( 236 ) 



plaitpoint temperature). Tlie conditions for the occurrence of these 



cases were defined by us by means of the equations (2) and (3) 

 there. From this appeared that with very feeble attraction the case 

 a) occurs, with greater attraction the case b), whereas with still 

 greater attraction case c) occurs (supposing the system to belong to 

 type I). 



We have found neither the case a) as we already observed above, 

 nor the case c) in van Laar. We did tind the case b), chiefly with 

 regard to the treatment of what takes place at lower temperatures, 

 when three-phase-equilibria occur. For this treatment we referred 

 to van Laar (of. These Proc. March '07 p. 797). 



From the fact that van Laar has declared this shape b) to hold 

 universally for type I (cf. p. 235 footnote 3 ; see also van Laar p. 36) 

 it appears in our opinion, that van Laar has not only left the cases 

 a) and c) unmentioned, but has decidedly overlooked them. J ) 



II. One more remark remains to be discussed. In § 7 we put 

 as the two criteria of the case b), the course of the plaitpoint 

 curve being from K^ to K m (see above), in which case a minimum 

 plaitpoint temperature occurs' (supposing 6j2M <C ^hm) : 



J^a22M./aiiM>— J— 1 + V\ + 3 6;>2m/&iim[ 

 and 



J^a22M/ailM <C — (1 — &22m/6um) + ^ ~~ &22.Vl/6|lM + (^22M/^11.M) 2 - 



Mr. van Laar points out (These Proc. May '07, p. 45, appendix), 

 that the tirst-mentioned condition corresponds with a condition for the 

 occurrence of a minimum plaitpoint temperature, derived by him These 

 Proc. Dec. '05, p. 581 (and Verschaffelt These Proc. March. '06 

 p. 751). In our opinion, however, Mr. van Laar is mistaken when 

 he thinks that the one, condition stated by him is sufficient in all 

 cases to decide as to the occurrence of a minimum plaitpoint tem- 



l ) We might consider the course of the spinodal curves in case b), if this is 

 also extended to values of X > 1 and < 0, and of v < ft, as a more general case, 

 from which the cases a) and c) might be obtained, at least qualitatively and 

 when we restrict ourselves to the region of the Ji-surface (1 > .r > and v < b) 

 that is of importance for the treatment of mixtures. This might be done by cutting 

 out a region bounded by re = and x—\, and a suitable line v = b in the same 

 way as van der Waals These Proc. Feb. '07, p 621 sqq. treats the course of the 

 isobars (cf. § 7 p. 796 of this Communication). We have not found a single indication 

 that van Laar's description of case b) is to be interpreted in this way; from the 

 phrase, quoted p. 235 footnote 3 e.g. we should much sooner conclude to the contrary. 



At any rate the distinctions which are of physical importance, have not been 

 made. 



