Page:Encyclopædia Britannica, Ninth Edition, v. 20.djvu/571

R I E R I E 551 suggested for his trial lecture, that " On the Hypo- theses which form the Foundation of Geometry " was chosen at the instance of Gauss, who Avas curious to hear what so young a man had to say on this difficult subject, on which he himself had in private speculated so pro- foundly (see PARALLELS, vol. xviii. p. 254). Dedekind tells us that Riemann's lecture, which surpassed his utmost expectation, filled him with the greatest astonish- ment, and that on the way back from the faculty meeting he spoke to Wilhelm Weber with the highest apprecia- tion, and with an excitement rare with him, regarding the depth of the thoughts to which Riemann had given utterance. In 1855 Gauss died and was succeeded by Dirichlet, who along with others made an effort to obtain Riemann's nomination as extraordinary professor. In this they were not successful ; but a Government stipendium of 200 thalers was given him, and even this miserable pittance was of great importance, so straitened were his circum- stances. But this small beginning of good fortune was embittered by the deaths of his father and his eldest sister, and by the breaking up of the home at Quickborn, where he had so often found solace when ill and dejected. Meantime he was lecturing and writing the great memoir (Borchardt 's Journal, vol. liv., 1857) in which he applied the theory developed in his doctor's dissertation to the Abelian functions. It is amusing to find him speaking jubilantly of the unexpectedly large audience of eight which assembled to hear his first lecture (in 1854) on partial differential equations and their application to physical problems. The rustic shyness which had troubled his schoolboyhood seems still to have haunted him ; for he says, speaking of these lectures, " The nervousness which I had at first has pretty well subsided, and I accustom my- self to think more of my hearers than of myself, and to read in their faces whether I may go on, or whether the matter requires further explanation." Riemann's health had never been strong. Even in his boyhood he had shown symptoms of consumption, the disease that was working such havoc in his family ; and now under the strain of work he broke down altogether, and had to retire to the Harz with his friends Patter and Dedekind, where he gave himself up to excursions and " Naturphilosophie." After his return to Gottingen (November 1857) he was made extraordinary professor, and his salary raised to three hundred thalers. As usual with him, misfortune followed close behind ; for he lost in quick succession his brother Wilhelm and another sister. In 1859 he lost his friend Dirichlet; but his reputation was now so well established that he was at once appointed to succeed him. It now seemed for a little as if the world was to go smoothly with him. Well-merited honours began to reach him ; and in 1860 he visited Paris, and met with a warm reception there. He married, and married happily, Fraulein Elise Koch in June 1862, but the following month he had an attack of pleurisy which proved the beginning of a long illness that ended only with his death. His physician recommended a sojourn in Italy, for the benefit of his health, and Weber and Sartorius von Waltershausen obtained from the Government leave of absence and means to defray the cost of the journey. At first it seemed that he would recover ; but on his return in June 1863 he caught cold on the Spliigen Pass, and in August of the same year had to go back to Italy. In November 1865 he returned again to Gottingen, but, although he was able to live through the winter, and even to work a few hours every day, it became clear to his friends, and clearest of all to himself, that he was dying. He was very desirous to finish some of the many investi- gations which had presented themselves to him, and eagerly asked his doctors to tell him how long he might reasonably expect to live, so that he might take up what he had most chance of finishing. In order to husband his few remaining days he resolved in June 1866 to return once more to Italy. Thither he journeyed through the confusion of the first days of the Austro-Prussian war, and settled in a villa at Selasca near Intra on Lago Maggiore. Here his strength rapidly ebbed away, but his mental faculties remained brilliant to the last. On the 19th of July 1866, attended by his wife, he lay under a fig-tree greatly enjoying the beautiful landscape and working at his last unfinished investigation on the mechanism of the ear. The day following he died. There are few more pathetic stories than the life of Riemann, few finer instances of victory gained by inborn genius over a host of adverse circumstances. Few as were the years of work allotted to him, and few as are the printed pages covered by the record of his researches, his name is, and will remain, a household word among mathe- maticians. Most of his memoirs are masterpieces full of original methods, profound ideas, and far-reaching imagina- tion. Few sources, we imagine, have been fuller of inspira- tion for the younger mathematicians of our day than the octavo volume of five hundred pages or so that contains his works ; and many an advance in mathematical science will yet be made, with increase of reputation to the maker, by carrying out his suggestions. The collected works of Riemann were published by H. Weber assisted by R. Dedekind (Svo, Leipsic, 1876). At the end of this volume there is a touching account of Ins life by the latter, from which the above sketch is almost entirely taken. " (G. CH.) RIENZI, COLA DI (1313-1354). See ROME. RIESENER, JEAN HENRI (1725-1806), the celebrated cabinet-maker of Louis XVL, was born at Gladbeck near Cologne in 1725. He was employed by Jean Frai^ois Oeben in the arsenal, and in 1769 married Oeben's widow, by whom he had one son. A number of fine examples of Riesener's cabinets are described in the catalogue of furniture in the South Kensington Museum. He employed tulip, rosewood, holly, maple, laburnum, and purple wood in their construction. Wreaths and bunches of flowers form the centres of his panels ; on the sides are diaper patterns in quiet colours. The name of Riesener is stamped sometimes on the panel itself, sometimes on the oak lining of the furniture made by him. The best pieces at the South Kensington Museum are from the collection of Sir Richard Wallace ; perhaps the most remarkable is the bureau made for Stanislaus, king of Poland, which is signed by the maker, as is also a similar piece in the Louvre which is accompanied by gilt bronze candle branches by Gouthiere. This last Avork, which bears the date 1769, it is believed that Riesener only finished; and indeed towards the close of his life, after his second marriage (1782) to Marie A. C. Grezel (from whom he was divorced), he ceased to produce anything, and became a collector, buying up his own Avorks. He died January 6, 1806. His son, HENRI FRANCOIS (1767-1828), was one of the most noted portrait-painters of the first empire. The portrait of M. Ravrio, a Avorker in bronze (Louvre), is a good example of his talent. RIESENGEBIRGE (Bohemian Krlconose), or Giant Mountains, a lofty and rugged group on the common boundary of Silesia and Bohemia, between the upper courses of the Elbe and the Oder. They form the highest portion of the Sudetic system, which separates south-east Prussia from the Austrian empire, and finds its natural continuation towards the north-Avest in the Erzgebirge, the Thuringian Forest, and the Harz Mountains. Adjoining the Isergebirge and the Lausitzergebirge on the Avest, and the Eulengebirge and the Adlergebirge on the east and