( 227 ) 



line running from C^ to Cj was ttince touched by a spinodal line. 

 Here also the hrancli C^A is touched hy a spinodal line [in the tirst 

 two cases this took place oidy once, either (in fig. 1 , loc. cit.) on the 

 branch C^A {A is the point x =zO, v^ b), or (in fig. 2 loc. cit.) on 

 the branch C^A (C„ is the before-mentioned third critical point)]. 



So it appeared that all the abnormal cases found bj Kuenen may 

 already appear for mixtures of 2)erfectly normal substances. 



It is certainly of importance for the theory of the critical phenomena 

 that the existence of two different brandies of the plaitpoint curve 

 has been ascertained, because now numerous phenomena, also in 

 connection with different "critical mixing points" may be easily 

 explained. 



c. In the third paper in These Proceedings (June 24, 1905)^) the 

 equation : 



1 fdT\ , 1 



■^1 V«'^Vo ^ 



^i/^fv.-V,i/^)-i) ..(3) 



^ V ^ 



was derived for the molecular increase of the lower critical temperature 



for the quite general case a^^a,, b, ^b„ which equation is reduced 



to the very simple expression 



A = ^i^-i) (3„) 



for the case Jt = 1 {p^ = p^). 



This formula was confirmed by some observations of Centnekszwer 

 and BÜCHNER. 



d. The fourth paper appeared in the Archives Teyler of Nov. 1905. 

 Now the restricting supposition /? =: (see b) was relinquished for the 

 determination of the double point of the plaitpoint line, and the quite 



general case a,^a,, b^ < b, was considered. This gave rise to very 



intricate calculations, but finally expressions were derived from which 



for every value of ^ = -^ the corresponding value ot' jr = — and 



^1 Pi ' 



also the values of x and v in tiic double point can be calculated. 



Besides the special case & = jt (see b) also the case .t = 1 was 

 examined, and it was found that then the double point exists for 

 <9 ^ 9,90. This point lies then on the line v =z b. 



^) The three papers mentioned have together been published in the Arch. Néerl. of 

 Nov. 1905. * . 



