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 or, and was probably a son or grandson of Wynebald de Balun of Eastington Manor, in Gloncestershire, brother of Hameline de Balun.

[Foss's Lives of the Judges; Dugdale's Origines Juridic. (Chron. Ser.); Courthope's Historic Peerage.]

 BAAN. [See .]

BABBAGE, CHARLES (1792–1871), mathematician and scientific mechanician, was the son of Mr. Benjamin Babbage, of the banking firm of Praed, Mackworth, and Babbage, and was born near Teignmouth in Devonshire on 26 Dec. 1792. Being a sickly child he received a somewhat desultory education at private schools, first at Alphington near Exeter, and later at Enfield. He was, however, his own instructor in algebra, of which he was passionately fond, and, previous to his entry at Trinity College, Cambridge, in 1811, he had read Ditton's 'Fluxions,' Woodhouse's 'Principles of Analytical Calculation,' Lagrange's 'Theorie des Fonctions,' and other similar works. He thus found himself far in advance of his tutors' mathematical attainments, and becoming with further study more and more impressed with the advantages of the Leibnitzian notation, he joined with Herschel, Peacock (afterwards Dean of Ely), and some others, to found in 1812 the 'Analytical Society' for promoting (as Babbage humorously expressed it) 'the principles of pure D-ism in opposition to the Dot-age of the university.' The translation, by the three friends conjointly (in pursuance of the same design), of Lacroix's 'Elementary Treatise on the Differential and Integral Calculus' (Cambridge, 1816), and their publication in 1820 of two volumes of 'Examples' with their solutions, gave the first impulse to a mathematical revival in England, by the introduction of the refined analytical methods and the more perfect notation in use on the continent.

Babbage graduated from Peterhouse in 1814 and took an M.A. degree in 1817. He did not compete for honours, believing Herschel sure of the first place, and not caring to come out second. In 1815 he became possessed of a house in London at No. 5 Devonshire Street, Portland Place, in which he resided until 1827. His scientific activity was henceforth untiring and conspicuous. In 1815-17 he contributed to the 'Philosophical Transactions' three essays on the calculus of functions, which helped to found a new, and even yet little explored, branch of analysis. He was elected a fellow of the Royal Society in 1816. He took a prominent part in the foundation of the Astronomical Society in 1820, and acted as one of its secretaries until 1824, subsequently filling the offices, successively, of vice-president, foreign secretary, and member of council. In 1825 he joined with Herschel in repeating and extending Arago's experiments on the magnetisation of rotating plates, reaching the conclusion that 'in the induction of magnetism, time enters as an essential element' (Phil. Trans. cxv. 484). The 'astatic' needle in its present form was devised for use in these researches (ib. p. 476).

It was at Cambridge about 1812 that the first idea of calculating numerical tables by machinery occurred to Babbage. The favourable opinion of Wollaston encouraged him in 1819 to make a serious effort towards its realisation. Machines, such as had existed since Pascal's time, for performing single arithmetical operations, afforded neither saving of time nor security against error, since the selection and placing of a number of arbitrary figures was no less laborious and uncertain than the calculation itself. The essential novelty of Babbage's design consisted in setting wheelwork to develop the numerical consequences of the law of any given series, thus insuring the accurate calculation of an entire table without any further trouble to the operator than a few original adjustments. The mathematical principle selected by him as the basis of his invention was the 'method of differences,' by which it appears that the numbers composing nearly all arithmetical series can be formed by the repeated addition to fundamental numbers of a common difference or 'element'—a process eminently capable of being performed by machinery.

A small engine, of which he constructed a model on this system between 1820 and 1822, was described by Babbage in a note read before the Astronomical Society on 14 June 1822 (Memoirs, i. 309). The announcement was received with enthusiasm, and the highest anticipations were formed as to the results eventually to be derived from the invention (see in Phil. Mag. lxiii. (1824) 355, and Astr. Nach. No. 46). It was rewarded on 13 June 1823 with the first gold medal bestowed by the society, in presenting which the president, Mr. Colebrooke, declared it to be 'in scope, as in execution, unlike anything before accomplished to aid operose computations' (Mem. R. A. Soc. i. 509).

Babbage now proposed to construct a machine upon a greatly enlarged scale, and made his views on the subject public in a letter dated 3 July 1822, addressed to Sir Humphry