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Rh guardian of the kingdom. In this office he set himself to reorganize the army and to regulate the affairs of the country. His measures were marked by much wisdom and vigour, and for a short time succeeded in securing order, even in the face of the jealousy and opposition of the nobles. Edward was in Flanders when the news of this successful revolt reached him. He hastened home, and at the head of a great army entered Scotland in July 1298. Wallace was obliged to adopt the only plan of campaign which could give any hope of success. He slowly retired before the English monarch, driving off all supplies and wasting the country. The nobles as usual for the most part deserted his standard. Those that remained thwarted his councils by their jealousies. His plan, however, came very near being successful. Edward, compelled by famine, had already given orders for a retreat when he received information of Wallace's position and intentions. The army, then at Kirkliston, was immediately set in motion, and next morning (July 22, 1298) Wallace was brought to battle in the vicinity of Falkirk. After an obstinate fight the Scots were overpowered and defeated with great loss. Among the slain was Sir John de Graham, the bosom friend of Wallace, whose death, as Blind Harry tells, threw the hero into a frenzy of rage and grief. The account of his distress is one of the finest and most touching passages in the poem. With the remains of his army Wallace found refuge for the night in the Torwood—known to him from his boyish life at Dunipace. He then retreated to the north, burning the town and castle of Stirling on his way. He resigned the office of guardian, and betook himself again to a wandering life and a desultory and predatory warfare against the English. At this point his history again becomes obscure. He is known to have paid a visit to France, with the purpose of obtaining aid for his country from the French king. This visit is narrated with many untrustworthy details by Blind Harry; but the fact is established by other and indisputable evidence. When in the winter of 1303-1304 Edward received the submission of the Scottish nobles, Wallace was expressly excepted from all terms. And after the capture of Stirling Castle and Sir William Oliphant, and the submission of Sir Simon Fraser, he was left alone, but resolute as ever in refusing allegiance to the English king. A price was set upon his head, and the English governors and captains in Scotland had orders to use every means for his capture. On the 5th of August 1305 he was taken—as is generally alleged, through treachery—at Robroyston, near Glasgow, by Sir John Menteith, carried to the castle of Dumbarton, and thence conveyed in fetters and strongly guarded to London. He reached London on the 22nd of August, and next day was taken to Westminster Hall, where he was impeached as a traitor by Sir Peter Mallorie, the king's justice. To the accusation Wallace made the simple reply that he could not be a traitor to the king of England, for he never was his subject, and never swore fealty to him. He was found guilty and condemned to death. The sentence was executed the same day with circumstances of unusual cruelty.

The cause of national independence was not lost with the life of Wallace. Notwithstanding the cruelty and indignity amid which it terminated, that life was not a failure. It has been an inspiration to his countrymen ever since. The popular ideas regarding his stature, strength, bodily prowess and undaunted courage are confirmed by the writers nearest his own time—Wyntoun and Fordun. And indeed no man could in that age have secured the personal ascendancy which he did without the possession of these qualities. The little we know of his statesmanship during the short period he was in power gives proof of political wisdom. His patriotism was conspicuous and disinterested. He was well skilled in the modes of warfare that suited the country and the times. That he failed in freeing his country from the yoke of England was due chiefly to the jealousy with which he was regarded by the men of rank and power. But he had a nobler success in inspiring his countrymen with a spirit which made their ultimate conquest impossible.

For bibliography see the article in the ''Dict. Nat. Biog.'' The principal modern lives are James Moir's (1886), and A. F. Murison's (1898).

 WALLACE, WILLIAM (1768–1843), Scottish mathematician, was born on the 23rd of September 1768 at Dysart in Fifeshire, where he received his school education. In 1784 his family removed to Edinburgh, where he himself was set to learn the trade of a bookbinder; but his taste for mathematics had already developed itself, and he made such use of his leisure hours that before the completion of his apprenticeship he had made considerable acquirements in geometry, algebra and astronomy. He was further assisted in his studies by John Robison (1739–1805) and John Playfair, to whom his abilities had become known. After various changes of situation, dictated mainly by a desire to gain time for study, he became assistant teacher of mathematics in the academy of Perth in 1794, and this post he exchanged in 1803 for a mathematical mastership in the Royal Military College at Great Marlow (afterwards at Sandhurst). In 1819 he was chosen to succeed John Leslie in the chair of mathematics at Edinburgh, and in 1838, when compelled by ill-health to retire, he received a government pension for life. He died in Edinburgh on the 28th of April 1843.

In his earlier years Wallace was an occasional contributor to Leybourne's Mathematical Repository and the Gentleman's Mathematical Companion. Between 1801 and 1810 he contributed articles on “Algebra,” “Conic Sections,” “Trigonometry,” and several others in mathematical and physical science to the fourth edition of the Encyclopaedia Britannica, and some of these were retained in subsequent editions from the fifth to the eighth inclusive. He was also the author of the principal mathematical articles in the Edinburgh Encyclopaedia, edited by David Brewster (1808–1830). He also contributed many important papers to the Transactions of the Royal Society of Edinburgh.

See ''Transactions of the Roy. Ast. Soc.'', 1844.  WALLACE, WILLIAM (1844–1897), Scottish philosopher, was born at Cupar-Fife on the 11th of May 1844, the son of a house-builder. Between the ages of sixteen and twenty-two he was educated at St Andrews, whence he proceeded as an exhibitioner in 1864 to Balliol College, Oxford. He took a first class in Moderations, and in Lit. Hum. (1867), was Gaisford prizeman in 1867 (Greek prose) and Craven Scholar in 1869. Three years later he was appointed fellow, and in 1871 librarian, of Merton College. In 1882 he was elected Whyte's professor of moral philosophy in succession to T. H. Green, and retained the position until his death. He died on the 18th of February 1897 from the effects of a bicycle accident near Oxford. His manner was somewhat brusque and sarcastic, and on this account, in his undergraduate days at Balliol, he was known as &ldquo; The Dorian.&rdquo; But he was greatly respected both as a man and as a lecturer. His philosophical works are almost entirely devoted to German, and especially to Hegelian, doctrines, which he expounded and criticized with great clearness and literary skill. In dealing with Hegel he was, unlike many other writers, successful in expressing himself in a lucid literary manner, without artificial and incomprehensible terminology.

His principal works were The Logic of Hegel (1873), which contains a translation of the Encyklopädie with an introduction, a second edition of which, with a volume entitled Prolegomena, appeared in 1892; Epicureanism (1880); Kant (Blackwood's Philosophical Classics, 1882); Life of Arthur Schopenhauer (1890); Hegel's Philosophy of Mind (translated from the Encyklopädie, with five introductory essays); Lectures and Essays on Natural Theology and Ethics, being a selection from his papers edited with a biographical introduction by Edward Caird. He wrote several important articles for the 9th edition of the ''Ency. Brit.'', which, with some revision, have been repeated in the present work.  WALLACE, WILLIAM VINCENT (1814-1865), British composer, was born at Waterford, Ireland, his father, of Scottish family, being a regimental bandmaster. Vincent Wallace learnt as a boy to play several instruments, and became a leading violinist in Dublin. But in 1835 he married and went off to Australia, sheep farming. A concert in Sydney revived his musical passion; and having separated from his wife, he began a roving career, which had many romantic episodes, in Australia, the South Seas, India and South America. He returned to London in 1845 and made various appearances as a pianist; and in November of that year his opera Maritana was performed at Drury Lane with great success. This was followed by Matilda of Hungary (1847), Lurline (1860), The Amber Witch