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 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 The powers foreseen by him for the 'analytical engine' not only transcended, but superseded, those of its predecessor.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