122 



viz. ill {I'\F,), (F^F,). . .{FJ\+2); in iil' "le otiier [viz. in ^ /i(vt-|-l) 

 regions] it is present however. The same applies to every other phase. 



Now we imagine in tig 1 the curves {F^), (F,) . . . (i^„+2) to be 

 draw». The n -f- -I regions in wliicli the phase F^ does not occur, 

 all start from the stable part of the curve [F^); none of those 

 regions can tlierefore, extend itself over the stable part of curve 

 (i^i). When, therefore a region extends itself over the stable part 

 of the curve (F^), then it must consequently contain the phase F^. 

 As every region-angle is however smaller than 180°, none of the 

 71 -{- 1 regions, in which the phase F^ does not occur, can extend 

 itself over the metastable part of the curve (F^); the regions, which 

 extend themselves over this part, consequently contain all the phase F^. 



Consequently we find : each region, wliieii extends itself over the 

 metastable or stable part of a curve {F/,), contains the phase F/j. 



We must keep in mind with this that the metastable part of a 

 curve is always coxered by one or more regions, but this is not 

 always the case with the stable part. Further it is also apparent 

 that the reverse of the previous thesis viz. "all regions which contain 

 themselves the phase F,, extend themselves over the metastable or 

 stable part of the curve (i'),)" need not be true; this is only always 

 the case in unary systems. Later we shall still refer to these and 

 other properties. 



Now we shall deduce a thesis, which is of great importance for 

 the determination of the position of the curves with respect to one 

 another. For fixing tiie ideas we take an invariant point with the 

 phases F^, F.„ F,, F, and F^ and we consider the curve (i^J =..F, + 

 _(- i^j -|- Ft + F^ starting from tliis point. Between the four phases 

 of this equilibrium on addition or withdrawal of heat a reaction 

 occurs, which is, as we have seen above, completely defined by the 

 compositions of the phases. Let this reaction be for instance: 



/; + i^, ^ /% + i-; ....... (Ö) 



Consequently four bivariant regions start from the curve (i^,) 

 viz. F,F,F„'fJ\F„ F,F,F, and F,F,F,. It follows from (6) 

 that the regions F, F^ F, and F^ F, F, are situated at the one side 

 and the regions F, F, F, and F, F, F, at the other side of curve 

 [F,). We write this: 



F, + F, :;± F, + F, 



F,F,F. I F„FJ'\] (7) 



F,F,P, I F,F,F 

 When we should know the changes in entropy and volume. 



