58 Prof. H. Lamb on the Theory of Electric 



difference of pressure in the absence of electrical forces. This 

 follows at once from the linearity of the equations. Wiede- 

 mann and Quincke have made experiments in which the 

 fluxes of liquid due to the two causes just balance one another, 

 the subject of measurement being the difference of pressure 

 which exists between the two sides when this equilibrium is 

 established. In Wiedemann's experiments the difference of 

 pressure maintained in this way between the two sides of a 

 porous partition was found to vary directly as the strength of 

 the electric current, inversely as the area of the porous wall, 

 and directly as its thickness. For solutions of different 

 degrees of concentration the pressure was proportional to the 

 electric resistance. 



In the case of a tube of uniform circular section treated by 

 von Helmholtz, taking the axis of x along the axis of the tube, 

 and using cylindrical coordinates x, r, the first of the equations 

 (12) becomes 



dp _ ti {d?u j_ 1 du y 



dx 



Here p is a function of x only, u one of r only. Hence each 

 side of the equation must be constant and = P/L, where L is 

 the length of the tube, and P the difference of pressure between 

 its ends. Hence 



Determining C so that the integral flux across the section is 

 zero, we find 



~ &(•*-?) w 



The velocities close to the wall and in the axis of the tube are 

 equal and opposite. The surface condition, viz. 



^* _*,;_„#_, 



x 



/d?u , 1 du\ ,., - N 



■"£-^-<>I= . («) 



leads, since 



to 



d<b _ a~J 

 dx'~~^K 2 ' 



p_ 8>L _ aJ 



7rR 4 (l + 4/V/3R)' ' P 



2o-JL I 



7r 2 K 4 (l + 4//K)'d 



E. 



