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half-measures. He acquiesced in the republic and gave his adhesion to General Cavaignac. He became the chief of Louis Napoleon's first ministry in the hope of extracting Liberal measures, but was dismissed in 1849 as soon as he had served the president's purpose of avoiding open conflict. After the coup d'état of December 1851 he was one of those who sought to accuse Napoleon of high treason. He was imprisoned for a short time and retired from active politics for some ten years. He was drawn once more into affairs by the hopes of reform held out by Émile Ollivier, accepting in 1869 the presidency of an extra-parliamentary committee on decentralization. After the fall of the empire he was nominated by Thiers, whom he had supported under Louis Philippe, president of the council of state. But his powers were now failing, and he had only filled his new office for about a year when he died at Bougival on the 6th of August 1873. He had been sufficiently an optimist to believe in the triumph of the liberal but non-republican institutions dear to him under the restoration, under Louis Philippe and Louis Napoleon successively. He was unable to foresee and unwilling to accept the consequences of his political agitation in 1830 and 1848, and in spite of his talents and acknowledged influence he thus failed to secure the honours won by more uncompromising politicians. He was described by Thureau-Dangin as "le plus solennel des indécis, le plus méditatif des irréfléchis, le plus heureux des ambitieux, le plus austère des courtisans de la foule."

His personal relations with Louis Philippe and Napoleon, with his views on the events in which he was concerned, are described in the four volumes of his Mémoires, edited by Duvergier de Hauranne in 1875-1876. See also Thureau-Dangin, Hist. de la monarchie de juillet.

BARROW, ISAAC (1630-1677), English mathematician and divine, was the son of Thomas Barrow, a linen-draper in London, belonging to an old Suffolk and Cambridgeshire family. His uncle was Bishop Isaac Barrow of St Asaph (1614-1680). He was at first placed for two or three years at the Charterhouse school. There, however, his conduct gave but little hopes of his ever succeeding as a scholar. But after his removal from this establishment to Felsted school in Essex, where Martin Holbeach was master, his disposition took a happier turn; and having soon made considerable progress in learning, he was in 1643 entered at St Peter's College, and afterwards at Trinity College, Cambridge, where he applied himself to the study of literature and science, especially of natural philosophy. He at first intended to adopt the medical profession, and made some progress in anatomy, botany and chemistry, after which he studied chronology, geometry and astronomy. He then travelled in France and Italy, and in a voyage from Leghorn to Smyrna gave proofs of great personal bravery during an attack made by an Algerine pirate. At Smyrna he met with a kind reception from the English consul, Mr Bretton, upon whose death he afterwards wrote a Latin elegy. From this place he proceeded to Constantinople, where he received similar civilities from Sir Thomas Bendish, the English ambassador, and Sir Jonathan Dawes, with whom he afterwards contracted an intimate friendship. While at Constantinople he read and studied the works of St Chrysostom, whom he preferred to all the other Fathers. He resided in Turkey somewhat more than a year, after which he proceeded to Venice, and thence returned home through Germany and Holland in 1659.

Immediately on his reaching England he received ordination from Bishop Brownrig, and in 1660 he was appointed to the Greek professorship at Cambridge. When he entered upon this office he intended to have prelected upon the tragedies of Sophocles; but he altered his intention and made choice of Aristotle's rhetoric. His lectures on this subject, having been lent to a friend who never returned them, are irrecoverably lost. In July 1662 he was elected professor of geometry in Gresham College, on the recommendation of Dr John Wilkins, master of Trinity College and afterwards bishop of Chester; and in May 1663 he was chosen a fellow of the Royal Society, at the first election made by the council after obtaining their charter. The same year the executors of Henry Lucas, who, according to the terms of his will, had founded a mathematical chair at Cambridge, fixed upon Barrow as the first professor; and although his two professorships were not inconsistent with each other, he chose to resign that of Gresham College, which he did on the 20th of May 1664. In 1669 he resigned his mathematical chair to his pupil, Isaac Newton, having now determined to renounce the study of mathematics for that of divinity. Upon quitting his professorship Barrow was only a fellow of Trinity College; but his uncle gave him a small sinecure in Wales, and Dr Seth Ward, bishop of Salisbury, conferred upon him a prebend in that church. In the year 1670 he was created doctor in divinity by mandate; and, upon the promotion of Dr Pearson to the see of Chester, he was appointed to succeed him as master of Trinity College by the king's patent, bearing the date of the 13th of February 1672. In 1675 Dr Barrow was chosen vice-chancellor of the university. He died on the 4th of May 1677, and was interred in Westminster Abbey, where a monument, surmounted by his bust, was soon after erected by the contributions of his friends.

By his English contemporaries Barrow was considered a mathematician second only to Newton. Continental writers do not place him so high, and their judgment is probably the more correct one. He was undoubtedly a clear-sighted and able mathematician, who handled admirably the severe geometrical method, and who in his Method of Tangents approximated to the course of reasoning by which Newton was afterwards led to the doctrine of ultimate ratios; but his substantial contributions to the science are of no great importance, and his lectures upon elementary principles do not throw much light on the difficulties surrounding the border-land between mathematics and philosophy. (See Infinitesimal Calculus.) His Sermons have long enjoyed a high reputation; they are weighty pieces of reasoning, elaborate in construction and ponderous in style.

His scientific works are very numerous. The most important are:—Euclid's Elements; Euclid's Data; Optical Lectures, read in the public school of Cambridge; Thirteen Geometrical Lectures; The Works of Archimedes, the Four Books of Apollonius's Conic Sections, and Theodosius's Spherics, explained in a New Method; A Lecture, in which Archimedes' Theorems of the Sphere and Cylinder are investigated and briefly demonstrated; Mathematical Lectures, read in the public schools of the university of Cambridge. The above were all written in Latin. His English works have been collected and published in four volumes folio.

See Ward, Lives of the Gresham Professors; Whewell's biography prefixed to the 9th volume of Napier's edition of Barrow's Sermons.

BARROW, SIR JOHN (1764–1848), English statesman, was born in the village of Dragley Beck in the parish of Ulverston in Lancashire, on the 19th of June 1764. He started in life as superintending clerk of an iron foundry at Liverpool and afterwards taught mathematics at a school in Greenwich. Through the interest of Sir George Staunton, to whose son he taught mathematics, he was attached on the first British embassy to China as comptroller of the household to Lord Macartney. He soon acquired a good knowledge of the Chinese language, on which he subsequently contributed interesting articles to the Quarterly Review; and the account of the embassy published by Sir George Staunton records many of Barrow's valuable contributions to literature and science connected with China.

Although Barrow ceased to be officially connected with Chinese affairs after the return of the embassy in 1794, he always took much interest in them, and on critical occasions was frequently consulted by the British government. In 1797 he accompanied Lord Macartney, as private secretary, in his important and delicate mission to settle the government of the newly acquired colony of the Cape of Good Hope. Barrow was entrusted with the task of reconciling the Boers and Kaffirs and of reporting on the country in the interior. On his return from his journey, in the course of which he visited all parts of the colony, he was appointed auditor-general of public accounts. He now decided to settle in South Africa, married Anne Maria Trüter, and in 1800 bought a house in Cape Town. But the surrender of the colony at the peace of Amiens (1802) upset this plan. He returned to England in 1804, was appointed by Lord Melville second secretary to the admiralty, a post which he held for