Endosmose and other Allied Phenomena. 59 



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

 small term Z/R in the denominator, we get 



p =^-!r B > < 18 > 



which again differs from von Helmholtz's result only in con- 

 taining the factor l/d. The comparison with Quincke's expe- 

 riments on the discharge of Leyden jars, &c, through a column 

 of liquid in a slightly inclined capillary tube can then be made 

 exactly as in von Helmholtz's paper. 



The result contained in (18) can be generalized. Taking, 

 for example, the case of a porous vessel, it has been shown 

 that the flux of liquid due to electrical causes is 



—=— x flux of electricity. 



The flux due to the difference of pressure P on the two sides is 

 -P/K, 



where K is a constant depending on the form and arrange- 

 ment of the channels and on the values of /j, and /3. This 

 constant might be called the "hydraulic resistance " of the 

 system of channels. Equating the total flux of liquid to zero, 

 we find 



P= — ^ — x flux of electricity. . . (19) 



For a tube of uniform circular section we have, neglecting l/R, 



K=8/*L/ttR 4 , 



leading to our previous result. 



3. Quincke has also made observations on the motion of 

 fine particles, suspended in a liquid through which electric 

 currents are flowing. For instance, in the case discussed in 

 § 2, where, under the influence of an electric current, the fluid 

 in a tube of circular section flows (as a rule) forwards along 

 the walls and backwards along the axis, the integral flux across 

 any section being zero, he found, using a glass tube -4 millim. 

 in diameter, thai; for a certain strength of current the particles 

 near the axis move backwards, whilst those near the walls 

 move forwards, though with less velocity. For stronger cur- 

 rents the motion of the suspended particles is everywhere 

 backwards, but more rapid the nearer to the axis. In nar- 

 rower tubes the motion was everywhere backwards, even with 

 the feeblest currents which were sufficient to produce percep- 

 tible motion at all. 



