recovered, in the death (15 April 1859) of his wife, the youngest daughter of Professor Wilson (Christopher North), whom he had married in April 1849, and to whom he was devotedly attached. He sought relief in hard work, but life had thenceforth lost much of its zest for him. Being childless, its loneliness became intolerable, and in December 1863 he married again. But by this time his constitution was seriously shaken, and on 4 Aug. 1865 he died at Blackhills, near Elgin, whither he had gone to spend the summer in the hope of recruiting his health. Aytoun's life had been, upon the whole, a happy one. He was of a genial, kindly disposition, full of playfulness, and of original and cultured humour, warmly esteemed by his friends, and constant in his attachments to them. Nature and education fitted him for a man of letters, and he took delight in the very varied literary labours by which his free and facile pen enriched the pages of Blackwood's Magazine,' and added a few books to literature of permanent interest.

sity of Edinburgh. Here he was in his
element; and he made his lectures so attrac-
tive that he raised the number of students
from 30 in 1846 to upwards of 1,850 in 1864.
His professorial duties did not interfere with
his position at the bar, and in 1852, when
the tory party came into power, they re-
quited his services as a political writer by
appointing him sheriff of Orkney. In the
following year Oxford conferred on him the
honorary degree of D.C.L. The duties of
Aytoun's sheriff'ship did not engross much
of his time. These, and his work as pro-
fessor, both most conscientiously discharged,
left him leisure for literary work. In 1854
he produced the dramatic poem 'Firmilian,'
perhaps the most brilliant of his works,
which was written in ridicule of the ex-
travagant themes and style of Bailey, Dobell,
and Alexander Smith. It was, however, so
full of imagination and fine rhythmical
swing, that its object was mistaken, and
what was meant for caricature was accepted
as serious poetry. In 1856 Aytoun pub-
lished Bothwell,' a poetical monologue, deal-
ing with the relations between the hero and
Mary Queen of Scots. It contained many
fine passages, and three editions of it were
published. In 1858 he published a collec-
tion, in two volumes, of the Ballads of
Scotland,' carefully collated and annotated,
of which four editions, the last in 1860, have
been published. In 1861 his novel of Nor-
man Sinclair' was published: it had already
appeared in 'Blackwood's Magazine,' and is
interesting for its pictures of society in
Scotland, as Aytoun saw it in his youth, and
for many passages which are, in fact, auto-
biographical. About this time Aytoun's
health began to fail, and his spirits had sus-
tained a shock, from which he never wholly | 1867.]

B

BAALUN, or BALUN, JOHN DE (d. 1235), justice itinerant, was a baron who possessed estates in Gloucestershire, Herefordshire, and Wiltshire, and was descended from one Hameline de Baalun, who came over with the Conqueror, built the castle of Abergavenny, and died in 1089. His father was, Reginald de Balun, and in 1207 John de Balun paid a fine for the lands of Hameline, on behalf of his father, to Geoffrey Fitz-Ace and Agnes, his wife, and 100 marks and a palfrey to the king. In 12 John (1210-11) Balun accompanied the king to Ireland, but at the end of John's reign lost his lands for taking part in

His published works are:-1. 'Poland, Homer, and other Poems,' Edinburgh, 1832. 2. 'The Life and Times of Richard the First,' London, 1840. 3. Lays of the Cavaliers,' Edinburgh, 1848, 29th edition 1883. 4. bun Gaultier's Ballads' (jointly with Theodore Martin), London, 1855, 13th edition 1877. 5. Bothwell,' London, 1856. 6. 'Firmilian,' 1854. 7. 'Poems and Ballads of Goethe' (jointly with Theodore Martin), London, 1858. 8. Ballads of Scotland,' 2 vols. London, 1858, 4th edition 1870. 9. Nuptial Ode to the Princess Alexandra,' London, 1863. 10. 'Norman Sinclair,' 3 vols. London, 1861.

[W. E. Aytoun's Life, by-Theodore Martin,

T. M.

the barons' attack upon thing. On the accession of Henry III he was restored on returning to his allegiance, and in 9 Henry III (1224-5) was appointed a justice itinerant for Gloucestershire along with Matthew de Pateshull, archdeacon of Norfolk, Richard de Veym, and the abbot of Tewkesbury. He died in 1235. His son John paid 1007. for his relief, and did homage for his inheritance, and, dying in 1274, was succeeded by another of John's sons, Walter (Abb. Rot. Orig. i. 24). A justice itinerant who was appointed 9 Henry III and died in the following year (1226) bore the name of ROGER DE BAALUN

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).

BABBAGE, CHARLES (1792-1871), mathematician and scientific mechanician, was the son of Mr. Benjamin Babbage, of the banking firm of Praed, Mackworth, and It was at Cambridge about 1812 that the Babbage, and was born near Teignmouth in first idea of calculating numerical tables by Devonshire on 26 Dec. 1792. Being a sickly machinery occurred to Babbage. The favourchild he received a somewhat desultory edu- able opinion of Wollaston encouraged him cation at private schools, first at Alphington in 1819 to make a serious effort towards its near Exeter, and later at Enfield. He was, realisation. Machines, such as had existed however, his own instructor in algebra, of since Pascal's time, for performing single which he was passionately fond, and, previous arithmetical operations, afforded neither to his entry at Trinity College, Cambridge, saving of time nor security against error, in 1811, he had read Ditton's 'Fluxions,' since the selection and placing of a number Woodhouse's 'Principles of Analytical Cal- of arbitrary figures was no less laborious culation,' Lagrange's Théorie des Fonctions,' and uncertain than the calculation itself. and other similar works. He thus found The essential novelty of Babbage's design himself far in advance of his tutors' mathe- consisted in setting wheelwork to develop matical attainments, and becoming with fur- the numerical consequences of the law of ther study more and more impressed with any given series, thus insuring the accurate the advantages of the Leibnitzian notation, calculation of an entire table without any he joined with Herschel, Peacock (after- further trouble to the operator than a few wards Dean of Ely), and some others, to original adjustments. The mathematical found in 1812 the Analytical Society' for principle selected by him as the basis of his promoting (as Babbage humorously ex- invention was the method of differences,' pressed it) the principles of pure D-ism in by which it appears that the numbers comopposition to the Dot-age of the university.' posing nearly all arithmetical series can be The translation, by the three friends con- formed by the repeated addition to fundajointly (in pursuance of the same design), of mental numbers of a common difference or Lacroix's Elementary Treatise on the Dif-element'-a process eminently capable of ferential and Integral Calculus' (Cambridge, being performed by machinery. 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.

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, Babbage graduated from Peterhouse in and the highest anticipations were formed as 1814 and took an M.A. degree in 1817. He to the results eventually to be derived from did not compete for honours, believing Her- the invention (see BAILY in Phil. Mag. schel sure of the first place, and not caring | lxiii. (1824) 355, and Astr. Nach. No. 46). to come out second. In 1815 he became pos- | sessed 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

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 ac-
curacy 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 judg-
ment of the Royal Society. Having been
favourably reported upon, an interview took
place in July between Babbage and the chan-
cellor 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 de-
voted a year to completing his extensive ac-
quaintance with the resources of British
mechanical art by the study of foreign work-
shops and factories. The results were em-
bodied 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 lan-
guages, and by reprints in America.

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.

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 The capabilities of the new machine, to made at the expense of his employers, and the perfecting of which Babbage devoted thus brought about a complete deadlock in thirty-seven years of his life and no inconthe construction of the machine. In the in- siderable share of his fortune, were not terval of a year and a quarter which elapsed limited, like those of the difference engine, before an accommodation could be arrived to the tabulation of a particular function, at, Babbage's speculative mind had grasped but extended over a wide range of analysis. the principle of an entirely new invention. Two sets of perforated cards, similar to those The powers foreseen by him for the analy-used in Jacquard's looms, prescribed in the tical 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

VOL. II.

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