34 Mr. 0.. Heaviside on MaxwelFs Electromagnetic 



steady flux instantaneously ; and all variations of e in time 

 and in space are kept time to without lag by the conduction- 

 current in spite of the electric displacement. 



This property is seemingly completely at variance with ideas 

 founded upon the retardation usually asLOciated with combi- 

 nations of resistances and condensers. But, being a special 

 case of the nondistortional theory, we can now understand it. 

 For suppose we start with a nonconducting dielectric, and put 

 on e uniform within a spherical portion thereof, aud send out 

 an electromagnetic wave to infinity and set up the steady flux. 

 On now removing e, we send out another wave to infinity, 

 and the flux vanishes. Now make the medium conducting, 

 with both conductivities balanced, as in (10). Starting with 

 the same steady flux, its vanishing will take place in the same 

 manner precisely, but with an attenuation factor e~P*. Now 

 gradually reduce g and /j, at the same time, in the same ratio. 

 The vanishing of the flux will take place faster and faster, 

 and in the limit, when both /u, and g are zero, will take place 

 instantly, not by subsidence, but by instantaneous transference 

 to an infinite distance when the impresi^ed force is removed, 

 owing to V being made infinite. 



7. Second Special Case. — There is clearly a similar property 

 v/hen k = and c= 0, that is, in a medium possessing mag- 

 netic inductivity and conductivity, but deprived of the electric 

 correspondences. Thus, when g/fi is constant, the solution 

 due to any polar field Hq is 



'H=Hoe-p', E = 0; .... (13) 



wherein p = 4:7rgf/jb. But a solenoidal field of fiR disappears at 

 once, by instantaneous transference to infinity. Thus any 

 varying impressed force h is accompanied without delay by 

 the corresponding steady flux, the magnetic induction. 



When the inertia associated with /u, is considered the result 

 is rather striking and difficult to understand. It appears, 

 however, to belong to the same class of (theoretical) pheno- 

 mena as the forowing. If a coil in which there is an electric 

 cuirent be instantaneously shunted on to a second coil in 

 which there is no current, then, according to Maxwell, the 

 first coil instantly loses current and the second gains it, in 

 such a way as to keep the momentum unchanged. Now we 

 cannot set rp a current in a coil instantly, so that we have a 

 contradiction. But the disagreement admits of easy re- 

 conciliation. We cannot set up current instantly with a 

 firite impressed force, but if it be infinite we can. In the case 

 of the coils there is an electromotive impulse, or infinite elec- 

 tromotive force acting for an infinitely short time, when the 



