ON ELECIBIC ENDOSMOSE AND OTHER ALLIED PHENOMENA. 501 



■which again differs from von HelmLoltz's result only in containing the 

 factor Ijd. The comparison with Quincke's experiments 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 pajDer. 



The result contained in (18) can be generalised. 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 arrangement of the 

 channels and on the values of fi and /3. This constant might bo called 

 the ' hydraulic resistance ' of the system of channels. Equating the total 

 flux of liquid to zero, we find 



^ KcrcE „ 



P=- — ^ X flux of electricity . . . (19) 



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



K = S/xL/ttR^ 

 leading to our previous result. 



3. Qnincke has also made observations on the motion of fine particles 

 suspended in a liquid through which electric currents are flowino-. Por 

 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 '-i mm. in dia- 

 meter, that for a certain strength of current the particles near the axis 

 move backwards, whilst those near the walls move forwards, thouo-h with 

 less velocity. For stronger currents the motion of the suspended particles 

 is everywhere backwards, but more rapid the nearer to the axis. In 

 narrower tubes the motion was everywhere backwards, even with the 

 feeblest currents which were sufficient to produce perceptible motion 

 at all. 



These phenomena have been explained in a general manner by Quincke 

 and von Helmholtz. If E denote the contact-difference of potential 

 between the solid particle and the fluid, we have electrifications ip cE on 

 the opposed surfaces, which are therefore urged in opposite directions by 

 the electric forces whose components are —dxpld-x, —d<pjdy, —df/dz. 



The principles of this paper lead to a very simple expression for the 

 velocity of an isolated particle when the motion has become steady, viz., 

 the velocity relative to the fluid in this neighbourhood is in the direction 

 of the electric current, and its amount is 



Y=-Cplf3 (20) 



where C denotes the gradient of electric potential, and p, (i have the same 

 meanings as before. To prove this take the axis of x parallel to the 

 general direction of the electric current in the neighbourhood of the 

 particle. The problem is virtually unaltered if we suppose the fluid to 

 flow \yith the general velocity — V past the solid, which is at rest. The 

 electric potential at a distance from the solid will be of the form 



