Mr. Moon in Reply to Jesuiticus. 217 



mark what follows: — " It is to this that the undulatory theory 

 owes its great celebrity, and of all parts of the undulatory 

 theory, that of double refraction is the most extraordinary. It 

 ought to be regarded as a stupendous monument of human 

 ingenuity. It must not be forgotten how admirably the pro- 

 perties of uniaxal crystals follow from the general investiga- 

 tion of the biaxal class ; but above all, how from this same 

 investigation, conical and cylindrical refraction were disco- 

 vered by Sir William Hamilton." 



I would ask of Jesuiticus, what is the hypothesis upon 

 which Fresnel professes to explain the separation of the ray ? 

 Whether it is not substantially what I have stated it to be in 

 the early part of this paper ? And if so, I appeal to the world 

 whether 1 have not shown incontrovertibly in my two papers 

 on this subject contained in the last two Numbers of the Phi- 

 losophical Magazine, that Fresnel entirely fails to explain the 

 separation of the ray on that hypothesis. It may be true that 

 some of Fresnel's expressions for the disturbance in doubly 

 refracted and other polarized waves may involve in them cer- 

 tain elements of truth (though for my own part 1 should be 

 sorry to answer for any of them) ; but they do not on that ac- 

 count afford any evidence of the truth of his principles, for 

 this plain reason, that they do not follow from them. It may 

 happen, that from the ruins to which this great theory must 

 soon, if it be not already reduced, may be gathered some 

 useful fragments which may form part of a new and more du- 

 rable edifice ; but Jesuiticus may take my word for it, or if he 

 do not choose to do that, he will not have long to wait for the 

 verification of the prediction, that the time is at hand when 

 Fresnel's theory will be considered as a " stupendous monu- 

 ment " of anything else but ingenuity. As to the supposed 

 discoveries of conical and cylindrical refraction, if Jesuiticus 

 had been aware of their very doubtful character, he would 

 hardly have ventured to have brought them so prominently 

 forward. # i; '*•'•»' • * 



As to the investigation which I examined in the first of my 

 two papers, I do not doubt that Mr. Airy considered it merely 

 as an illustration ; but even in that point of view, and without 

 adverting to the error which I pointed out in his reasoning, 

 it would be entirely worthless, as it is obvious that the state 

 of things he contemplates could only exist for a single mo- 

 ment, whereas the results he deduces are supposed to be 

 always subsisting. His object is to show that an undulation 

 consisting of transversal vibrations might be propagated ac- 

 cording to a certain law, when even on his own premises it is 

 quite obvious that if the disturbance originally communicated 



