498 KEPORT— 1887. 



as before, and 



^t|f5 = l (8) 



The constant I, whicli is of the nature of a line, measures, as it were, the 

 facility of slipping. In ordinary hydrodynamical problems, in which 

 there is no question of external surface-forces, the surface condition (1) 

 reduces to 



^ = ^dn (9) 



The motion will then be sensibly the same as it would be on the hypo- 

 thesis of no slipping, provided a layer of thickness I were removed from 

 the surface of the solid and replaced by fluid, it being supposed that I 

 is small compared with all the dimensions of the space occupied by fluid. 

 On making the substitutions (7) and (8), the formula (6) becomes 



U=^^.i.E (10) 



whicli differs from von Helmholtz's result only in containing the 

 factor l/d. 



In one respect the difference between the view here taken and that 

 adopted by von Helmholtz is little more than verbal. Von Helmholtz 

 considers that the velocity u is practically uniform over the section of 

 the tube, except near the wall, where it falls rapidly to zero. The 

 stratum within which this fall is supposed to take place is that occupied 

 by the (probably) molecular charges of electricity, whose aggregate is 

 represented by p. The two views might perliaps be reconciled by inter- 

 preting von Helmholtz's investigation as virtually a proof that l=:d, if ib 

 were not for the assumption that the equations of motion of a viscous 

 fluid, as well as the electrostatic equation 



V^^ + 4/xE = 



(where ^^^^d^ jd.v"^ + d'/dy"^ + d~/dz-, and e is the volume-density of 

 free electricity), may be supposed to hold through the thickness of the 

 stratum in question. Since these equations are only true in a statistical 

 sense, when the linear elements dx, dif, dz are taken to be large in com- 

 parison with the average distance between neighbouring molecules, 

 whereas the thickness of the stratum is almost certainly not more than 

 a very moderate multiple of this distance, it seems doubtful whether 

 they can fairly be pressed into service in the manner indicated. 



Althougli we have only somewhat vague probabilities to guide us, it 

 appears reasonable to suppose, from what we know of contact difierences 

 of potential in cases where they can be measured, that the ratio E/D will 

 not very greatly exceed or fall below unity ; that it will lie, say, between 

 about '1 and 10. If this be so, the comparison of our theory with the 

 observations entitles us to say that the sliding coefiicient I is at all events 

 of the same order of magnitude as d. If for water in contact with glass I 

 were equal to 10"* cm., this would make 



^ = /,/Z = l-4xl06 C.G.S. ; 



in other words, the shearing stress necessary (in the absence of electrical 

 surface forces) to produce a sliding of one centimetre per second would 

 be 1'4 megadynes per square centimetre. It follows that the effects of 

 slipping would be utterly insensible in ordinary hydrodynamical questions, 



