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burgh Philosophical Magazine, for the months of February and March, 1833 ; 
and they will be found with fuller details in the present Volume of the Irish Trans- 
actions. 
I am informed that James Mac Cutxacu, Esq. F.T.C.D. who published in the last 
preceding Volume of these Transactions a series of elegant Geometrical Illustrations 
of Fresnev’s theory, has, since he heard of the experiments of Professor Luoyp, em- 
ployed his own geometrical methods to confirm my results respecting the existence of 
those conoidal cusps and circles of contact on FREsNEL’s wave, from which I had been 
led to the expectation of conical refraction. And on my lately mentioning to him 
that I had connected these cusps and circles on FRESNEL’s wave, with circles and cusps 
of the same kind on a certain other surface discovered by M. Caucuy, by a general 
theory of reciprocal surfaces, which I stated last year at a general meeting of the Royal 
Irish Academy, Mr. Mac Cuxtacu said that he had arrived independently at similar 
results, and put into my hands a paper on the subject, which I have not yet been able 
to examine, but which will (I hope) be soon presented to the Academy, and published 
in their Transactions. 
{ ought also to mention, that on my writing in last November to Professor Airy, 
and communicating to him my results respecting the cusps and circles on FREsNEL’s 
wave, and my expectation of conical refraction which had not then been verified, Pro- 
fessor Arry replied that he had long been aware of the existence of the conoidal cusps, 
which indeed it is surprising that Fresvex did not perceive. Professor Arry, how- 
ever, had not perceived the existence of the circles of contact, nor had he drawn from 
either cusps or circles any theory of conical refraction. 
This latter theory was deduced, by my general methods, from the hypothesis of 
transversal vibrations in a luminous ether, which hypothesis seems to have been first 
proposed by Dr. Youne, but to have been independently framed and far more per- 
fectly developed by Fresnex ; and from Fresnev’s other principle, of the existence of 
three rectangular axes of elasticity within a biaxal crystallised medium. The verifi- 
cation, therefore, of this theory of conical refraction, by the experiments of Professor 
Lioyp, must be considered as affording a new and important probability in favour of 
FRESNEL’s views: that is, a new encouragement to reason from those views, in com- 
bining and predicting appearances. 
