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LX XXIII. On some Optical Effects including Refraction and 

 Rotation of the Plane of Polarization due to the Scattering 

 of Light by Electrons. By Sir J. J. Thomson, O.M., 

 P.R.&* 



WE begin by considering the radiation along the axis 

 of x emitted by the electrons in a very thin slab 

 bounded by planes at right angles to this axis; all the elec- 

 trons in the slab are supposed to be moving in the same way 

 at the same instant. 



If an electron has an acceleration / in a direction at 

 right angles to OP the electric force at P at the time T due 

 to this acceleration is parallel to /and equal to — efijc 2 . OP, 

 where /i is the acceleration at the time T—OP/c, e being the 

 charge on the electron and c the velocity of light. Let P 

 be a point in front of the slab on the axis of x; if the 

 acceleration parallel to y of an electron Q in the slab is 

 d 2 y/dt 2 , the electron will produce an electric force parallel 

 to y at P at the time T equal to 





PQ \uc i T- 



PQ 



provided PQ is at right angles to y. Since the optical 

 effects at P of a plane wave arise from the parts adjacent 

 to 0, where is the foot of the perpendicular let fall from 

 P on the plane of the wave, we may make this supposition 

 without loss of generality. 



If D is the thickness of the slab, cr the density of the 

 electrons, Y 1 the electric force parallel to y at P at the 

 time T is giveii by the equation 



^ C 



where p = 0Q, r=PQ. 



Now r 2 =p 2 + OF 2 , 



hence rdr — pdp, 



and therefore 



2ireaJ) CfcV 



eaB ( d\,j\ 



* Communicated by the Author. 



PhiL May. S. 6. Vol. 40. No. 240. Dec. 1920. 3 A . 



