( 56 ) 



:;rr=p-J.„=^(-%(l-.^•)) , .... (2) 



the expression already derived by me in 1894. ^) 



1) Gf. Z. f. Ph. Gh. 15, 1894; Arch. Teyler 1898; Lehrbiich der matli. Ghemie, 

 1901; Arch. Teyler 1903; Ghem. Weekbl. 1905, N". 9; These Proceedings, June 

 21, 1905. 



hi the original Dutch paper another note followed, which Mr. van Laar has 

 replaced by the following in the English translation. 



A conversation with Dr. Kohnstamm suggested the following observations lo me. 



db 

 Dr. Kohnstamm finds (These Proceedings, May 27, 1905) the quantity v — x —— 



aw 



in the denominator of the expression for ?r. This is quite correct, and harmonizes 



perfectly with the general expression, which according to equation (1) on p. 54, 



would also have been found by me for non-linear variability of v. 



Then we should viz. have: 



Ir-iilatinfT t.\ o' 



'P 



where, when calculating (o — x ^— by means of van der Waals' equation of state, 



ó{v — b) . .,.,/' db\ 



also a term — px — ^^ appears, m consequence of which p [v — x-^] occurs 



ox \ ax J 



H^-^) :„ „„„ „„„ „.„..;„. „, A. . db^, 



in the first member. 



... öü db 



Now it IS of no importance whether v is diminished by x ^^~ or by x -j- , as 



o.v dx 



d(v—b) 

 2) - — 5 approaches to both for small and for very large values of ^9. I therefore 



obtained a correction term in the denominator, in connection with the size of the 



molecules of exactly the same value as Dr. Kohn.stamm. That this did not always clearly 



appear in my previous papers, is due to the fact that I then always introduced the 



dv 

 approximation v — ^ v- — ^'i, which was perfectly justifiable for my purpose. 



dv /'d^v\ 



For as v — x-^ = Vi — V2 ^^[ ^~^ ) ~ etc., this is sufficiently accurate for prac- 

 tical purposes, (for ideal mixtures, where v is a Hnear function of x, it is of 

 course quite accurate). 



Yet in a so early paper as the one cited by K. of 1894 (Z. f. Ph. Gh. 15, 



p. 464) it is clearly to be seen that the result obtained by me agrees perfectly 



with his. For it says (line 4 from the top) that Va' (the index a' is there always 



dv 

 used for the liquid phase) = ^ — . But this is in the a;-notation nothing but 



OUa' 



dv . 



V — x^— , tke physical meaning of which is : the molecular volume of the water 

 Ox 



in the solution with the concentration x. 



The phrase occurring on page 466 : "und niemals etwa Vn' — b im Sinne etc." 



refers there to the well-known attempts of Ewan and others. The same is the 



case with the phrase in the paper on non-diluted solutions in the Gh. Weekblad 



of June 7th 1905: "Ook heeft men getracht, etc." (j). 5). 



