﻿626 Dr. (j. V. Burton on the Scattering and 



is an essentially similar transition from diffuse to regular 

 reflexion as the distribution of the vibrators becomes denser. 



2. The present investigations deal exclusively with vibrators 

 which scatter, without absorbing, wave-energy of definite 

 frequency, though their extension to molecules which absorb 

 some part of the incident energy should present no difficulty. 

 Wood * has lately emphasized the importance of determining 

 experimentally to which category the resonant atoms of 

 mercury vapour belong, and in the second part of this paper 

 some tentative suggestions are made towards that end. 



3. The case of an isolated " simple aerial resonator, excited 

 by plane waves," has been dealt with by Eayleigh in the 

 paper already cited ; and the result (with a changed notation) 

 may be stated as follows. Let the primary waves be defined 

 by the velocity-potential 



T|r = Acos (pt — vat), (1) 



where p/'2tt is the frequency and 2tt/v the wave-length ; 

 then the secondary disturbance due to a resonator at the 



origin is 



c 



V=- cos (pt-vr-y), (2) 



where y is the lag in phase and 



C=£sin-y (3) 



This last relation is deduced from the sole assumption 

 that the resonator merely scatters sonorous energy without 

 changing its total amount. 



4. Consider next a square, forming part of the plane of 

 yz and having for its sides y = +J6, x=+^h. Let simple 

 Helmholtz vibrators be distributed over the surface of this 

 square with complete irregularity like the molecules of a gas, 

 the average number of vibrators per unit of area being <r. 

 For the moment, the only restriction made regarding a is 

 that the aggregate surface occupied by the vibrators is 

 insignificant in comparison with the spaces between them. 

 It is simply postulated that all the vibrators are sending out 

 vibrations of the same amplitude and phase, represented 

 typically for the nth vibrator by 



C 

 yjr n = — cos (j)t — vr n ) (4) 



The manner in which the vibrators are kept going is not the 

 * Guthrie Lecture, Proc. Phys. Soc. xxyi. p. 185 (1914). 



