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* CLEBSCH. 16 CLEISTOGAMOUS FLOWERS. maximum number possible in sueh a curve. (See CuBVES.) C'lebsc-li and t^reuioiia studied llie representation of cubic surfaces on a plane tliroufjli a one-to-one correspondence — a notion tliat has led to the study of higher correspond- ences between surfaces by Cayley (q.v.) and Nother. Clebsch solved, by aid of the addition theorem of elliptic functions (see Functions), the generalized form of iMalfatti's Problem. He also solved (1S(>2) the so-ealled 'Pfallian Prob- lem' of ditVerential equations, by making it de- pend upon a system of simultaneous linear partial dillerential equations whose statement is possible without integration. Clebsch took a leading ])art in showing the great significance of the theory of invariants for the theory of hy])er- ellijilic and Abelian functions; and to bini is due the transformation of the theory of binary to that of ternary forms. (See FoBMS. ) He died at Gdttingen, November 7, 1872. Vol. vii. of the Matheiiialinclte Aimalen contains an excellent article on Clebsch, in which the value of his works is estimated by Brill, Gordan. Klein, Mayer, Nother, and other contemjxiraries. His ^'orlcsull<^en iiber (Iconietrie were edited by Linde- mann (Leipzig, vol. i.. 1875-76. vol. ii.. 1891). CLE'BUKNE. A town and the county-scat of .Johnson County. Tex., .'iS miles southwest of Dallas; on the Gulf. Colorado and Santa Fe Kailroad (ilap: Texas. F 3). It has a large trade in grain, live stock, cotton, wool, hides, and produce, besides considerable interests as a dis- tributing centre. The town contains eotton-eom- preeses. cottonseed-oil mills, flour-mills, foundry and machine-shop, etc. : and division offices and shops of the Gulf. Colorado and Santa Fc Kail- road. Population, in 1890. 3278; in 1900. 7493. CLEBURNE, P.trick Ronayne (1828-64). An American soldier, prominent as a Confederate officer during the Civil War. He was born in Countj- Cork, Ireland; stiulied medicine for a time at Trinity College, England; ran away from home, and served for several years in the ]5ritish Army. In 1855 he emigrated to the United States, and settled in Helena, Ark., where he . studied law, was admitted to the bar, and prac- ticed with considerable success. On the outbreak of the Civil War, he enlisted in the Confederate Army as a private, but by Mareli, 1862. rose to the rank of brigadier-general. He commanded a brigade at the battle of Shiloh; was wounded in the battle of Perryville, Ky., on October 8, 1862 : was promoted to be major-general in December of that year; was distinguished for gallantry at Murfreesboro, and at Chiekamauga led a brilliant charge, and earned the title, 'The Stonewall of the West.' In the battle of Uh- sionary Kidge he commanded the right Aving of the Confederate army; subsequently took a con- spicuous iiart, as division commander under Johnston, against Sherman, and as a corps com- mander under Hood, in the Atlanta campaign against Sherman, and later, in the Tennessee campaign against Thomas and Schofield; and at the battle of Franklin, on November 30, 1864, he was killed while leading a charge on the Federal works. He was one of the organizers of the 'Order of the Southem Cross,' and was one of the first men in the Confederacy to advo- cate the use of colored troops. Consult the bio- graphical sketch, by General Gordon, in Hovthern Historical Society Papers, vol. xviii. (Richmond, 1889). CLECK'HEATON. A town in the West Rid- ing of Yorksliiri'. Kngland, two and one-half miles southwest of Ijradford (Map: England, F 3). It has manufactures of woolens, worsteds, and blank- ets. Population, in 1891, 11,800; in 1901, 12,500. CLEDON'ISMAN'CY. See Superstition. CLEE'THORPE WITH THRUNS'COE. A progressive town and niilway-jiuiitiuii in hin- eolnshire, F^ngland. two and one-fourth miles east-southeast of Grimsby (Map: England. F 3). It owns a new market and recreatiim- grounds. There is an electric-lighting plant. Population, in 1891, 4.300; in 1901, 12.600. CLEF (Fr., key). A musical symbol, which is placed on the staff, to fix the pitch of one note, and thereby also to determine that of the sueeeed- iiig notes. There are three kinds of clefs — viz. the G (treble), and C (tenor), and the F (bass). The G clef is placed on the second line, thus: m the C clef on the third line, thus: and the F clef on the fourth line, thus: m The C clef is a fifth below the G clef, and a fifth aoove the F clef, thus: f

m The G clef is also placed on the fourth line for some instruments, and for the tenor part in vocal music, thus: 4yj_ E^ and in old vocal music the C clef placed on the first line was used for the soprano. The tendency at present, in vocalization, is to do away with the C clef. The signature zt is a descendant of G, through many stages of transformation. The development of the two other clef-symbols from the letters C and F, though not so obvious to the eye, is as much a matter of history as is the former case. CLEISHBOTHAM, klesh'boTH-om, .Jedediah. The imaginary 'collector' in Scott's series of novels, Tales of My Landlord. He claims to be selioolmaster and parish clerk of Gandereleuch, in which cajiacity he meets Peter Pattieson. the equally fictitious writer of the stories. CLEISTHENES, klis'the-nez. See Clisthenes. CLEISTOG'AMOUS FLOWERS (Gk. Kei,r- rdsjcleistos, that which may be closed, from Kekty, klcifiit, to close + fdfios, r/ainos, mar- riage). Relatively inconspicuous andnever-open flo-vers, which occur, along with the ordinary flowers, in many plants, representing all of the principal alliances of the flowering plants. Cleis- togamous flowers are seldom in a conspicuous position. One of the best-known illustrations is in the stemless species of violets. In these, in addition to the well-known conspicuous flowers, cleistogamous flowers occur more or less con- cealed near the base of the cluster of leaves and