44 Mr. 0. Heaviside on Maxwell^s Electromagnetic 



Now, lastly, the wires have resistance, and this is without 

 any representation whatever in a real dielectric. But, as I 

 have before shown, the effect of the resistance of the wires in 

 attenuating and distorting waves is, to a first approximation 

 (ignoring the effects of imperfect penetration of the magnetic 

 field into the wires), representable in the same manner exactly 

 as the corresponding efi'ects due to g, the hypothetical mag- 

 netic conductivity of a dielectric*. Thus, in addition to the 

 above, 



47r^ becomes E, 

 R being the resistance of the circuit per unit length. 



16. In the circuit, if infinitely long and perfectly insulated, 

 the total charge is constant. This property is independent of 

 the resistance of the wires. If there be leakage, the charge 

 Q at time t is expressed in terms of the initial charge Qo by 



independent of the way the charge redistributes itself. 



In the general medium, the corresponding property is per- 

 sistence of displacement, no matter how it redistributes itself, 

 provided k be zero, whatever g may be. And, if there be 

 electric conductivity. 



/^ 00 / /"* CO 



where Dq is the initial displacement, and D that at time t, 

 functions of z. 



In the circuit, if the wires have no resistance, the total 

 momentum remains constant, however it may redistribute 

 itself. This is an extension of MaxwelFs well-known theory 

 of a linear circuit of no resistance. The conductivity of the 

 dielectric makes no difference in this property, though it 

 causes a loss of energy. When the wires have resistance, 

 then 



PlC dz= ( I LCo dzy-^'l^ 



expresses the subsidence of total momentum ; and this is 

 independent of the manner of redistribution of the magnetic 

 field and of the leakage. 



In the general medium, when real, the corresponding pro- 

 perty is persistence of the induction (or momentum) ; and 

 when g is finite, 



I ixRdz=(^ /iHo dz\ e-^^stlt>., 

 * '<■ Electromagnetic Waves," § 6 (Phil. Mag. Feb. 1888). 



