[macgregor] conductivity OF ELECTROLYTES 73 



region occupied by itself and one otlier electrolyte having a coniinon ion, 

 it gives thirty-six equations such as, 



A + A A 



^1 + l\ Vi -\- u, 



Tliese forty-five equations, however, are not independent, but may be 

 reduced to eight, viz. : 



(10) . . . . El ^ El ^ _A, 



which are thus necessarj^ conditions of equilibrium. 



Applied to each electrolyte throughout the region occupied by itself 

 and two other electrolytes having a common ion, we obtain 18 equations, 

 such as, 



fh A + A + A A 



Vi + i\ -j- v^ Vi + i\ + Vg c, + i\ H- v^ 



These, however, as in Case III., may be deduced from those given above. 



Applied to each electrolyte throughout the region occupied by it, 



another electrolyte having no ion in common with it, and the products of 



their double decomposition, the equilibrium law gives 36 equations, such as, 



^1 (/^i + A) (A + A) 



I'l + ^2 + tu + ^^5 iVi-{-V2-\-V^-{- Vj' 



These equations, when combined, give 9 equations, such as, 

 which, however, are not independent, but reduce to four, say, 



(11) 





which thus form additional necessary conditions of equilibrium. 



Applied to each electrolyte throughout the whole volume of the 

 solution, the equilibrium law gives 9 equations, such as 



^ W _ /A + A + (h . A + A + A ^ 



which, however, may be deduced from the twelve equations (10) and (11). 

 These twelve equations thus express the necessary conditions of equili- 

 brium. 



