Endosmose and other Allied Phenomena. 63 



If E is positive (as it appears to be in most cases ) the higher 

 potential is at the end towards which the liquid is forced. 

 With the same substitutions as before, this becomes 



&A- e > ■ < 28 > 



differing from von Helmholtz's result by the factor l/d, as in 

 the previous cases *. 



This result does not involve the dimensions of the tube, and 

 may therefore be surmised, like that contained in (10), to be 

 of much wider application than to the particular form of 

 channel above considered. It may be shown, in fact, that if 

 a liquid is forced by pressure through any system of channels 

 with homogeneous walls, and no external path is provided for 

 the electricity set free at various points of these, the resulting 

 distribution of electric potential is given by 



<£ =-5£j9 + const. " .... (29) 

 P 



In the first place it follows from (12) that this value of <£ 

 satisfies V 2 <£ = 0. 



We have next to take account of the fact that the integral 

 amount of electricity which, in consequence of the slipping of 

 the superficial film of liquid, crosses the contour of any 

 elementary area dS of the wall is not in general accurately 

 zero, and that each such element dS must be regarded, in 

 relation to the conducting mass of liquid, as a (positive or 

 negative) " source " of electricity. If the origin be taken in 

 this element, and the axis of z normal to it, the strength of 

 this source is 



-»(M> s 



4> 



Now at the origin we have 



w=0 -\ 



^jfdu^dw^ | 



(30) 



\dz dy 



* Dorn infers from a comparison of his experimental results with von 

 Helmholtz's formula that for water in contact with the glass of his tubes 

 ED=3-9, about. 



