Forced Vibrations of Electromagnetic Systems. 133 



because the waves cannot return, as there is no reflecting 

 barrier in the infinite dielectric. 



3. If the impressed force be confined to the region between 

 two parallel planes distant 2a from one another, there are now 

 two sources of disturbances, which are of opposite natures, 

 because the vorticity of e is oppositely directed on the two 

 planes, so that the left plane sends out both ways disturbances 

 which are the negatives of those simultaneously emitted by 

 the right plane. Thus, if the origin of z be midway between 

 the planes, we shall have 



E=^H=-t/(*-tf} + i/( i -^) . (13) 



on the right side of the stratum of e, and 



-E=,™H= -*/(*+ f^) +*/(«+ ^) . (14) 



on the left side. If therefore e vary periodically in such a 

 way that 



f(t) = -At + 2a), (15) 



there is no disturbance outside the stratum, after the initial 

 waves have gone off, the disturbance being then confined to 

 the stratum of impressed force. 



Decreasing the thickness of the stratum indefinitely leads to 

 the result that the effect due to e=f(t) in a layer of thickness 

 dz at z=0 is, on the right side, 



*=-i{/K)-4-^)} 

 =-t/'K> <to 



since /ncv 2 =l ; on the left side the -f sign is required. 



We can now, by integration, express the effect due to 



e =A z , *), ^ iz - 



In these, however, a certain assumption is involved, viz. that 

 e vanishes at co both ways, because we base the formulse upon 

 (16), which concerns a layer of e on both sides of which e is 

 zero. Now the disturbances really depend upon de/dz, for 

 there can be none if this be zero. By (12) the elementary 



