496 REroRT— 1887. 



In the present paper a slightly different view is adopted on this latter 

 point. It is assumed that a solid offers a very p^reat, but not an infinite, 

 resistance to the sliding of a fluid orer it, and that this sliding is aa 

 essential factor in the phenomena referred to. On this modified hypo- 

 thesis the varions 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 Jjd, where Z is a linear magnitude measur- 

 ing 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 instance, compai'ing with the experimental results of Wiede- 

 mann, von Helmholtz infers that for a certain solution of CUSO4 in con- 

 tact with the material of a porous clay vessel, 



E/D=177, 

 where E is the contact difference of potential, and D the E.M.F. of a 

 Daniell's cell. On the views adopted in this paper, the inference 

 would be — 



E Z __ 



Since this involves two unknown ratios, no such definite conclusion aa to 

 the value of B can be drawn ; but it is evident that the phenomena are con- 

 sistent even with very small values of B/D, provided Z be a suSicient mul- 

 tijDle of d. Since this quantity d is of molecular order of magnitude (com- 

 parable probably with 10-*cm.), I may still be so small that the effects of 

 slipping would be entirely insensible in such experiments as those of 

 Poiseuille. 



1. In Wiedemann's experiments the poles of a galvanic battery were 

 connected with two metal plates immersed in a conducting liquid (for 

 instance, copper plates in a solution of CUSO4) and separated by a porous 

 partition. In one set of experiments the liquid was maintained at the 

 same level on the two sides, and the amount carried by ' electric 

 endosmose ' through the pores was measured by the overflow on the 

 further side. This amount was found to be proportional to the total 

 amount of electricity conveyed by the current, and independent of the 

 area or of the thickness of the porous partition. For solutions of the 

 same salt, but of different degrees of concentration, the amount of fluid 

 carried across was roughly proportional to the specific electric 

 resistance. 



As typical of this class of experiment, von Helmholtz considers the 

 case of a straight tube of uniform section, made of insulating material, 

 and containing a liquid through which an electric current is made to 

 flow. Taking the axis of x parallel to the length of the tube, let u be the 

 velocity of the fluid at any point, jj. the coefficient of viscosity, /3 the 

 coefficient of sliding friction of the fluid in contact with the wall of the 

 tube. Considering the forces acting on a thin surface film, and denoting 

 by dn an element of the inwardly directed normal, we find — 



i"^|-/3«-l-X=0 (1) 



where the first term is due to the fluid friction on the inner surface of 

 the film, the second to the friction between the outer surface and the 

 tube, while the third term represents the external forces reckoned per 

 unit area. In all ordinary hydrodynamical questions the latter term is 



