193 



The writer may take this opportunity of mentioning a re- 

 sult which lately occurred to him, respeeting two arbitrary, 

 but reciprocal conical surfaces, of which each is the locus of 

 all the normals to the others, erected at their common vertex ; 

 namely, that two such cones have always one common conical 

 surface of centres of curvature. 



The President read the following Address : 



Gentlemen, — We have this night reached the close of a Ses- 

 sion of more than usual activity ; and I might, therefore, naturally 

 have desired — before leaving this Chair and adjourning the Aca- 

 demy to another winter — to trespass for a short time upon your 

 attention, and to lay before you a brief summary of the results of 

 our toil. On the present occasion, however, my duty is narrowed 

 and defined ; and the recent award of the Cunningham Medals by 

 the Council renders it imperative on me to submit to the Academy 

 the grounds of their decision. In doing this, it will be necessary 

 for me to present a brief analysis of the results of those labours 

 whose value your Council have thus honourably recognised ; and 

 in the execution of this task I must request the indulgence of the 

 Academy, and still more that of the gentlemen of whose discove- 

 ries I am to speak, if, in my imperfect acquaintance with them, I 

 should fail to do justice to their merits. 



You are aware that, during the past Session, the laws respect- 

 ing the award of medals have occupied the attention of the Council ; 

 and that certain new regulations relating to it were, upon their sug- 

 gestion, adopted by the Academy. It is unnecessary for me to 

 recapitulate these regulations, or to state the grounds for the changes 

 therein made, as this has been already fully done by the Council, in 

 their last Annual Report. It will be sufficient for me, on the pre- 

 sent occasion, to remind you, that the principal alteration in the 

 rules respecting the award of medals under the Cunningham be- 

 quest, has been to extend the limit within which the Council are 

 enabled to bestow such rewards, and to confine them only to 

 Memoirs or Works printed and published in Ireland, or relating 

 to Irish subjects. 



A considerable interval having elapsed since the last award of 

 VOL. IV- Q 



