830 



When the triangle in fig. 2a (order ftj 6, ii^ ?i,) is represented by 

 ABC, tlie two binodal lines lie entirely outside the triangle, when 

 by ABD, they lie both [>artly inside it, whereas in tig. 2b (order 

 6, 71, b, 71, ) one l)inodal line lies partly inside, one entirely outside 

 the triangle both for the three-phase equilibrium J ^6' and for .4^Z). 



Fig. 26. 



3. Of the conclusions discussed in ^ 2 the last of those mentioned 

 under a is not new. Some years ago Kuenen proved this thesis by 

 another method ^). 1 think I have demonstrated in what precedes 

 that the relative situation of nodal lines and binodal lines can directly 

 be derived in a general way from the already long known properties 

 of the i^-surface'). 



Though the realizable parts of the i^-surface are only indicated 

 by elliptical poinis, the general discussion of ^ 2 has the advantage 

 that it points out a regularity for the whole i|--surface. The above 

 discussed conclusions are of great importance when we want to 

 examine the possible coexistences of solid by the side of fluid. By 

 the aid of . the rules discussed in § 2 it is possible to indicate the 

 relative situation of the binodal lines solid-fluid and fluid-fluid in 

 every point. They are almost indispensable in this study, because 

 when these rules are not observed, we are often in danger in the 

 more intricate cases of mistaking impossible cases for possible ones, 

 especially in the metastable and unstable region. And for a complete 

 survey of these existences the not realizable parts of the xp-surface 

 cannot be dispensed with. 



1) Kuenen. These Proceedings. XIV p. 420. 



^) Note added during the correction of the Dutch proofs. The theses of § 2 

 are not only valid for the j^-surface, but for any surface, hence also for the ^-surface. 

 In Bakhujs Roozeboom's Heterogene Gleichgewichte HI. 2. Scheeikemakers thus 

 discusses analogous rules (p. 115 et seq.) ; the situations in the metastable region 

 have, however, been only partly treated (p. 340 et seq.)- 



