Forced Vibrations of Electromagnetic Systems. 389 



The reflected wave, superimposed on the primary, annuls 

 the H disturbance, which is therefore, after the reflexion, 

 confined to a spherical shell of depth 2a containing the un- 

 cancelled part of the primary wave outward. 



The amplitude of H at the fronts of the two primary waves, 

 in and out, before the former reaches the centre, is 



(f 1 va)^-(2fi vr). 



After the inward wave has reached the centre, however, the 

 amplitude of H on the front of the reflected wave is the 

 negative of that of the primary wave at the same distance, 

 which is itself negative. 



The process of reflexion is a very remarkable one, and 

 difficult to fully understand. At the moment t=a/v that the 

 disturbance reaches the centre, we have H = (/ 1 v)-r-(4 ( u, 'i;), 

 constant, all the way from r=Q to 2a, which is just half the 

 initial value of H on leaving the surface of the sphere. But 

 just before reaching the centre, H runs up infinitely for an 

 infinitely short time, infinitely near the centre ; and just 

 after the centre is reached we have H = — c© infinitely near 

 the centre, where the H disturbance is always zero, except 

 in this singular case when it is seemingly finite for an infinitely 

 short time, though, of course, v is indeterminate. 



With respect to this running-up of the value of H in the 

 inward primary wave, it is to be observed that whilst H 

 is increasing so fast at and near its front, it is falling else- 

 where, viz. between near the front and the surface of the 

 sphere ; so that just before the centre is reached H has only 

 half the initial value, except close to the centre, where it 

 is enormously great. 



After reflexion has commenced, the H disturbance is 

 negative in the hinder part of the shell of depth 2a which 

 goes out to infinity, positive of course still in the forward 

 part. At a great distance these portions become of equal 

 depth a; at its front H= (/ 1 va)(2/* ?;r)~ 1 , at its back 

 H= — ditto; using of course a different value of r. 



22. As regards the electric field, we have, by (133), 



which, expanded, is 



~~2r\ \ qa)\ qr q 2 r 2 ) 



+ £ -,<« + ,( 1+ i)(l + l + l 5 )j /i; . (144) 

 Phil. Mag. S. 5. Vol. 25. No. 156. May 1888. 2 D 



