^ Mr. Moon on Fresnel's Thecrry of Diffraction. 



plete proof, such as Mr. Cayley professes his to be, all these 

 things ought to have been done. And I heartily wish he had 

 done them, and done them rightly, for the sake of the result. 

 Mr. Cayley thinks that his paper just referred to will lead 

 to the complete determination of H and H'. I think so too; 



CO 



and I say that H = ^, and that this follows from (2.) of this 



paper. But from the last three forms of » I cannot determine 

 H. And if I could, it is easy to see from (3.) that they would 

 give different values to this quantity ; another proof of the 

 faulty nature of these forms. For the transformation being 

 but one, H ought to have but one value. I suppose the dif- 

 ferent forms of CO derived from one another, as in this paper. 

 With regard to Mr. Cayley's last paper, I have to observe 



that I had made trial of the form co = , and did not 



3 



make it to be a transformation. But on going over the subject 

 again, I find I somewhere made a mistake. It is complemen*^ 

 tary however, and makes no part of the direct transformation, 

 although somehow strangely derived from it, without the pro- 

 cess by which the complementary is derived from the direct 

 one. I pass over the rest of this paper, because it would be 

 an endless and useless task to discuss every minute parti- 

 cular. 



Gunthwaite Hall, May 13, 1845. 



XIII. On Fresnel's Theory of Diffraction. By R. Moon, 

 M.A., Fello'w of Qiieen's College, -Cambridge, and of the 

 Cambridge Philosophical Society. 



[Continued from vol. xxvi. p, 94. J 



IN a paper which appeared in a recent Number of this 

 Journal (see vol. xxvi. p. 89), I endeavoured to point out 

 some remarkable errors in Fresnel's investigation of the fringes 

 produced by an opake body illuminated from a single point ; 

 and in particular I endeavoured to stigmatize an erroneous 

 principle of approximation adopted by Fresnel, and which I 

 then stated, and now assert to be such, as to vitiate every in- 

 vestigation of that ingenious person in this department of 

 optics. 1 thence proceeded to show that Fresnel's mode of 

 investigation, when properly conducted, leads to conclusions 

 very different from what he supposes, and such in fact as are 

 completely at variance with the observed phaenomena which 

 he wholly fails to account for; and I further drew the con- 

 elusion, that the principle of small waves emanating from the 



