Regular Reflexion of Light hy Gas Molecules. 97 



It' we are dealing (as in § 22) with a thin lamina 

 0<x<8x\ with v secondary vibrators of type I. per unit of 

 volume, <t in (56) must be replaced by vSx, and corresponding 

 to the resultant incident waves (55), the secondary waves 

 emitted are 



0, 0, — %8 t e . A exp i(pt + vx) y 

 where 



[Type I.] % = 37rvy~ 2 sin7 exp ?' [\ir — y). . (57a) 



46. Under the primary stimulus (55), when the secondary 

 radiators are of type II., with axes promiscuously oriented, 

 the average radiator gives out a disturbance which differs 

 from that for a type 1. radiator only in having an additional 

 factor ^, as explained in § 42. Thus 



[Type II.] x = *nw~- sin 7 exp i (i 73 "— *y)» • (576) 



47. Either (57a) or (576) — according to the type of 

 secondary radiator witli which we have to deal — may now 

 be made use of in adapting some results already obtained 

 to the circumstances of optical problems. For instance, 

 equations (9) and (24) still hold good, with the single 

 emendation that the value attributed to w is multipled by -g- 

 or by \ as the case may be. In particular, when the 

 radiators are tuned as resonators, w = ?>tt<jv~ 2 (Type I.) or 

 w = 7T(tv~ 2 (Type II.), and as before the validity of (9) 

 and (24) is limited only by the conditions that the radiators 

 must scatter without absorbing wave-energy of frequencv 

 p/27r, and must be distributed with perfect irregularity like 

 gas-molecules. The expressions (50), (51) likewise hold 

 good rigorously provided the same conditions are fulfilled. 

 It appears from Wood's researches that, as the density of a 

 swarm of resonant molecules is increased, the condition that 

 true absorption should be absent fails long before any marked 

 departure from the laws of ideal gases has become apparent. 

 This is so even in the case of mercury vapour, which can be 

 raised to a pressure of several atmospheres without destroying 

 the property of resonance. 



48. Equation (36), giving the amplitude of waves regularly 

 reflected from an attenuated swarm of secondary vibrators, 

 must now be replaced by 



[Type I.] A"'= -§Aiwvv~ 3 = -3AtV\ 3 /16ir» 1 



[Type II.] A'"=-\A;>7rvv-*=-Ah\*/16 7 r 2 J" ( } 

 Phil. Mag. S. 6. Vol. 30. No. 175. July 1915. H 



