Among his most remarkable works may be mentioned his ten memoirs on quantics, commenced in 1854 and completed in 1878; his creation of the theory of matrices; his researches on the theory of groups; his memoir on abstract geometry, a subject which he created; his introduction into geometry of the "absolute"; his researches on the higher singularities of curves and surfaces; the classification of cubic curves; additions to the theories of rational transformation and correspondence; the theory of the twenty-seven lines that lie on a cubic surface; the theory of elliptic functions; the attraction of ellipsoids; the British Association Reports, 1857 and 1862, on recent progress in general and special theoretical dynamics, and on the secular acceleration of the moon's mean motion.
1-a'5 Accounts of further attempts in this direction will be found in Cayley's Memoirs on Quantics (Collected"Papers), in the papers of Sylvester and Franklin (Amer.
I.-iv.), and in Elliott's Algebra of Quantics, chap. viii.
Cayley, " Memoirs on Quantics," in the Collected Mathematical Papers (Cambridge, 1898); Salmon, Lessons Introductory to the Modern Higher Algebra (Dublin, 1885); E.