CURVE. 681 CUSA. completed by Cayley (1800) and Brill (1873). Cajiey's iiillueiice was also very great. He ad- vanced tbe work of PHicker, investigated bi- tangents and osculating conies, extended the properties of covariants and invariants, as well as Salmon's theory of reciprocal surfaces and the theorj- of double curvature, ileution should also be made of the labors of Jean-Claude Bou- quet (1819-85) and Charles - Auguste - Albert ISriot (1817-82), two of Cauchy's most eminent pupils, whose labors in the field of geometry and theory of functions are well known. Their Lccons dc geometric annlytique (Paris, 1847) has been translated into English (Chicago, 1896) and forms an excellent intioduction to the sub- ject. Besides the works of those mentioned in connection with the development of curves, con- sult, for theory: Salmon, Treatise on the Higher PJaiw Curves (Dublin, 18o2) ; Clebsch, Vorlesun- gen iiber Geometrie (Leipzig, vol. i., 1875-70; vol. ii., 1891): and for history, Merriman and Woodward, Higher ilathetiuitics, chap. xi. (New York, 1890) ; Broeard, Notes de bibliographie des courbes geometriques (Bar-le-Duc, 1897-09). CURVE OF PURSUIT. The problem of the curve of pursuit first attracted attention in the following form: To find the path of a dog which takes the shortest course to reach his master. This problem, though stated in various forms, resolves itself mathematically into finding the curve traced bj- a point .1 whose movement is always directed toward a point B moving on a known curve. The curve seems to have been studied first by Pierre Bouguer (1732). The re- sult is, in general, an algebraic curve; in par- ticular cases logarithmic. For a solution of the problem, consult Salmon, Treatise on the Higher Plane Curves (Dublin, 1852). CURVE OF SINES. A curve whose ordi- nates are equal or proportional to the sines of a variable angle and whose abscissas are equal to the corresponding ares of the unit circle. This curve is also called an harmonic curve, it being the curve in which a musical string vibrates when sounded. TJT ABC Y« CURVE OF BINES. In the figure. OA represents the length of an arc whose sine is j/„ OB the length of an arc whose sine is y,, and so on. The ordinate 1/3 is the sine of 90°, and is the maximum ordi- nate of the curve. D, which corresponds to an angle of 180°, is a point of inflection, tbe radius of curvature being infinite. Similarly the curves of the other trigonometric functions may be represented graphically. CURVES, Anticuxal and Synclinal. See .V.NTici.iNK and Sy.ncline. CUR'WEN, Joii. (1810-80). An English music reformer and writer. He was born at lleclvuiondwike, in Yorkshire, and was earlv in- fiuenced l)y the community music, in those "days cliaractcristie of every Yorksliire village. The inlluence of Handel, and his oratorios, more tlian
- iny other single factor, had caused clioral and
l)liilluirmc>nic s(K-iclics to spring uj) tliroughotit the nortlicrn counties of Kngland. In order to develop these and the numerous local band organizations, Curwen, then a dissenting minis- ter, resigned his pastorate, and becoming inter- ested in the 'tonic sol-fa' system, invented by Miss S. A. Glover, spent his entire time in propagating it. In 1853 he had begun to found associations for spreading the theory, and in 1802 established the Tonic Sol-Fa College. He was sticcessful enough to start a pulilishing house in London, where he ])ul>lished the Tanic ttol-Fa Reporter. Nearly all of his many publica- tions are for the s.ystem of liis choice. He died at Heaton Jlersey, near Slanehester. CURZOLA, koUr'ts(j-la (Slav. Kordula, an- cient Ciirei/ra Xigra, so called from the sombre color of its pine forests ) . An island of the Adriatic, situated ofT the coast of the Aus- trian Crownland of Dalmatia, in latitude 43° N. and longitude 17° E. (Jlap: Austria, E 5). It is almost 25 miles long, has an area of about 100 square miles, and is hilly, the greatest alti- tude being 1880 feet. It is well wooded and produces grain, wine, and olives. The inhabit- ants are engaged chiefly in ship-building, sea- faring, and fisheries. It has a number of good harbors. Population, in 1900, 18,749. The prin- cipal towns are Curzola, the capital, with a population of 0487, and Blatta, with 7320 in- habitants. CUR'ZON, George Nathaniel, Baron Curzon of Kc^lcston (1859 — ). An English statesman, bom at Ivedleston. He studied at Balliol Col- lege, Oxford, became assistant private .secretary to the Marquis of Salisbury in 1885, and from 1880 to 1898 sat as a Conservative for the South- port division of Southwest Lancashire. In 1891- 92 he was Under-Secretary of State for India, and in 1895-98 Under-Secretary of State for Foreign Affairs, He was appointed, in 1898, Viceroy and (Jovernor-General of India. Ilis ad- ministration has proved most acceptable to both the Indian natives and the English Government. His policy aims at the promotion of education, the increased efficiency of the military, and op- position to Russian advance in the East. He has ptiblished Russia in Central Asia (1889); Persia and the Persian Question (1892); and Problems of the Far Fast { 1894) . CU'SA, Xiivoi.As OP or Xikolavs Cf.SANrs (1401-04). A Roman Catholic philosopher and theologian. He was born at Kues. on the Moselle, in the Diocese of Treves: educated at Deventer by the Brethren of the Conunon Life, and at the University of Padua ; became .rchdeacon of Li^ge and attended the Council of Basel (1431-49), where he opposed the Papal claims; but, altering his views, lie entered the Pajial service and was made a cardinal in 1448; Bishop of Brixen in the Tyrol, and Papal legate for Germany in 1450.
