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 1900); V. Sella and D. Vallino, Nel Caucaso Centrale (Turin, 1890); K. Koch, Der Kaukasus (Berlin, 1882); C. Phillipps Woolley, Savage Svanetia (2 vols., London, 1883); E. Levier, À travers le Caucase (Paris, ed. 1905), especially valuable for botany; G. Merzbacher, Aus den Hochregionen des Kaukasus (2 vols., Leipzig, 1901); A. Fischer, Zwei Kaukasische Expeditionen (Berne, 1891); E. Fournier, Description géologique du Caucase central (Marseilles, 1896); G. Radde, Reisen an der persisch-russischen Grenze. Talysch und seine Bewohner (Leipzig, 1886), Die Fauna und Flora des südwestlichen Kaspigebiets (Leipzig, 1886), Karabagh (Gotha, 1890), and Aus den daghestanischen Hochalpen (Gotha, 1887); and Count J. Zichy, Voyages au Caucase (2 vols., Budapest, 1897). F. Loewinson-Lessing has an account of the geology of the district along the military road from Vladikavkaz to Tiflis in the Guide des Excursions du VIIe Congrès géol. internat. (St Petersburg, 1897). N. Y. Dinnik writes on the fauna in Bull. Soc. Impériale des Naturalistes de Moscou (1901); J. Mourier on the folk-tales in Contes et légendes du Caucase (1888); and on modern history G. Baumgarten, Sechzig Jahre des kaukasischen Krieges (Leipzig, 1861). But a very great amount of most valuable information about the Caucasus is preserved in articles in encyclopaedias and scientific periodicals, especially the Izvestia and Zapiski of the Russian and Caucasian geographical societies, in P. P. Semenov’s Geographical Dictionary (in Russian, 5 vols., St Petersburg, 1863–1884), and in the Russkiy encyklopedicheskiy slovar (1894), and in the Kavkazskiy kalendar (annually at Tiflis). See also G. Radde and E. Koenig, “Der Nordfuss des Daghestan und das vorlagernde Tiefland bis zur Kuma” (Ergänzungsheft No. 117 to Petermanns Mitteilungen), and “Das Ostufer des Pontus und seine kulturelle Entwickelung im Verlaufe der letzten 30 Jahre” (Ergänzungsheft No. 112 of the same); by V. Dingelstedt in ''Scot. Geog. Mag''.—“Geography of the Caucasus” (July 1889); “The Caucasian Highlands” (June 1895); “The Hydrography of the Caucasus” (June 1899); “The Riviera of Russia” (June 1904), “The Small Trades of the Caucasus” (March 1892); and “Caucasian Idioms” (June 1888). The best map is that of the Russian General Staff on the scale of 1:210,000 (ed. 1895–1901).

 CAUCHOIS-LEMAIRE, LOUIS FRANÇOIS AUGUSTE (1789–1861), French journalist, was born in Paris on the 28th of August 1789. Towards the end of the First Empire he was proprietor of the Journal de la littérature et des arts, which he transformed at the Restoration into a political journal of Liberal tendencies, the Nain jaune, in which Louis XVIII. himself had little satirical articles secretly inserted. After the return from Elba the Nain jaune became Bonapartist and fell into discredit. It was suppressed at the second Restoration. Cauchois-Lemaire then threw himself impetuously into the Liberal agitation, and had to take refuge in Brussels in 1816, and in the following year at the Hague, whence he was expelled for publishing an Appel à l’opinion publique et aux États Généraux en faveur des patriotes français. Returning to France in 1819, he resumed the struggle against the ultra-royalist party with such temerity that he was condemned to one year’s imprisonment in 1821 and fifteen months’ imprisonment in 1827. After the revolution of July 1830 he refused a pension of 6000 francs offered to him by King Louis Philippe, on the ground that he wished to retain his independence even in his relations with a government which he had helped to establish. He made a bitter attack upon the Périer ministry in his journal Bon sens, and in 1836 was one of the founders of a new opposition journal, the Siècle. He soon, however, abandoned journalism for history and, having no private means, in 1840 accepted the post of head of a department in the Royal Archives. Of a Histoire de la Révolution de Juillet, which he then undertook, he published only the first volume (1842), which contains a historical summary of the Restoration and a preliminary sketch of the democratic movement. He died in Paris on the 9th of August 1861.

 CAUCHON, PIERRE (d. 1442), French bishop, was born near Reims in the latter half of the 14th century. We find him rector of the university of Paris in October 1397. In 1413 he joined the Burgundian faction, and was exiled by the parlement of Paris. But on the triumph of his party this decree was annulled, and Philip the Good, duke of Burgundy, gave him a canonry at Beauvais, sent him to the council of Constance, procured him the post of maître des requêtes in 1418, and finally in 1420 had him made bishop of Beauvais. But the people were hostile to him, and he was driven from his bishopric in 1429; whereupon he attached himself to the English court, and in 1431 endeavoured to procure the surrender of Reims to the English, so that Henry VI. might be crowned there. In this he failed, and Henry was crowned in Paris on the 17th of December 1431 by Henry Beaufort, cardinal bishop of Winchester, assisted by the bishops of Beauvais and Noyon. On the 24th of May 1430, Joan of Arc having been taken prisoner at Compiègne, within the limits of his diocese, Cauchon acted as her accuser, and demanded the right of judging her. Joan was taken to Rouen, whither Cauchon followed her, having been driven from Beauvais. He conducted the trial with marked partiality and malevolence, condemned the maid to imprisonment for life, and then, under pressure from the populace and the English, had recourse to fresh perfidies, declared Joan a relapsed heretic, excommunicated her, and handed her over to the secular arm on the 30th of May 1431. As, in consequence of this, it was impossible for him to return to his own diocese, he obtained the bishopric of Lisieux in 1432 by favour of the king of England. He assisted at the council of Basel in 1435, and died suddenly on the 18th of December 1442. Excommunicated posthumously by Pope Calixtus IV., his body was exhumed and thrown in the common sewer.

 CAUCHY, AUGUSTIN LOUIS, BARON (1789–1857), French mathematician, was born at Paris on the 21st of August 1789, and died at Sceaux (Seine) on the 23rd of May 1857. Having received his early education from his father Louis François Cauchy (1760–1848), who held several minor public appointments and counted Lagrange and Laplace among his friends, Cauchy entered École Centrale du Panthéon in 1802, and proceeded to the École Polytechnique in 1805, and to the École des Ponts et Chaussées in 1807. Having adopted the profession of an engineer, he left Paris for Cherbourg in 1810, but returned in 1813 on account of his health, whereupon Lagrange and Laplace persuaded him to renounce engineering and to devote himself to mathematics. He obtained an appointment at the École Polytechnique, which, however, he relinquished in 1830 on the accession of Louis Philippe, finding it impossible to take the necessary oaths. A short sojourn at Freiburg in Switzerland was followed by his appointment in 1831 to the newly-created chair of mathematical physics at the university of Turin. In 1833 the deposed king Charles X. summoned him to be tutor to his grandson, the duke of Bordeaux, an appointment which enabled Cauchy to travel and thereby become acquainted with the favourable impression which his investigations had made. Charles created him a baron in return for his services. Returning to Paris in 1838, he refused a proffered chair at the Collège de France, but in 1848, the oath having been suspended, he resumed his post at the École Polytechnique, and when the oath was reinstituted after the coup d'état of 1851, Cauchy and Arago were exempted from it. A profound mathematician, Cauchy exercised by his perspicuous and rigorous methods a great influence over his contemporaries and successors. His writings cover the entire range of mathematics and mathematical physics.

Cauchy had two brothers: (1792–1857), who became a president of a division of the court of appeal in 1847, and a judge of the court of cassation in 1849; and  (1802–1877), a publicist who also wrote several mathematical works.

The genius of Cauchy was promised in his simple solution of the problem of Apollonius, i.e. to describe a circle touching three given circles, which he discovered in 1805, his generalization of Euler’s theorem on polyhedra in 1811, and in several other elegant problems. More important is his memoir on wave-propagation which obtained the Grand Prix of the Institut in 1816. His greatest contributions to mathematical science are enveloped in the rigorous methods which he introduced. These are mainly embodied in his three great treatises, Cours d’analyse de l’École Polytechnique (1821); Le Calcul infinitésimal (1823); Leçons sur les applications du calcul infinitésimal à la géométrie (1826–1828); and also in his courses of mechanics (for the École Polytechnique), higher algebra (for the Faculté des Sciences), and of mathematical physics (for the Collège de France). His treatises and contributions to scientific journals (to the number of 789) contain investigations on the theory of series (where he developed with perspicuous skill the notion of convergency), on the theory of numbers and complex quantities, the theory of groups and