194 Mr. G. A. Schott on the Electron 



force (P, 0, II), and of the magnetic force (A, M, N). At 

 a point so distant that terms of order -^ may be neglected 

 in comparison with those of order - I find 



n 2 cot 6 X s Jgn (sn/3 sin 6) sin sn [col t — ^ ) -f 8 + - — <£] , 



P = A = 0, 



^eB 



By Povnting's Theorem we easily find 



R= ?^« 2 T[^ 2 J / 2sB (257 ? )8)-A 2 (l-6 2 ) f J 2s «(2^r)^r]. 



P s=l Jo 



Using DuhamePs asymptotic value for the Bessel function 



we see that the series converges, and that for large values 

 of ™ we may take the first term only. 



When up is small we may content ourselves with the 

 lowest power ; in that case we get J. J. Thomson's result. 

 Generally we cannot neglect the higher powers and must 

 write 



-,. CVyS 2 ATV / M l+7\ 



approximately for n large. 



For ?i=l the series gives by (]irect summation 



3/> 2 (l-/3 2 ) 2 ' 



in agreement with the general result of §4. 



The reduction in the intensity of the radiation in the 

 present case is clearly due to interference between the waves 

 emitted by the several electrons of the ring. Each electron 

 may be supposed to emit the same amount of energy as if it 

 alone were present ; but to absorb a great portion of the 

 energy of the same type emitted by the remaining electrons 

 of the ring. From this point of view, the reduction in the 

 radiation from the electron is due to resonance. It is clear 

 that the electron can in the same way absorb energy from 

 any wave which passes it, provided the wave be properly 

 attuned to the motion of the electron. 



