332 Royal Irish Academy. 



Charles Graves was born in Dublin in 1812. He was the youngest 

 son of John Crosbie Graves, a member of the Irish Bar, and Chief 

 Police Magistrate of this city. Having received his early education 

 at a private school in England, he entered Trinity College. He 

 became successively Scholar and Fellow, and in 1843 was elected 

 Professor of Mathematics. He became a member of this Academy in 

 1837, was elected on the Council in 1844, Secretary of the Council in 

 1846, Secretary of the Academy in 1856, and, finally, President in 

 1861. He was appointed Dean of the Chapel Royal, Dublin, in 1860, 

 and Bishop of Limerick in 1866. 



His admission to our body took place at a time when, under the 

 influence of Provost Bartholomew Lloyd, the Mathematical School of 

 Trinity College was exhibiting a remarkable revival ; and Hamilton, 

 M'CuUagh, and Humphrey Lloyd were prosecuting with energy the 

 researches with which their names are associated. The results at which 

 they arrived were usually announced at our meetings. Graves was in 

 intimate relation with these distinguished men, and, as their junior 

 associate, naturally followed in their footsteps. He contributed to our 

 " Proceedings" a great number of memoirs on subjects belonging to 

 almost every province of Mathematical Science. Only a few of these 

 can here be summarily noticed. In 1841 he published a translation 

 of the two elegant treatises of Chasles on the Properties of Cones of 

 the Second Degree and Spherical Conies, and appended to it a new 

 method of treating curves traced on the sphere by the use of co- 

 ordinates similar to the Cartesian. These researches he explained in 

 communications to the Academy, and from them he was led to con- 

 sider the geometry of curves traced on any surface, and in particular 

 on surfaces of the second degree, and gave a demonstration of the cele- 

 brated proposition of Joachimsthal, from which is most easily deduced 

 the beautiful theorem of our countryman, Michael Roberts, respecting 

 the lines of curvature on the Ellipsoid. 



Sir W. Hamilton's Calculus of Quaternions led many contem- 

 porary mathematicians to devise other systems involving new 

 imaginaries, and Graves brought before the Academy a system of 

 Algebraic Triplets of this kind ; but though it was curious and 

 interesting, he was himself the first to confess that it was far inferior 

 "in power, symmetry, and flexibility" to the Quaternions. Other 

 papers of his related to the theory of linear differential equations, to 



