[macgregok] conductivity OF f:LECTROLVTES 71 



thi-onghout the regions occupied by it and 3, and by it and 4, respec- 

 tively, gives the equations, 



c. 



^'1 4- (-3 r, + c, r, + r, 



, h, /^i + A /^i . 



(_ J — . ■ , 



Vx + ^\ '"i + V, i\ + i\ 



iind a simihir application to the other electrol3'tes gives six other similar 

 equations. These twelve equations may be reduced, as in Case I., to the 

 three indejiendent equations, 



(7) . . . . A ^ j^ ^ A ^ A. 



'"i i"r. ''3 ^\ 



It is, therefore, a necessar}' condition of equilibrium that the concentra- 

 tions of ions, in the regions occupied by the four electrolytes, respectively, 

 shall be equal. 



We may obtain other equations of equilibrium by expressing the fact 

 that each electrolyte is in equilibrium throughout the whole solution. 

 Thus we obtain for electrolyte 1, 



(8) . . . . .^ ^'^ _ (^x + ^ A + A 



and similar equations for 2, 3 and 4. From (G) we have, 

 and from (8), 





, (A + A) (A + A) 



C\'>\ = 



Hence El ^ (A + f±ù (A + /JJ 



From the other equations similar to (6) and (8) we obtain 



From these four equations and (7), we obtain : 



A (A + A:) (A -f A) = A (/:^, + /i,,) (/i, + /ij, 

 A (A + A) (A + A) = A (A + /A) (A + A), 

 A (A + A) (/:^. + A) = A (/^, + A) (A + A) ; 



