TRANSACTIONS OF THE SECTIONS. 369 



the appearance as very beautiful when he employed a lamp, 

 and received the emergent rays on a lens : he seemed to see 

 the two points of light, which the double refraction usually 

 produced, spread out on a sudden, when the critical incidence 

 was obtained, into a ring of gold viewed on a dark ground. 

 His account is contained (with Professor Hamilton's theoretical 

 investigation) in the First Part of the seventeenth volume of 

 the Transactions of the Royal Irish Academy ; a shorter state- 

 ment was also published in the numbers of the London and 

 Edinburgh Philosophical Magazine for the months of February 

 and March 1833. 



From the connexion of the surface of components with the 

 wave-surface propagated from a point, the author saw that the 

 existence of four conoidal cusps on the one surface in Fresnel's 

 theory involved the existence of four such cusps upon the 

 other, namely, at the points of intersection of Fresnel's circle 

 and ellipse in the plane of the extreme axes of elasticity : and 

 thus he was led to expect an external conical refraction, 

 corresponding to the internal incidence of a cusp-ray when 

 emerging into air from a crystal with two axes. On this point 

 also he requested Professor Lloyd to undertake a series of ex- 

 periments ; and on this point also (indeed, somewhat sooner 

 than on the other,) he obtained a complete verification. His 

 experimental determinations of the size and position of this 

 emergent cone, as of the former emergent cylinder, and of the 

 laws of polarization in each, for the same large piece of arra- 

 gonite, agreed with the theoretical results deduced from the 

 principles of Fresnel by the method of the Characteristic 

 Function. 



Although this method appears likely to be adopted by 

 analysts at some future time in the researches of theoretical 

 optics, the author does not pretend that its results cannot be 

 obtained in other ways ; and with respect to the two kinds of 

 conical refraction, in particular, Mr. MacCullagh (F.T.C.D.) 

 has published, in the London and Edinburgh Philosophical 

 Magazine for the months of August and September in the 

 present year, an elegant geometrical investigation, together 

 with some account of the progress of his thoughts upon the 

 subject. The surface which Professor Hamilton has called the 

 surface of components, (of normal slowness of propagation,) and 

 to which he was conducted some years ago, as constructing a 

 fundamental equation between the partial differential coefficients 

 of his Characteristic Function, occurred to Mr. MacCullagh 

 also, as he has informed the author, independently from consi- 

 derations of a geometrical kind. The same important surface 



1833. 2 B 



