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C A W N P O H E — CAYLEY 625 literature was first emphasized by the late bishop of Cayley, Arthur (1821 -1895), English mathemaLondon, Dr Mandell Creighton, who insisted over and tician, born at Richmond in Surrey, 16th August 1821, was over again on the claim of Cavendish to be recognized the second son of Henry Cayley, a Russian merchant, and as the earliest of the great English biographers and an Maria Antonia Doughty. Mr Henry Cayley retired from individual writer of particular charm and originality. He business in 1829 and settled in Blackheath, where Arthur writes with simplicity and with a certain vivid picturesque- was sent to a private school kept by the Rev. G. B. F. ness, rarely yielding to the rhetorical impulses which Potticary; at the age of fourteen he was transferred to governed the ordinary prose of his age. (e. g.) King’s College School, London. He soon showed that he was a boy of great capacity, and in particular that he was Cawnpore (Khanpur), a city and district of possessed of remarkable mathematical ability. On the British India, in the Allahabad division of the North-West advice of the school authorities he was entered at Trinity Provinces. The city is situated on the right bank of College, Cambridge, as a pensioner. He was there coached the Ganges, 417 feet above the sea; 684 miles by rail by William Hopkins of Peterhouse, was admitted a scholar from Calcutta. In 1881 it had a population of 151,444 ; of the college in May 1840, and graduated as Senior in 1891, of 188,712, showing an increase of nearly 25 Wrangler in 1842, and obtained the first Smith’s Prize at per cent. In 1901 the population was 197,000, showing the next examination. In 1842, also, he was elected a a further increase of 4 per cent. The municipal income in Fellow of Trinity, and became a Major Fellow in 1845, 1896-97 was Rs.3,61,899. In 1897 the death-rate was the year in which he proceeded to the M.A. degree. He 49'59 per thousand. The municipality, with a population was assistant tutor of Trinity for three years. In 1846, of 163,779, is governed by a board of 24 members, having decided to adopt the law as a profession, he left of whom 22 are elected. The waterworks provide an Cambridge, entered at Lincoln’s Inn, and became a pupil of annual supply of about 480 million gallons of filtered the conveyancer Mr Christie. He was called to the Bar water, being 8 gallons a head daily, at a total cost of in 1849, and remained at the Bar fourteen years, till 1863, four annas per thousand gallons. In 1897-98 the chief when he was elected to the new Sadlerian Chair of Pure items of expenditure were : Rs.72,234 on water-supply, Mathematics in the University of Cambridge. He settled Rs. 14,657 on drainage, and Rs.56,459 on other public at Cambridge in the same year, and married Susan, works. The principal educational institutions are : the daughter of Robert Moline of Greenwich. He continued aided Christ Church College, with 36 students in to reside in Cambridge and to hold the professorship till 1896-97; the Government agricultural school for the he died, 26th January 1895. From the time he went first province; industrial schools maintained by the S.P.G. to Cambridge till his death he was constantly engaged in and the American mission; and several high schools. mathematical investigation. The number of his papers There are 29 printing-presses, issuing 5 English and and memoirs, some of them of considerable length, exceeds 5 vernacular newspapers. Besides Government manu- 800; they were published, at the time they were composed, factories of leather and flour, Cawnpore possesses 4 in various scientific journals in Europe and America, and cotton-mills, having a total capital of Rs. 59,00,000, with are now embodied, through the enterprise of the syndics of 1638 looms and 230,000 spindles, employing more than the Cambridge University Press, in thirteen large quarto 6000 hands, producing 25,000,000 3b of yarn and woven volumes. These form an enduring monument to his fame. goods valued at Rs. 30,43,000; a woollen mill, having a He wrote upon nearly every subject of Pure Mathematics, capital of Rs.20,00,000, with 302 looms and 12,000 and also upon Theoretical Dynamics and Spherical and spindles, employing 1500 hands, producing all kinds of Physical Astronomy. He was quite as much a geometrician goods valued at Rs.15,35,000; a jute mill, having a as he was an analyst. Among his most remarkable works capital of Rs. 3,75,000, with 73 looms and 1574 spindles, may be mentioned his ten Memoirs on Qualities, comemploying 345 hands; two flour-mills, employing 132 menced in 1854 and completed in 1878 ; his creation of the hands, with an out-turn valued at Rs. 9,70,000; four large Theory of Matrices; his researches on the Theory of Groups; tanneries and leather factories; a small iron-foundry; and his Memoir on Abstract Geometry, a subject which he factories of ice and mineral waters. Cawnpore is also a created; his introduction into geometry of the “ Absolute ”; great railway centre, where the lines of the East Indian, his researches on the higher singularities of curves and the Oudh and Rohilkhand, the Indian Midland, and the surfaces; the classification of cubic curves; additions to Rajputana railways all meet. Since 1875 the Ganges the Theories of Rational Transformation and Correhas been crossed by an iron girder bridge of 25 spans, spondence; the theory of the twenty-seven lines that lie superseding the former bridge of boats. The cantonments, on a cubic surface; the theory of elliptic functions; the to the east of the native quarter, contain accommodation attraction of ellipsoids; the British Association Reports, for a battery of artillery, a European and native infantry 1857 and 1862, on recent progress in general and special regiment, and a native cavalry regiment. theoretical dynamics and on the secular acceleration of the The district of Cawnpore has an area of 2363 square moon’s mean motion. He is justly regarded as one of miles. It had a population in 1881 of 1,181,396, and in the greatest of mathematicians. Competent judges have 1891 of 1,209,695, showing an increase of 2 per cent., compared him to Euler for his range, analytical power, and an average density of 512 persons per square mile. and introduction of new and fertile theories. He was In 1901 the population was 1,259,243, showing a further the recipient of nearly every academic distinction that increase of 4 per cent. The land revenue and rates were can be conferred upon an eminent man of science. Rs.24,47,361, the incidence of assessment being R.l:6:7 Amongst others may be noted honorary degrees by the per acre ; the cultivated area in 1896-97 was 737,218 acres, universities of Oxford, Dublin, Edinburgh, Gottingen, of which 241,883 were irrigated ; the number of police was Heidelberg, Leyden, and Bologna. He was Fellow or 3606 ; the number of vernacular schools in 1896-97 was foreign corresponding member of the French Institute, the 140, with 6435 pupils; the registered death-rate in 1897 Academies of Berlin, Gottingen, St Petersburg, Milan, was 41‘IS per thousand. The district is watered by four Rome, Leyden, Upsala, and Hungary; and he was branches of the Ganges canal, and traversed by two lines nominated an officer of the Legion of Honour by Presiof railway. There are 98 indigo factories, employing dent Carnot. At various times he was President of 5000 persons, with an out-turn valued at Rs.8,84,000, and the Cambridge Philosophical Society, of the London sugar-works with an out-turn valued at Rs. 3,00,000. Mathematical Society, and of the Royal Astronomical S. II. — 79