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 for the graphic solution of astronomical problems for nautical purposes, and which he had brought to the notice of the admiralty in 1845. The instrument was for the purpose of approximately determining the latitude from two observations taken before 9 a.m. and at noon, and also of finding the latitude by a south altitude, from the time of day, and of finding the amplitude and azimuth. The invention was considered ingenious, and its principle correct; but its adoption was not recommended for the royal navy, lest its general use might induce neglect of even the slight acquaintance with nautical astronomy which officers were then required to possess.

Warren married, first, on 17 April 1830, at the British embassy at Paris, Mary Anne (d. 20 Jan. 1846), daughter of William and Margaret Hughes of Dublin and Carlow, by whom he had six children, two of whom died young; secondly, on 4 Oct. 1859, Mary (d. 22 Dec. 1860), daughter of George Bethell, rector of Worplesden and vice-provost of Eton College. The eldest son, John, a captain in the 55th regiment, served with his father in the Crimea, and died of a wound in Scutari hospital after the battle of Inkerman. Another son is Sir Charles Warren, chief commissioner of the metropolitan police 1886–8.

General Warren's elder brother, (1796–1852), mathematician, eldest son of the dean of Bangor, born on 4 Oct. 1796 at Bangor deanery, was educated at Westminster school and Jesus College, Cambridge, of which he was a fellow and tutor. In 1818 he was fifth wrangler, and in 1825 and 1826 served the office of moderator and examiner. In 1830 he was elected a fellow of the Royal Society. In 1828 he published at Cambridge ‘A Treatise on the Geometrical Representation of the Square Roots of Negative Quantities,’ a subject which had previously attracted the attention of Wallis, Professor Heinrich Kühn of Danzig, M. Buée, and M. Mourey, whose researches were, however, unknown to Warren. The work bears evident marks of originality, and has received honourable mention as well from continental as from English mathematicians. The title hardly conveys an exact idea of the main object, which is to represent every kind of quantity geometrically by the intervention of symbolical expressions, which involve the square roots of negative quantities, and designate lines in position as well as magnitude. He was strongly convinced of the superiority of geometry as a means of demonstration to the use of mere symbols of quantity, and thought that the obscurity attaching to the proofs of some of the fundamental rules of algebraic and analytical operations might be removed by adopting a geometrical representation of quantity such as he proposed.

On 19 Feb. 1829 Warren read a paper before the Royal Society entitled ‘Considerations of the Objections raised against the Geometrical Representation of the Square Roots of Negative Quantities,’ which was followed on the 4th of June by another ‘On the Geometrical Representation of the Powers of Quantities whose Indices involve the Square Roots of Negative Quantities,’ in which he came to the conclusion ‘that all algebraic quantity may be geometrically represented, both in length and direction, by lines drawn in a given plane from a given point.’

Warren was chancellor of the diocese of Bangor and rector of Graveley in Cambridgeshire, and of Caldecott in Huntingdonshire. He owned the advowson of the latter, which, as well as an adjoining parish, was without a resident clergyman. To remedy this evil he proposed to unite the two parishes. He sold the advowson of Caldecott to the patron of the other parish, and gave the purchase-money to build a parsonage for the united parishes—an incident characteristic of the man. He married his cousin, Caroline Elizabeth, daughter of Captain and Lieutenant-colonel Richard Warren of the 3rd foot guards. He died at Bangor on 16 Aug. 1852, without issue.

 WARREN, FREDERICK (1775–1848), vice-admiral, born in March 1775, was son of [q. v.], physician to George III, and elder brother of [q. v.] He was admitted to Westminster school on 15 Jan. 1783, and entered the navy in March 1789, on board the Adamant, flagship of Sir [q. v.] on the Halifax station. When the Adamant was paid off in 1792, Warren was sent to the Lion with Captain [q. v.], and in her made the voyage to China. Shortly after his return, on 24 Oct. 1794, he was confirmed in the rank of lieutenant and appointed to the Prince George. He after