PROCEEDINGS 



OP 



THE ROYAL IRISH ACADEMY. 



1846. No. 52. 



January 12, 1846. 



GEORGE PETRIE, Esq, Vice-President, in the Chair. 



The Earl of Enniskillen, William Lloyd, M.D., The Ven. 

 Henry Cotton, D. C. L., Archdeacon of Cashel, Rev. John 

 Connell, John C. Deane, Rickard Deasy, Conyngham Ellis, 

 Arthur Nugent, Edward King Tenison, John Tyrrell, and T. 

 JoUifFe TufFnell, Esquires, were elected Members of the 

 Academy. 



Resolved, — " That the recommendation of the Council, 

 to place £50 lis. at their disposal, for the purchase of a con- 

 voluted Gold Bracelet, be adopted." 



The Rev. Professor Graves read a paper on the discussion 

 of Algebraic Curves and Surfaces, with special references to 

 the theory of Curves of the third degree. 



The general equation of an algebraic curve or surface of 

 the n"^ degree being written in the form 



Un -\-Vn-i-\- U„_2 -I- -I- U2-I- Ui 4-Uo = O, (1) 



where u„ stands for a homogeneous function of the n"^ degree 

 of the rectilinear coordinates, any equation such as 



A„,Uto-|- A,„_iU,„_i -f- A„t_2 U„i-2 + . • • + A2U2 -I- AiUi 4- AqUo = o (2) 



in which m is not greater than n, and Aq, a,, A2, . • . a„, are con- 



VOL. III. o 



