MiO PROFESSOR AIRY, ON THE DIFFRACTION OF 



The quantity under the bracket, if p is very small, is equal to 



X) ft 



2p .<p {fi) + pn<p' (n) = - . -J— {n^<p{n)}. 



In the case of a very narrow annulus therefore the diameters of the 

 black rings will be determined by making ?i^(p (») maximum or 

 minimum. It appears then that there ought to be only one black 

 ring corresponding to each black ring with the full aperture, and that 

 its diameter ought to be somewhat smaller. This conclusion does not 

 agree with the experiments recorded by Sir J. Herschel, in the Encyc. 

 Metrop. Article Light, page 488 : but it is acknowledged there that 

 the results are discordant with Fraunhofer's : and I am inclined there- 

 fore to attribvite the phasnomena observed by Sir J. Herschel to some 

 other cause. 



The investigation of cases of diffraction similar to that discussed 

 here appears to me a matter of great interest to those who are 

 occupied with the examination of theories of light. The assumption 

 of transversal vibrations is not necessary here as for the explanation 

 of the phasnomena of polarization : and they therefore offer no argu- 

 ments for the support of that principle. But they require absolutely 

 the supposition of almost unlimited divergence of the waves coming 

 not merely from a small aperture, but also from every point of a large 

 wave : and the results to which they lead us, shew strikingly how 

 small foundation there was for the original objection to the undulatory 

 theory of light, viz. that if waves spread equally in all directions. 



there could be no such thing as darkness. 



Obsbrvatory, Cambridge, 



November 20, 1834. 



G. B. AIRY. 



