( 228 ) 



e. The fifth paper (These Proceedings, Dec. 30, 1905) ^) contained 

 the condition for a minimum critical {plaitpoint) temperature, and 

 that for a maximum vapour pressure at higher temperatures (i. e. 

 when at lower temperatures the three-phase-pressure is greater than 

 the vapour pressures of the components). For the first condition 

 was found: 



for the second 



4 Jt [/ Ji 



'<W^i' <'' 



which conditions, therefore, do not always include each other ''). 



After this the connodal relations for the three pi'incipal types were 

 discussed in connection with what had already been written before 

 by KoKTEWEG (Arch. Néerl. 189J) and later by van der Waals (These 

 Proceedings, March 25, J 905). The successive transformations of main 

 and branch plait were now thrown into relief in connection ivith the 

 shape of the jilcLitjwint line, and its splitting up into tivo branches as 

 examiried by me. 



ƒ. In the sixth paper (Arch. Teyler of May 1906) the connodal 

 relations mentioned were first treated somewhat more fully, in which 

 also the p, .^'-diagrams were given. There it was proved, that the 

 points i?i, R^ and R\, where the spinodal lines touch the plaitpoint 

 line, are cusps in the jj>,T-diagram. 



Then a graphical representation was plotted of the corresponding 

 values of 6 and Jt for the double point in the plaitpoint line, in 

 connection with the calculations mentioned under d. 



Both the graphical representation and the corresponding table are 

 here reproduced. The results are of sufficient importance to justify 

 a short discussion. 



We can, namelj^ characterize all possible pairs of substances by 

 the values of 6 and üt, and finally it will only depend on these 

 values, which of the three main types will appear. To understand 

 this better, it is of importance to examine for what combination 

 {:t, 6) one type passes into another. As to the transition of type I 

 to II (III), it is exactly those combinations for which the plaitpoint 

 line has a double point. In fig. 1 (see the plate) every point of the 



t) Inserted in the Arch. Néerl. of May 1906. 



2; These results were afterwards confirmed by Verschaffelt (These Proceedings 

 March 31, 1906; cf. also the footnote on p. 749 of the English translation). 



