﻿216 



Lord Rayleigh on the Mutual Influence of 



The following table gives the values o£ F for values of 2m 



not greater than 2 :■ 



2m. 



F. 



2m. 



F. 



2m. 



F. 



0-05 



0-0459 



0-70 



0-7042 



1-40 



1-266 



0-10 



01514 



0-80 



0-7588 



1-50 



1-269 



020 



0-3582 



0-90 



0-8256 



1-60 



1226 



0-30 



0-4836 



1-00 



0-9080 



1-70 



1-159 



040 



0-5583 



110 



1-006 



1-80 



1-088 



0-50 



0-6110 



1-20 



1-113 



1-90 



1-026 



060 



0-6569 



1-30 



1 



1-208 



j 2-00 



0-975 



In the case of two resonators the integration in (23) 

 presents no difficulty ; but when there are a larger number, 

 it is preferable to calculate the emission of energy in the 

 dispersed waves from the work which would have to be done 

 to generate them at the resonntors (in the absence of 

 primary waves) — a method which entails no integration. 

 We continue to suppose that all the resonators are 

 similarly situated, so that it suffices to consider the work 

 done at one of them — say the first. From (15) 



-\Jr = a \ — 



ilcr ^ e 



r — * ~ 



-ikR 



dr 



a 



^2* 



The pressure is proportional to iyfr, and the part of it 

 which is in the same phase as d-^rjdr is proportional to 



J v sin&B,l 



Accordingly the work done at each source is proportional to 



sin 



*{i+*T?} 



(28) 



Hence altogether by (19) the energy dispersed by 

 n resonators is that carried by an area S of primary wave- 

 front, where 



^ sin A-R 



s = 



n\ 2 



IT 



kU 



. (29) 



the constant factor being determined most simply by a 



