the Theory of Solutions. 593 



change, the exterior work will consist of two parts, and we 

 have 



$A=-p8v+8a, 



p is the pressure, v the volume, and 8a the work done by the 

 force in the field, on account of the variation. The equili- 

 brium condition will in our case then be 



8yjr-{-p8v = 8a; 

 and as p is constant, 



$(yfr+pv) = 8a, 



(^+/>r) is the exterior thermodynamic potential or the 

 thermodynamic potential under constant pressure. If this 

 function is indicated by o>, we get 



8ra = 8a (3) 



We will now consider a small volume element dx, dy, dz, 

 containing n 1 molecules of the first component, and n 2 mole- 

 cules of the second component. We select the X axis 

 parallel to the force at the point considered. Let us suppose 

 that the thermodynamic potential for the element — neglecting 

 quantities of a higher order — has the same value as it would 

 have had if the system had been homogeneous, and pressure 

 and concentration had had the same value as is to be found 

 in the centre of the element, to then becomes for the element 

 a homogeneous function of the first order ; and according to 

 a well-known theorem of Euler 



a>(M ini , M,a g1 p, T) = M^^ig^ + M s n 3 ^|g^ . (4a) 



The two partial derivatives are again homogeneous functions 

 of the Oth degree of the components. We put 



If we once more make use of Euler's theorem the result 

 will be 



ALi?? .,,, + Motto.— =-= N ^ /iyT .- = 0. 



Phil. Mag. IS. 6. Vol. 13. No. 77. May 1907. 2 S 



