ADSORPTION POTENTIALS AND ELECTROKINETIC PHENOMENA 249 



the layer set in motion and the wall. Hence, in our stationary con- 

 dition we have 



d 



where d is the distance between the moving electric layer and the 

 resting laA^er, hence it is the thickness of the double layer. 



If, on the other hand, the volume >f> of the fluid displaced per 

 unit of time is measured, then the velocity v can be expressed in 

 the following terms, on the assumption that the diaphragm is rep- 

 resented by a single capillary whose average cross section has the 

 radius r: 



TT r^ V = ^5 



from which it follows that 



<r d = ^^ X :g 



IT r^ H 



This equation permits us to calculate the potential f at the phase 

 boundary surface from the velocity of the water transport. The 

 potential difference between the moving and the resting layer is, 

 according to the laws of theoretical physics, 



f=-X47r(rd 

 K 



K represents here the dielectric constant of water (Helmholtz left 

 this value out of consideration, and it was first applied by Pellat and 

 Perrin), therefore, 



4 IT 77 <p 



K TT r^ H 



If the diaphragm consists of a large number, n, of similar capil- 

 laries of radius r, the total cross section of all of them being s, and the 

 amount of water transferred in a unit of time being $, then cor- 

 respondingly: 



4 TT 77 $ 



f = T^ X - X - 

 Iv s H 



It follows, therefore, that the transfer of the water is proportional 

 to the intensity of the electric field and to the cross section of the 

 diaphragm, but that it is independent of the length of the capil- 



