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XXIV. How to apply the Resolution of Light into Uniform 

 Undulations of Flat Wavelets to the Investigation of Optical 

 Phenomena. By G. JOHNSTONE STONEY, M.A., Sc.D. 9 

 I.R.S* 



[The letters ufic are used throughout the preseut paper as an 

 abbreviation for undulation of fiat wavelets.'] 



Introduction. 

 1. IGHT while within a uniform transparent medium, or 



.Li an}' other event which the medium can without 

 external assistance propagate forward as w r aves. may be 

 resolved within that medium in an infinite number of ways, 

 and among them into undulations of convex or of concave or 

 of flat wavelets. That a resolution into uniform flat wavelets 

 is always possible is proved in the October number of the 

 Philosophical Magazine of 1896, p. 335, where this theorem 

 is enunciated and deduced from an already known theorem f 

 in optics ; and a more direct proof of the resolution by the 

 Principle of Reversal is given in a paper published at p. 570 

 of the Report of the British Association for 1901. This 

 proof is better than that previously given, because it is more 

 direct and less inelegant, and also because it furnishes addi- 

 tional information which is useful. A third and extremely 

 elegant proof has recently been published by Mr. Edmund 

 Whittaker, Secretary of the Royal Astronomical Society, at 

 p. 619 of the ' Monthly Xotices ' of that Society issued in 

 September 1902, where he shows that the general solution 

 of the equation 



w-4!? ■■ ■ « 



may be made to assume the form 



V= p P* F . d6 dyfr, .... (2) 



where F is an arbitrary function of the three arguments 

 O sin 6 cos yjr -f- y sin 6 sin ^ +.zco<6 + Id), 6, and ty : 



* Communicated by the Author, having been read in September 1902 

 before Section A of the British Association. 



t The theorem here referred to is enunciated at the foot of p. 335 

 (loc. cit,), and illustrated by the diagram on p. 310. It is the theorem 

 by which Fraunhofer"s beautiful experiments with crossed gratings, 

 which were then recent, were explained in the University of Dublin 

 when the author was a student of Trinity College in the forties of the 

 last century. There were two proofs of it current— one an analytical 

 proof by Professor, afterwards Provost. Jellett, based on an extension of 

 one of Airy's theorems in his Tract on Light ; and the other a proof by 

 the Principle of Reversal, a new and powerful tool of investigation which 

 3]acCiilla<rh had then recentlv introduced. 



