﻿634 Dr. C. V. Barton on the Scattering and 



Similarly, when f =77 (20) becomes 

 A( y u, 2 -l) = C 1 {(/^ 2 --l)x- 1 expi(^ + l)7 ? -fiv- 1 (^-l)expi(/x+l)77 



-iw-^M— 1)} 



+ 2 {( A 6 2 -l)x- 1 exp{-/( / .-l)}-^-VH-l)exp{-z(^-l)7 7 } 



+ iv- 1 ( f ju+l)}, . . . (22) 



21. The constants C 1? C 2 are thns determined, and the 

 solution of the proposed problem, in terms of the single 

 complex constant %, is fully indicated. The results, more- 

 over, are not limited in their scope to the acoustical type of 

 problem which has so far claimed our attention ; in the form 

 (18), (21), (22) they would be equally applicable to a cloud 

 of light-scattering molecules or particles, whether the scatter- 

 ing is accompanied by absorption or not : it would only be 

 necessary to assign to ^ its proper value in each case. 



22. There are two cases in which the results of § 20 

 assume a specially simple form ; in the one case L is very 

 small compared with X, that is, 77 is very small ; in the other 

 case L (or 77) is infinite. When rj is very small, it is most 

 convenient to go back to the integral equation (16), which 

 now takes the form 



X^B + A + v-'T B'd?=0. 



This shows that, to our degree of approximation, B is a 

 constant, so that the above definite integral =B?; = Bl'L, 

 and we get 



1+ X L 



The waves emitted by the total of the vibrators are now 

 by (14) 



<ty'\ ^srBL exyi(pt + va?) 



= -TT^L exp ^ 4w) I . . . (23) 



fL or 2ttL\\ being small. 



23. If we now introduce the condition that through the 

 lamina 0<#<L the secondary vibrators are distributed like 

 gas-molecules, (13) holds good and (23) takes the form 



V, ty" = — Aw {l + iv exp i(±7r - 7) \ -1 exp i(pt T vx 4 \tt — 7) 



where w = 2ira sin 7/u 2 , 



and <7 = vJj, the number of vibrators per unit area of the 



