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 substitutions, the theory of functions, differential equations and determinants. He clarified the principles of the calculus by developing them with the aid of limits and continuity, and was the first to prove Taylor’s theorem rigorously, establishing his well-known form of the remainder. In mechanics, he made many researches, substituting the notion of the continuity of geometrical displacements for the principle of the continuity of matter. In optics, he developed the wave theory, and his name is associated with the simple dispersion formula. In elasticity, he originated the theory of stress, and his results are nearly as valuable as those of S. D. Poisson. His collected works, Œuvres complètes d’Augustin Cauchy, have been published in 27 volumes.

See C. A. Valson, Le Baron Augustin Cauchy: sa vie et ses travaux (Paris, 1868).

 CAUCUS, a political term used in America of a special form of party meeting, and in Great Britain of a system of party organization. The word originated in Boston, Massachusetts, in the early part of the 18th century, when it was used as the name of a political club, the “Caucus” or “Caucas” club. Here public matters were discussed, and arrangements made for local elections and the choosing of candidates for offices. The first mention of the club in contemporary documents occurs in the diary of John Adams in 1763, but William Gordon (History of the Independence of the United States of America, 1788) speaks of the Caucus as having been in existence some fifty years before the time of writing (1774), and describes the methods used for securing the election of the candidates the club had selected. The derivation of the word has been much disputed. It was early connected with “caulkers,” and it was supposed referred to meetings of the caulkers in the dockyard at Boston in 1770, to protest against the action of the British troops, or with a contemptuous allusion to the lower class of workmen frequenting the club. This is, however, a mere guess, and does not agree with the earlier date at which the club is known to have existed, nor with the accounts given of it. That it was a fanciful classical name for a convivial club, derived from the late Greek , a cup, is far-fetched, and the most plausible origin is an Algonquin word kaw-kaw-was, meaning to talk. Indian words and names have been popular in America as titles for societies and clubs; cf. “Tammany” (see Notes and Queries. sixth series, vols. xi. and xii.). In the United States “caucus” is used strictly of a meeting either of party managers or of party voters. Such might be a “nominating caucus,” either for nominating candidates for office or for selecting delegates for a nominating convention. The caucus of the party in Congress nominated the candidates for the offices of president and vice-president from 1800 till 1824, when the convention system was adopted, and the place of the local “nominating caucus” is taken by the “primaries” and conventions. The word is used in America of the meetings of a party in Congress and other legislative bodies and elsewhere which decide matters of policy and plan campaigns. “Caucus” came first into use in Great Britain in 1878. The Liberal Association of Birmingham (see ) was organized by Mr Joseph Chamberlain and Mr F. Schnadhorst on strict disciplinary lines, more particularly with a view to election management and the control of voters on the principle of “vote as you are told.” This managing body of the association, known locally as the “Six Hundred,” became the model for other Liberal associations throughout the country, and the Federation of Liberal Associations was organized on the same plan. It was to this supposed imitation of the American political “machine” that Lord Beaconsfield gave the name “caucus,” and the name came to be used, not in the American sense of a meeting, but of a closely disciplined system of party organization, chiefly used as a stock term of abuse applied by opponents to each other’s party machinery.

 CAUDEBEC-EN-CAUX, a town of France, in the department of Seine-Inférieure, 27 m. W.N.W. of Rouen by the Ouest-État railway. Pop. (1906) 2141. It is situated on the right bank of the Seine, the tidal wave of which (mascaret) can be well seen at this point. The chief interest of the town lies in its church, a building of the 15th and the early 16th centuries. Round its top run balustrades formed of Gothic letters, which read as part of the Magnificat. Its west portal, the decoration of the spire of the tower, and its stained glass are among the features which make it one of the finest churches of the Rouen diocese. The town also possesses several old houses. Its industries include tanning and leather-currying, and there is trade in grain. The port has a small trade in coal, live-stock and farm produce.

 CAUDINE FORKS (Furculae Caudinae), a pass in Samnium, famous for the disaster which befell the Roman army in the second Samnite War (321 ). Livy (ix, 2) describes it as formed by two narrow wooded gorges, between which lay a plain, grassy and well-watered, but entirely enclosed by mountains. Through this plain the road (later the Via Appia) led. The Romans, marching from Calatia to the relief of Luceria, entered the valley unopposed, but found the exit blocked by the enemy; on marching back they saw that the entrance and the hills surrounding the plain were also occupied, and there was no way of escape. The plain which lies west of Caudium (Montesarchio) seems, despite the older views, to be the only possible site for such a disaster to an army of as many as 40,000 men; and there is no doubt that the Romans wished to leave it by the defile on the east, through which later ran the Via Appia to Beneventum. The existence of three ancient bridges on the line of the modern road renders it impossible to suppose that its course can be essentially different from that of the ancient, though Hülsen makes the two diverge considerably after passing Montesarchio. There are, however, two possible entrances—one on the north by Moiano, and one on the west by Arpaia; the former seems to answer better to Livy’s description (via alia per cavam rupem), while the latter is the shortest route, having been, later on, followed by the Via Appia, and bore the name Furculae Caudinae in the middle ages.

See C. Hülsen in Pauly-Wissowa, Realencyclopädie, iii. (1802).

 CAUDLE (through the O. Fr. caudel, from the Med. Lat. caldellum, a diminutive of caldum, a warm drink, from calidus, hot), a drink of warm gruel, mixed with spice and wine, formerly given to women in childbed.

 CAUL (from O. Eng. calle, Fr. cale, a cap), a close-fitting woman’s cap, especially one made of network worn in the 16th and 17th centuries; hence the membranous covering to the heart or brain, the omentum, or the similar covering to the intestines, and particularly, a portion of the amnion, which is sometimes found remaining round the head of a child after birth. To this, called in Scotland “sely how,” holy or lucky hood, many superstitions have been attached; it was looked on as a sign of good luck, and when preserved, was kept as a protection against drowning.

 CAULAINCOURT, ARMAND AUGUSTIN LOUIS, (1773–1827), French general and diplomatist, was born of a noble family. He early entered the army, did not emigrate in the revolution, but was deprived of his grade as captain in 1793 and served in the ranks. In 1795, through the protection of L. Hoche, he became captain again, was colonel in the Army of the Rhine in 1799–1800, and after the peace of Lunéville (1801) was sent to St Petersburg to negotiate an understanding between Russia and France. On his return he was named aide-de-camp of the First Consul. He was employed to seize some agents of the English government in Baden in 1804, which led to the accusation that he was concerned in the arrest of the duc d’Enghien, an accusation against which he never ceased to protest. After the establishment of the empire he received various honours and the title of duke of Vicenza (1808). Napoleon sent him in 1807 as ambassador to St Petersburg, where Caulaincourt tried to maintain the alliance of Tilsit, and although Napoleon’s ambition made the task a difficult one, Caulaincourt succeeded in it for some years. In 1811 he strongly advised Napoleon to renounce his proposed expedition to Russia. During the war he accompanied the emperor, and was one of those whom Napoleon took along with him when he suddenly abandoned his army in Poland to return to Paris (December 1812). During the last years of the empire, Caulaincourt was charged with all the diplomatic negotiations. He signed the armistice of Pleswitz, June 1813, represented France at the congress of Prague, in August 1813, at the congress of Chatillon, in February 1814, and concluded the