of Mixed Solutions. 283 



Thus we see that also in the general case the concentration in the 

 equilibrium state must be constant along a potential surface, and 

 for the same concentration pressure and temperature the con- 

 centration gradient will be proportional to the force intensity at 

 the point considered. 



The equations (21) determining the concentration fall in any 

 direction are perfectly symmetrical with regard to the (r + 1) 

 components. The solution found holds regardless of compressi- 

 bility of the solution and of the aggregate form of the single 

 components, and for any concentration whatever, that may have 

 physical existence. 



§ 5. Transformations. 



During the theoretical development we have assumed that the 

 concentration is defined as the number of gram-molecules per unit 

 volume. There are, however, several other ways of expressing the 

 concentrations, and it may be useful to find the expression of our 

 equation system corresponding to the most usual forms of concen- 

 tration. 



1. The concentration is defined as the mass of each component 

 contained in unit volume. Let us call these concentrations 

 Co, (7i ... Or, then 



Ci = Mini. * = 0, 1, 2...r. 



Introducing <^i = Mifi, 



and — = Qi, 



dfdC^dfdG, k.^-^(,a-l) i~0 12 r 



dCo dx '^dG, dx ^•■' dCr dx dx ^P^' ^' *-"'-^'^-"^- 



I cZC/q , dCi dUr ^ 



qi is the volume which unit mass of the component (i) occupies 

 in solution under the conditions present. 



2. The concentration is given as the amount of mass of each 

 component contained in unit mass of solution. Call these con- 

 centrations ao,(Ti ... (Tr, then 



Ci Ci 

 ai= ~ = . 



" 20. 







Employing well-known rules for transformation 



li^da^^^pd^^ JJ,d^M _ .^ 0, 1. 2 ... r. 



ocTo dx dcTi ax oar dx dx ' 



(23) -i 



(24). 



d(Tn ttCi ttCTj. ^ 



— - + ■ — - + ... — - = 0. 

 dx dx '" dx 



