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VIII. On the Theory of Electric Endosmose and other Allied 

 Flwnomena, and on the Existence of a Sliding Coefficient for 

 a Fluid in contact with a Solid. By Professor Horace 

 Lamb, M.A., F.R.S* 



THE laws governing the electric transport of conducting 

 liquids through the walls of porous vessels or along 

 capillary tubes, and other related phenomena, have been in- 

 vestigated experimentally by Wiedemann f and Quincke}, 

 and explained by the latter writer on the assumption of a 

 contact difference of potential between the fluid and its solid 

 boundaries. This explanation has been developed mathema- 

 tically by von Helmholtz in his well-known paper on electric 

 double layers §. Applying the known laws of motion of 

 viscous fluids, he finds that the calculated results, so far as 

 they depend on quantities which admit of measurement, are 

 in satisfactory agreement with the experiments, and that the 

 values which it is necessary to assign to the contact difference 

 above spoken of are in all cases comparable with the electro- 

 motive force of a Daniell's cell. Incidentally he arrives also 

 at the conclusion that in the cases considered there is no 

 slipping of the fluid over the surface of the solids with which 

 it is in contact. 



In the present paper a slightly different view is adopted on 

 this latter point. It is assumed that a solid offers a very 

 great, but not an infinite, resistance to the sliding of a fluid 

 over it, and that this sliding is an essential factor in the phe- 

 nomena referred to. On this modified hypothesis the various 

 cases treated by von Helmholtz are discussed, and in some 

 respects extended. In all cases the results differ from those 

 obtained by von Helmholtz by a factor l/d, where Z is a linear 

 magnitude measuring the " slip," and d is the distance between 

 the plates of an air-condenser equivalent to that virtually 

 formed by the opposed surfaces of solid and fluid. For in- 

 stance, comparing with the experimental results of "Wiede- 

 mann, von Helmholtz infers that for a certain solution of 

 CuS0 4 in contact with the material of a porous clay vessel, 



E/D = l-77, 

 where E is the contact difference of potential, and D the 



* Communicated by the Author : read before Section A of the British 



Association at the Manchester meeting, September 1, 1887. 



t Pogg. Ann. lxxxvii. 1852, and xcix. 1856. 



| Ibid, cxiii. 1861. An excellent summary is given in "Wiedemann's 

 Eektricitdt, ii. pp. 166 et seq. 



§ AVied. Ann. vii. 1^79 ; or Collected Papers, i. p. 855. 



