ON THE VORTEX THEORY OF THE LUMINIFERODS iETHER. 495 



upper part of the diagram represents the state of affairs when t = ; 

 the lower when i = 7r/ (2w), But it must not be overlooked, that all 

 this (§§ 22, 23) depends on the unproved assumption that the symmetrical 

 arrangement is stable. 



24. It is exceedingly doubtful, so far as I can judge after much 

 anxious consideration from time to time during these last twenty years, 

 whether the configuration represented in fig. 1, or any other symmetrical 

 arrano-ement, is stable when the rigidity of the ideal partitions enclosing 

 each ring separately is annulled throughout space. It is possible that the 

 rigidity of two, three, or more of the partitions may be annulled without 

 vitiating the stability of the steady symmetric motion ; but that if it be 

 annulled through the whole of space, for all the partitions, the symmetric 

 motion is unstable, and the rings shuSle themselves into perpetually vary- 

 ing relative positions, with average homogeneousness, like the ultimate 

 molecules of a homogeneous liquid. I cannot see how, under these 

 conditions, the ' vitiating rearrangement ' referred to at the end of § 20 

 can be expected not to take place within the period of a wave or vibration. 

 To suppose the overall diameter of each ring to be ■\ery small in pro- 

 portion to its average distances from neighbours, so that the crowd would 

 be analogous rather to the molecules of a gas than to those of a liquid, 

 would not help us to escape the yitiating rearrangement which would be 

 analogous to that investigated by Maxwell in his admirable kinetic theory 

 of the viscosity of gases. I am thus driven to admit, in conclusion, that 

 the most favourable verdict I can ask for the propagation of laminar 

 waves through a turbulently moving inviscid liquid is the Scottish verdict 

 of not proven. 



Oil the Theory of Electric Endosmose and other Allied Phenomena, 

 and on the Existence of a Sliding Coefficient for a Fluid in 

 contact with a Solid. By Professor Horace Lamb, 31. A., F.R.8. 



[A communication ordered by the General Committee to be printed in extenso 

 among the Reports.] 



The laws governing the electric transport of conducting liquids through 

 the walls of porous vessels or along capillary tubes, and other related 

 plienomena, have been investigated experimentally by Wiedemann • 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 mathematically by von HelmhoUz 

 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 electromotive force of a Daniell's cell. In- 

 cidentally 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. 



• Pogg. Ann. Ixxxvii. 1852, and xcix. 1856. 



- Ibiil. cxiii. 1861. An excellent summary is given in Wiedemann's EleHricitdt 

 ii. pp. 166 et seq. 



* Wied. Ann. vii. 1879; or Collected Papers, i. p. 855. 



