CAYLEY, ARTHUR (1821-1895), English mathematician, was born at Richmond, Surrey, on Aug. 16, 1821. He entered Trinity college, Cambridge, as a pensioner, became a scholar in May 184o, senior wrangler, first Smith's prizeman and fellow of Trinity in 1842, and a major fellow in 1845. In 1846, he entered at Lincoln's Inn, and became a pupil of the conveyancer Mr. Christie. He was called to the bar in 1849, and remained at the bar till he was elected to the new Sadlerian chair of pure mathe matics at Cambridge in 1863, when he married Susan, daughter of Robert Moline of Greenwich. He held this chair till his death, on Jan. 26, 1895. His Boo mathematical papers, published in 13 large quarto volumes by the Cambridge University Press, treat of nearly every subject of pure mathematics, and also of theo retical dynamics and spherical and physical astronomy. He was as much a geometrician as an analyst. We may especially mention his ten memoirs on quantics (18S4-1878), 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 to 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, and 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. Com petent judges have compared him to Leonhard Euler for his range, analytical power and introduction of new and fertile theo ries. He was the recipient of nearly every academic distinction that can be conferred upon an eminent man of science. His nature was noble and generous, and the universal appreciation of this fact gave him great influence in his university. His portrait, by Lowes Dickinson, was placed in the hall of Trinity college in and his bust, by Henry Wiles, in the library of the same college in 1888.