UNPUBLISHED FRAGMENTS. 431 



Integrating from one point to another in the electrolyte, 



C l /C 1 y l 



The evaluation of these integrals which denote the resistance and 

 electromotive force for a finite part of the electrolyte depends on 

 the distribution of the ions in the cell. For one salt with varying 

 concentration, 



dx 



or, since C 1 y 1 = c 2 y 2 and C 1 c?y 1 = c 2 (iy 2 , 



I- 

 \ 



dx 



Vl 

 i ^2 



The resistance depends on the concentration throughout the part of 

 the cell considered, but the electromotive force depends only on the 

 concentration at the terminal points (' and "). 



/y <y 



For C 1 M 1 and c z M 2 we may write and - 1 , where v l and v z are 



a n a n 



the " valencies " of the molecules. This gives 



2i _ ^2 

 V"- V 7 = a H At-~ z log^j f , for = (circuit open). 



I think this is identical with your equation (V) when your ions 

 have the same valency. 



Planck's problem is less simple.* We may regard it as relating to a 

 tube connecting the two great reservoirs filled with different electro- 

 lytes of same concentration, i.e., ^oyo' = 2 Coyo"' I use (o) f r an y 

 ion, (J for any cation, ( 2 ) for any anion. [The accents Q and (") 

 refer to the two reservoirs.] 



The tube is supposed to have reached a stationary state and 

 dissociation is complete. The number of ions is immaterial, but they 



all must have the same valency v. 



v 



Now by equations (3) and (4), since cJJ/ = , 



H 



dV 



[Planck, Wied. Ann., vol. xl (1890), p. 561.] 



