420 Mr. 0. Heaviside on the 



gation of magnetic induction into it is concerned, may be 

 regarded as independent of the rest of the line ; the variation 

 of the boundary magnetic force or of C fully determining the 

 internal state of the conductors, exactly as it would do were 

 there no electrostatic induction. 



In a copper wire, in which />t=l, and &= 1/1 700, the value 

 of the quantity Airfikp is p/135. On the other hand, the 

 quantity m in — s 2 = 4:7r/j,kp + m 2 has values 0, irjl, 2ir/l, &c, 

 or a similar series, in which I is the length of the line in cen- 

 timetres, so that jtt 1 1 is a minute fraction, unless^' be exces- 

 sively large. But then it would correspond to an utterly 

 insignificant normal system. We may therefore take 

 — s 2 = ^irfjbkp r 



It will be as well to repeat the system that results, from 

 Part II. The line-integral of the radial electric force across 

 the dielectric being V, from the inner to the outer conductor 

 (concentric tubes), and the line-integral of the magnetic force 

 round the inner conductor being 47rC, so that is the total 

 current in it, accompanied by an oppositely direct current of 

 equal strength in the outer conductor, V and C are connected 

 by two equations, one of continuity of C, the other the equa- 

 tion of electric force, thus : — 



_^=SV, e-^=L C + E 1 "C + R/C . (141) 



Here e is impressed force, S the electrostatic capacity, and L 

 the electromagnetic capacity, or the inductance, of the dielec- 

 tric, all per unit length of line ; and R/' and R 2 " are certain 

 functions of d/dt and constants such that R/'C and — R 2 "C 

 are the longitudinal electric forces of the field at the inner and 

 outer boundaries of the dielectric, which, when only the first 

 differential coefficient dC/dt is counted, become 



R^R. + L.I, E/=R 2 + L 2 | 



respectively, where R 1? L a , and R 2 , L 2 are the steady-flow 

 resistance and inductance of the two conductors. 



The forms of R/ and R 2 " are known when the conductors 

 are concentric circular tubes, of which the inner may be solid, 

 making it an ordinary round wire. Now t if the return con- 

 ductor be a parallel wire or tube externally placed, it is clear 

 that we may regard R/ and R 2 " as known in the same manner, 

 provided their distance apart be sufficiently great to make the 

 departure of the distribution of current in them from symmetry 

 insensible. We have merely to remember that it is now the 

 inner boundary of the return tube that corresponds to the 



