﻿Regular Reflexion of Light by Gas Molecules. 633 



% -iB" + Aexpz'(-i^+ B'expiu(— d'+x^dx' 

 + ¥> 1 Qvpiv(x n -x')dx , = ®. 

 The double accents being dropped, this may be written 

 X-'B+Aexp (-t^ + ir^exp (-tf) P B'expif'df 



+"u- 1 exptf pB'exp(— «f)if=0; (16) 



where %=vx = 2wx\\, rj = vL. . . . (17) 



20. To (16) add the equation obtained by differentiating 

 (16) twice with respect to f. The definite integrals are 

 eliminated, and we set 



d 2 B 



"-o-v>. 



of which the solution is 



B = C i exp i[jL% -f C 2 exp ( — I/jl^) ; . . . (18) 

 where /jl= \Z(l-2i x /v), (19) 



and Ci, C 2 are constants, to be determined by substituting 

 the expression found for B in (16). This now becomes 



=%"H Ci exp ^f + C 2 exp (-«>£)}+ A exp (-if) 



+ i/- l exp(—ig) {Cjexpz>f + C 2 exp (— ijif)} expipdp 



+ w- 1 exp*f f' {C 1 exp^f'H-C 2 exp(-i/*|0}exp(-?f)^ (20) 



which must hold good for all values of £ from to 77. Thus, 

 when £=0 



expz(/*-l)r *' 



Q=A + % - 1 (C 1 + C 2 ) + C 1 i;- 1 

 + C2V 1 



»0*-l) 



exp^ -?'(/* +!)£'} 



■*(/* + !) 



g'=0 



or 



+ C 2 { ^-llrHiv-V-l) e X p{-t(/»+l)ij}-tv- , (f.-l) I • 



.... (21) 



