DISTRIBUTION OF ELECTRICITY ON LINEAR CONDUCTORS. 207 



we get 



or 



According to this, the total resistance R of the medium is ex- 

 pressed by 



The same reasoning would apply to the case of a medium 

 unlimited on one side, and bounded on the other by a plane on 

 which two hemispherical electrodes A x and A 2 are placed. The 

 resistance would then be the double of the preceding, and we should 

 have 



TTCp 



It is remarkable that the resistance is independent of the dis- 

 tance of the two electrodes, and only depends on their dimensions 

 and on the conductivity of the medium. This case may be regarded 

 as corresponding to that of the earth when two points of the soil are 

 connected with electrodes kept at potentials of equal values and 

 opposite signs. 



219. DISTRIBUTION OF ELECTRICITY ON LINEAR CONDUCTORS. 

 When the state is permanent, as the density is zero in the interior of 

 the conductor (203), the potential is simply due to the electricity 

 which exists on the surface; this electrical layer is distributed ac- 

 cording to a law which can be determined in a few simple cases. 



Let us consider a rectilinear cylindrical wire, the diameter ot 

 which is very small as compared with its length, and placed in its 

 whole extent in conditions which are the same in reference to neigh- 

 bouring conductors. If this wire were electrified and in equilibrium, 

 the distribution of the superficial layer at some distance from its 

 ends would be uniform that is, that any portion of a surface 

 comprised between two planes perpendicular to the axis, and at 

 unit distance, would have the same quantity of electricity: let 

 A be this quantity, which may be called the linear density of 

 the wire. 



