THE RAINBOW DUE TO A CIRCULAR SOURCE OF LIGHT. 



13 



when tliis is not the case, the consideration is more complicated. 

 Firstly, let us consider the case where the source of light con- 

 sists of three points 8,, .s\,, s,-, lying in a plane perpendicular to 

 SiC at a great distance. In tlio plane SiC o, the intensity of 

 tlie rainbow due to s^, is 



where (i represents the angle Bi Ai O, Bj Ai being the direction 

 of the minimum deviation due to Si. Suppose that s-, lies in 

 the 2:)lane s^co, and its angular distance (f from Si, is small; 

 then the intensity due to s-, in the direction AiO or A2O is 



i,{d)=c,AfLo + <f)i 



Next suppose that S3 lies in another plane s^co, and its position 

 is represented by (p' and 9'', where (p' is the small angular dis- 

 tance of .<?:; from .9, and </' the angle subtended by .s, .% and Si .s.;. 

 Now then, in the plane SgCo there is no direction parallel to 



