[ 37 ] 



V. The Scattering and Regular Reflexion of Light by Gas 

 Molecules.— -Part IT. ^ By C. V. Burton, 'D.Sc* 



i 



obtained in Part I.f The region < x < L is 

 occupied by a cloud of Rayleigh resonators (or more gene- 

 rally secondary vibrators) and plane sound-waves specified 

 by the velocity-potential 



yjr — A exp i (pt — vx), 



are incident normally on this region. A complex constant % 

 characteristic of the swarm is defined by the condition 

 that if the resultant regular disturbance at the plane x' is 

 E' exp ipt, them the secondary plane-waves emitted by the 

 elementary lamina dx' are 



— %E' exp i { pt^fv(x — x / ) } dx ; 



B', or — x^'i as a function of x\ being given by 



B' = d exp ifju% -f C 2 exp ( — £/*(■ ) , 



where fi = N(l — 2i^u _1 ), £ = t/« = 2-nxj\, 



and the constants C b C 2 are determined by (21), (22); which 

 may be written 



2xA=C J [-(/*+l)exp»>-l)i ? +0*-l)] 



+ C 2 [O-l)exp{-;0 i +lh}-( /i +l)], (25) 



2 x A = C 1 [-(/ i + l)expt( /4 + l), + (/ t -l)] 



+ C s [0*-l)exp{-»( /t -lM-O' + l)]. (26) 



29. In the most general case (cf. § 21) we may write 



X = %i + z 'X2, /* = Mi — >>2, .... (27) 



where % 1? % 2 , /x 1? /a 2 are all real. Then from (19) /x u fi 2 may 

 be found in terms of xi> %2 ; the positive sign being con- 

 veniently retained where a choice of sigus is open. The 

 results obtained are 



Ml = v{i(i + 2 X^')+i V[( 1 + 2 x.«- 1 ) , +4xi*"- I ] , f. • (88) 

 h= vi-Ki+s^O+i V[(i+2»« _1 ) , +J=xi s «'-*]}; (89) 



and evidently both y^ and yu, 2 are always positive. 



* Communicated bv tbe Author. 

 t May 1915. 



