﻿214 Lord Rayleigh on tlie Mutual Influence of 



such that each singly would respond as much as possible 

 to the primary waves. The ratio of (16) to (17) must then, 

 as we have seen, be equal to — 1\, when i\ is indefinitely 

 diminished. Accordingly 



1 p -ikK 



,H- 2 V> c«o 



which, of course, includes (10). If we write a = A^ 7a , 

 then 



A '"[^#H^?r ,(I9> 



The other case arises when the resonators are so tuned 

 that the aggregate responds as much as possible to the 

 primary waves. We may then proceed as in the investi- 

 gation for a single resonator. In order that no work may 

 be done at the disturbing centres, (<^4-^) and d(<f)-\-yjr)jdr 

 must be in the same phase, and this requires that 



f+i_ t -jfe+2* =rea i, 



a r Y K 

 or - = TQ&\ + ik+i2, R ('20) 



The condition of maximum resonance is that the real part 

 in (20) shall vanish, so that 



1 . f ^sin&IT] 



«='H +2 ~ho • • • • (21) 



A =— ^Smffi ^ 



The present value of A 2 is greater than that in (19), as 

 was of course to be expected. In either case the disturb- 

 ance is given bv (15) with the value of a determined by 

 (18), or {21). 



The simplest example is when there are only two re- 

 sonators and the sign of summation may be omitted in (18). 

 In order to reckon the energy dispersed, we may proceed 

 by either of two methods. In the first we consider the 

 value of yjr and its modulus at a great distance r from 

 the resonators. It is evident that t|t is symmetrical with 



