( 230 ) 



region of the normal type II (III) is practically bounded by the 

 lines ABD, AA' and A' C. On the right of ABB we have the 

 abnormal type I (C,H, + CH.OH, ether +H,0); on the left of^'C 

 we have also the type I. But whereas in the first region of I the 

 branches of the plaitpoint line are C^C\ and C\A, they are C\Co 

 and C\B (see figs. 23 — 25 loc. cit.) in the second region. It is namely 

 easy to show, (loc. cit.), that for jr > 1 the branches of the plait- 

 point line are either C\C\ and C^A (type II and III), or C,A and 

 CC (type I), while for jr <[ 1 these branches are C^C^ and C^B 

 (type II and III) or C\B and C,C\ (type I). The line jt = 1 divides 

 therefore the region of type II (III) into two portions, where we 

 shall resp. find the shape of the plaitpoint line branches mentioned 

 (viz. for ^>1)- But in practice it will most likely never happen, 

 that with ^ > 1 a value of j1 corresponds which is much smaller 

 than 1, for a higher critical pressure goes generally together with a 

 higher critical temperature. We may therefore say that with a given 

 value of Jt the abnormal type I is found when 6 is comparatively 

 large [larger than the double point (of the plaitpoint line) value of 

 6'], whereas the normal type II (or III) appears when 8 is compara- 

 tively small (smaller than the said double point value). 



It is now of the greatest importance to examine, when type II 

 passes into III, where the plaitpoint line C^C^ is twice touched by 

 a spinodal line (in R^ and /?/). This investigation forms the con- 

 clusion of the last paper in the Arch. Teyler. 



The calculations get, however, so exceedingly intricate, that they 



proved practically unfeasible for the general case a^^a^ , b^-^b^. 



Only the special cases ^=0{b^=:b, or üt = 8) and ji = 1 admitted 

 of calculation, though even then the latter was still pretty complicated. 

 Then it appeared, that for ^ = the region of type III is exactly 

 = 0, that it simultaneously appears and disappears in the double 

 point P, where jr = ^ = 2,89. But in the case ^i- = 1 the region 

 lies between 8 = 4,44 and 8 = 9,9 (the double point). This is 

 therefore QB in fig, 1 ; i. e. for values of <9 > 1 and < 4,44 we 

 find type II (see fig. 2«); for <9 = 4,44 (in Q) the plaitpoint line 

 gets a point of inflection (see fig. 2^), whereas from 6 = 4,44 to 

 6 = 9,9 we meet with type III (fig. 2^) with two points R, and R/, 

 where the spinodal lines touches the plaitpoint line. This type 

 disappears in the double point P, where (9 = 9,9 and R, and R^' 

 coincide in P (fig. 2^), and passes for values of 6» > 9,9 into type I 

 (fig. 2^). We point out, that the figs. 2«— 2« represent an intermediate 

 case (i.e. between Jt = 8 and ji~l, see fig. 1), for in the case of 



