1897.] Mr Mai/all, On the Diffraction Pattern etc. 259 



The following Communications were made to the Society : 



(1) On the Diffraction Pattern near the Focus of a Telescope. 

 By R. H. D. Mayall, M.A., Sidney Sussex College. 



The problem here considered is the diffraction pattern formed 

 by the light from a star on a screen placed near the focus of a 

 telescope. The exact theory of the diffraction of light through a 

 circular opening has been developed by Lommel, in his well-known 

 memoir on the subject*. It will be convenient to give here the 

 general conclusions at which he arrived, as applied to the case 

 under consideration. 



If h be the distance of the screen from the focus measured 

 towards the object-glass, f and r the focal length and radius 

 respectively of the object-glass, £ the distance of any point on 

 the screen from the centre of the image, and if we use the 

 abbreviations 



_ 2-7T Sr 2 2-7T £r 



the intensity of light at the point £ is 



where U,= (|) J,{z)- (jj)V,(*) + — , 



and tf 2 =(|)V 2 (*)-(f)V 4 (*) + ..., 



in which the J's are Bessel's functions with the usual notation, 

 and both series are continued to infinity. 



Now — f = ^ ) expresses the ratio of the distance of the point 



£ from the centre of the image to the radius of the geometrical 

 image, and is therefore < 1 for points inside the geometrical 

 boundary and > 1 for points outside. Hence for points inside the 

 geometrical image the series U^ and U 2 , although absolutely con- 

 vergent, are not adapted to numerical calculation. They are 

 however related to two other series 



r>-®w-®' '-to*.... 



V (l = .T a ( 2 )-{^p,(z)+..., 



* Abh. der K'dn. Bayer. Akad. vol. xv. 



