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government, Heredia is held in high esteem not only for his political poems like the Himno del desterrado, but also for his descriptive poems like the Niágara, the Teocalli de Cholula, and the Tempestad, pervaded by a melancholy sentiment, and full of most noble imagery. Among Heredia's works are many translations and imitations of the poems of English, French, and Italian writers, such as Young, Campbell, the pseudoOssian, Lamartine, Delavigne, Millevoye, Arnault, Foscolo, and Pindemonte (cf. the edition of Heredia's poems and his translations and imitations of foreign dramas, published at New York, 1875; his prose Lecciones de historia universal, Toluca, 1831, and other prose works; and consult: Villemain, Essai sur le génie de Pindare et sur la poésie lyrique, Paris, 1859; J. Kennedy, Modern Poets and Poetry of Spain, London, 1852). Among the lesser lights must be counted Domingo del Monté, a Venezuelan, who, residing in Cuba, there composed pleasing romances, played the part of a generous patron of other poets, and strove energetically to have purity of idiom maintained in the Cuban use of the Castilian speech; Ignacio Valdés Machuca, who imitated Meléndez Valdés in his Ocios poéticos (1819), and also translated and imitated JeanJacques Rousseau; Manuel González del Valle, a teacher of philosophy, and the author of a Diccionario de las Musas (1827), etc., etc. A protégé of del Monte's was the romantic spirit José Jacinto Milanés (1814-63), a man of superior powers, whose lyrics are now gently sentimental, and again madly socialistic. Milanés is also deemed one of the best playwrights that the island has had so far. His pieces include El Conde Alarcos, El poeta en la corte, Por el puente ó por el río, and A buena hambre no hay pan duro. Pictures of manners in dialogue form are to be seen in his Mirón cubano (cf. the first ed. of his Obras, Havana, 1846; second ed., New York, 1865). Another true poet was Gabriel de la Concepción Valdés, best known by his pseudonym Plácido (1809-44). He was a mulatto and a foundling, and had but slight training, yet few Cuban lyrics will live longer than his romance entitled Xicotencal, and his sonnets, La muerte de Gessler, Fatalidad, and Plegaria (cf. the eds. of his verse, New York, 1856; and Havana, 1886). Of undisputed excel lence is the work of the poetess Gertrudis Gómez de Avellaneda (1814-73). She was eminently successful as a lyric poet and as a dramatist, less so as a novelist (cf. an edition of her works, Madrid, 1869).

Among the countless writers of verse that have arisen in Cuba later than Avellaneda, three are of particular merit: Joaquín Lorenzo Luaces (1826-67), the author of war songs (the Caída de Misolonghi, etc.), of odes (see especially the Oración de Matatias of biblical inspiration and the ode A Cyrus Field, on the laying of the Atlantic cable), and of one or another drama (cf. the Poesías de J. L. Luaces, Havana, 1857, and the Noches literarias en casa de N. Azsárate, Havana, 1866); Juan Clemente Zenea (183271), whose elegiac verse is full of a tender melancholy (cf. the complete edition of his Poesías, New York, 1872); and Rafael María de Mendive (1821-86), noted for his translation of the Irish Melodies of Thomas Moore, whose influence is also easily discernible in his original Cuban verse (cf. the Poesías of Mendive, Havana, 1883; and

VOL. V.-33.

the Melodías irlandesas, New York, 1875). To the list of the nineteenth-century poets there may further be added the names of Ramón Vélez y Herrera (born 1808), Miguel Teúrbe de Tolón (1820-58), Francisco Orgáz (1815-73), Ramón de Palma y Romay (1812-60), Ramón Zambrana (1817-66), José Fornaris (1827-90), José Güell y Renté, etc.

As compared with her poets, it is clear that the prose writers of Cuba are distinctly inferior in importance. In the eighteenth century, she has the historians Arrati and Urrutia; in the nineteenth, Valdéz, José Arrango y Castillo, etc. Among her legal writers have figured Conde, Ayala, Armas, Bermúdez, Cintra, etc., and among her moralists and writers on philosophical matters, Barea, Veranes, José Augustín Caballero, Félix Varela, José de la Luz Caballero, etc. In the fine arts Vermay and Perouani 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 hispanocubana de prosistas and the Antología de poesía cubana, which a commission of littérateurs has presented to the Spanish Academy. On Cuban lyric poets an excellent essay has been written by M. Menéndez y Pelayo and now appears as the preface to the second volume of the Antología de poetas hispano-americanos (Madrid, 1893), which contains very good selections from the works of the most important Cuban poets. Consult also: the Parnaso cubano, Colección de poesías selectas de autores cubanos desde Zequeira, etc. (Havana, 1881); the Cuba poética, colección escogida de las composiciones en verso de los poetas cubanos desde Zequeira, prepared by Fornaris and Luaces (2d ed., Havana, 1861); Hills, Bardos cubanos, antología de las mejores poesías líricas de Heredia, 'Plácido' Avellaneda, Milanés, Mendive, Luaces, y Zenea, with biographical notices of each of the poets and a comprehensive bibliography of their works and of Cuban poetry in general (Boston, 1901); Bachiller y Morales, Apuntes para la historia de las letras y de la instrucción pública en la isla de Cuba (Havana, 1860); Mitjans, Estudio sobre el movimiento científico y literario de Cuba (Havana, 1890); Merchán, Estudios críticos (Bogotá, 1886); Calcagno, Diccionario biográfico cubano (New York, 1878); González del Valle, La poesía lirica en Cuba (new ed., Barcelona, 1900).

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CUBE (Lat. cubus, Gr. kúßos, kybos, 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 occurrence in nature, especially among crystals. The cube or third power of a number is the product formed by taking the number three times as a factor, e.g. the cube of 4, or 43 4 · 4 · 4 = 64. This use of the term arises from the circumstance that the solid contents of a cube may be expressed by the third power of the number which expresses the length of one of its edges. Thus, if the edge of a cube is 4 inches, its volume 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 8 is 2, since 22·2 = 8. The number of which the root is sought is called the power, and

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if it is a power of a commensurable (q.v.) number, it is called a perfect power. Roots of perfect powers are often readily obtained by factoring; e.g. to find the cube root of 216; 216 = 666, therefore 6 is the cube root of 216. If the root is incommensurable, the binomial formula, logarithms, or the equation (q.v.) is available. Every number which satisfies the

equation 3 1, or a3. 10 is a cube root of i. But 10 is the same as (-1) (x2+ + 1) = 0, and equating each factor to 0 and solving, a = 1, − 1 + √ √ −3,− 1 − 1 √ —3, the three cube roots of unity. (See COMPLEX NUMBER.) The three cube roots of 8 are

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CUBIC EQUATION. A rational integral equation of the third degree is called a cubie equation. It is called binary, ternary, or quaternary according as it is homogeneous of the third degree in two, three, or four unknowns. ̧ The general form of a cubic equation of one unknown is a3 + bx2 + cx + d = 0. It is shown in algebra that this equation can be reduced to one of the form a3 + pa + q = 0. Every cubic equation of this form has three roots, of which one is real and the others real or imaginary. The roots will all be real when p is negative, and p3 g2 27 4

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> This is known as the irreducible case in solving the equation. Only one root is real when p is positive, or when it is negative and p3 p❜ If < P is negative and = two of 27 4 27 4 the roots are equal. The cubic equation may be solved by the following formula, due to Tartaglia and Ferro, Italian mathematicians of the sixteenth century, but known as Cardan's formula:

x=

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+

27

3 9
2

q

+
4 27

+ √

2,2(+√−3), 2(—1—1 √−3). Thus any number has three cube roots, one real and two imaginary. In extensive calculations, 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 contents. The problem reduces to the solution of the continued proportion a: x = x: y = y: 2a, or to the solution of a 2a3. This was effected geometrically by Hippocrates, Plato, Menæchmus, Archytas, and others, but 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); Vorträge über ausgewählte Fragen der Elementargeometrie (Leipzig, 1895); Famous Problems of Elementary Geometry, trans. by Beman and Smith ing corresponding coefficients of cosa, and solv(Boston, 1897).

Klein,

Besides Ferro, Tartaglia, and Cardan, Vieta, Euler, and others contributed to the early the ory of cubic equations. In case the roots of a cubic equation are all real their values are more readily calculated by means of trigonometric formulas-e.g. assume an cosa, and the equation x3px+q=0 may be expressed by cos3a 9 + cosa + = 0. But from trigonometry cos 3a

n

cos'a cosa

3

4p

x = n ·

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CU BEBS, or CUBEB PEPPER (Fr. cubebe, ing the equations, n = √ and cos3a=— from Ar. kababa). The dried unripe berries of Piper officinalis, a species of climbing shrub of the natural order Piperaceæ, very closely allied to the true peppers. Piper officinalis is a native of Penang, Java, New Guinea, etc., and is said to be extensively cultivated in some parts of Java. Its spikes are solitary, opposite to the leaves, and usually produce about fifty berries, which are globular, and, when dried, have much resemblance to black pepper, except in their lighter color and the stalk with which they are furnished. Piper canina, a native of the Sunda and Molucca islands, is supposed also to vield part of the cubebs of commerce, and the berries of Piper ribesioides possess similar properties. Cubebs are less pungent and more pleasantly aromatic than black pepper; they are used in the East as a condiment, but in

cosa; n cos For history and methods, consult Matthiessen, Grundzüge der antiken und modernen Algebra der litteralen Gleichungen (Leipzig, 1896). See also CARDAN, JEROME.

CUBIC ULUM (Lat., bedroom, from cubare, to lie down). A term used to designate a small room or cell in a Roman house, containing a bed or couch, and opening off the court; also a recess or alcove, a box at the theatre or circus; and lastly, a final resting-place or burial-recess for one or more bodies in the early Christian catacombs.

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YELLOW-BILLED

Americanus).

CUCKOO

(Coccyzus

1. AMERICAN 2. BLUEHEADED KOEL (Eudynamis cyanocephala). 3. COMMON EUROPEAN PARASITIC CUCKOO (Cuculus canorus).

4. ANI, or RAIN CROW (Crotophaga ani).

5. CRESTED CUCKOO (Lepidogrammus Cummingi). 6. CHANNEL-BILL (Scythrops Nova-Hollandiæ). 7. CHAPARRAL COCK (Geococcyx Californianus).

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CUBIT (Lat. cubitus, elbow). A measure employed by the ancients, equal to the length of the arm from the elbow to the tip of the middle finger. The cubit of the Romans was about 17% inches, and that of the Hebrews 22 inches, but its length is now generally stated at 18 English inches.

An

CUBITT, Sir WILLIAM (1785-1861). English civil engineer, born at Dilham, Norfolk. In 1800-04 he was apprenticed to a cabinetmaker at Stalham, and at Swanton was associated with a manufacturer of agricultural machines and devised self-regulating sails for windmills. In 1818 he began the manufacture of his invention known as the treadmill, which was quickly introduced into the principal jails of Great Britain. From 1826 he was connected as engineer with important works in the improve ment of canals and rivers, and the construction

of bridges and railways. He conducted the improvement of the Severn and the building of the Southeastern Railway. The water-works of Berlin were also executed by him. In 1850-51 he was president of the Institution of Civil Engi

neers.

CUCKOO, kukoo (Fr. coucou, Lat. cuculus, Gk. Kokkuğ, kokkyx, cuckoo, Skt. kōkila, cuckoo). A name given to many birds of the picarian family Cuculidæ, which contains about 175 species, mostly confined to the warmer regions of the globe, although some of them are summer visitors to cool climates. Only 35 of the known species live in the New World. The beak is slightly compressed and somewhat arched; the tail long, rounded, and usually of ten feathers; the wings rather long; the tarsi short, with two toes directed forward and two backward, the outer hind toe capable of being brought half round to the front. The feet are thus adapted for grasping and moving about upon branches rather than for climbing.

Cuckoos of the Old World.-The name cuckoo is derived from the note of the male of the common European cuckoo (Cuculus canorus), which, although monotonous, is always heard with pleasure, being associated with all that is delightful in returning spring. A similar name is given to the bird in many languages. This common cuckoo is very widely diffused, as it is also found in India, Africa, and, in summer, even in Lapland and Kamchatka. It appears in Great Britain in April, and all except the young birds are believed to migrate southward again before the middle of August. The adult cuckoo is about a foot in length; ashy-gray, barred beneath with black; the wings are black, and the tail is black, marked with white. It frequents both cultivated districts and moors. There is no pairing or continued attachment of the male and female; and the female, after having laid an egg on the ground, takes it in her mouth and deposits it, by means of her beak, in the nest of some other smaller bird, leaving the egg to be hatched and the young one to be fed by the proper owners of the nest. This egg is very small for so large a bird, not larger than a skylark's; and the number laid is uncertain. The Young one, soon after hatching, acquires size and strength enough to eject from the nest any eggs or young birds-the true offspring of its foster-parents-which may remain in it, and it seems restless and uneasy till this is accom

plished. It works itself under them, and then jerks them out by a motion of its rump. Other species of cuckoo, closely allied to the European cuckoo, inhabit Africa, Asia, and Australia, and have essentially the same habits, one, about the Mediterranean, victimizing pies alone, its eggs having a remarkable resemblance to those of the magpie. Equally parasitic are many Old-World tropical species of various other genera; yet some of them (see COUCAL) do not shirk parenta! responsibility, but incubate and rear their own offspring. This extraordinary practice of bird parasitism, in respect to its facts and probable origin and development, is thoroughly discussed by A. Newton, Dictionary of Birds, article "Cuckoo" (London, 1896).

The American cuckoos represent three differthe tree-cuckoos. ent subfamilies-the anis, the road-runners, and The last compose the group

Coccyzinæ, and are characteristic of and confined to America. The best-known species are the black-billed cuckoo (Coccyzus erythrophthalmus) and the yellow-billed (Coccyzus Americanus). Both species occur commonly in summer throughout the United States and eastern Canada, but pass the winter in Central and South America. The black-billed cuckoo does not occur west of the Rocky Mountains. two species are of about the same size, a foot long, and are olive-brown above, white beneath, but are easily distinguished by the color of the bill and the amount of white on the tail.

YELLOW-BILLED CUCKOO.

The

Unlike the Old-World cuckoos, they are not parasites, but build their own nests and incubate their own eggs. The nests are flimsy structures of twigs, the eggs large and pale blue. Incubation begins when the first egg is laid, so that no two of the eggs or young are in just the same stage of development. The American cuckoos are insectivorous and are very useful birds. Their note or call is a series of accelerated chucks,' not exactly harsh, but far from musical. In the Middle, Western, and Southern States the yellow-bill is known as 'rain-crow,' because its note is supposed to predict rainan idea prevalent in regard to these birds in other parts of the world. Consult Beal, Food of Cuckoos (Department of Agriculture, Washington, 1898). See Plate of CUCKOO FAMILY; and Colored Plate of EGGS OF SONG-BIRDS.

CUCKOO AND THE NIGHTINGALE, THE. A poem attributed in the sixteenth century to Chaucer, but probably not composed by him. The subject is the discussion between a nightingale and a cuckoo on the comparative blessings of love.

CUCKOO-BEE. A naked, somewhat wasplike bee of the family Nomadida, all the many species of which are parasitic in the nests of other bees, after the manner of the European

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