54 Prof. H. Lamb on the Theory of Electric 



excess of potential of the liquid in contact with the wall of 

 the tube over that of the wall itself. It has been pointed out 

 by von Helmholtz that a discontinuity of potential implies the 

 existence, over the surface of discontinuity, of a " double 

 layer'" of positive and negative electricity (analogous to the 

 magnetic shells of Ampere), the difference of potential on the 

 two sides being equal to Air times the electrical moment of the 

 layer. We therefore suppose that in our present case there 

 exists in a thin superficial stratum of the fluid a distribution 

 of electricity whose amount per unit area is p, say, whilst in 

 a thin superficial stratum of the solid there is a complementary 

 distribution —p. If d denote (in an obvious sense) the mean 

 distance between these distributions, we have 



E=47r i od, 

 or 



p=cE (2) 



if 



c =l/4:7rd, 



that is, c denotes the capacity per unit area of the quasi- 

 condenser formed by the opposed surfaces of solid and fluid. 

 For the case of metallic electrodes (platinum, mercury) in 

 contact with acidulated water, von Helmholtz and Lippmann 

 have independently found the value of d to be comparable 

 with 10~ 8 centim., and we may reasonably suppose it to be 

 of a similar order of magnitude in the cases at present under 

 consideration. 



If <f> denote the electric potential at any point in the interior 

 of the fluid, we have 



*--£• .... (3) 



If Q be the sectional area of the tube, J the electric current 

 through it, a the specific resistance of the liquid, we have, by 

 Ohm's law — 



a<f>_ o-J 



da Q ' 



When the motion has become steady, there being no dif- 

 ference of fluid pressure between the two ends of the tube, 

 the velocity u will be uniform over the section, so that the 

 equation (1) becomes 



P U =%P> (5) 



and therefore the total flux per second is 



U = uQ=°3 J E (6) 



(4) 



