Page:EB1911 - Volume 16.djvu/713

 central conic for the focus, and the first positive pedal of a circle for any point. The form of the limaçon depends on the ratio of the two constants; if a be greater than b, the curve lies entirely outside the circle; if a equals b, it is known as a (q.v.); if a is less than b, the curve has a node within the circle; the particular case when b＝2a is known as the (q.v.). In the figure (1) is a limaçon, (2) the cardioid, (3) the trisectrix.

Properties of the limaçon may be deduced from its mechanical construction; thus the length of a focal chord is constant and the normals at the extremities of a focal chord intersect on a fixed circle. The area is (b2+a2/2), and the length is expressible as an elliptic integral.

LIMASOL, a seaport of Cyprus, on Akrotiri Bay of the south coast. Pop. (1901) 8298. Excepting a fort attributed to the close of the 12th century the town is without antiquities of interest, but in the neighbourhood are the ancient sites of Amathus and Curium. Limasol has a considerable trade in wine and carobs. The town was the scene of the marriage of Richard I., king of England, with Berengaria, in 1191.

 LIMB. (1) (In O. Eng. lim, cognate with the O. Nor. and Icel. limr, Swed. and Dan. lem; probably the word is to be referred to a root li- seen in an obsolete English word “lith,” a limb, and in the Ger. Glied), originally any portion or member of the body, but now restricted in meaning to the external members of the body of an animal apart from the head and trunk, the legs and arms, or, in a bird, the wings. It is sometimes used of the lower limbs only, and is synonymous with “leg.” The word is also used of the main branches of a tree, of the projecting spurs of a range of mountains, of the arms of a cross, &c. As a translation of the Lat. membrum, and with special reference to the church as the “body of Christ,” “limb” was frequently used by ecclesiastical writers of the 16th and 17th centuries of a person as being a component part of the church; cf. such expressions as “limb of Satan,” “limb of the law,” &c. From the use of membrum in medieval Latin for an estate dependent on another, the name “limb” is given to an outlying portion of another, or to the subordinate members of the Cinque Ports, attached to one of the principal towns; Pevensey was thus a “limb” of Hastings. (2) An edge or border, frequently used in scientific language for the boundary of a surface. It is thus used of the edge of the disk of the sun or moon, of the expanded part of a petal or sepal in botany, &c. This word is a shortened form of “limbo” or “limbus,” Lat. for an edge, for the theological use of which see.

 LIMBACH, a town in the kingdom of Saxony, in the manufacturing district of Chemnitz, 6 m. N.W. of that city. Pop. (1905) 13,723. It has a public park and a monument to the composer Pache. Its industries include the making of worsteds, cloth, silk and sewing-machines, and dyeing and bleaching.

 LIMBER, an homonymous word, having three meanings. (1) A two-wheeled carriage forming a detachable part of the equipment of all guns on travelling carriages and having on it a framework to contain ammunition boxes, and, in most cases, seats for two or three gunners. The French equivalent is avant-train, the Ger. Protz (see and ). (2) An adjective meaning pliant or flexible and so used with reference to a person’s mental or bodily qualities, quick, nimble, adroit. (3) A nautical term for the holes cut in the flooring in a ship above the keelson, to allow water to drain to the pumps.

LIMBORCH, PHILIPP VAN (1633–1712), Dutch Remonstrant theologian, was born on the 19th of June 1633, at Amsterdam, where his father was a lawyer. He received his education at Utrecht, at Leiden, in his native city, and finally at Utrecht University, which he entered in 1652. In 1657 he became a Remonstrant pastor at Gouda, and in 1667 he was transferred to Amsterdam, where, in the following year, the office of professor of theology in the Remonstrant seminary was added to his pastoral charge. He was a friend of John Locke. He died at Amsterdam on the 30th of April 1712.

LIMBURG, one of the many small feudal states into which the duchy of Lower Lorraine was split up in the second half of the 11th century. The first count, Walram of Arlon, married Judith the daughter of Frederick of Luxemburg, duke of Lower Lorraine (d. 1065), who bestowed upon him a portion of his possessions lying upon both sides of the river Meuse. It received its name from the strong castle built by Count Walram on the river Vesdre, where the town of Limburg now stands. Henry, Walram’s son (d. 1119), was turbulent and ambitious. On the death of Godfrey of Bouillon (1089) he forced the emperor Henry IV. to recognize him as duke of Lower Lorraine. He was afterwards deposed and imprisoned by Count Godfrey of Louvain on whom the ducal title had been bestowed by the emperor Henry V. (1106). For three generations the possession of the ducal title was disputed between the rival houses of Limburg and Louvain. At length a reconciliation took place (1155); the name of duke of Lower Lorraine henceforth disappears, the rulers of the territory on the Meuse become dukes of Limburg, those of the larger territory to the west dukes of Brabant. With the death of Duke Walram IV. (1280) the succession passed to his daughter, Irmingardis, who was married to Reinald I., count of Guelders. Irmingardis died without issue (1282), and her cousin, Count Adolph of Berg, laid claim to the duchy. His rights were disputed by Reinald, who was in possession and was recognized by the emperor. Too weak to assert his claim by force of arms Adolph sold his rights (1283) to (q.v.). This led to a long and desolating war for five years, at the end of which (1288), finding the power of Brabant superior to his own Reinald in his turn sold his rights to count Henry III. of Luxemburg. Henry and Reinald, supported by the archbishop of Cologne and other allies, now raised a great army. The rival forces met at Woeringen (5th of June 1288) and (q.v.) gained a complete victory. It proved decisive, the duchies of Limburg and Brabant passing under the rule of a common sovereign. The duchy comprised during this period the bailiwicks of Hervé, Montzen, Baelen, Sprimont and Wallhorn, and the counties of Rolduc, Daelhem and Falkenberg, to which was added in 1530 the town of 