﻿its Polarization and Colour. 1 ] 9 



And if R= vV+y*, 



__ ocuT 9 —yuj i _ — TZ / d j/\ 6- jA '' 



= ~ TZ A . £^ _ TZ sin a _rf > e-^ 

 47r6 2 dR r 47r6 2 dr r 



where a denotes the angle between r and z. 



The resultant rotation at any point is thus about an axis per- 

 pendicular to the plane passing through the point and the axis 



G -ikr 



of Z ; and its magnitude is given by ot. In differentiating 



with respect to r, we may neglect the term divided by r 2 as alto- 

 gether insensible, kr being an exceedingly great quantity at any 

 ordinary distance from the origin of disturbance. Thus 



...(E) 



4tt6 2 



which completely determines the rotation at any point. For a 

 given disturbance it is seen to be everywhere about an axis per- 

 pendicular to r and the direction of the force, and in magnitude 

 dependent only on the angle between these two directions (a) 

 and on the distance (r). 



The intensity of the light, however, is more usually expressed 

 in terms of the actual displacement in the plane of the wave. 

 In order to find the connexion between the two quantities, it 

 will be more convenient to suppose the scattered ray parallel to 

 x, and that the force F (for Z is no longer appropriate) acts in 

 the plane of zx at an angle a with Ox, -ot becomes identical 



with ot 2 ; that is, with —■ ; for f as well as rj is zero ; so that 



J 



TF sin a €~ ikr 

 tzar-. 



Restoring the factor e int t we have 



TF sin a. e j(*t-*r ) 

 ^~ 4tt6 2 ' r 



or throwing away the imaginary part, 



,, TFsiua 27r /z , . fm 



f=^r- cos xr^- r) (F) 



