358 Prof. F. L. 0. Wadsworth on the Effect of 



Then integrating each of the two terms of (7) by parts we 

 obtain 



, B6 BZk 7.7, - B5 _ B6 \ l.J, 



S=&(«2+* ,z Jsin-s- -t-Bl e * — e * Icos— j 



(8) 



and therefore 



1^-O+b- - A2 + B , .... (J) 



Resubstituting for £ its value in terms of f, and also ex- 

 pressing cos kh in terms of sin-~- we finally obtain 



When the origin of coordinates is not at the centre of the 

 horizontal aperture, and the limits of integration, b 1 and 

 —b 2 , are unequal, we obtain similarly 



I f =1 '° 2 xy(^+B a ") [^ 2B6l + ^ 2B62 -2 cos tji, + «r^] 



. . . (11) 



When there is no absorption B = and i—1, and both (9) and 

 (10) reduce at once to the usual form for rectangular aper- 

 ture, i.e., 



. ir%b 



V -™L *L (ii) 



\Xf) 



For very small values of B the distribution in intensity is 

 practically the same as when there is no absorption. For 

 very large values of B, on the other hand, the term e Bb remains 

 the only one of importance in the numerator, and we have 



b\P e m 



<V (BJ)* + 4(^) 



