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tricity. In real cases the numerical value of this product is small 

 as compared with unity; the variation in the direction of motion is 

 only slight; lience we are allowed to assume this force to be always 

 perpendicular to the axis of X. If the magnetic force is along the 

 axis of ¥, the ions will obtain on additional velocity in the direc- 

 tion of the axis of Z i). 



These vclocities will cause difleiences of potential and of concen- 

 tration. Wiit'u the state of equilibrium has been reached it is not 

 necessary tliat the velocities should be zero, but it will be suf- 

 ficient if 



P. The velocities of positive and negative ions are equal. 



2"^. As much of the dissolved material wanders back by diffusion 

 in the molecular state as is transported in the form of ions by the 

 said velocities. 



For completing the image formed in this way we ought to ima- 

 gine at the borders of the liquid, or at all events outside the space 

 now considered, on one side molecules dividing into ions, on the 

 other side ions combining again into molecules. For the moment 

 we suppose the reaction-velocities for these processes to be infinitely 

 great. 



We will now work out the two conditions. 



]f we call the E. M. F. in the direction of the axis oï Z E, ^ the 

 ions obtain velocities in the direction of this axis equal to 



{U HE^-\- £-) U and ( V H Ej, — E,) V. 



Writing cj for the concentration of both ions and fj for the con- 

 centration of the salt, we may represent the velocities of diffusion 

 of the ions by 



A dc^ A dc-i 



■ . £/ and . V 



Cj dz t'l ds 



and that of the salt by . U. 



'•2 '/- 



Here A is a constant closely related to the diffusion constant of 

 completely dissociated electrolytes; B has a similar signification for 

 the diffusion of a non dissociated salt. 



') A calculation which takes into account the irregular thermal motion of the ions 

 leads to the same results. 



