590 Mr. L. Vegard : Contributions to 



If in a small volume element of the solution there are n± 

 molecules of the first and n 2 of the second component, the 

 concentration will be defined by the equation 



M 2 n 2 



The task we now set before us, is to find c as a function 

 of the coordinates when equilibrium has set in, and the 

 temperature is the same all over the system. 



To keep the system in equilibrium, two conditions must be 

 present — one mechanical and one thermodynamic. If the 

 pressure at a point in the fluid is given by p, it gives the 

 following mechanical condition for equilibrium : 



7 ^U BU 3TJ \ 



p is the density of the solution at the point considered. To 

 maintain equilibrium it is absolutely necessary for p to be a 

 function of the coordinates, i. e., dp must be an exact differ- 

 ential. Consequently: 





*S) »(< 



dp 





B7 





On differentiation and rearrangement ; 



dp dp 

 d~# bv 



d# d,y 



where K denotes the resultant of the force intensity at the 



point, and - *- the change of density per unit of length in 



the direction of thejforce. 



As the density is a function of the coordinates, 



dp^dx+^dy + ^dz, 

 ox dy oz 



or by use of the above equation 



