Babbage, Charles (DNB00)

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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 Baily 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 Davy, president of the Royal Society. The prospect of vastly increased facility and accuracy in the production of the innumerable tables needed in navigation, astronomy, &c., could not be overlooked by the government, and the practicability of the scheme was on 1 April 1823 officially submitted to the judgment of the Royal Society. Having been favourably reported upon, an interview took place in July between Babbage and the chancellor of the exchequer (Mr. Robinson), at which some indistinct verbal agreement was come to. The upshot was that, aided by a grant of 1,500l. from the Civil Contingencies Fund, the works were without delay set on foot, and were continued actively for four years. At the end of that time Babbage went abroad under medical advice, and devoted a year to completing his extensive acquaintance with the resources of British mechanical art by the study of foreign workshops and factories. The results were embodied in an admirable little treatise 'On the Economy of Machinery and Manufactures' (1832, 4th edition 1835), of which the merit was attested by translation into four languages, and by reprints in America.

On his return to England towards the close of 1828 fresh applications to the treasury became necessary, which, after the council of the Royal Society had repeated its verdict of encouragement, and the Duke of Wellington, by a personal inspection of the works, had convinced himself of their satisfactory progress, were liberally responded to. Nevertheless, little more was done. Misunderstandings arose with Clement, the engineer; the previous prompt payment of his bills was suspended; and the removal of his business from Lambeth to the neighbourhood of Babbage's residence. No. 1 Dorset Street, Manchester Square, where the government had caused fire-proof buildings to be erected for the reception of the drawings and workshops, was made the occasion of an extravagant claim for compensation. On its refusal he withdrew his men, carried off (as he was legally entitled to do) the valuable tools made at the expense of his employers, and thus brought about a complete deadlock in the construction of the machine. In the interval of a year and a quarter which elapsed before an accommodation could be arrived at, Babbage's speculative mind had grasped the principle of an entirely new invention. The powers foreseen by him for the 'analytical engine' not only transcended, but superseded, those of its predecessor. It promised to do the work of the 'difference engine' with greatly increased rapidity, besides executing operations of a far higher range of complexity. These views he considered it his duty to communicate to the government, but failed, during eight years, to elicit any answer to the question whether, under the altered circumstances, they desired the fulfilment of his original (implied) engagement with them. At length, on 4 Nov. 1842, Mr. Goulburn (Sir Robert Peel's chancellor of the exchequer) acquainted him with the final decision to abandon, on the ground of excessive and indefinite expense, a construction which had already cost 17,000l. of public money, besides (probably) about 6,000l. of the inventor's private means.

The machine, of which the plan was thus rendered abortive, was to have had twenty places of figures with six orders of differences, and included mechanism for printing its results. A small portion, put together in 1833, capable of calculating to the third difference, gave a highly satisfactory earnest of the working of the whole. It was shown at the International Exhibition of 1862, and is now in the South Kensington Museum. An elaborate article on the subject by Dr. Lardner, published in the 'Edinburgh Review' for July 1834, led to the construction of the Swedish difference engines by Scheutz of Stockholm (whose original inventiveness Babbage was foremost in acknowledging), one of which was used by the late Dr. Farr in computing the 'English Life Table,' No. 3 (1864). As further secondary, but most important, results of Babbage's labours may be mentioned, first, improvements in machinery and tools, stated by Lord Rosse (Proc. R. Soc. vii. 257) to have more than repaid the sum expended on the unfinished machine: secondly, the invention of a scheme of notation applicable to the interpretation of all mechanical actions whatever, first explained in a communication by Babbage to the Royal Society, 16 March 1826 ('On a Method of expressing by Signs the Action of Machinery,' Phil. Trans, cxvi. part ii. 250), and afterwards more fully developed to meet the requirements of the analytical engine.

The capabilities of the new machine, to the perfecting of which Babbage devoted thirty-seven years of his life and no inconsiderable share of his fortune, were not limited, like those of the difference engine, to the tabulation of a particular function, but extended over a wide range of analysis. Two sets of perforated cards, similar to those used in Jacquard's looms, prescribed in the one case the numbers to be worked with ('variable cards'), and in the other the kind and sequence of operations to be performed upon them ('operation cards'). A committee appointed by the British Association in 1872 (including the names of Cayley and Clifford), to report upon the feasibility of the design, recorded their opinion that its successful realisation might mark an epoch in the history of computation equally memorable with that of the introduction of logarithms {Report, 1878, p. 100); yet did not counsel the attempt, the state of the drawings not being such as to admit of any reasonable estimate as to cost, strength, or durability, being founded upon them. This extraordinary monument of inventive genius accordingly remains, and will doubtless for ever remain, a 'theoretical possibility.'

Babbage occupied the Lucasian chair of mathematics at Cambridge during eleven years (1828-39), but delivered no lectures. He attended in 1828 the meeting of 'Naturforscher' at Berlin, and the scientific congress of Turin in 1840, when he was received with singular and unexpected favour by the king, Charles Albert (see chap. xxiv. of his Passages in the Life of a Philosopher). The drawings and models of the analytical engine exhibited by him on that occasion formed the subject of a valuable essay by Menabrea {Bibl. Tin. de Genève, t. xli. October 1842), translated, with copious notes, by Ada, Lady Lovelace (Taylor's Scientific Memoirs, iii. 666). His outspoken attack upon the management of the Royal Society in a volume entitled 'The Decline of Science in England' (1830) contributed materially to the origin of the British Association in the following year. Of this body he acted as one of the trustees during six years (1832-8), and originated the statistical section at the Cambridge meeting in 1833. The foundation, moreover, of the Statistical Society of London on 15 March 1834 was mainly his work. Amongst his ingenious ideas, that of signalling by 'occulting solar lights,' brought into practice by the Russians during the siege of Sebastopol, deserves mention. It had been recommended by him as a mode of identification for lighthouses (see his tract. Notes respecting Lighthouses, 1852). He twice—in 1832 and 1834—unsuccessfully contested the borough of Finsbury on liberal principles. Nor were what he regarded as his equitable claims to remunerative employment under government recognised. He was, however, a, member of scientific bodies in all parts of the world, including the Paris Academy of Moral Sciences, the Royal Irish and American Academies.

In his latter years Babbage came before the public chiefly as the implacable foe of organ-grinders. He considered that one-fourth of his entire working power had been destroyed by audible nuisances, to which his highly-strung nerves rendered him peculiarly sensitive. In the decay of other faculties, his interest and memory never failed for the operations of the extensive workshops attached to his house. There what might be called the wreckage of a brilliant and strenuous career lay scattered, and thence, after his death on 18 Oct. 1871, some fragmentary portions of the marvellous engine destined to have indefinitely quickened the application of science to every department of human life, were collected and removed to the South Kensington Museum.

Of the eighty works enumerated by Babbage himself (Passages, &c pp. 493-6) scarcely one, except the 'Economy of Manufactures,' can be regarded as a finished performance. The rest are mostly sketches or enlarged pamphlets, keen and suggestive, but incomplete. The 'Comparative View of the various Institutions for the Assurance of Lives' (1826), however, though not exempt from error, was a highly useful work, and one of the first attempts to popularise the subject. It contained a table of mortality deduced from the experience of the Equitable Society, to the construction of which Babbage had been led by his appointment as actuary to the Protector Life Assurance Company (No. 1) on its establishment in 1824 (see Walford's Insurance Cyclopædia, iii. 10), The book was reviewed at length in the 'Quarterly' and 'Edinburgh' Reviews (January and March, 1827), was translated into German, and its table of mortality adopted by the Life Assurance Bank of Gotha, founded in 1829. The 'Table of Logarithms of the Natural Numbers from 1 to 108000' (1827), to the preparation of which Babbage devoted singular care, is still in repute. Several foreign editions were printed from the stereotyped plates. The 'Ninth Bridgewater Treatise' (1837, 2nd edition 1838), a work nobly planned, but very partially executed, was remarkable as one of the earliest attempts to reconcile breaches of continuity with the government of the universe by law, and vindicated the serviceableness of mathematics to religion. A volume entitled 'The Exposition of 1851; or Views of the Industry, the Science, and the Government of England' (1851), is the diatribe of a disappointed man, and, like his autobiographical 'Passages from the Life of a Philosopher' (1864), is disfigured by personal allusions, in giving utterance to which he wronged his better nature.

[Month. Not. R. Astr. Soc. xxxii. 101; Times, 23 Oct. 1871; Athenæum, 28 Oct. 1871; Ib. 14 Oct. and 16 Dec. 1848 (De Morgan); Weld's Hist. R. Society, ii. chap. xi.; Nature, v. 28; Ann. Reg. 1871, p. 159.]

A. M. C.