Regular Reflexion of Light by Gas Molecules. 89 



second order of x v_1 



and, as far as the first order of x^ -1 , 



A'" = -A + Ail + iixv- 1 )^ - iAixv' 1 - • (35) 



On the other hand, when %v _1 becomes large (a condition 

 which does not necessarily result from a large value of v if 

 absorption is then present), /^ and /x 2 both approach the 

 value X* v ~^> aR d (32) becomes in the limit 



A'"=-A; 



which implies that the reflexion has become complete. 



32. So long as the (aerial) secondary vibrators are not too 

 closely crowded to allow of their being distributed like the 

 molecules of a gas, and so long as absorption is absent, the 

 relation between % and v (the number of vibrators per unit 

 of volume) is given by (13) ; while in the special case of 

 resonators 7 = -j7r, so that % is real as in the last paragraph, 

 and the approximation (35) is equivalent to 



A'"= -AiTTvv- 3 ^ -AIv\ 3 /Stt' 2 . . . . (36) 



This result is true only when x v ~ 1 or v\*/<±7r 2 i s small ; 

 moreover it applies only to the acoustical case considered. 

 The corresponding electromagnetic (or optical) case is re- 

 ferred to in § 48. 



33. Some practical interest attaches to the transmission 

 of normally incident plane-waves through a lamina of finite 

 thickness occupied by a swarm of secondary vibrators ; for 

 it is on this that certain interferometer measurements of 

 anomalous dispersion are based. From (18), (19) we obtain, 

 with the help of (21), (22), 



E =-X" ,B =-%" 1 L C i ex P / >f + C , 2 exp(-?>f)] 

 ■2A{[( f i-l)ex V {-i( f M-l) v }-( f i + l)]cx V irf 



— [0*— l)exp \-i((/ji + l)v\ — Ou + l)]expz>f 

 + [-(/*+ l)exp* (^-l^ + ^-l)] eX p (-*>£) 



-[-(^+l)expt> + l)^ + (M-l)]exp(-t/4f)} 

 {^+l) 2 ex V i(fi-l) V + (fi-iyex V {-i(fM-l) v } 



-fa— l) 2 exp{— i(fi+l)ri} — (ii+l) a expi(tJk+l)y}i 



