XII. On the Diffraction of an Ohject-glass with Circular Aperture. By 

 George Biddell Airy, A.M. late Fellow of Trinity College, 

 and Plumian Professor of Astronomy and Experimental Philosophy 

 in the University of Cambridge. 



[Read Nov. 24, 1834.] 



The investigation of the form and brightness of the rings or rays 

 surrounding the image of a star as seen in a good telescope, when a 

 diaphragm bounded by a reetihnear contour is placed upon the object- 

 glass, though sometimes tedious is never difficult. The expressions 

 which it is necessary to integrate are always sines and cosines of mul- 

 tiples of the independent variable, and the only trouble consists in 

 taking properly the limits of integration. Several cases of this problem 

 have been completely worked out, and the result, in every instance, 

 has been entirely in accordance with observation. These experiments, 

 I need scarcely remark, have seldom been made except by those whose 

 immediate object was to illustrate the undulatory theory of light. 

 There is however a case of a somewhat different kind; which in 

 practice recurs perpetually, and which in theory requires for its com- 

 plete investigation the value of a more difficult integral ; I mean the 

 usual case of an object-glass with a circular aperture. The desire of 

 submitting to mathematical investigation every optical phaenomenon of 

 frequent occurrence has induced me to procure the computation of the 

 numerical values of the integral that presents itself in this inquiry : 

 and I now beg leave to lay before the Society tlie calculated table, 

 with a few remarks upon its application. 



Let a be the radius of the aperture of the object-glass, f the focal 

 length, h the lateral distance of a point (in the plane which is normal 

 Vol. V. Part III. Pp 



