( 234 ) 



The calculation teaches that the transition case presents itself when 

 the proportion 6 of the critical temperatures of the two components 

 is in the neighbourhood of 1, and the proportion n of the critical 

 pressures is at the same time pretty large. 



A clear representation of these different relations is also given by 

 the two ih T-diagrams of fig. 7 and fig. 7«. (The temperature of C^ 

 is there assumed to be lower than that of R^, but it may just as 

 well be higher). The plaitpoints 7/ on the part R^A below the cusp 

 are the unrealizable plaitpoints (see also figs. 3— 6); the plaitpoints 

 p on the part RJ^I before M also (then the isolated closed connodal 

 curve has not yet got outside the main plait); the plaitpoints F 

 beyond M are all realizable. 



So after the above we arrive at the conclusion that in all cases 

 in which a distinct longitudinal plait appears of the shape as in 

 figs. 4'^ or 6^ (so when the minimum B lies near R^, the critical 

 mixing point M of the three phases need not always lie on the 

 longitudinal plait (see fig. 4'^), and also that the longitudinal plait 

 with its plaitpoint P will not always coincide with the transverse 

 plait itself, but it can also coincide with the branch plait of the 

 transverse plait, so that at that moment no three phase equilibrium, 

 i. e. no vapour phase is found (see fig. 4''). The two liquid phases 

 1 and 2, however, coincide in this case. 



The case drawn in figs. 5« and 5* remains of course an exception, 

 and the conditions for its occurrence may be calculated (see above). 

 But this calculation, as well as that which in general indicates the 

 situation of the points /?,, D and M, will be published elsewhere 

 (in the Arch. Teyler). It is, however, self-evident that the above 

 general considerations are by no means dependent on these special 

 calculations. 



It is perhaps not superfluous to call attention to the fact that the 

 concentration x^ of the vapour phase is neither in fig. 4^^, nor in 

 fig. 5« or 6«, the same as the concentration of the two coinciding 

 liquid phases .^1,2, as van der Lee wrongly believes to have shown 

 in his Thesis for the doctorate (1898), [see p. 66—69, 73—74 and 

 Thesis III; also van der Waals, Cont. II, p. 181 (1900)]. Now we 

 know namely, that when x^ lies between x^ and x^ at lower tem- 

 peratures, this need not continue to be so till x^ and x^ have coincided. 

 The latter would be quite accidental; in general one of the maxima, 

 e. g. in the j9,A^-line, which lie in the unstable region between x^ and 

 x^, will get outside the plait before x^ and .x', have coincided. 

 Cf. the figs. 12« to 12/ in my Paper in These Proceedings of March 

 25 1905 and ^ 8 p. 669—670, and also the footnote on p. 665. 



