156 Prof. J. J. Thomson on the 



If e is the charge on one of the atoms of the electrolyte, 

 m the number of molecules per unit of area of a plane in the 

 electrolyte parallel to the electrodes, then, when the molecules 

 are polarized, the charge per unit area on the end of the chain 

 of molecules is me ; this equals the surface-density on the 

 electrodes KE/4-7T, where E is the electromotive intensity and 

 K the specific inductive capacity of the electrolyte. Hence 



4-7T 



If c be the conductivity of the electrolyte, N the number of 

 molecules in unit volume, we have 



-r- n = c, m = Nd. 



4-7T 



Making these substitutions, we find 



cE 



which is the same as the expression for the sum of the 

 velocities given by Kohlrausch. The ratio of the velocities 

 will follow exactly the same way from the migration-data 

 whichever theory we adopt ; so that there is nothing in 

 Prof. Lodge's confirmation of Kohlrausch's expressions for 

 the velocity of the ions inconsistent with the theory of con- 

 duction we are describing. 



We will now leave the consideration of thes behaviour of 

 these tubes in conductors, and proceed to discuss their pro- 

 perties when moving through the dielectric. 



Let /, g, h denote the number of unit tubes parallel to the 

 axes of x, y, z respectively — in other words, the components 

 of the electric displacement ; and let us suppose that these 

 tubes are moving with the velocity u, v, w parallel to the 

 axes of coordinates. 



Let us consider the increase in the number of tubes parallel 

 to x which occurs in a time 8t in an element of volume 

 dx, dy, dz. 



The increase due to the passage of the tubes across the 

 faces of the element is 



-*(aW+£o*)+ £0*0)1.**. 



The increase due to the deformation of the tubes inside 

 the element is 



*(>£ + '£ + *£) <te * <fc 



