On the Calculation of Newton's Experiments on Diffraction. By 

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

 and Plumian Professor of Astronomy and Experimental Philosophy 

 in the University of Cambridge. 



[Read May 7, 1833.] 



Since the publication of Fresnel's experiments on Diffraction, it has 

 been usual to employ as the source of light, in all experiments of this 

 class, the image of the Sun formed by a lens of short focal length. On 

 the undulatory theory, the effect of light thus produced is precisely 

 the same as if the minute image of the Sun were the real origin of 

 the light diverging with equal intensity through a solid angle whose 

 diameter is many degrees. The spherical or chromatic aberration of 

 the lens produces no sensible effect in any of the common experiments, 

 in all which the angle, made by rays which afterwards interfere, is small. 

 In calculating experiments thus conducted we proceed therefore with 

 full confidence that no consideration is left out of sight, the omission 

 of which could cause sensible error. 



Newton's experiments however were conducted in a different way. 

 His origin of light was a hole, from Jg^ to ^ of an inch in diameter, 

 through which the Sun's light was made to pass. The effect of this 

 light, on the undulatory theory, is not the same as if the bright hole 

 were the origin of light. It becomes then a matter of some interest 

 to examine mathematically what is the effect produced by transmitting 

 the sun-beams directly through a hole of sensible size ; and whether this 

 effect, in practice, will differ much from the effect produced by forming 

 an image of the Sun with a lens of short focal length. 



The integrals which occur in this investigation are of such a kind 

 that their values cannot be exhibited even in tables of numbers (except 

 Vol. V. Part II. O 



