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 "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.

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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-what brusque and sarcastic, and on this account, in his underat 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.

WALLACE, WILLIAM (1844-1897), Scottish philosopher, was born at Cupar-Fife on the 11th of May 1844, the son of a housebuilder. 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 somegraduate days at Ball, he was known as "The Dorian." 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 Philo Ethics, being a selection from his papers edited with a biographical ductory essays); Lectures and Essays on Natural Theology and 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.

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 inspira-sophy of Mind (translated from the Encyklopädie, with five introtion 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). (A. F. H.)

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 per formed at Drury Lane with great success. This was followed by Matilda of Hungary (1847), Lurline (1860), The Amber Witch

sometimes worked on the paper with stencil patterns cut out of zinc sheets. These are laid upon the paper and thick colour applied through the perforations with a stiff brush.

trouble and without any danger of its sagging. When the cement has properly set, the paper is washed off from the face of the work. Much improvement has been effected in the design and manufacture of wall-tiles. Especially has the design of tiles reached a very The cheaper wall-papers are printed by machinery. The paper is high level of excellence, and as a material which combines made to travel round a large drum around which are grouped the Tiles. the qualities of being hard in wear, durable, damp-resist-printing cylinders, each with its separate inking roller to supply the ing and easily washable, with beauty of design, colouring and surface, special colour for its use. On each of the wooden printing rollers is tiling may perhaps be placed next in order of merit as a wall-covering set copper "type," representing as much of the pattern as is to be to mosaic. A thin, opaque glass material, manufactured under printed in one colour. It is a difficult and tedious matter to get all various trade names, is now much used, especially for tiling existing the rollers to work together to form one perfect pattern, and when walls. It has all the sanitary qualities of tiles, but is perhaps printing in several colours it may take a skilled workman a week or somewhat more fragile and liable to be damaged under hard wear. more to set "his machine, a very large quantity of paper being It is made in opal and other colours and is usually fixed with a spoilt during the process. special cement or mastic which allows for slight movements of expansion and contraction. The thickness of the material varies with different makers from to in.

Metal sheeting, though somewhat inartistic in appearance, is useful where a durable, waterproof and sanitary wall protection is needed, and is therefore often used for sculleries, wash-houses and Metal lavatorics. Thin sheets of zinc with slightly embossed sheeting. patterns and enamelled in colours can be hung upon the wall with a composition of white lead (one part) and whiting (two parts) mixed to a thick paste with varnish or gold size. Sheets of iron or steel can be more elaborately embossed and fixed to the wall with nails or screws; they are either previously enamelled or are painted after being fixed. They are used more for ceilings than for wall-coverings, but are adapted for use in either position. Tapestry of good design and workmanship is a really beautiful wall-covering. It is usually hung upon frames fitted to the wall, and may either cover the entire wall surface or be fixed Tapestry. in the form of panels, friezes, dados or fillings. It is not at all a sanitary covering, for it harbours a very large quantity of dust and dirt. The same remark applies, but perhaps in a less degree, to brocades of silk and damask. These materials are of a delicate nature and become easily soiled by the fumes of gas or oil lamps. Substitutes for these materials on stout paper and on cotton are made with a prepared back to facilitate pasting and hanging, and are a very good imitation of the better material. A coarse canvas, specially prepared with a smooth back for pasting, and stained in several plain colours, can now be purchased. Having a rough surface it naturally holds the dust, but this can easily be brushed off without damaging the material. It is a pleasing wall-wall the colour chosen should be capable of withstanding the bleaching covering, which will stand hard wear, and it forms a good background for pictures and furniture.

papers.

The term" wall-paper " embraces a very large variety of materials of many kinds, designs and qualities, ranging from the cheapest machine-printed papers of the most flimsy description and Wall- often hideous design, to the Japanese and similar leather papers, skilfully modelled in relief and richly decorated in gold and colours. The design of the paper, of whatever description it may be, should preferably be of a conventional pattern, unobtrusive and restful to the eye, and presenting no strong contrasts of colour. The wall must be treated as a background, consisting of a plane surface, and no attempt made to introduce a pictorial element into the decoration. The wall surface, regarded from the paperhanger's point of view, is often divided into three sections, the dado or base, the field or filling, and the frieze at the top immediately beneath the cornice. This subdivision is not always adhered to, and a wall may be papered uniformly all over its surface, or may consist of dado and filling without the frieze, or frieze and filling without the dado, The division between the sections is usually formed, in the

case of the frieze and filling, with a wood picture rail, and between the

filling and dado with a moulded dado or chair rail.

Wall-papers may be printed either in distemper colours or oil colours, and the patterns upon them are printed either by hand or by machine. There are also self-coloured papers which have different kinds of surface finish, and with some of these a pattern is formed by contrasting a smooth with a rough or granulated surface or vice versa. Typical of such papers are the ingrain papers, which have the colour penetrating through their substance. Plain filling papers are often used in conjunction with a boldly designed and strongly coloured frieze of considerable depth. The dado is either of similar plain paper or of an unobtrusive pattern. Often the filling is taken down to the skirting without the intervention of a dado rail. Papers printed in oil colours can be sized and varnished, and when treated in this way can be washed repeatedly and are very durable. This treatment gives an unpleasant glazed surface to the wall, but in spite of this it is often adopted for bathrooms, kitchens and in similar positions, because it is economical.

The best papers are printed from blocks manipulated by hand. The pattern, or as much of it as is to be printed in one colour, is carved upon a pear-wood board, small and delicate members being represented by strips and dots of copper inserted in the block. With large blocks a treadle and pulley arrangement gives the workman assistance in applying and removing the pattern, which is first fed with colour by being pressed on a felt blanket soaked in pigment and then applied to the surface of the paper to be decorated. One tint is applied at a time, and this when dry is followed by others necessary to complete the design. This drying of the previous colour ensures sharpness of outline and accuracy of colour. Designs are

The colours used for hand-printed work, whether applied with blocks or stencil plates, are much thicker in consistency than those for machine work. One advantage of hand-worked paper is the comparative ease with which a paper can be matched even after it has gone out of stock. At a slight extra cost the manufacturer will print a few pieces for his customer from the blocks he has retained. With machine-printed paper this, from a practical point of view, is impossible, for it would necessitate the printer's going through the long and costly process of "setting" the machine. Wall-papers are sold in rolls called " pieces." In England the standard size for a piece of paper is 12 yds. long and 21 in. wide. The printed surface is only 20 in. in width, as a margin of half an inch is left on each edge. One or both of these plain margins must be removed prior to hanging. French wall-papers are 9 yds. long and 18 in. wide and only contain 40 sq. ft. compared with 63 ft. in a piece of English paper. To ascertain the number of pieces required for a room take the superficies in feet of the surface to be covered (deduction being made for the doors, windows, &c.) and divide by 60. This gives the net amount required; an allowance of about oneseventh must be added to allow for waste in matching patterns and of odd lengths. If French papers are to be used the division should be 38 instead of 60, these figures representing in feet the area of the printed surface in cach roll. The surface of the wall should before papering be carefully prepared so as to be quite smooth and regular. If the wall has been previously papered it should be stripped, and any irregularities filled in with stopping. To remove varnished paper use hot water to which borax has been added in the proportions of 2 oz. to each pint of water. In selecting a paper for a newly plastered action of the lime in the plaster. Greens, blues and pinks especially are affected in this manner. For heavy papers glue paste should be used. Papering which has become dirty may be effectually cleaned with new bread or stiff dough; when gently rubbed over the surface in one direction this speedily removes the dirt. When the wall is damp, tinfoil, pitch-coated paper or Willesden waterproofed paper is used behind the paper to prevent the paper from becoming damaged by the wet. (J. Br.)

WALLENSTEIN' (properly WALDSTEIN), ALBRECHT WENZEL EUSEBIUS VON, duke of Friedland, Sagan and Mecklenburg (1583-1634), German soldier and statesman, was born of a noble but by no means wealthy or influential family at Herrmanic, Bohemia, on the 15th of September 1583. His parents were Lutherans, and in early youth he attended the school of the Brothers of the Common Life at Koschumberg. After the death of his parents he was sent by his uncle, Slawata, fessed, but hardly accepted, the Roman Catholic faith. to the Jesuit college of nobles at Olmütz, after which he proIn 1599 he went to the university of Altdorf, which he had to leave in consequence of some boyish follies. Afterwards he studied at Bologna and Padua, and visited many places in southern and western Europe. While in Padua he gave much attention to astrology, and during the rest of his life he never wavered in the conviction that he might trust to the stars for indications as to his destiny. For some time Wallenstein served in the army of the emperor Rudolph II. in Hungary, which was commanded by a methodical professional soldier, Giorgio Basta. His personal gallantry at the siege of Gran won for him a company without purchase. In 1606 he returned to Bohemia, and soon afterwards he married an elderly widow, Lucretia Nikossie von Landeck, whose great estates in Moravia he inherited after her death in 1614. His new wealth enabled him to offer two hundred horse, splendidly equipped, to the archduke Ferdinand for his war with Venice in 1617. Wallenstein commanded them in person, and from that time he enjoyed both favour at court and popularity in the army. His wealth and influence were further increased by his marriage with Isabella Katharina, daughter of Count Harrach, a confidential adviser of the emperor Matthias.

In the disturbances which broke out in Bohemia in 1618 and proved to be the beginning of the Thirty Years' War, advances

were made to Wallenstein by the revolutionary party, but he spoken of the arrogance of the princes, and it appeared probable preferred to associate himself with the imperial cause, and he that he would try to bring them, Catholics and Protestants carried off the treasure-chest of the Moravian estates to Vienna, alike, into rigid subjection to the crown. Again and again part of its contents being given him for the equipment of a regi- the emperor was advised to dismiss him. Ferdinand was very ment of cuirassiers. At the head of this regiment Wallenstein unwilling to part with one who had served him so well, but the won great distinction under Buquoy in the war against Mansfeld. demand was pressed so urgently in 1630 that he had no alterHe was not present at the battle of the Weisser Berg, but he did native, and in September of that year envoys were sent to brilliant service as second-in-command of the army which opposed Wallenstein to announce his removal. Had the emperor declined Gabriel Bethlen in Moravia, and recovered his estates which the to take this course, the princes would probably have combined nationalists had seized. The battle of the Weisser Berg placed against him, and the result would have been a civil war even Bohemia at the mercy of the emperor Ferdinand, and Wallenstein more serious than that which had already brought so many turned the prevailing confusion to his own advantage. He disasters upon the country. Wallenstein perfectly understood secured the great estates belonging to his mother's family, and this, and he therefore accepted the emperor's decision calmly, the emperor sold to him on easy terms vast tracts of confiscated gave over his army to Tilly, and retired to Gitschin, the capital lands. His possessions he was allowed to form into a territory of his duchy of Friedland. There, and at his palace in Prague, called Friedland, and he was raised in 1622 to the rank of an he lived in an atmosphere of mysterious magnificence, the rumours imperial count palatine, in 1623 to that of a prince. In 1625 of which penetrated all Germany. The enigma of his projects he was made duke of Friedland Meantime he fought with was intensified, and the princes who had secured his disgrace skill and success against Gabriel Bethlen, and so enhanced his became more suspicious than ever. But ere long the emperor was reputation at the dark moment when Vienna was in peril and the forced by events to call him into the field again. emperor's general Buquoy dead on the field of battle. At this stage in his life the enigma of his personality is complicated by the fact that he was not only the cold, detached visionary with vast ambitions and dreams, but also the model ruler of his principality In everyday matters of administration he displayed vigour and foresight He not only placed the administration of justice on a firm basis and founded schools, but by many wise measures developed agriculture and mining and manufacturing industries. At the same time he enlisted in the service of his ambition and his authority a pomp and refinement in his court which contrasted forcibly with the way of life of the smaller established rulers.

When the war against the Bohemians had become a widespread conflagration, Ferdinand found he had no forces to oppose to the Danes and the Northern Protestants other than the Army of the League, which was not his, but the powerful and independent Maximilian's, instrument Wallenstein saw his opportunity and early in 1626 he offered to raise not a regiment or two, but a whole army for the imperial service After some negotiations the offer was accepted, the understanding being that the troops were to be maintained at the cost of the countries they might occupy. Wallenstein's popularity soon brought great numbers of recruits to his standard. He soon found himself at the head of 30,000 (not long afterwards of 50,000) men. The campaigns of this army in 1625, 1626 and 1627, against Mansfeld, the Northern Protestants and Gabriel Bethlen, are described under THIRTY YEARS' WAR.

Having established peace in Hungary, Wallenstein proceeded, in 1627, to clear Silesia of some remnants of Mansfeld's army, and at this time he bought from the emperor the duchy of Sagan, his outlay in the conduct of the war being taken into account in the conclusion of the bargain. He then joined Tilly in the struggle with Christian IV., and afterwards took possession of the duchy of Mecklenburg, which was granted to him in reward for his services, the hereditary dukes being displaced on the ground that they had helped the Danish king. He failed to capture Stralsund, which he besieged for several months in 1628. This important reverse caused him bitter disappointment, for he had hoped that by obtaining free access to the Baltic he might be able to make the emperor as supreme at sea as he seemed to be on land It was a part of Wallenstein's scheme of German unity that he should obtain possession of the Hanseatic towns, and through them destroy or at least defy the naval power of the Scandinavian kingdom, the Netherlands and England. This plan was completely frustrated by the resistance of Stralsund, and even more by the emperor's "Edict of Restitution" that not only rallied against him all the Protestants but brought in a great soldier and a model army, Gustavus and the Swedes.

At the same time the victory of the principles of the League involved the fall of Wallenstein's influence. By his ambitions, his high dreams of unity and the incessant exactions of his army, he had made for himself a host of enemies. He was reported to have

Shortly before the dismissal of Wallenstein, Gustavus Adolphus had landed in Germany, and it soon became obvious that he was far more formidable than the enemies with whom the emperor had yet had to contend. Tilly was defeated at Breitenfeld and on the Lech, where he received a mortal wound, and Gustavus advanced to Munich, while Bohemia was occupied by his allies the Saxons. The emperor entreated Wallenstein to come once more to his aid. Wallenstein at first declined; he had, indeed, been secretly negotiating with Gustavus Adolphus, in the hope of destroying the League and its projects and of building his new Germany without French assistance. However, he accepted Ferdinand's offers, and in the spring of 1632 he raised a fresh army as strong as the first within a few weeks and took the field. This army was placed absolutely under his control, so that he assumed the position of an independent prince rather than of a subject. His first aim was to drive the Saxons from Bohemiaan object which he accomplished without serious difficulty. Then he advanced against Gustavus Adolphus, whom he opposed near Nuremberg and after the battle of the Alte Veste dislodged. In November came the great battle of Lützen (q.v.), in which the imperialists were defeated, but Gustavus Adolphus was killed.

To the dismay of Ferdinand, Wallenstein made no use of the opportunity provided for him by the death of the Swedish king, but withdrew to winter quarters in Bohemia. In the campaign of 1633 much astonishment was caused by his apparent unwillingness to attack the enemy. He was in fact preparing to desert the emperor. In the war against the Saxons he had offered them as terms of peace the revocation of the Edict. Religious toleration and the destruction of the separatist régime, as well as not inconsiderable aggrandisements for his own power, formed his programme, so far as historians Have been able to reconstruct it, and becoming convinced from Ferdinand's obstinacy that the Edict would never be rescinded, he began to prepare to "force a just peace on the emperor in the interests of united Germany." With this object he entered into negotiations with Saxony, Brandenburg, Sweden and France. He had vast and vague schemes for the reorganization of the entire constitutional system of the empire, and he himself was to have supreme authority in determining the political destinies of his country. But as the mere commander of mercenaries he was trusted by no one, and could only play the part of Cassandra to the end.

Irritated by the distrust excited by his proposals, and anxious to make his power felt, he at last assumed the offensive against the Swedes and Saxons, winning his last victory at Steinau on the Oder in October. He then resumed the negotiations. In December he retired with his army to Bohemia, fixing his headquarters at Pilsen. It had soon been suspected in Vienna that Wallenstein was playing a double part, and the emperor, encouraged by the Spaniards at his court, anxiously sought for means of getting rid of him. Wallenstein was well aware of the designs formed against him, but displayed little energy in his

attempts to thwart them. This was due in part, no doubt, to ill- | at Coleshill and migrated to Beaconsfield. Of Waller's early health, in part to the fact that he trusted to the assurances of his astrologer, Battista Seni. He also felt confident that when the time came for his army to decide between him and the emperor the decision would be in his own favour