430 UNPUBLISHED FRAGMENTS. 



the cation d) has the charge c lt the force necessary to prevent its 

 migration would be 



d/UL, , dV 



' * L yi ..__,_, 



dx 1 dx' 

 For an anion ( 2 ) the force would be 



dx 2 dx' 



Now we may suppose that the same ion in different parts of a 

 dilute solution will have velocities proportional to the forces which 

 would be required to prevent its motion. We may therefore write 

 for the velocity of the cation ( l ), 



, dV 

 " H C * 



and for the flux of the cation ( 1 ), 



~ , - .--- 



7 l 7l \~fa l dx ' - C.M, dx dx 



for the flux of the anion ( 2 ), 



dV 



,.. 



where k ly k 2 are constants ('migration velocities') depending on the 

 solvent, the temperature, and the ion.t Now whatever the number 

 of ions the flux of electricity is given by the equation 



where the upper sign is for cations and the lower for anions, and the 

 summation for all ions. This gives 



That is, J 



2 HFi 



A 1Y* , T _ 



-At l dV. 



/y /yi 



The form of this equation shows that since is the current, 



is the "resistance" of an elementary slice of the cell, and the next 

 term the (internal) electromotive force of that slice. 



* [c, is a positive number equal numerically to the negative charge on unit mass of 

 the anion.] 



t[Th e positive direction for both these fluxes is the direction of increasing x.] 

 t [The sign of the charge is not included in c. Honce the double sign is necessary.] 



