1 20 



The n -\- \ regiDiis starting in tig. 1 IVoni cnive (F,), arc situated 

 partly at tiie one and partly at the other wide of this curve; also 

 it is evident liiat the regions, which are situated on the same side 

 of the curve, cover one another. Hence it follows immediately that 

 several bivariant equilibria can occur under a given P and at a 

 given 7\ 



In order to determine on which side of the curve (F,) the stable 

 part e.g. {FiF^) of a bivariant region is situated, we let the reaction 

 (5) take i)lacc in such a way, that the phase F., disappears from 

 the equilibrium [F^). This may always take place, when the quantity 

 of F., in the equilibrium [F^) has been taken small enough. If we 

 let this reaction proceed under a constant pressure, we have to state 

 whether heat must be added or supplied, when we let it take place 

 at a constant tempei'ature, we must determine whether the volume 

 increases or decreases. We may then apply the following rules : 

 at the right of the curve we find the bivariant equilibria, which 

 arise on addition of heat ; at the left of the curve those which arise 

 on withdrawal of heat. Above the curve we tind the bivariant equi- 

 libi'ia, which arise on decrease of volume ; beneath the curve those, 

 which arise on increase of volume. 



Foi' the meaning of "at the right", "at the left", "beneath" and 

 "above" is assumed that the P- and 7-axes are situated as in fig. 1. 



When we apply the considerations, mentioned above, to each of 

 IliP If _|_ 2 curves (F^) . . . (F.+j) then we obtain the division of 

 the ii (n-\-2) {n-\-l) di variant regions between the different curves and 

 around the point (}. 



The following is apparent from the previous considerations. When 

 we know the compositions of the phases, which occur in an inva- 

 riant point and the changes in entropy and volume which take place 

 at the reactions, then we are able to determine in the P, 7-diagram 

 the curves starting from this point and the division of the bivariant 

 regions. 



2. Soj)ie (general properties. 



Now we will put the question whether anything may be deduced 

 concerning the position of the curves and the regions with respect 

 to one another, when we know the compositions of the phases only 

 and not the changes of entropy and volume which the reactions involve. 



This question is already dissolved for binary ^) and ternary ') 



1) F. A. H. ScHREiNEMAKERS, Z. 1'. Pliys. Chemie 82 59 (1913) and F. E. C. 

 ScHEFFER, those Coiiimunicalions October 1912. 



-) F. A. H. SoHREiNEMAKERS, Die heterogenen Gleicligewichte von Bakhuis 



ROOZEBOOM 111' 218. 



