curvical bundles, ete. 
It is evident that also the metastable parts of the curves form 
bundles, so that we may also speak of one- and morecurvical meta- 
stable bundles. 
