es »? 
? . 
PROCEEDINGS 
OF 
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. 
Jolliffe Tuffnell, Esquires, were elected Members of the 
Academy. 
Resotvep,—‘ That the recommendation of the Council, 
_ to place £50 11s. 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 
Unt Un-1 + Un-o+---s- + U,+0,4+0),=0, (1) 
where v,, stands for a homogeneous function of the n degree 
- of the rectilinear coordinates, any equation such as 
AmUm- Am—1Um—1-+ Am—2Um—2+ «++ + AgUa+ AU) + AgUy = 0 (2) 
in which m is not greater than », and Ay, Aj, Ag, ... Am are con- 
VOL. Ilr. Ce) 
