Sir William, the heroic defender of Scottish independence against the aggressions of Edward I. of England, was the second of three sons of Sir Malcolm Wallace (or Walays) of Elderslie and Auchinbothe, properties near the town of Paisley, in the county of Renfrew, and was born probably about 1270. The earlier years of Wallace appear to have been spent at Dunipace, in Stirlingshire, in the society of his uncle, a wealthy priest, who gave him an education far above what was usual in those times, and whose strong love of liberty fostered his nephew's youthful enmity against the English. The rudiments of education thus acquired were afterwards strengthened by the instruction which he received at Dundee. At this period of life he also acquired those hardy and warlike accomplishments which insured his frame to fatigue, and gave him the ready command of weapons of war. His early hatred of the English led him into many brawls and adventures; but it was not till after the battle of Dunbar, in 1296, when Scotland was completely subdued, that he first came prominently before his countrymen. Early in 1297, in a skirmish or quarrel which took place in the town of Lanark, in which several were killed, Wallace slew with his dagger the son of the sheriff of Clydesdale. For this deed he was proclaimed a traitor, outlawed, and compelled to leave home for the wilds and fastnesses of the country, where he joined himself to men whose fortunes were as desperate as his own, and who, in consequence of his courage and higher rank, chose him for their chief. From this time he was constantly engaged against the English with various results, but ultimately, as his adherents increased, and his plans became more matured, with decided advantage. This guerilla warfare was of the utmost importance in his future proceedings.

1 See Henry's ("Blind Harry's") Wallace, by Dr Jamieson; Carrick's Life of Wallace; and the first volume of Tytler's History of Scotland. Wallace. By it he became acquainted with the strongest passes and the best positions for defence in the country; his men were inured to a life of fatigue and privation, to feel the benefits of discipline and obedience, and to rest with the most perfect confidence in the abilities, courage, and great strength of their intrepid commander.

The success which attended these desultory efforts induced him to undertake an enterprise of greater importance. By a forced march he surprised Ormesby, the English justiciary, at Scone, defeated his troops, nearly captured him, and took a rich booty. This exploit led the younger Bruce (afterwards king) and a number of the nobility to join him with their vassals; and their united forces, led by Wallace, in a few months cleared the country of the English. This intelligence reached Edward when about to embark for Flanders, who immediately despatched an army of 40,000 foot and 300 horse into Scotland, under the command of Henry Percy, which, on the 9th of July 1297, came up with that of the Scots, encamped at Irvine, and consisting of nearly the same strength. Dissensions had however broken out among the leaders; the feudal barons, from pride and jealousy, would not submit to the orders of Wallace, and they therefore entered into negotiations with Percy, which ended in their submission to Edward. Sir Andrew Murray of Bothwell was the only man of rank who adhered to Wallace; and, with a large body of tried and veteran followers, they retired indignantly to the north. Percy, considering that he had put an end to the revolt, returned to England; but Wallace and Murray, dividing their forces, carried on their operations against the English, and with such vigour, that in a short time all the strongholds north of the river Forth, except the castle of Dundee, were retaken. Wallace had just laid siege to that fortress, when his scouts informed him of the approach of a powerful force, under the command of the Earl of Surrey, and Cressingham the treasurer. He instantly left the siege to be continued by the citizens, and by a forced march took possession of the high ground on the north side of the river Forth, above Cambuskenneth, at Stirling, before the English forces reached the south side of the river. On the morning of September 11, 1297, Surrey, urged by the taunts of Cressingham, and against the advice of those who knew the nature of the ground, ordered his troops to deploy over the narrow bridge which at that time crossed the river; but when only half their number had passed, and before their ranks could be arrayed on the narrow peninsula which formed the field of battle, Wallace attacked them with his whole force, and nearly every soldier that crossed was either slain or drowned. This decisive defeat was followed by the expulsion of the English from the kingdom. To lessen the severity of a dreadful dearth and famine which now spread over Scotland, Wallace resolved on an expedition into England, not only to procure subsistence for his numerous army, but also to retaliate for the calamities to which Scotland had been subjected. After collecting his forces, he proceeded as far as Newcastle, wasting the northern country with fire and sword, sparing neither age nor sex, and carrying off a large and valuable booty. Soon after his return from this successful expedition, he was elected governor of Scotland, and, strengthened by this high title, he proceeded to regulate the affairs of the kingdom; and so firm and determined was his rule, so beneficial his measures, that the powerful nobility were compelled to submit to his authority, while the lesser barons and the people willingly supported him. This state did not long continue. Edward, in July 1298, at the head of an army of nearly 100,000 foot and 8000 horsemen, entered Scotland, while Wallace retired before him as he advanced, wasting the country, so as to make the English army depend on its own supplies. This mode of warfare reduced it to such straits, that the king had to order an inglorious retreat. At this critical moment, when the military skill of Wallace predicted the most complete success, the treachery of two Scottish nobles, Patrick, earl of Dunbar, and the Earl of Angus, revealed to the English monarch the dispositions of Wallace. Edward immediately ordered his army to readvance, and by a rapid night-march came up with the Scottish army at Torwood, near Falkirk; and Wallace, with not one-third of the number of foot-soldiers, and unsupported by horse, was compelled by his position to fight at disadvantage, and was defeated with great loss. Shortly after this disastrous event, he resigned his high office as governor, and, apparently with the consent of the regents who succeeded him, proceeded to France, with the expectation of obtaining assistance for Scotland from its sovereign. In this he was deceived, as, on arriving at Amiens, he was thrown into prison, and a letter was written by Philip to Edward, offering to send him to London. Philip, however, in this offer, showed more policy than sincerity; for Wallace was secretly released from prison, and furnished with letters, dated November 3, 1298, to the French agents at the court of Rome, ordering them to solicit Pope Boniface to give Wallace an attentive hearing regarding the affairs of Scotland. There is no positive proof that Wallace was at Rome; but certain it is that Boniface, in his bull to Edward, exhibited a knowledge of Scottish history and affairs which he could only have derived from such a source as Wallace. This noble-minded patriot remained on the continent until late in the year 1303, when he returned into Scotland, and immediately commenced active operations in assisting those who still defended the liberties of their country. Their efforts were however of no avail, and Wallace, by his resolute and unflinching conduct, rendered himself so obnoxious to Edward, that when mercy was extended to the few remaining patriots on certain conditions, Edward excluded him, and set a reward of 300 merks on his head. At last, by the treachery of a servant who waited on him, of the name of Jack Short, this great man was betrayed to Sir John Monteith, a Scottish baron, who captured him at night in bed in the house of a certain Ralph Rae, at Robroyston, in the neighbourhood of Glasgow. For this service Monteith received from the English privy council a grant of land of the annual value of L.100. Wallace was taken to Dumbarton Castle, and from thence to London, where he arrived upon Sunday, the 22nd of August 1305. On the following day he was tried in Westminster Hall, with mock splendour and ceremony, by the form of English law, but without the least regard to its justice, and, in accordance with the predetermined resolution of Edward, was condemned to death. The sentence was executed the same day, with disgraceful and revolting cruelty.

Thus ended the career of this noble-minded patriot, but not without leaving a name which will ever be revered. He found his country overpowered and disorganized, her people disheartened, her nobles and leaders in prison, or in the pay of one of the ablest monarchs that ever swayed the English sceptre, himself without wealth or influence, and an outlaw; yet, under all these disadvantages, his love of freedom and hatred of oppression, his fearless courage and continued perseverance, his military skill, his political sagacity, his natural eloquence, and the ardour with which he animated his companions and followers, all conspired to restore the confidence of his countrymen and the freedom of the nation; and had it not been for the pride, jealousy, and treachery of her nobles, the measures that he pursued for organizing the strength and extending the commerce of the kingdom would have given it a stability which the warlike power of the English, aided by the experience, military tactics, and judgment of her monarch, would not have been able to overturn. As it was, both he and his country suffered from the venality of those who by birth and power were her natural protectors. His person was of the most perfect form, and of a stature approaching the gigantic. In strength he was superior to the strongest men of his day; and his frame was such that it was capable of bearing the greatest fatigue. At his execution it is probable that he was not thirty-five years of age.

Wallace, William, an eminent Scottish mathematician, was born at Dysart, in Fifeshire, on the 23rd of September 1768. He acquired the art of reading at a school in his native town, and was indebted for his instruction in arithmetic to his father's tuition. His father, not succeeding as a leather-merchant in Dysart, removed in 1784 to Edinburgh, where young Wallace was apprenticed to a bookbinder in that city. During his leisure hours, he was busy in the pursuit of knowledge, and on the completion of his apprenticeship he was a tolerable proficient in geometry, algebra, and astronomy. Being introduced by the assistant of Dr Robison to the notice of that distinguished professor, Wallace obtained permission to attend his class for the study of natural philosophy, and received private instructions in the higher geometry from the same generous individual. Professor Playfair likewise contributed much to his advancement in the study of the mathematics. After various changes of situations, dictated mainly by a desire to gain time for his books, he became, in 1794, an assistant teacher of mathematics in the academy of Perth; and ultimately, in 1803, one of the mathematical masters to the Royal Military College in Great Marlow, Bucks, and subsequently in Sandhurst, Berks. In 1819, while Wallace was steadily adding to his fame as a lecturer in England, a more important situation was open for him in Edinburgh, the scene of his early struggles and victories. This was the professorship of mathematics, which he filled with great success till 1838, when, on account of ill health, he was obliged to retire. Wallace received the honorary degree of L.L.D. from the university where he had taught for nearly twenty years; and, in consideration of his eminent attainments in science, he received a government pension for life. He died at Edinburgh, after a lingering illness, on the 29th of April 1843. He was fellow or honorary member of numerous scientific societies both in Edinburgh and elsewhere.

The contributions of Dr Wallace to mathematical literature were select and important, if not very extensive. He wrote a considerable number of papers for the Royal Society of Edinburgh, as well as contributing on various subjects to other scientific associations. He produced the principal mathematical articles for the Edinburgh Encyclopedia, and for the fourth edition of the Encyclopaedia Britannica, some of which, from their abiding excellence, have still a place in the present issue of that work. The following is a list of his more important papers contributed to the Transactions of the Royal Society of Edinburgh:

"Geometrical Problems, with Examples of their Applications to the Solution of Problems," was written in 1796; in 1802, "A New Method of expressing the Co-efficients in the Development of the Formula which represents the Mutual Perturbation of two Planets." In 1808, he read an important paper to the Society, entitled "New Series for the Calculation of the Cosine Series and the Calculation of Logarithms." A fourth paper was read before it in 1823, on the "Investigation of Formulas for finding the Logarithms of Trigonometrical Quantities from one another." In 1831, another entitled "Account of the Invention of the Pantograph, and a Description of the Eidograph," the latter being an instrument of his own invention; in 1839, a paper on "The Analogous Properties of Elliptic and Hyperbolic Sectors;" and his last contribution to the Transactions of the Society was entitled "Solution of a Functional Equation with its Application to the Parallelograms of Forces, and the Curve of Equilibration." In 1836, he contributed "Two Elementary Solutions of Kepler's Problem by the Angular Calculus" to the Royal Astronomical Society; and, for the Cambridge Philosophical Society, he wrote a paper on "Geometrical Theorems and Formulae, particularly applicable to some Geodetical Problems."

At the outset of his career, Wallace was an occasional contributor to Leybourne's Mathematical Repository, and to the Gentleman's Mathematical Companion.