1187 
now as a schematical reaction-diagram. From the position of the 
phases with respect to one another, the reactions follow: 
24345 1452384 Dee eo 
gs 5) cE VS sec So \ 
Consequently we find the same reactions as from the concentration- 
diagram [fig. 1 (II)]; the difference is only that they may be deduced 
schematically from fig. 2, quantitatively from fig. 1. 
When we consider also the other P,7-diagrams of binary, ternary 
and quaternary systems, then we find perfect concordance between 
(53) 
those and the corresponding concentration-diagrams. 
It is apparent from the previous that we may deduce the sche- 
matical reactions from both the diagram-types and that the concen- 
tration-diagrams have the advantage that they indicate the reactions 
also quantitatively ; the schematical reaction-diagrams have, however 
the advantage, that they can be drawn in a plane for each 
system of 2 components; the concentration-diagrams, however, are 
situated in a space with n— 1 dimensions and consequently they are 
difficult to draw for systems with more than four components. 
We can also obtain schematical reaction-diagrams in other ways. 
When we wish to know the reactions quantitatively, then the 
concentration-diagram has to be known. A similar diagram of a 
system of m components is represented however in a space with 
n—1 dimensions and it is difficuit to draw it for systems with 5 and 
more components; but this is unnecessary for our purpose. It is 
viz. unnecessary for the deduction of the P,7-diagrams to know 
the reactions quantitatively, but it is sufficient when we know them 
schematically. 
Consequently we put the following question : is it possible to draw 
for each system with 2 components without using a space with more 
than three dimensions, a diagram, which represents all reactions 
schematically 7 
We shall discuss one of the different ways, in which this is 
possible. We imagine an invariant point with the phases A, B, C, 
D, E, and F’; suppose in the monovariant equilibrium (A) the reaction : 
Bei Ee Die, A oo ots. eoa ane (O4) 
occurs. We represent each of the phases by a point on a closed 
curve, e. g. a circle, in this we shall place at the outer side of the 
cirele the letters or figure-signs, belonging to these points). 
First we draw in fig. 1 on the circle the point A and we 
imagine through this point the diameter AA, which is not drawn ; 
