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 Turvy’s Wonderful Magic Lantern; or, The World Turned Upside Down (1810), and Original Hymns for Sunday School (1812). In 1813 Ann married a Congregational minister, the Rev. Josiah Gilbert, and Jane went to live at Ilfracombe with her brother Isaac. In 1816 Jane returned to Ongar, where the family had been settled for some years, and died there on the 13th of April 1824. Mrs Gilbert died at Nottingham on the 20th of December 1866. Both sisters wrote after their separation, but none of their later works had the same vogue. Jane showed more wit and vivacity than her sister, notably in the Contributions of Q. Q. (2 vols., 1824), and in Display, a Tale for Young People (1815); but, though she was generally supposed to be the chief writer of the two, some of the most famous pieces in their joint works, such as “I thank the goodness and the grace,” “Meddlesome Matty,” “The Notorious Glutton,” &c., are by Ann.

TAYLOR, BAYARD (1825–1878), American author, was born at Kennett Square in Chester county, Pennsylvania, on the 11th of January 1825. The son of a well-to-do farmer, he received his early instruction in an academy at West Chester, and later at Unionville. At the age of seventeen he was apprenticed to a printer in West Chester. A little volume, published at Philadelphia in 1844 under the title Ximena, or the Battle of the Sierra Morena, and other Poems, brought its author a little cash; and indirectly it did him better service as the means of his introduction to The New York Tribune. With the money thus obtained, and with an advance made to him on account of some journalistic work to be done in Europe, “J. B. Taylor” (as he had up to this time signed himself, though he bore no other Christian name than Bayard) set sail for the East. The young poet spent a happy time in roaming through certain districts of England, France, Germany and Italy; that he was a born traveller is evident from the fact that this pedestrian tour of almost two years cost him only £100. The graphic accounts which he sent from Europe to The New York Tribune, The Saturday Evening Post, and The United States Gazette were so highly appreciated that on Taylor’s return to America he was advised to throw his articles into book form. In 1846, accordingly, appeared his Views Afoot, or Europe seen with Knapsack and Staff (2 vols., New York). This pleasant book had considerable popularity, and its author now found himself a recognized man of letters; moreover, Horace Greeley, then editor of the Tribune, placed Taylor on the Tribune staff (1848) thus securing him a certain if a moderate income. His next journey, made when the gold-fever was at its height, was to California, as correspondent for the Tribune; from this expedition he returned by way of Mexico, and, seeing his opportunity, published (2 vols., New York, 1850) a highly successful book of travels, entitled El Dorado; or, Adventures in the Path of Empire. Ten thousand copies were said to have been sold in America, and thirty thousand in Great Britain, within a fortnight from the date of issue. Bayard Taylor always considered himself native to the East, and it was with great delight that in 1851 he found himself on the banks of the Nile. He ascended as far as 12° 30′ N., and stored his memory with countless sights and delights, to many of which he afterwards gave expression in metrical form. From England, towards the end of 1852, he sailed for Calcutta, proceeding thence to China, where he joined the expedition of Commodore Perry to Japan. The results of these journeys (besides his poetical memorials) were A Journey to Central Africa; or, Life and Landscapes from Egypt to the Negro Kingdoms of the White Nile (New York, 1854); The Lands of the Saracen; or, Pictures of Palestine, Asia Minor, Sicily and Spain (1854); and A Visit to India, China and Japan in the Year 1853 (1855). On his return (December 20, 1853) from these various journeyings he entered, with marked success, upon the career of a public lecturer, delivering addresses in every town of importance from Maine to Wisconsin. After two years' experience of this lucrative profession, he again started on his travels, on this occasion for northern Europe, his special object being the study of Swedish life, language and literature. The most noteworthy result was the long narrative poem Lars, but his “Swedish Letters ” to the Tribune were also republished, under the title Northern Travel: Summer and Winter Pictures (London, 1857). His first wife, May Agnew, died (1850) within a year of her marriage, and in October 1857 he married Maria Hansen, the daughter of Peter Hansen, the German astronomer. The ensuing winter was spent in Greece. In 1859 Taylor once more traversed the whole extent of the western American gold region, the primary cause of the journey lying in an invitation to lecture at San Francisco. About three years later he entered the diplomatic service as secretary of legation at St Petersburg, and the following year (1863) became chargé d'affaires at the Russian capital. In 1864 he returned to the United States and resumed his active literary labours, and it was at this period that Hannah Thurston (New York, 1863), the first of his four novels, was published. This book had a moderate success, but neither in it nor in its successors did Bayard Taylor betray any special talent as a novelist. In 1874 he, went to Iceland, to report for the Tribune the one thousandth anniversary of the first settlement there. In June 1878 he was accredited United States minister at Berlin. Notwithstanding the resistless passion for travel which had always possessed him, Bayard Taylor was (when not actually en route) sedentary in his habits, especially in the later years of his life. His death occurred on the 19th of December, only a few months after his arrival in Berlin.

TAYLOR, BROOK (1685–1731), English mathematician, was the son of John Taylor, of Bifrons House, Kent, by Olivia, daughter of Sir Nicholas Tempest, Bart., of Durham, and was born at Edmonton in Middlesex on the 18th of August 1685. He entered St John’s College, Cambridge, as a fellow-commoner in 1701, and took degrees of LL.B. and LL.D. respectively in 1709 and 1714. Having studied mathematics under John Machin and John Keill, he obtained in 1708 a remarkable solution of the problem of the “centre of oscillation,” which, however, remaining unpublished until May 1714 (Phil. Trans., vol. xxviii. p. 11), his claim to priority was unjustly disputed by John Bernoulli. Taylor’s Methodus Incrementorum Directa et Inversa (London, 1715) added a new branch to the higher mathematics, now designated the “calculus of finite differences.” Among other ingenious applications, he used it to determine