and Conductance Operators. 491 



matically equivalent to distributing the impressed force 

 throughout the whole circuit, and therefore its vortex-lines 

 over the whole boundary*. In reality, with finite speed, the 

 disturbances come from the real vortex-lines in time. 



There is still a limitation of the disturbances to the neigh- 

 bourhood of the vortex-lines when they are on the boundary 

 of the conductor, and the frequency of alternations is suffi- 

 ciently great, the impressed force being within the con- 

 ductor. 



But in a non-conducting dielectric this effect does not 

 occur, at least in any case I have examined. On the con- 

 trary, as the frequency is raised, there is a tendency to 

 constancy of amplitude of the waves sent out from the edge 

 of a simple sheet of impressed force, or from a shell of 

 vortex-lines of the same, in a dielectric. Very remarkable 

 results follow from the coexistence of the primary and re- 

 flected waves. Thus : — 



(d) If a spherical portion of an infinitely extended di- 

 electric have a uniform field of alternating impressed force 

 within it, and the radius a, the frequency w/27r, and the 

 speed v be so related that 



na na 

 tan — — — , 



v v 



there is no disturbance outside the sphere. There are nume- 

 rous similar cases ; but this is a striking one, because, from 

 the distribution of the impressed force, it looks as if there 

 must be external displacement produced by it. There is not, 

 because the above relation makes the primary wave outward 

 from the surface of the sphere, which is a shell of vorticity, 

 be exactly neutralized by the reflexion, from the centre, 

 of the primary wave inward from the surface. 



(e) If, instead of alternating, the uniform field of impressed 

 force in (d) be steady, the final steady electric field due to it 

 takes the time (r + a)/v to be established at distance r from 

 the centre. The moment the primary wave inward reaches 

 the centre, the steady state is set up there ; and as the 

 reflected wave travels out, its front marks the boundary 

 between the steady field (final) and a spherical shell of 

 depth 2<2, within which is the uncancelled first portion of 

 the primary wave outward from the surface ; which carries 

 out to an infinite distance an amount of energy equal to that 

 of the final steady electric field. This is the Joss by radiation. 

 [The magnetic energy in this shell equals half the final 



* ' Electrician/ June 25, 1886, p. 129. 



