KREYDEB. 613 KRONECKER. and Fuchs, took a studio in Paris in 1859, and made his first api>earance in the Salon four years afterwards with "Le rosier blanc." He ex- hibited afterwards "L'n rosier en automne" )18(i7): "Poramier en tieur" (187-2) ; '•Champ de blO" ( 1876) ; "Une corbeille de raisin" ( 1879) ; "Cerisier en fleur" (1878); Roses tremiferes" (1879) ; "Un ruisseau en Alsace," and Lilas" (1880); '-PiToines" (1888); "L'Ancien puits" (1889); '-Torrent de la Wormsa" (1891); and '-Raisins et Coquelicots" (1892). His "Offrande i liacehus" (1868) was placed in the Luxem- bourfT, and La source" (1870) was bought by the (jovernment. KRIEGER, kre'ger, JoHAXX PniLiPP (1649- 1 'i -J.') I . A German composer, bom at Xurembcrg. He studied the harpsichord and organ, became kapellmeister at Bayreuth. then went to Italy, upon his return was kapellmeister in Cassel, Court organist at Halle, and finally Court kapell- meister to the Duke of Saxe-Weissenfels. He wrote several operas, which were produced at dillerent courts. -24 sonatas, quartets, and arias. He died at Wei^senfels. KRIEGSSPIEIi, kreK'shpM. See War Game. KRIEKER. A gunners' name for one of the 'jack-snipe' {Tringa pcctoralis) . KRIMMITSCHAU, krim'mit-shou. A town in Saxony. See CniMMiTscuAL'. KRIS, KRES, CREESE, or CREASE CSla- lay. dagt'cr ) . The universal weapon of the in- habitants of the JIalayan Archipelago. It' is made of many different forms, short or long, straight or crooked. The hilt and scabbard are often much ornamented. Men of all ranks wear this weapon; and those of high rank, when in full dress, sometimes carry three or four. In Java, women sometimes wear it. KRISHABER, kre'sha'bar', INUuBlCE (1836- 83 ) . A French laryngologist, one of the founders of the modern treatment of diseases of the larj-n.K. He was born in Hungary, and studied medicine at Vienna and Prague, and at Paris, where he began to practice in 1864. He founded the Annalcs des Maladies dc VOreille et du Larynx (187.5); devoted himself to nervous diseases; and wrote: Des laryngopathies pen- dant les premieres phases de la syphilis, with Mauriac (1870) ; "Sur le cancer du larynx," in the AniHiles (1879); and. on 'Krishaber's dis- ease.' De la neuropathie cerehro ■ eardiaque (lS7:Vi. KRISH'NA (Sk-t. ln>ia, black). The eighth Avatara or incarnation of the Hindu god Vishnu. See Vishnu. KRISHNA. A river of India. See Kistna. KRISTIANIA, kristi-a'nf-a. A city of Nor- way. See ClIRISTIAMA. KRIZHANITCH, krC-'zha-nich, YvKi (1017- c.16801. A Russian author, a promoter of pan- Slavism, and one of the earliest students of Slavic philology. He was a Serb by birth ; was educated at the school in Agram. his birthplace, at Vienna. Bologna, and (1640) Rome, where he was trained for the work of converting the orthodox Slavs to Catholicism. This was ap- parently the germ in his mind of the idea of an ecclesiastical, political, and literary union of the Slavs. Russia seemed to him a promising field for this scheme, but his plan w-as not well re- ceived in that country, and he was sent to Si- beria. While there he wrote his pan-Slavonic grammar, (Jrammatischno Iskaziniye. In this work the pan-Slavic language is a jargon manu- factured by the author, largely from Russian, with admixtures of the south-Slavic languages; but the author shows no small .scientific insight in his ability to see cognates. Even more impor- tant among his works and in the history of pan- Slavism was ICrizhanitch's Politics, published by Bezsonow {Uussland uni die Hiilfte des sieb- z'ehnteii Jahrhunderts, 18.59-60). Here he criti- cises contemporary conditions in Russia, and pro- poses remedies. He returned from Siberia in 1076, and after that date nothing is known of him. KROLEVETZ, kro'ly6'v6ts. The capital of a district in the Russian Government of Tcliemi- gov, situated on two small streams, 160 miles east of Tchemigov. It carries on some manu- facturing of textiles, and is the seat of an im- portant annual fair. Population, in 1897. 10,375. KRONBERG, kroon'bar-y', .Irurs (1850—). A Swedish painter, born at Karlskrona. He entered the Academy at Stockholm at the age of thirteen, and before he was twenty re- ceived a gold medal for his "Gustavus Vasa Receiving the Translation of the Bible." A Government stipend in 1873 enabled him to con- tinue his studies in Diisseldorf and Paris, and in 1875 he sprang suddenly into fame with Xymphs and Fauns" (Xational Museum, Stockliolm ) , a composition of great coloristic charm in the manner of ilakart. His other works include Amorettes" (1878). '-David and Saul" (1885). both in the Xational Museum, Stockholm: "Death of Cleopatra" (1883), and "Queen of Sheba" (1888). He was elected a member of the Stockholm Academy in 1880, and appointed professor in 1885. KRONECKER, krO'nSk-er, Leopold (18-23- 91). A German mathematician, born at Liegnitz. He studied at the universities of Berlin. Bonn, and Breslau, and received his doctor's degree at Berlin in 1845. In 1800 he became a member of the Academy of Sciences at Berlin, and the next year he began giving lectures on mathe- matics in the university. In 1883 he was made ])rofessor of mathematics. Kronecker was one of the greatest of German algebraists. He gave a simpler treatment of cyclotomic equa- tions than Gauss, improved the proof of Abel for the insolubility of the general algebraic equation of degree higher than the fourth, and made a thorougli investigation of Abclian equa- tions. He also worked out the arithmetical and algebraic problems involved in the theory of elliptic functions, and materially improved the general thcoi-j". He attempted to do away with all special ideas of number, such as frac- tions and irrational numt)ers. and to construct a scientific arithmetic on the basis of the one concept 'number.' 'die Anzahl.' This problem was. more recently, further elaborated by Klein. Kronecker's most important works are: Grand- ziige 'einer arithmetischen Theorie der alge- braischen Orossen (1882); Veber den Zahlbegriff (1887); Vorlesiingen (edited bv Hensel and Xetto. vol. i.. 1S94)'. His n'rrke. edited by Hen- sel. were published at Leipzig in 1895-99. He assisted also in editing Crelle's Journal fur ilathematik. Many of his published articles
