626 



CURWEN 



GUST 



expressed by an equation between the co-ordinates 

 of any point in it referred to a fixed point ; and thus 

 the doctrine of carves becomes matter of algebra 

 (see CO-ORDINATES). When the equation of a 

 curve contains only powers of x and y, the curve 

 is algebraic ; when the equation contains other 

 functions, logarithms, for instance, of x and y, the 

 curve is called transcendental. The cycloid, e.g., 

 is a transcendental curve. 



There are also curves, like some spirals, that do 

 not continue in one plane ; these are called curves 

 of double curvature, and require, in analysis, three 

 co-ordinates and two equations. Curves are said to 

 be of the first, second, third, &c. order, according 

 as their equations involve the first, second, third 

 powers of x or y. The circle, ellipse, parabola, and 

 hyperbola are of the second order of curves. There 

 is only one line of the first order viz. the straight 

 line, which is also reckoned among the curves. 

 The higher geometry investigates the amount of 

 curvature of curves, their length, the surface they 

 inclose, their tangents, normals, asymptotes, 

 evolutes and involutes, &c. 



The number of curves that might be drawn is of 

 course infinite. A large number have received 

 names, and are objects of great interest to the 

 mathematician in some cases, for their beauty, in 

 others, for their geometrical properties. Among 

 the most interesting are the following : ( 1 ) Circle ; 

 ( 2 ) ellipse ; ( 3 ) hyperbola ; ( 4 ) parabola ; ( 5 ) cissoid of 

 Diocles ; ( 6 ) conchoid of Nicomedes ; ( 7 ) lemniscata ; 

 ( 8 ) cycloid ; ( 9 ) harmonic curve ; ( 10 ) trochoid ; ( 1 1 ) 

 the witch; (12) cardioid ; (13) curves of circular 

 functions e.g. curve of sines ; ( 14) the logarithmic 

 curve and other plane spirals, such as that of Archi- 

 medes, the lituus, the reciprocal or hyperbolic, and 

 the involute (q.v. ) of the circle ; ( 15) the catenary ; 

 ( 16 ) the tractory ; ( 17 ) the tractrix ; ( 18 ) the ovals 

 of Cassini. 



Curwen, JOHN, the apostle of the Tonic Solfa- 

 system of teaching music, was the son of an In- 

 dependent minister, and was born at Heckmond- 

 wike, Yorkshire, 14th November 1816. He was 

 trained for the ministry, and after having served 

 as assistant in various charges, was settled as 

 minister of the Independent chapel at Plaistow. 

 In 1841 he began to advocate the Sol-fa System 

 (q.v.); in 1843 his Grammar of Vocal Music ap- 



E eared ; in 1864 he resigned his ministry and gave 

 imself wholly to the cause. He died 6th May 

 1880. See Memorials of John Curwen ( 1882). 



l'nr'/ol:i, a Dalmatian island, 30 miles by 5, 

 with a pop. of 15,000, of whom 2000 are in the town 

 of Cur/ola. 



Cusa, NlCOLAUS OF (1401-64), born at Cusa or 

 Kues on the Moselle, studied at Deventer with 

 the Brothers of the Common Life and at Padua. 

 As archdeacon of Liege he took the anti-papal side 

 at the Council of Basel ; but was ultimately Bishop 

 of Brixen in Tyrol, cardinal, and papal legate to 

 Constantinople. He exposed the false Isidorian 

 decretals, denounced perverted scholasticism in 

 De Docta Ignorantia, taught that the earth went 

 round the sun, and in pantheistic tendencies and 

 otherwise was a precursor of Giordano Bruno. 

 See German monographs by Dux (1848), Scharpff 

 (1871 ), and Glossner (1891)! 



C II SOUS, a marsupial akin to the Phalanger (q.v.). 



dish, the son of Ham (q.v.), and father of the 

 Cushites. See ETHIOPIA, SEMITES. 



4'nsliiiur, CALEB, American statesman, born in 

 Salisbury, Massachusetts, in 1800, was admitted to 

 the bar in 1821, sat in the state legislature and 

 senate, and was elected to congress in 1835-43. He 

 arranged the first treaty between China and the 

 United States in 1844 ; raised and commanded a 

 regiment in the war with Mexico ; and was United 



States attorney-general in 1853-57, counsel for the 

 United States at the Geneva Conference in 1872, 

 and minister to Spain in 1874-77. He died in 1879. 



Cushman, CHARLOTTE SATJNDERS, a distin- 

 guished American actress, born in Boston in 1816, 

 appeared first in opera in 1834, and as Lady 

 Macbeth in 1835. Miss Cushman played some- 

 times in high comedy, but her name is identified 

 with tragic parts. In 1844 she accompanied 

 Macready on a tour through the northern states, 

 and afterwards appeared in London, where she was 

 well received in a range of characters that included 

 Lady Macbeth, Rosalind, Meg Merrilees, and 

 Romeo her sister Susan ( 1822-59 ) playing Juliet. 

 Miss Cushman retired from the stage in 1875, and 

 died in Boston, 18th February 1876. 



Cusk. See TORSK. 



Cusp (Lat. cuspis, ' a lance-point '). If we con- 

 ceive a curve to be generated ty a moving point, 

 then a cusp is where the point suddenly stops arid 



Fig. 1. 



Fig. 2. 



returns for a time in the same general direction as 

 that in which it was moving when it reached the 

 cusp point. A later name is ' spinode. ' When two 

 branches (as BA, CA) meet a common tangent 

 without extending further, the point of contact is 

 a cusp. Fig. 1 is an example of the first species, 

 and 2 of the second. 



Cusparia. See ANGOSTURA BARK. 



Cusps, curved projections or featherings in 

 Gothic tracery, 

 arches, panels, &c. 

 They began in the 

 Early English period, 

 when they projected 

 from the fiat soffit 

 of the arch ; but 

 they were soon com- 

 prised in the mould- 

 ings, and generally 

 spring from the inner 

 splay or cavetto. In 

 Decorated and Per- 

 pendicular work the 

 points were length- 

 ened, and were frequently ornamented with flowers, 

 heads, &c. 



Cusset, a small town in the French department 

 of Allier, 2 miles NE. of Vichy, with two mineral 

 springs. Pop. 5356. 



< lisso. Kusso, or CABOTZ (Brayera anthelmin- 

 tica), a small Abyssinian tree of the order Rosacese, 

 sub-order Spiraeaceae, the dried flowers of which 

 have been long infused in Abyssinia as an anthel- 

 mintic, and have been found so efficacious in the 

 removal of tapeworm, that they were in 1874 

 introduced into European pharmacy as Flares 

 Kusso. 



4 usf. ROBERT NEEDHAM, was born in 1821, at 

 Cockayne-Hatley, Bedfordshire, studied at Eton, 

 and entered the Indian civil service. He held 

 various important administrative and judicial posts 

 in North India, in 1864-65 was a member ot the 

 legislative council, and returned to England in 1869. 

 He is a member of many learned societies at home 

 and abroad, has contributed extensively to their 

 Transactions, and has published works on the 



Cusp. 



