( 512 ) 



(i, :=/{T) + RTlog (l-.r) + («, w^ + ,?, ..^ + ...), 

 a very good agreement is obtained between the caJciihited values of 

 the melting-temperatures at various values of .v, and the temperatures 

 observed by van Heteren (compare his Dissertation), at least up till 

 about 80° C. 



In a conference, 1 had since with prof, van der Waals, he called 

 my attention to an expression for the correction term in ft^, which 

 may be taken as a fairly good approximation ^). This expression is : 



(1 + «)' 



After he had first shown (}). 193), that the correctionterm is 

 really of the order .v- — this I also showed in my previous com- 

 munication, but in a different manner — and had observed, that (in 

 the case investigated by him) the value of rfj does not remain constant, 

 but decreases when ,r increases (p. 198), he afterwards arrived at 

 the said approximate expression (p. 213, 214), in agreement with 

 an empirical relation of Thomsen. 



Though Prof, van der Waals has lu'ietly gi\en the deduction of 

 his formula, it may he useful to state once more how" this expression 

 can be arrived at. The matter is of great importance, because the 

 Sf'ime quantity (i^ — (,Mi)x=o constantly occurs in a great number of 

 formulae, such as those for the lowering of the freezing-point, elevation 

 of the boiling-point, alteration in vapour pressures, etc. If therefore 

 this quantity is once for all accurately known, ^^e may get a better 

 insight into a great number of problems relating to binary mixtures. 



2. As the total thermodynamic potential is represented by 



^=-:S{u,k,)Tilo<,T-l}i- 



J' 



:<:{n,{e,\)-T2{n,{,M 



pd V — p V 



-{- RT:S {,1 florin,). 



1 of the compone 



^RT-^-ETlogn,. 



we obtain for the molecular potential of the component n^ : 



With 



2 n^.RT a 

 ^' ~ V—h F* 



1) Zeitschrift fur I^li. Gh. 8, pg. 18S (1891). Also compare different passages in 

 the second part of liis "Coutimntat'' on p. 43—45: 148; 152. 



Recently, Prof, van der Waals has returned to this question in his "" Ternary 

 Systems'' (Proc. March to July 1902). He gives there a more general and accurate 

 expression, wherein occur tlie critical temperature and pressure of the mixture 

 (Compare in particular IV, p. 92 — 96). 



