338 H. NAGA0KA; DIFFRACTION PHENOMENA 



p = {la + o)y/i — h? siri z <p , where */ = v 



when lies external to the circle. We see from the expression 

 for hi and & a that both are smaller than 1. 

 We can easily prove that 



dd. 



:(l-\ ; . I l . ., — r— )d<p for an internal point ; 



\ (L-kf si>r<f) ) r * 



(, wl — = ^_) 



and 



dd = (\ — n — 7 e • •> s W for an external point : 

 \ (1— k e snv<p) J r 



The intensity at an external point becomes 

 1 ttJo J r 



7t ,/o 



At an external point 



U«r>WrL drde 



7rJ_ a J 9 > r 



where p'=op' , p=op, and o. = /_aoi\ 



Patting the values for p and 6, we obtain for 



If the point be not very near the rim of the circle 



* See Halphen, Fonctions Elliptiques, Torn. 1, Chap. 1. 



