Unsymmetrical Broadoung of Spectral Lines. 537 



quite ditfert lit tVoni (Mtlier the Dopiiler effect or tlie effect of 

 clainpin*^' of the motion. 



Several years ago 1 proved * that a charoed particle under 

 the influence o£ plane Avaves Avould vibrate in a period which 

 differed from the period of the incident waves ; but as the 

 calculation has not been published, and is quite simple, I 

 reproduce it here. 



Let m be the mass of the particle, x^ y, z the coordinates 

 ol: its centre of mass, e its electrical charge ; and let plane 

 waves given by 



electrical force X^XqCOS (j!9i — a:^) ") 2 



K S' wli(^re ^^ V i^ 



magnetic force M= -XqCos {pt — Kz) \ k^ ' 



be incident on the particle. 



Then the equations of motion of the particle are 



mi^ = e(X-Mz) = ^i sin (pt- kz), 

 ^ ^ p (it ^^ " 



my = 0, 



** * K ' 



mz = e}Ax =-- e^QX COS (pt^KZ 



p 



Let us take a new variable L so that 



.=ii.+, 



Then the equations become 



Ccosa:C, 



p m 



^ = 0, 



•■ K ^Xo • y 



L= M COS KL. 



p m 



As integrals of these equations we get 



^Xo . ^ 

 mp 



\ 



' mp \iiip / 



where a, h, and c are constants of integration. 



* Proc. Royal Society, London, vol. Ixix. p. 394. 



