250 HYDROGEN ION CONCENTRATION 



laries, i.e., of the thickness of the diaphragm, as long as the intensitj' 

 of the field (or the fall of potential per sq. cm.) in the diaphragm 

 remains constant. In other words : The amount of water transported 

 through a diaphragm is proportional to the total current intensity and is 

 independent of the length and of the width of the pores of the diaphragm. 

 It is dependent, however, upon the nature of the substance of the 

 diaphragm as well as of the liquid used. These are exactly the laws 

 which Wiedemann (1. c.) had previously established experimentally. 



In the above discussion the assumption was made that the adher- 

 ing layer is completely motionless. If this were not exactly true, then 

 the value of f as calculated from the above equation becomes some- 

 what too great. Further, it is also assumed that the dielectric con- 

 stant K is the same in the boundary layer of the water as the usual 

 dielectric constant of water. Furthermore, the friction coefficient, 

 77, must only be applied when it is assumed that the distance between 

 the double layers is indeed small, and yet quite great in relation to 

 the size of a molecule. Lamb'^ developed a theory in which he ne- 

 glected these assumptions. But since formally a quite similar equa- 

 tion is derived and only the absolute value of f is affected by it, we 

 shall limit ourselves merely to this mention. 



Helmholtz's theory also demands that the diaphragm should con- 

 sist of only similar and lengthwise parallel capillaries. Smoluchowski 

 extended the theory to diaphragms with capillaries running in any 

 desired direction and found no demonstrable deviations from Helm- 

 holtz's laws. 



The entire phenomenon of electroendosmosis can be pictured as 

 follows: A thin laj^er of water lying adjacent to the walls of the pores 

 of the diaphragm is displaced tangentially along these walls by the 

 field of force of the electric current; and this layer carries along with 

 it, because of cohesion, water layers further removed from the walls 

 of the pores. The water is to a certain extent pulled tangentially 

 at its boundary layer. 



73. The theory of electrophoresis 



In a wide U-tube filled with water are suspended fine insoluble 

 (either solid or fluid) particles, and an electric current is sent through 

 the suspension. The current affects, conversely to the preceding case, 



22 H. Lamb, Phil. Mag. 25, 52 (1888). 



