208 PROPAGATION OF ELECTRICITY. 



The potential V of the wire is, moreover, proportional to the 

 total charge, and therefore to the charge of each unit length. 

 We have then 



A being a constant which depends on the section of the wire, and on 

 its position in reference to external conductors. 



If the charge of the wire varies from one point to the other of 

 the length, the linear density at a point, is the limit of the ratio of 

 the charge to the corresponding lengths. 



When equilibrium does not hold, it is not generally speaking 

 exact that the potential at each point is proportional to the 

 density; but this proportionality is evidently in particular true for 

 cables, in which the conducting wire is surrounded by a dielectric 

 layer of constant thickness, which in turn is surrounded by a con- 

 ductor in connection with the earth. The various parts of the wire 

 are then without appreciable action on each other, and the potential 

 at each point is that due solely to the nearest electrical masses. If 7 

 be the capacity of unit length of the wire that is to say, the charge 

 which would correspond to unit potential the charge of a length dx 

 at potential V would be equal to yVdx. 



220. PROPAGATION IN A WIRE WHEN THERE is A Loss ON 

 THE SURFACE. Let us still consider a cylindrical wire traversed by 

 a current, and let us suppose that the permanent state has been 

 attained, but that there is a loss of electricity on the surface. The 

 flow is no longer parallel to the axis throughout the entire extent of a 

 perpendicular section ; it tends to become perpendicular to the wire 

 close to the external surface. The equipotential surfaces S, S' 

 (Fig. 55) are still planes throughout the greater part of their extent, 



but they bend just near the edges and then join with the outer 

 surface of the wire. 



