mom — is the produce of Elettaria repens, or
Elettaria cardanwmtnii, a native of the moun-
tains of Malabar, and is cultivated in India,
Ceylon, etc. I'lie seeds depend for their qualities
on a peculiar, pungent essential oil, called oil of
cardamom, which may be obtained from them
by distilling with water, and which, when fresh,
is colorless. They also contain 10 per cent,
fixed oil. Other kinds of cardamom occur in
conmierce, but none is equal to the true carda-
mom in commercial value. The different kinds
of cardamom differ not only in strength, but in
the character of their aroma, though the plants
producing them have much general similarity.
CAR'DAN, JEROME, often referred to as HlEKOXYMlS CaRDANUS or GiBOLAMO Cabdano (1501-70). An Italian mathematician, born at Pavia, the illegitimate son of Facio Cardan, a jurist. He was at once an astrologer and a genu- ine philosopher; a gambler and charlatan, and a true devotee of science. As early as 1523 Car- dan taught mathematics at Pavia. In 1526 he took the degree of doctor of medicine at Padua, and spent the following seven years practicing medicine at Sacco. Here Cardan met his wife, and is said to have squandered her fortune in gambling. In 1534 he was appointed to the chair of mathematics at Milan, and while holding this post, and at the .same time practicing and teach- ing medicine, he produced his principal works, ^^hieh are noticed below.
In 1552 he started on an extensive journey through central and northern Europe, and in 1559 obtained the chair of medicine at Pavia, and later at Bologna, remaining there from 1562 until 1570. While living in Bologna he was im- prisoned for debt, or on the charge of heresy for having pul>lished the horoscope of Christ, and on his release resigned his professorship at the uni- versity. He then went to Rome, and was admit- ted by Pope Gregory XIII. to the College of Phy- sicians, and allowed a pension. He died in Rome in 1576.
The Ars ilar/na (1545), by far the greatest work of Cardan, contains the celebrated solu- tion of the cubic equation. Tlie solution had been discovered in 1541 by Tartaglia, who com- municated it to Cardan under the most solemn vows of secrecy. Cardan, nevertheless, published the solution under his own name, and hence arose a dispute over the authorship of the discovery. After ten years of controversy, challenge and counter-challenge, Tartaglia began publishing his own work (1556), but died before reaching the chapter on the cubic equation. Thus the great- est mathematical discovery of the Sixteenth Cen- tury came to be known as Cardan's method. The solution, as given by Cardan in geometrical terms, is, briefly, as follows: To solve the equa- tion x^ 4- C)x =: 20, take two culies such that the rectangle of their respective edges is 2 and the difference of their volumes is 20; then x is equal to the difference between the edges of the cubes. In the general equation xi' -- px =^ q, the rect- angle of the edges is a third of p, and the dif- ference of the volumes of the cubes is q. The publication of the Ars Magna stimulated mathe- matical research, and hastened the general solu- tion of biquadratic equations, of which Cardan himself had solved special cases, as ISo-' = r' + 2x^ + 2x + : although the credit of producing the first general solution belongs to his pupil Ferrari. Cardan recognized negative roots, which he designated as fictitious ; he also ob- served that imaginary roots occur in pairs, but discarded them as impossible, and failed to un- derstand the irreducible case of the cubic. He found the relation of the roots to the coellicienta of an equation, recognized that the change of sign of a function implies a solution, and gave a method of approximating the roots of nu- merical equations. His discussions of quadratic equations are hardly superior to those of Mo- hammed ben Musa.
Besides the Ars Magna, his most important works include: I'raitica Arithmctinr Uniicrsalis (1539); Dc Sublilitate lierum (1551), and its sequel. De Varictate licriim. Artis Magiiw siie (le liegulis Algebraicis lib. iiniis (1545) : Oc Vila Propria and Dc Libris Propriis (1571-75) ; En- comiutn Geometrice (1535); Ue liegula Aliza, Exwreton Mathcmaticorum, Sermo de plus et minus (1540-50). The standard collection of Cardan's works is that of Sponius (Lyons, 1663). Consult: Morley, Jerome Cardan (Lon- don, 1854), and Rixner and Siber, Leben und Lehrmeinungen beriihmter Physiker am Ende des XVI. und am Anfange des XVII. Jahrhun- derts (Sulzbach, 1820).
CARDBOARD. A material prepared by past- ing together several layers of paper, according to the thickness and quality required. Liris- tol-board, used by artists, is made entirely of white paper; ordinary cardboard, of tine white paper outside, with one or more sheets of coarse cartridge paper between. According to the number of layers, they are called three, four, six, or eight sheet boards. Millboard, used by book- binders as the basis of book-covers, is made of coarse brown paper, glued and strongly pressed. The enameling of visiting-cards and fine card- board is produced by brushing over the card- board a mixture of China or Kremnitz white (a fine variety of white lead) and size. After drying, this surface is rubbed lightly over with a piece of flannel, previously dipped in (incly powdered talc : it is then polished by rubbing vigorously with a hard, close-set brush.
CARDENAL, kar'dc-nal', or CABDINAL, PiEBRE or Peire (C.1205-C.1305). A French trou- badour, born at Puy-en-Velay. He passed most of his life at various courts, and found esi)ecial favor with James I. of Aragon. His poems, which consist chiefly of sirventes, satirizing the clergy and nobles of his day, are both original and vigorous. About seventy are published in !Mahn's Gedichte dcr Troubadours (4 vols., Ber- lin, 1856-73). Consult: Fauricl, Jlistoirc de la litterature provcntale (3 vols., Paris, 1846), and Diez, Leben und Werke der Troubadours (Leipzig. 1882).
CARDENAS, kiir'dft-nAs. A seaport of Cuba, in the Province of Matanzas, situated on the northern coast of the island, about 80 miles east of Havana, with which it is connected by rail (Map: Cuba, D 3). It is regularly built with wide streets and broad plazas, one of which is the site of a statue of Columbus, and has sev- eral notable buildings. Cardenas is one of the important eonuncrcial centres of the island, its chiet export being sugar. The trade is, to a large extent, conducted by American firms. On May 11, 1898, Cardenas Bay was the scene of an
