Among the countless writers of verse that have arisen in Cuba later than Avellaneda, three are of particular merit: Joaquin Lorenzo Luaces (1826-67) , the author of war songs (the Caida de Misolonghi, etc.), of odes (see especially the Oration dc Matatias of biblical inspiration and the ode A Cyrus Field, on the laying of the At lantic cable). and of one or another drama (cf. the Poesias de J. L. Luaccs, Havana, 1857, and the Noches literarias cn easa dc N. Acsaratc, Havana, 1866) : Juan Clemente Zenea (1832 71) , whose elegiac verse is full of a tender melan chol• (cf. the complete edition of his POCS taS, New York, 1872) : and Rafael Maria de Mendive (1s21-86), noted for his translation of the Irish Melodies of Thomas "Moore, whose influence is also easily discernible in his original Cuban verse (cf. the Poesfas of Mendive, Havana, 1883; and the .Uclodias irlandesas, New York, 1875). To the list of the nineteenth-century poets there may further be added the names of Ramon Velez y Herrera (born 1808), Miguel Teurbe de TolOn (1820-58), Francisco Orgaz (1815-73), RamOn de Palma y Romay (1812-60), Ramon Zambrana (1817-66), Jose Fornaris (1827-90), Jose Giiell y Re:lie, etc.
As compared with her poets, it is clear that the prose writers of Cuba are distinctly inferior in importance. In the eighteenth cen tury, she has the historians Arrati and Ur rutia; in the nineteenth. Valdez, Jose Arrango y Castillo. etc. Among her legal writers have figured Conde, Ayala, Armes, Bermudez, Cintra, etc., and among her moralists and writers on philosophical matters, Berea, Veranes. Jose Augustin Caballero, Felix Varela, Jose de In Luz Caballero, etc. In the fine arts Vermay and Perounni have earned some recognition, and in music Villate has gained notice by his operatic compositions. A really good critical account of Cuban prose and poetry has yet to be written; more light on the subject may be expected from the publication of the Biblioteca selecta hispano cabana de prosistas and the Antologia de poesia cabana, which a commission of littera teurs has presented to the Spanish Academy. On Cuban lyric poets an excellent essay has been written by M. Menendez y Pelayo and now ap pears as the preface to the second volume of the Antologia de poctas hispano-antcricanos (Madrid, 1S93), which contains very good selections from the works of the most important Cuban poets. Consult also: the I'arnaso eubano, ColcceiOn do pocsias selectas dc autorcs cubanos dcsde Ze qucira, etc. (Havana. 1881) : the Cuba poetica, colcccidn cscogida de las composiciones en rcrso dc los poetas cubanos desde Zequairu, prepared by Fornaris and Luaces (2d ed., Havana, 1861) ; Hills, Bardos cubanos, antologia dc las inciorcs . pocsias linens de Hcredia, 'Phicido' Arellancda, Milanes, Mendire, Lituccs, y Zenea, with bio graphical notices of each of the poets and a com prehensive bibliography of their works and of Cuban poetry in general (Boston, 1901) ; y Morales, Apuntes porn la historia dc las kerns p de in instruction pliblica en in isla dc Cuba (Havana, 1860) ; Estudio sobre el niorimiento cientifico y litcrario de Cuba (Ha vana, 18901: Merchan. Est udios erfticos (Bogottl,
1886) ; Caleagno, Diccionario biogrdfico cubano (New York. 1878) ; Gonzalez del Valle. La pocsia lirica cn Cuba (new ed.. Barcelona, 1900).
CUBE (Lat. cubits, Or. silgos, 7•ybos, cube), or REGULAR HEXAHEDRON. A regular solid with six square faces, each of which is parallel to the one opposite to it. It is a form of frequent oc currence in nature, especially among crystals. The cube or third power of a number is the prod uct formed by taking the number three times as a factor, e.g. the cube of 4, or = 4 • 4 • 4 = 64. This use of the term arises from the circum stance that the solid contents of a cube may he expressed by the third power of the munber which expresses the length of one of its edges. Thus, if the edge of a cube is 4 inches. its vol ume is 4 • 4 • 4 • 1 cubic inch, or 64 cubic? inches. The cube root of a number is one of the three equal factors of the number: e.g. the cube root of S is 2, since 2 • 2 • 2 = 8. The number of which the root is sought is called the power. and if it is a power of a commensurable (q.v.) num ber, it is called a perfect power. Roots of per fect powers are often readily obtained by factor ing; e.g. to find the cube root of 216; 216 = 6 • 6 • 6, therefore 6 is the cube root of 216. If the root is incommensurable, the binomial for mula, logarithms, or the equation (q.v.) is available. Every number which satisfies the equation 1, or = 0 is a cube root of i. But = 0 is the same as (x— 1) (A' + x+ 1) = 0, and equating each factor to 0 and solving, x = 1, — + V-3,-1-11 V —3, the three cube roots of unity. (See COMPLEX NUMBER.) The three cube roots of S are 2, 2(-3 + ), 2 (—i-1 V-3 ). Thus any number has three cube roots. one real and two imaginary. lm extensive cklculations, tables of roots and of logarithms are employed. Duplication of the cube or the Delian problem, according to tradition, originated with the oracle of Delos, which declared to the Athenians that a pestilence prevailing among them would cease if they doubled the altar of Apollo—i.e. replaced his cubical altar by another of twice its con tents. The problem reduces to the solution of the continued proportion a : x = x: y = y: 2a, or to the solution of 20. This was effected geometrically by Hippocrates, Plato, 1\lenrech nms, Archytas, and others, hut not by elementary geometry. This is one of the three great prob lems whose appearance has been of wonderful significance in the development of mathematics. Consult: Gow, History of Greek Mathematics (Cambridge, 1884) ; Klein, Vortragc ii bur ansgewahlte Fragen der Elementargeometric (Leipzig, 1895) ; Famous Problems of Elemen tary Geometry, trans. by Beman and Smith (Boston, 1897).