IN FOCAL PLANE OF TELESCOPE. 323 



JJij) 



where J^ (7) denotes Bessel function of the first kind and of order 1. 

 If the source of light he not a geometrical point, we must consider a ß 

 as variable when finding the illumination at points corresponding to 

 o' ß' , and sum the effects due to all elements of the luminous plane. 

 In other words, the illumination is proportional to 



J:(r) 



./T 



da 



where da represents an element of the luminous area. For effecting 

 the integration, we can, for nearly normal incidence, assume «' = /?1=0, 

 and put 



_ ZTiB^/fS + ß* _ ItzBA 



r ~ ;, ~ ;. 



A denoting the angular interval of the incident and diffracted rays. 

 Thus, expressed in polar coordinates r, 0, the present problem reverts 

 to the evaluation of 



the integration extending over the whole luminous source. It is to be 

 remarked that, for ;, = 0.589 fx, r=l, A = V ', the value of E = 1.93 cm. 

 The intensity of illumination is consequently given b} 7 



K 1 icing a constant to be afterwards determined. 

 Since 



we can write 



^ff^M+Jx\r)\drdd 



* Louiuiel, Mathematische Annalen, 14» 1870. 

 Kayleigh, Phil. Mag., 11 (5), 1881. 



