328 W A L W A L Mathematical Companion. Between 1801 and 1810 he contributed the 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 re tained in subsequent editions from the fifth to the eighth inclusive. He was also the author of the principal mathematical articles in the Edinburgh Encyclopedia, edited by Brewster (1808-30). Sub joined is a list of his more important papers contributed to the Transactions of the Royal Society of Edinburgh: "Geometrical Porisms, with Examples of their Applications to the Solution of Problems" (1796); "A new Method of expressing the Coefficients in the Development of the Formula which represents the Mutual Perturbation of two Planets " (1802) ; " New Series for the Quadra ture of the Conic Sections, and the Computation of Logarithms " (1808); "Investigation of Formulae for finding the Logarithms of Trigonometrical Quantities from one another" (1823); "Account of the Invention of the Pantograph, and a Description of the Eidograph," the latter being an instrument of his own invention (1831) ; "Analogous Properties of Elliptic and Hyperbolic Sectors " (1839); and "Solution of a Functional Equation, with its Applica tion to the Parallelogram 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 tho Cambridge Philosophical Society he wrote a paper on "Geometrical Theorems and Formuke, particularly ap plicable to some Geodetical Problems." WALLASEY, a town of Cheshire, England, on rising ground near a branch of the Mersey called Vallasey Pool, which bounds it on the S.E., while to the N.W. is the Irish Sea. It is about 2 miles north-west of Birkenhead, of which part of it is practically a suburb, and Wallasey Pool is now occupied by the Great Float, forming an immense dock of about 150 acres. The church of St Hilary, rebuilt in the 18th century, with the exception of the tower bearing date 1536, having been gutted by fire in 1857, the whole, except the tower, was rebuilt in the Early English style. The free grammar school, built and endowed by Major Henry Meols in 1656-57, was re-estab lished under a scheme of the charity commissioners, and reopened in 1876. On the shore of the Irish Sea is Leasowe Castle, once known as Mock-Beggar Hall, and supposed to have been erected by the earls of Derby in the reign of Elizabeth, in order to witness the races. On the sides of Wallasey Pool are remains of a submarine forest bed, in which various animal skeletons have been found. The population of the urban sanitary district (which includes Liscard and Poulton, with Seacomb, the total area being 3408 acres) in 1871 was 14,944, and in 1881 it was 21,192. At the Conquest Wallasey formed part of the possessions of Robert de Rhuddlan, and on his decease became part of the fee of Halton. In the reign of Elizabeth it had a small port, to which there belonged three barques and fourteen men. In 1668 the manor was possessed by the earl of Derby, but various parts afterwards became alienated. For a considerable time the horse races held on what was then a common had considerable reputation, but they were discontinued in 1760. At these races the duke of Monmouth, son of Charles II., once rode his own horse and won the plate. WALLA WALLA, a city and the county seat of Walla Walla county, AVashington Territory, United States, is situated in a valley on Mill Creek, a tributary of the Walla Walla, in a fertile agricultural region, devoted mainly to the growth of wheat, fruit, and vegetables. The population, which in 1880 was 3588, was estimated at 5000 in 1888. WALLENSTEIN (properly WALDSTEIN), ADALBERT EUSEBIUS VON (1583-1634), duke of Friedland, Sagan, and Mecklenburg, was born on the hereditary estate of his family, Hermanic, in Bohemia, on 15th September 1583. His parents were Protestants, 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, to the Jesuit college at Olmiitz, where he joined the Roman Catholic Church. In 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, according to the custom of the young nobles of the time, visited many places in southern and western Europe. While in Padua, he gave much atten tion to astrology, and during the rest of his life he seems never to have 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. In 1606 he returned to Bohemia, and soon afterwards he married a rich widow, Lucretia Nikossie von Landeck, whose lands in Moravia he inherited after her death in 1614. Supporting the arch duke Ferdinand in his war with Venice, he became favour ably known at court, and his influence was 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 disturbances which proved to be the beginning of the Thirty Years War advances were made to Wallenstein by the revolutionary party ; but he preferred to associate himself with the imperial cause, for which he repeatedly fought with marked success. In 1620 he was made quartermaster-general of the army of the League, com manded by Tilly. Wallenstein was not present at the battle of the Weissenberg (1620), but soon afterwards he did brilliant service as second in command of the army which opposed Bethlen Gabor in Moravia. The battle of the Weissenberg placed Bohemia absolutely at the mercy of the emperor Ferdinand; and Wallenstein, who was a man of insatiable ambition, knew how to turn the prevailing confusion to his own advantage. Through no very honourable means he secured the inheritance of the great estates belonging to his mother s family, and the emperor sold to him on easy terms vast tracts of confiscated lands. His possessions he was allowed to form into a territory called Friedland, and he was raised in 1622 to the rank of an imperial count and palsgrave, in 1623 to that of a prince. In 1625 he was made duke of Fried- land. In the government of his principality he displayed much vigour and foresight. He not only placed the ad ministration of justice on a firm basis, but by many wise measures developed agriculture and mining and manufac turing industries. The early successes of the emperor Ferdinand in the Thirty Years War were due chiefly to the army of the League, which he could only indirectly control. When he was threatened with a coalition of the Protestant powers, with Christian IV. of Denmark as his most active enemy, he was anxious to have an army of his own, which should be more devoted than that of the League to the interests of his dynasty. He had not, however, the means of secur ing the fulfilment of his wish. In these circumstances Wallenstein saw that he might have an opportunity of playing a great part in the events of the age ; and accord ingly, early in 1626, he offered to raise an 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 had always been a popular com mander, and great numbers of recruits flocked to his standard, so that he soon found himself at the head of an army of 30,000 men. With this force he marched north wards for the purpose of co-operating with Tilly against Christian IV. and Mansfeld. No engagement was fought in 1625; but on April 25, 1626, Wallenstein defeated Mansfeld at the bridge of Dessau, and later in the year Christian IV. was defeated by Tilly at Lutter. Wallenstein pursued Mansfeld into Hungary, where the Protestant general effected a junction with Bethlen Gabor. Before the end of the year Mansfeld died, and Bethlen Gabor came
to terms with the emperor.