from Faraday to jf . J . Thomson. 389 



unit electric field, the charge transferred across unit area in 

 unit time by the anions is 



vvcfdV^ RT dc\ 

 M\dx cv dx) 



We have therefore, if the total current be denoted by i, 

 . vc dV RT do 



- u+ M^- u - v >^Tdx> 



or 



dV 7 Mdx u-v RT dc , 



- - T - dx = - - ^ + -- dx. 

 dx (u + v)vc u + v vc dx 



The first term on the right evidently represents the product of 

 the current into the ohmic resistance of the parallelepiped dx, 

 while the second term represents the internal electromotive 

 force of the parallelepiped. It follows that if r denote the 

 specific resistance, we must have 



u + v = Mjrvc, 



in agreement with Kohlrausch's equation ;* while by integrating 

 the expression for the internal electromotive force of the 

 parallelepiped dx, we obtain for the electromotive force of a 

 cell whose activity depends on the transference of electrolyte 

 between the concentrations c, and c z , the value 



u-v RT fl dc . 



-- - T- <te> 

 u + v v c dx 



u-v RT , c, 



or log-, 



u + v v GI 



in agreement with the result already obtained. 



It may be remarked that although the current arising from 

 a concentration cell which is kept at a constant temperature is 

 capable of performing work, yet this work is provided, not by 

 any diminution in the total internal energy of the cell, but by 

 the abstraction of thermal energy from neighbouring bodies. 

 This indeed (as may be seen by reference to W. Thomson's general 



* Cf. P . 374. 



