Endosmose and other Allied Phenomena. 55 



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 us write 



c = l/±ird (7) 



as before, and 



HiP=l (8) 



The constant I, which 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 



u=A (9) 



dn K ' 



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

 the hypothesis 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 the fluid. 



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

 becomes 



U =£H- E > ao) 



which 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 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 aggre- 

 gate is represented by p. The two views might perhaps be 

 reconciled by interpreting von Helmholtz's investigation as 

 virtually a proof that l=d, if it were not for the assumption 

 that the equations of motion of a viscous fluid, as well as the 

 electrostatic equation 



V 3 <£ + 4^6=0 



(where \J 2 =d 2 /dx 2 + d 2 /dy 2 + d 2 /dz 2 , and e is the volume- 

 density of free electricity), may be supposed to hold through 



* The most noteworthy exception appears to be oil of turpentine in 

 contact with glass or clay. In contact with sulphur, on the other hand, 

 it appears to he positive (Quincke). 



