ON ELECXKIC ENDOSMOSE AND OTHER ALLIED PHENOMENA. 497 



absent, but in the present case we have forces due to the fall of potential 

 along the tube, acting on the superficial layer. Let E be the excess of 

 potential of the liquid in contact with the wall of the tube over that of 

 the wall itself. It has been pointed out by von Helmholtz that a discon- 

 tinuity of potential implies the existence, over the surface of discontinuity, 

 of a ' double layer ' of positive and negative electricity (analogous to the 

 magnetic shells of Ampere), the difference of potential on the two sides 

 being equal to 47r times the electrical moment of the layer. We therefore 

 suppose that in our present case there exists in a thin superficial stratum 

 of the fluid a distribution of electricity whose amount per unit area is p, 

 say, whilst in a thin superficial stratum of the solid there is a complement- 

 ary distribution — p. If d denote (in an obvious sense) the mean distance 

 between these distributions, we have 



E = 4<TTpd, 

 or 



P = cE . . . . (2) 



if 



C = Ij-iTrd, 



that is, c denotes the capacity per unit area of the quasi-condenser formed 

 by the opposed surfaces of solid and fluid. For the case of metallic 

 electrodes (platinum, mercury) in contact with acidulated water, von 

 Helmholtz and Lippmann have independently found the value of d to be 

 comparable with 10~* cm., and we may reasonably suppose it to be of a 

 similar order of magnitude in the cases at present under consideration. 



If (f> denote the electric potential at any point in the interior of the 

 fluid, we have 



^=-^g .... (3) 



If Q be the sectional area of the tube, J the electric current through 

 it, (7 the specific resistance of the liquid, we have, by Ohm's law — 



dcf) ffJ 



~dx-q (4) 



When the motion has become steady, there being no difierence of fluid 

 pressure between the two ends of the tube, the velocity u will be uniform 

 over the section, so that the equation (I) becomes 



/5« = qP (5) 



and therefore the total flax per second is 



U= mQ =j E . ; . . (6) 



Since in most cases the flux is in the positive direction of the electric 

 current, we must assume that, as a rule, E is positive, i.e., the fluid is 

 positive relatively to the solid. ^ 



To compare with von Helmholtz's result let ns write 



c = l/47rd: (7) 



' The most noteworth}'- exception appears to be oil of turpentine in contact with 

 glass or clay. In contact with sulphur, on the other hand, it appears to be positive. 

 (Quincke.) 



1887. ^ ^ 



