C 11* ] 



XXII I. Note on the subject of Conical Refraction, By J. Mac- 

 Cullagh, Fellow of Trinity College, Dublin*. 



"VI7"HEN Professor Hamilton announced his discovery of 

 * * Conical Refraction, he does not seem to have been aware 

 that it is an obvious and immediate consequence of the theo- 

 rems published by me, three years ago, in the Transactions of 

 the Royal Irish Academy, vol. xvi. part ii. p. 65, &c. The 

 indeterminate cases of my own theorems, which, optically in- 

 terpreted, mean conical refraction, 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, 

 O^, in the general statementf — 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 contact T 

 is variable, for the plane ROS in 

 which it lies changes with OR. 

 Thus we get a curve of contact 

 on the tangent plane of the wave 

 surface, and a cone of rays OT 

 derived from the same incident 

 ray. The vibrations of any ray OT are in the line TS pass- 

 ing through the fixed point S, as follows from a general re- 

 mark in the place referred to. 



The three right lines OQ, Or, OT, are at right angles to 

 each other, and a geometer will observe that the first two of 

 them are confined to given planes. For Or is always in the 

 plane of the circle ROr ; and the point Q must be in a given 

 plane, because the line OP, perpendicular to the plane that 

 touches the ellipsoid in Q, is in a given plane RO r. 



* Communicated by the Author. 



•f The right line Oqr is perpendicular to the plane of the figure, and 

 intersects the two ellipsoids in q and r. 



