Electric Endosmose and other Allied Phenomena. 53 



E.M.F. of a Daniell's cell. On the views adopted in this 

 paper the inference would be — 



Since this involves two unknown ratios, no such definite con- 

 clusion as to the value of E can be drawn • but it is evident 

 that the phenomena are consistent even with very small 

 values of E/D, provided I be a sufficient multiple of d. Since 

 this quantity d is of molecular order of magnitude (com- 

 parable probably with 10 -8 centim.), I may still be so small 

 that the effects of slipping would be entirely insensible in 

 such experiments as those of Poiseuille. 



1. In Wiedemann's experiments the poles of a galvanic 

 battery were connected with two metal plates immersed in a 

 conducting liquid (for instance, copper plates in a solution of 

 CuS0 4 ) and separated by a porous partition. In one set of 

 experiments the liquid was maintained at the same level on 

 the two sides, and the amount carried by " electric endos- 

 mose " through the pores was measured by the overflow on 

 the further side. This amount was found to be proportional 

 to the total amount of electricity conveyed by the current, 

 and independent of the area or of the thickness of the porous 

 partition. For solutions of the same salt, but of different 

 degrees of concentration, the amount of fluid carried across 

 was roughly proportional to the specific electric resistance. 



As typical of this class of experiment von Helmholtz con- 

 siders the case of a straight tube of uniform section, made of 

 insulating material, and containing a liquid through which 

 an electric current is made to flow. Taking the axis of x 

 parallel to the length of the tube, let u be the velocity of the 

 fluid at any point, fju the coefficient of viscosity, /3 the co- 

 efficient of sliding friction of the fluid in contact with the 

 wall of the tube. Considering the forces acting on a thin 

 surface film, and denoting by dn an element of the inwardly 

 directed normal, we find — 



^-^ +s=0 > w 



where the first term is due to the fluid friction on the inner 

 surface of the film, the second to the friction between the 

 outer surface and the tube, while the third term represents 

 the external forces reckoned per unit area. In all ordinary 

 hydrodynamical questions the latter term is absent, but in 

 the present case we have forces due to the fall of potential 

 along the tube, acting on the superficial layer. Let E be the 



