Self-induction of Wires. 127 



the magnetic force at a point without giving rotation to the 

 electric force. Now as in a steady state the electric force has 

 no rotation (away from the seat of impressed force) , it follows 

 that under no circumstances (except by artificial arrangements 

 of impressed force) can we set up the steady state in a con- 

 ductor strictly according to the linear theory. We may 

 approximate to it very closely throughout the greater part of 

 the variable period, but it will be widely departed from in the 

 very early stages. 



Let there be a straight round wire of radius a h conduc- 

 tivity k u inductivity /n l9 and dielectric capacity c x ; surrounded 

 up to radius a 2 by a dielectric of conductivity k 2 , inductivity^, 

 and dielectric capacity c 2 : in its turn surrounded to radius a z 

 by a conductor of Jc 3 , fju 3j and c 3 . This might be carried on to 

 any extent; but we stop at r = a 3 , r being distance from the 

 axis of the wire, as the outer conductor is to be the return to 

 the inner wire. 



Let the magnetic lines be such as would be produced by 

 longitudinal impressed electric force, viz. circles in planes 

 perpendicular to the axis of the wire and centered thereon. 

 Let H be the intensity of magnetic force at distance r from 

 the axis, and distance z along it from a fixed point. Use (6*), 

 with h = 0, to find the electric current. It has two compo- 

 nents, say r longitudinal or parallel to z, and y radial, or 

 parallel to r } given by 



47rr=-#rH, 47T 7 =-^. . . . (11) 

 r dr ; dz ' 



We have also E = pT, if p is a generalized resistivity, or 



'-'=* + &! < i2 > 



Now use equation (7), with e = 0. The curl of the longitu- 

 dinal and of the radial electric force are both circular, like H, 

 giving 



*-'(§-$) < 13 > 



In this use (11), and we get the H equation, which is 

 did -,-,- , d 2 H . 7T - T T --f 



The suifixes 1? 2 , and 3 to be used, according as the wire, dielec- 

 tric or sheath, is in question. 



In a normal state of free subsidence, d / dt = p a constant. 

 Let also d 2 /tlz 2 = —m 2 , where m 2 is a constant, depending upon 



