PROPAGATION OF ELECTRICITY. 



is permanent, the flow of electricity for a volume- element is zero : the 

 flow of force which is proportional to it is zero also ; but the latter is 

 equal to 477^2, m being the mass in the volume in question ; hence 

 m = 0. Thus, when a system of conductors has attained a permanent 

 state, the electrical density is zero at all points of the conductor ; the 

 electrical masses which produce the potential V, and whose action 

 determines the current, are therefore entirely on the surface of the 

 conductors. These masses are not in equilibrium of themselves, and 

 they produce at each point the electromotive force of the current. 



It follows from this that the flow, whatever it may be, if it has a 

 real existence, is not a flow of free electricity ; on the hypothesis 

 of two fluids, we must assume that at every instant there is the same 

 quantity of the two electricities in each volume-element in the 

 interior of the conductor, and that these move in two equal currents 

 in opposite directions. On the hypothesis of a single fluid, each 

 element must be looked upon as containing at each instant the 

 normal quantity of electricity, while we still assume that this may 

 be either wholly or partially displaced. 



204, LINEAR CONDUCTORS. OHM'S LAW. Imagine a cylin- 

 drical wire, very long as compared with its diameter, placed in a 

 perfectly insulating medium, and let us suppose that the permanent 

 state has been attained. 



If there is no loss of electricity, the flow of electricity is parallel 

 at each point to the generating lines of the cylinder; the equi- 

 potential surfaces are therefore planes perpendicular to the axis of 

 the wire. The flow of electricity across any given section in unit 

 time is the same throughout the whole length ; let us call this flow 

 the intensity or strength of the current, or more simply the current^ 

 and denote it by /. Let V be the potential at the point P at a 

 distance x from a fixed plane perpendicular to the wire, and let S be 

 the section of the wire. 



The potential is simply a function of x, and the expression for 

 the current is 



dV 



t=-cS- . 

 dx 



As this flow is independent of x, we have 



= a, and V = ax + b, 



dx 



where a and b are constants to be determined. 



