500 REPORT — 1887. 



direction as that of electricity, and stands to it in the ratio of x to — ^/o-, 

 that is, in the ratio a-pl /3. The formula (11) embraces all the laws dis- 

 covered experimentally by Wiedemann for the electric transport of liquids 

 through porous vessels. 



2. If a difference of pressure obtains between the two sides of a porous 

 wall, or between the two ends of a capillary tube, the flux above calcu- 

 lated must be superposed on that which would be maintained (as in 

 Poiseuille's experiments) by this difference of pressure in the absence of 

 electrical forces. This follows at once from the linearity of the equations. 

 Wiedemann 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 experi- 

 ments 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, tbe first of the equations (12) becomes 



dp fd^u 1 d'liX /-I r \ 



i = "Ur^+r^J • • • • ^^^^ 



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 



4/1 L 



Determining C so that the integral flux across the section is zero, we 

 find 



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

 opposite. The surface condition, viz. 



-^^-/5u-p^ = . . . (17) 



leads, since 



d<l> <tJ 



dx ttR'^' 

 to 



8/xL o-J 



^= 7rR4(i + 4^/^K) -^' P 



_ ^<tJL I 



If A denote the total E.M.P. along the tube, and if we neglect the 

 small term Z/R in the denominator, we get 



u^ — ir-^-^) .... (16) 



E. 



