CURVE 228 CURZON OF KEDLESTON prescribed kinematic movement of a point 1 or a line, according to the methods of an- alytic geometry, by an equation between co-ordinates, as the intersection of a plane by an irregular surface. The ellipse for example can be represented in all four of these methods: as the geometrical locus of all points for which the sum of the distances of two given points — the foci — is constant. Kinematically by an ellipsograph or oval; by an equation of the second rank, and by the section of a cone by a plane. The consideration of curves as geomet- rical loci is based on the principles of the geometry of Euclid and is the most an- cient method of studying curves and dis- covering new kinds. Far more fruitful and speedy in their results are the meth- ods of analytical geometry, the science of which was established by Descartes in 1637, especially through the use of the differential and integral calculus. In this way the peculiarities of curves may be investigated on purely mathematical methods, and on the other hand the ana- lytical geometry of the theory of func- tions offers a means of establishing the functions as curves and thereby giving a clear image of their course. According to the nature of the equation on which they are based, curves are called alge- braic, containing powers of x and y, or transcendental, where they involve loga- rithmxS. Algebraic curves are distin- guished according to the rank or order of the equation. Thus, we have curves of the 2d rank or conic sections, of the 3d rank or cubic curves, of which there are many varieties, including Newton's foli- ate or 41st species, and the 4th rank or quartic, and so on. The analytic investi- gation of a curve is especially directed toward the characteristics of its tangents and normals, toward its point of oscula- tion as well as toward its asymptotes and its peculiar points or singularities. Curves can be likewise defined according as one prescribes their tangents or nor- mals or the characteristics of their cur- vation from which the equation of the curve is deduced. A frequently recur- rent condition of curves is that they are regarded as inclusive of their tangents whereby, for example, the caustic curves, the trajectories and tractories are found. Also through investigation of the nadir- curves and the evolutes arise many forms of curves and relations among well- known kinds. The number of points in which a curve of any order in general is drawn is called its rank; the number of tangents which in general may be drawn from any given point to a curve is called its class. Between rank, class, and the number of their distinguished points and tangents, double points, return points, double tangents, periodic tangents, come a series of continuously valid relations, the Pliicker's Formulas. For example, every curve of the 3d rank without double point is of the 6th class, with double point is of the 4th class, with return point of the 3d class. Besides the an- alytical methods for the investigation of curves there are the synthetic methods devised especially by Poncelet, Steiner, and Staudt. Projection geometry has proved of great use in the investigation of cones. For description and illustra- tion of the principal curves, see their respective titles. CURWOOD, JAMES OLIVER, an American author, born at Owosso, Mich., in 1878. He studied in the literary de- partment of the University of Michigan, and for 7 years was engaged in news- paper work. Later he spent much time in the Canadian Northland, where he traveled as far north as the Arctic coast. He was employed by the Canadian Gov- ernment as an explorer and descriptive writer. Among his books are "The Cour- age of Captain Plum" (1908) ; "The Danger Trail" (1910); "The Valley of Silent Men" (1911); "Nomads of the North" (1919) ; and "The River's End" (1919). He was a frequent contributor to magazines. CURZOLA, the most beautiful of the Dalmatian islands, in the Adriatic, stretching W. to E. about 25 miles, with an average breadth of 4 miles; area, 85 square miles. It is covered in many places with magnificent timber. The fish- eries are very productive. It contains a town of the same name. CURZON OF KEDLESTON, GEORGE NATHANIEL, EARL, a British states- man; born in Kedleston, England, in 1859. He was educated at Eton and Bal- liol College, Oxford, In 1885 he was as- sistant private secetary to the Marquis of Salisbury; in 1891 and 1892, Under-Sec- retary of State for India; and from 1895 to 1898, Under-Secretary of State for Foreign Affairs. From 1899 to 1905 he was Viceroy and Governor-General of India. He represented the Southport di- vision of southwest Lancashire in Parlia- ment, from 1886 to 1898. In 1908 he was Irish Representative Peer, and since 1916 Leader of the House of Lords. In 1915- 1916 he was Lord Privy Seal; in 1916 President of the Air Board, later in that year becoming Lord President of the Council, and also member of the Im- perial War Cabinet. In 1920 he was Secretary of State for Foreign Affairs. In 1895 he married Mary Victoria, daughter of L. Z. Leiter, Washington,
