123 



occnrring witli reaction (6), I lieu we could, as we have seen above, 

 indicate at whicli side (viz. at the right, at the left, above or 

 beneath) of curve (i^,) each of these regions is situated. As this is 

 not the case, we only know that tiie regions, wiiich are written 

 in (7) at tlie right of the vertical line, are situated at the one side 

 and those, which are written at the left of this line, are situated at 

 the other side of (/^,). Each of the four regions is limited, besides 

 by curve (i^,) also still by another curve, viz. the region F^ t\ F^ 

 by (/;), F,F,F, by {F}), F,F,F, by {F,) and F,F,F, by (F,). 

 When we keep in mind now that every region-angle is smaller than 

 J80°, then it is evident that the curves [F^) and {F,) are situated 

 at the one side and the curves {P\) and (F^j at the other side of 

 curve (i'\). We shall represent this in future in the following way : 



F, + f\:^F, + F\ (8) 



This means: when reaction 8 occurs between the phases of curve 

 (i^i), then the curves {F^) and (F^) are situated at the one side and 

 the curves (F,) and {F^) are situated at the other side of curve (i^J. 



As the previous considerations are completely valid in general, we 

 find the following. When we know of a system of >j-components 

 the compositions of the n -\- 1 phases of a curve {F^), then also the 

 reaction is known between these n -\- 1 phases F^, F, . . . F„-^.2. 

 Willi the aid of this reaction we can divide the curves (i^,), (F,) ... {F„-^^) 

 into two groups in such a way, that the one grou(> is situated at 

 the one side and the other group at the other side of curve {F^). 



As we may act in the same way with each of the other curves, 

 we find : 



When we know the compositions of the?* -|- 2 phases F,, F^, . . . F„+2, 

 which occur in an invai-iant point, we can with respect to each of 

 the curves {F,), {I',) . . . (l^n-\-2) divide the n -{- 1 remaining curves 

 into two groups in such a way that the one group is situated at 

 the one side and the other group is situated at the other side of the 

 curve under consideration. 



Now we shall apply the rule which is treated above, to some 

 cases in order to deduce the position of the different curves with 

 respect to one another. In order to simplify the discussions, we shall 

 distinguish instead of "at the one" and "at the other side" of a 

 curve "at the right" and "at the left". For this we imagine that we 

 find ourselves on tliis curve facing the stable part and turning our 

 back towards the stable part. Consequently in fig. J (Fj is situated 

 at the right and {F,) at the left of (F,); (F,) is situated at the right 



