356 Lord Rayleigh on Light dispersed from 



the condition as regards polarization of the scattered light 

 turns upon the value of 



__ iBjsinasinc^ — B 2 sin 2^sin 2^>+ ... ,~.^ 



~~ Oo + i (Ji cos a cos <£ — 2 cos % a cos 2</> 4- . . . ' 



in which the values of B la B s , ... C , C, ... are to be sub- 

 stituted from (18), (19), (20), and from (22), (23), (24). 



If we stop at the first approximation, neglecting B 2 , C 2; &c, 

 we have 



„ 2 sin u sin <f> , Q . 



1 + 2 cos a cos <p 



From (34) or (35) we see that the value of II is symme- 

 trical as between a and <£, an example of the general law of 

 reciprocity (' Theory of Sound,' § 108 &c). 



If a = 0, or if <£ = 0, II vanishes without appeal to approxi- 

 mations. This means that c* preponderates, or that the 

 scattered light is polarized in a plane parallel to the length 

 of the cylinder. The conclusion follows approximately 

 although a be not very small, provided <£ be also small. 



According to (35) II becomes infinite when 



1 + 2 cos « cos </>= 0, (36) 



for example when a = 45°, <£ = 135°. 



If we take « = 40°, <£=130° so as to avoid the directly 

 reflected rays, we have II =—67, so that there is nearly 

 complete polarization in the plane perpendicular to the length 

 of the cylinder. 



If we suppose <£ = 180° — a, so that observation is made 

 nearly in the direction of the regularly reflected rays, (35) 

 becomes 



n =- 2|n^_ (37) 



1—2 COS 2 a v ' 



The scattered light is unpolarized when 11= +1. If we 

 make this supposition in (37) we find a =30°. This angle 

 separates the two kinds of polarization. Thus when a is 

 small, II = 2 sin 2 a; whena = 30°, 11 = 1; when a = 45°, II = go ; 

 whena=90°, 11 = -2. 



By use of (34) the approximation may be carried further. 

 As an example we may take the case of perpendicular in- 

 cidence and observation, so that a = 90°, <f> = 90°. Thus by 

 (34) 



n= 7r ^ T -=-2(l'+iiW). • . . (38) 



