III. NOTE ON THE SUBJECT OF CONICAL REFRACTION. 



[From the Philosophical Magazine, VOL. in., 1833.] 



WHEN Professor Hamilton announced his discovery of Conical 

 Eefraction, he did not seem to have been aware that it is an ob- 

 vious and immediate consequence of the theorems published by 

 me, three years ago, in the Transactions of the Royal Irish Aca- 

 demy, vol. xvi., pt. ii., p. 65, &c. The indeterminate cases of my 

 own theorems, which, optically interpreted, mean conical refrac- 

 tion, of course occurred to me at the time ; but they had nothing 

 to do with the subject of that Paper ; and the full examination 

 of them, along with the experiments they might suggest, was 

 reserved for a subsequent essay, which I expressed my intention 

 of writing. Business of a different nature, however, prevented 

 me from following up the inquiry. 



I shall suppose the reader to have studied the passage in 

 pp. 75, 76, of the volume referred to. He will see that when 

 the section of either of the two ellipsoids employed there is a 

 circle, the semiaxes answering to OR, Or, and to OQ, Oq, in 

 the general statement* are infinite in number, giving of course 

 an infinite number of corresponding rays. And this is conical 

 refraction. I shall add a few words on the two cases : 



1. When ROr is a circle, any two of its rectangular radii 

 may be taken for OR and Or. The line OS and the tangent 

 plane perpendicular to it at S are fixed ; but the point of con- 



* The right line Oqr is perpendicular to the plane of the figure, and intersects 

 the two ellipsoids in q and r. 



C 



