the Theory of Solutions. 595 



Here dn u dn 2 , dc, dp, mean the average changes of the 

 four quantities n 1? >? 2 , c, p from one element to the other ; or 

 rather the changes which these quantities undergo when we 

 go from the centre of the first element to the centre of the 

 second. Then we can write 



7 d»l 7 , 7 B"2 7 



#«,= ax. da.-)— cLc. 



7 CV' 7 7 d/' 7 



ac = ^— dx, dp = =-^- cfa?, 

 and when we take equations (1) and (5) into consideration : 



It must now be noticed that n x and 72 2 do not change inde- 

 pendently of each other ; for there must always he sufficient 

 substance of both hinds -in each element to keep the volume 

 element full of fluid. 



Supposing that the molecular volumes of the components 

 are indicated at the concentration c by v } and v 2 respectively, 

 the volume of the first element will then be 



dx . dy . dz = I*,;*! + c 2 n 2 . 



In the other the concentration is different ; and the pressure 

 also. Let us., however, suppose that the fluid is incompres- 

 sible, and that we leave out of consideration the change of 

 volume with pressure. The molecular volumes of both com- 

 ponents of the second element will then be 



and the volume of the second element 



(vi + —^ dc\(n! + dn x ) 4- L, + ~de)(n 2 + d> 



= dx.dy.dz — VjWj + Us 

 For brevity's sake let us write 



(7a) 



\7U\ 





•2 S 2 



