833 



lines and biiiodal lines passing (hrungh the nodes, amonnis to (liree. 

 When we assume tliat the Ihree-pljase coexistence takes place on 

 the stable part of the i|'-8iirface, the three Huid phases participating 

 in this equilil)riuni are indicated by elliptical points; the relative 

 situation of the three pairs of conjugate diameters is again deter- 

 mined by the rules of § 2(f in this sense that these theorems hold 

 good for every combination in sets of two of the 3 pairs of con- 

 jugate diainetei'S. 



6. Applications. 



In a treatise on the phenyl- and tolylcarbaminic acids recently 

 published in these Proceedings it was pointed out that the different 

 /'*-7-ligures which are found for these homologous compounds, can 

 be derived from each other by moving the quadruple point along 

 the three-phase line />,L,(r"). When the quadruple point reaches 

 the critical endpoint, it is still just stable; this is the ti-ausitiou case, 

 which connects this type of binary systems with the type sulphuretted 

 hydrogen-ammoniac, where the coexistence L^L^G does not appear 

 stable any more. 



Such a transition is also found for lunaiy systems without com- 

 pound, a fact which Büchnkr') already pointed out in his Thesis 

 for the Doctorate. We then get a transition from a system with a 

 quadruple point to the type diphenylamine-carbonic acid. The transi- 

 tion itself has not been studied by Büchneh ; as it is, however, 

 possible that by a suitable choice of the components we can get 

 close to this transition case — in the cited paper I drew attention 

 to the system as-o-xylidine-carbonic acid — the study of this 

 transition case has probably not only theoretical importance. 



This transition can now be simply followed by the aid of the 

 rules mentioned in ^^ 1 — 5; it has, indeed, been the study of this 

 transition that induced me to seek the regularities mentioned in 

 what precedes. 



A complete discussion of this transformation is not possible with 

 the aid of the above rules alone. For these only indicate the course 

 of binodal and nodal lines in the neighbourhood of the nodes. Yet 

 this is already sufficient to give us an insight into the phenomena 

 that will make their appearance in this transition case. 



For this purpose I will imagine the t|>-surface to be constructed 

 for the temperature of the critical endpoint (/v, = G). We may then 

 expect a situation as indicated by fig. '^a or 8/;. The plaitpoint /^, 



1) These Proceedings. 21. 661. (15)19). 



') BiicHNER. Thesis for the Doctorate. Amsterdam 1905. 



