372 Mr. 0. Heaviside on Electromagnetic Waves, and the 



and the oscillatory discharge follows. But the impressed 

 force keeping up the charge on the sphere need not be an 

 external cause, as supposed in the paper referred to. There 

 seems no other way of doing it than by having impressed 

 force with vorticity/j/ on the surface, but in other respects it 

 is immaterial whether it is internal or external, or superficial. 

 It may perhaps be questioned whether the sphere does 

 reflect, seeing that its surface is the seat of /. But we have 

 only to shift the seat of / to an outer spherical surface in the 

 dielectric, to see at once that the surface of the conductor is 

 the place of continuous reflexion of the wave incident upon it 

 coming from the surface of/. The reflexion is not, however, 

 of the same simple character that occurs when a plane wave 

 strikes a plane boundary (k = oo ) flush, which consists merely 

 in sending back again every element of H unchanged, but 

 with its E reversed ; the curvature makes it much more com- 

 plex. When we bring the surface of / right up to the con- 

 ducting sphere, we make the reflexion instantaneous. At the 

 front of the wave we have z=Q and 



H =fva/fjbvr = E//*u 



by (269) and (270), This is exactly double what it would 

 be were the conductor replaced by dielectric of the same kind 

 as outside, the doubling being due to the instantaneous re- 

 flexion of the inward going wave by the conductor. 



The other method of solution may also be applied, but is 

 rather more difficult. We have 



fivr 



M^IX 1 -^ 1 -^?)"/-- ( 272 > 



Expand the last factor in descending powers of (qa) 3 , and 

 integrate. The result may be written 



where x = a~ l (vt — r-\-a). Conversion to circular functions 

 reproduces (269). 



42 A. Same case with finite Conductivity. Sinusoidal Solution. 

 — It is to be expected that with finite conductivity, even with 

 the greatest at command, or & = (1600) -1 , the solution will be 

 considerably altered, being controlled by what now happens 

 in the conducting sphere. To examine this point, consider 

 only the value of H at the boundary. We have, by (264), 



H a =^>- 3 /v=( S £) 1 + ^)-yv. . . . (274) 



