of right lines. This theory he worked out in detail, supplying formulae for tangents, normals, osculating circles, &c., to spherical curves. This memoir was greatly admired by Sylvester and other distinguished mathematicians, but their high expectations of its fertility have not been fulfilled.
This was the only mathematical work published by Graves. His other investigations were either embodied in his lectures as professor, or in papers read before, and published by, the Royal Irish Academy. During this period Sir William Hamilton, McCullagh, and Humphry Lloyd were also members, and the meetings were often made the occasion of announcing the results of the spirit of scientific investigation which then remarkably prevailed in the university of Dublin.
While Hamilton was explaining in a series of communications his new calculus of quaternions, several contemporary mathematicians were led to conceive more or less analogous systems, likewise involving new imaginaries. Graces proposed a system of algebraic triplets of this kind. It must, however, be said of it, as of the other similar systems, that it could not lay claim to anything like the power of the quaternions, and was not so much a valuable working method as an interesting mathematical curiosity.
Other papers by Graves, published by the Royal Irish Academy, related to the theory of differential equations, to the equation of Laplace's functions, and to curves traced on surfaces of the second degree. For example, he gave an elementary geometrical proof of Joachimsthal's well-known and fundamental theorem—viz. that at all points on a line of curvature of an ellipsoid the rectangle pd is constant, where p is the central perpendicular on the tangent plane, and d is the diameter drawn parallel to the element of the line of curvature. He also gave some very important applications of the calculus of operations to the calculus of variations, and more especially arrived at an elegant and simple demonstration, by the operational method, of Jacobi's celebrated theorem for distinguishing between maxima and minima values in the application of the calculus of variations. Graves had much literary and artistic taste, and to these were largely due the symmetry and elegance, both of method and results, which are marked characteristics of his mathematical work.
On the death of Sir William Hamilton, in 1865, Graves delivered from the presidential chair an eloquent cloge upon him containing a valuable account both of his scientific labours and of his literary attainments. As a member of the academy Graves devoted much time and thought to Irish antiquarian subjects. It is a striking instance of his varied accomplishments that, the death of George Petrie [q. v.] having taken place shortly after that of Hamilton, Graves pronounced an eloge on him also, and gave as competent a survey of the archæological researches of the one as he had given of the scientific investigations of the other. Both these 'Eloges,' originally printed in the 'Transactions of the Royal Irish Academy,' were separately published (Dublin, 1865 and 1866).
He studied with special zeal the interpretation of the ogham inscriptions, so numerous in Ireland, and applied to them the accepted methods for the decipherment of writings, known or presumed to be alphabetical, and in this way confirmed the interpretation which is given of these symbols in some of the old Irish books. He thus gave readings and renderings of a number of the inscriptions on cromlechs and other stone monuments. The subject, however, is still surrounded with difficulties, and many archaeologists have been led to the conclusion that the inscriptions are intentionally cryptic, at least in some cases.
Graves, in some 'Suggestions' published at Dublin in 1851, brought before the government the importance of having the old Irish laws, commonly called the Brehon laws, edited and translated by competent scholars. His suggestion was adopted, and he was appointed a member of the commission charged with carrying it into effect, and held this office until his death.
[Private information ; Cotton's Fasti Eccl. Hiberniæ, Suppl. p. 33.]
GRAVES, HENRY (1806–1892), print-seller, son of Robert Graves (d. 1825), and younger brother of Robert Graves, A.R.A. [q. v.], was born on 16 July 1806. At the age of sixteen he became an assistant of Samuel Woodburn, the art dealer, and later was employed by Messrs. Hurst, Robinson, & Co., the successors of Boydell, as manager of their print department. On the failure of this firm in 1825 Graves, in conjunction with Francis Graham Moon [q. v.] and J. Boys, acquired the business which was carried on with various changes of partnership until 1844, when Graves became sole proprietor ; the title of the firm has since been Henry Graves & Co. In the course of an enterprising and successful career, throughout which he was recognised as the leading London printseller, Graves published