610 Mr. L. Vegard : Contributions to 



Planck * has expressed the law in the following terms : 



v dj) =vdp. 



v is the volume of 1 gr. solvent, v is the increase of volume 

 suffered by a very great quantity of the solution, when 1 gr. 

 of solvent is added to it. If equation (1) is taken into con- 

 sideration, we get 



£ = l-f (6) 



op v 



In order to find the proportion — we will take a limited 



instead of an unlimited quantity, and add to it an exceedingly 

 small quantity of the solvent. We have as before : 



Vp = M. 1 n ] +M 2 n 2 . 



If we add a quantity M. 1 dni=p dv of the first component 



we get : 



dv 

 dx 



■ = v =^(l + 1 ,(l + ,)^Y . . . (7) 

 o % P\ P Off 



From equations (6) and (7) we almost immediately get 

 equation (5). 



Duhem f has developed the following formula : 



P,_P Ui(T)-,>( c ,T)+c(l+c)^9 

 ^ = ~ <c> T)-o(l +C )^) 



QC 



The term to the left corresponds fully to what we have 



called ^— . Furthermore, we'i have : 

 op 



U!(T) = - and v(c,T)=- . 



Po P 



If this is introduced, we get : 



£_( 1 + i c(1+c) |?) 



q 73 ^ _ Po v p p es 



3p_ i + i C (i +C )l" 



P OC 



* VlRncli,Zeitschr{ft fur physih. Chemie, xliii. p 584, 

 f Mecanique Chimique. tome iv. livre vi. p. 65. 



