( 426 ) 



that is to Siiv into 



7; 



J =: .r 



the oi'diiuirv fornmhi of van 't Hoff for oxlreiiiclv dihitc solutiojis. 

 If, however, the sohitioiis are no longer extremely dihite, we can 

 no longer be satisfied with one or two terms in the develoi)ment of 

 loq (1 — .f), but kuj (1 — .*•) must remain. 



I will now show, that the approximative relation 



T 



l-Olog{l — .r) 



dT 



gives indeed the (tbser\ed course qualitatively. For -— we 



find 



dT 



~dr 



1\ 







Whilst T itself, for ,/■===(), passes into 7',,. and for ,r = 1 into 



7'=0, which already agrees with the steadily declining course — it 



dT 

 appears from - , that this (piantitv. for ,/' = 0, becomes: 



dx 



dT\ 



2 



the limiting value of van 't Hoff, whilst for 

 .(' = 1 it passes into — x . It may now 

 still be asked, whether there will be a point 

 of intloction or not. In the case, examined 

 by vanHeteren, a point of inlledion plainly 

 occurred at about ,v = 0.8, but it may also 

 be possible, that the course was like the 

 one in the following figure, without point 

 of iiillectio]). Let us therefore determine 

 d:'T 

 17' 



(y 



7'„ 







T. 



\~20 



■ dx' {i—oiofi{i-x)y {i-xy N'{i-xy A' {i-xy ix 



d' T 



1 



Evident Iv 



dx-' 



0, when 20 = N, that is to say, when 

 10 lo,j (1— ./■) - 

 ^log{V — a:) — 2 



W 

 1 

 "Ö 



As 



RT 



" will be positive, we see, that the point of iiillection can 



