The Project Gutenberg eBook ofEncyclopaedia Britannica, 11th Edition, "Cube" to "Daguerre, Louis Jacques Mandé"This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.Title: Encyclopaedia Britannica, 11th Edition, "Cube" to "Daguerre, Louis Jacques Mandé"Author: VariousRelease date: January 29, 2012 [eBook #38709]Most recently updated: January 8, 2021Language: EnglishCredits: Produced by Marius Masi, Don Kretz and the OnlineDistributed Proofreading Team at https://www.pgdp.net*** START OF THE PROJECT GUTENBERG EBOOK ENCYCLOPAEDIA BRITANNICA, 11TH EDITION, "CUBE" TO "DAGUERRE, LOUIS JACQUES MANDÉ" ***
This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.
Title: Encyclopaedia Britannica, 11th Edition, "Cube" to "Daguerre, Louis Jacques Mandé"Author: VariousRelease date: January 29, 2012 [eBook #38709]Most recently updated: January 8, 2021Language: EnglishCredits: Produced by Marius Masi, Don Kretz and the OnlineDistributed Proofreading Team at https://www.pgdp.net
Title: Encyclopaedia Britannica, 11th Edition, "Cube" to "Daguerre, Louis Jacques Mandé"
Author: Various
Author: Various
Release date: January 29, 2012 [eBook #38709]Most recently updated: January 8, 2021
Language: English
Credits: Produced by Marius Masi, Don Kretz and the OnlineDistributed Proofreading Team at https://www.pgdp.net
*** START OF THE PROJECT GUTENBERG EBOOK ENCYCLOPAEDIA BRITANNICA, 11TH EDITION, "CUBE" TO "DAGUERRE, LOUIS JACQUES MANDÉ" ***
Articles in This Slice
CUBE(Gr.κύβος, a cube), in geometry, a solid bounded by six equal squares, so placed that the angle between any pair of adjacent faces is a right angle. This solid played an all-important part in the geometry and cosmology of the Greeks. Plato (Timaeus) described the figure in the following terms:—“The isosceles triangle which has its vertical angle a right angle ... combined in sets of four, with the right angles meeting at the centre, form a single square. Six of these squares joined together formed eight solid angles, each produced by three plane right angles: and the shape of the body thus formed was cubical, having six square planes for its surfaces.” In his cosmology Plato assigned this solid to “earth,” for “‘earth’ is the least mobile of the four (elements—‘fire,’ ‘water,’ ‘air’ and ‘earth’) and most plastic of bodies: and that substance must possess this nature in the highest degree which has its bases most stable.” The mensuration of the cube, and its relations to other geometrical solids are treated in the articlePolyhedron; in the same article are treated the Archimedean solids, the truncated and snub-cube; reference should be made to the articleCrystallographyfor its significance as a crystal form.
A famous problem concerning the cube, namely, to construct a cube of twice the volume of a given cube, was attacked with great vigour by the Pythagoreans, Sophists and Platonists. It became known as the “Delian problem” or the “problem of the duplication of the cube,” and ranks in historical importance with the problems of “trisecting an angle” and “squaring the circle.” The origin of the problem is open to conjecture. The Pythagorean discovery of “squaring a square,”i.e.constructing a square of twice the area of a given square (which follows as a corollary to the Pythagorean property of a right-angled triangle, viz. the square of the hypotenuse equals the sum of the squares on the sides), may have suggested the strictly analogous problem of doubling a cube. Eratosthenes (c.200B.C.), however, gives a picturesque origin to the problem. In a letter to Ptolemy Euergetes he narrates the history of the problem. The Delians, suffering a dire pestilence, consulted their oracles, and were ordered to double the volume of the altar to their tutelary god, Apollo. An altar was built having an edge double the length of the original; but the plague was unabated, the oracles not having been obeyed. The error was discovered, and the Delians applied to Plato for his advice, and Plato referred them to Eudoxus. This story is mere fable, for the problem is far older than Plato.
Hippocrates of Chios (c.430B.C.), the discoverer of the square of a lune, showed that the problem reduced to the determination of two mean proportionals between two given lines, one of them being twice the length of the other. Algebraically expressed, if x and y be the required mean proportionals and a, 2a, the lines, we have a : x :: x : y :: y : 2a, from which it follows that x³ = 2a³. Although Hippocrates could not determine the proportionals, his statement of the problem in this form was a great advance, for it was perceived that the problem of trisecting an angle was reducible to a similar form which, in the language of algebraic geometry, is to solve geometrically a cubic equation. According to Proclus, a man named Hippias, probably Hippias of Elis (c.460B.C.), trisected an angle with a mechanical curve, named the quadratrix (q.v.). Archytas of Tarentum (c.430B.C.) solved the problems by means of sections of a half cylinder; according to Eutocius, Menaechmus solved them by means of the intersections of conic sections; and Eudoxus also gave a solution.
All these solutions were condemned by Plato on the ground that they were mechanical and not geometrical,i.e.they were not effected by means of circles and lines. However, no proper geometrical solution, in Plato’s sense, was obtained; in fact it is now generally agreed that, with such a restriction, the problem is insoluble. The pursuit of mechanical methods furnished a stimulus to the study of mechanical loci, for example, the locus of a point carried on a rod which is caused to move according to a definite rule. Thus Nicomedes invented the conchoid (q.v.); Diocles the cissoid (q.v.); Dinostratus studied the quadratrix invented by Hippias; all these curves furnished solutions, as is also the case with the trisectrix, a special form of Pascal’s limaçon (q.v.). These problems were also attacked by the Arabian mathematicians; Tobit ben Korra (836-901) is credited with a solution, while Abul Gud solved it by means of a parabola and an equilateral hyperbola.
In algebra, the “cube” of a quantity is the quantity multiplied by itself twice,i.e.if a be the quantity a × a × a (= a³) is its cube. Similarly the “cube root” of a quantity is another quantity which when multiplied by itself twice gives the original quantity; thus a1/3is the cube root of a (seeArithmeticandAlgebra). A “cubic equation” is one in which the highest power of the unknown is the cube (seeEquation); similarly, a “cubic curve” has an equation containing no term of a power higher than the third, the powers of a compound term being added together.
In mensuration, “cubature” is sometimes used to denote the volume of a solid; the word is parallel with “quadrature,” to determine the area of a surface (seeMensuration;Infinitesimal Calculus).
CUBEBS(Arab.kabábah), the fruit of several species of pepper (Piper), belonging to the natural order Piperaceae. The cubebs of pharmacy are produced byPiper Cubeba, a climbing woody shrub indigenous to south Borneo, Sumatra, Prince of Wales Island and Java. It has round, ash-coloured, smooth branches; lanceolate, or ovate-oblong, somewhat leathery, shining leaves, 4 to 6½ in. long and 1½ to 2 in. broad. Male and female flowers are borne on distinct plants. The fruits are small, globose, about1⁄5in. in diameter, and not so large as white pepper; their contracted stalk-like bases are between1⁄3and ½ in. in length; and from forty to fifty of them are borne upon a common stem. The cubeb is cultivated in Java and Sumatra, the fruits are gathered before they are ripe, and carefully dried. Commercial cubebs consist of the dried berries, usually with their stalks attached; the pericarp is greyish-brown, or blackish and wrinkled; and the seed, when present, is hard, white and oily. The odour of cubebs is agreeable and aromatic; the taste, pungent, acrid, slightly bitter and persistent. About 15% of a volatile oil is obtained by distilling cubebs with water; after rectification with water, or on keeping, this deposits rhombic crystals of camphor of cubebs, C15H26O; cubebene, the liquid portion, has the formula C15H24. Cubebin, CH2[O]2C6H3·CH:CH·CH2OH, is a crystalline substance existing in cubebs, discovered by Eugène Soubeiran and Capitaine in 1839; it may be prepared from cubebene, or from the pulp left after the distillation of the oil. The drug, along with gum, fatty oils, and malates of magnesium and calcium, contains also about 1% of cubebic acid, and about 6% of a resin.
The dose of the fruit is 30 to 60 grains, and the British Pharmacopoeia contains a tincture with a dose of ½ to 1 drachm. The volatile oil—oleum cubebae—is also official, and is the form in which this drug is most commonly used, the dose being 5 to 20 minims, which may be suspended in mucilage or given after meals in a cachet. The drug has the typical actions of a volatile oil, but exerts some of them in an exceptional degree. Thus it is liable to cause a cutaneous erythema in the course of its excretion by the skin; it has a marked diuretic action; and it is a fairly efficient disinfectant of the urinary passages. Its administration causes the appearance in the urine of a salt of cubebic acid which is precipitated by heat or nitric acid, and is therefore liable to be mistaken for albumin, when these two most common tests for the occurrence of albuminuria are applied. Cubebs is frequently used in the form of cigarettes for asthma, chronic pharyngitis and hay-fever. A small percentage of cubebs is also commonly included in lozenges designed for use in bronchitis, in which the antiseptic and expectoral properties of the drug are useful. But the most important therapeutic application of this drug is in gonorrhoea, where its antiseptic action is of much value. As compared with copaiba in this connexion cubebs has the advantages of being less disagreeable to take and somewhat less likely to disturb the digestive apparatus in prolonged administration. The introduction of the drug into medicine is supposed to have been due to the Arabian physicians in the middle ages. Cubebs were formerly candied and eaten whole, or used ground as a seasoning for meat. Their modern employment in England as a drug dates from 1815. “Cubebae” were purchased in 1284 and 1285 by Lord Clare at 2s. 3d. and 2s. 9d. per ℔ respectively; and in 1307 1 ℔ for the king’s wardrobe cost 9s., a sum representing about £3, 12s. in present value (Rogers,Hist. of Agriculture and Prices, i. 627-628, ii. 544).
A closely allied species,Piper Clusii, produces the African cubebs or West African black-pepper, the berry of which is smoother than that of common cubebs and usually has a curved pedicel. In the 14th century it was imported into Europe from the Grain Coast, under the name of pepper, by merchants of Rouen and Lippe.
CUBICLE(Lat.cubiculum), a small chamber containing a couch or a bed. The small rooms opening into the atrium of a Pompeian house are known as cubicula. In modern English schools “cubicle” is the term given to the separate small bedrooms into which the dormitories are divided, as opposed to the system of large open dormitories.
CUBITT, THOMAS(1788-1855), English builder, was born at Buxton, near Norwich, on the 25th of February 1788. Few men have exhibited greater self-reliance in early life in the pursuit of a successful career. In his nineteenth year, when he was working as a journeyman carpenter, his father died, and he tried to better his position by going on a voyage to India, as captain’s joiner. He returned to London, two years after, in the possession of a small capital, and began business as a carpenter. The growth of his establishment was steady and rapid. He was one of the first to combine several trades in a “builder’s” business; and this very much increased his success. One of the earlier works which gave him reputation was the London Institution in Finsbury Circus; but it is from 1824 that the vast building operations date which identify his name with many splendid ranges of London houses, such as Tavistock, Gordon, Belgrave and Lowndes Squares, and the district of South Belgravia. While these and similar extensive operations were in progress, a financial panic, which proved ruinous to many, was surmounted in his case by a determined spirit and his integrity of character. He took great interest in sanitary measures, and published, for private circulation, a pamphlet on the general drainage of London, the substance of which was afterwards embodied in a letter toThe Times; the plan he advocated was subsequently adopted by the conveyance of the sewage matter some distance below London. He advocated the provision of open spaces in the environs of London as places of public recreation, and was one of the originators of Battersea Park, the first of the people’s parks. At a late period he received professionally the recognition of royalty, the palace at Osborne being erected after his designs, and under his superintendence; and in theLife of the Prince Consorthe is described by Queen Victoria as one “than whom a better and kinder man did not exist.” In 1851, although he was not identified with the management of the Great Exhibition, he showed the warmest sympathy with its objects, and aided its projectors in many ways, especially in the profitable investment of their surplus funds. Cubitt, when he rose to be a capitalist, never forgot the interests and well-being of his workpeople. He was elected president of the Builders’ Society some time before his death, which took place at his seat Denbies, near Dorking, on the 20th of December 1855.
His son, George Cubitt (1828- ), who had a long and useful parliamentary career, as Conservative member for West Surrey (1860-1865) and Mid-Surrey (1885-1892), was in 1892 raised to the peerage as Baron Ashcombe.
CUBITT, SIR WILLIAM(1785-1861), English engineer, was born in 1785 at Dilham in Norfolk, where his father was a miller. After serving an apprenticeship of four years (1800-1804) as a joiner and cabinetmaker at Stalham, he became associated with an agricultural-machine maker, named Cook, who resided at Swanton. In 1807 he patented self-regulating sails for windmills, and in 1812 he entered the works of Messrs Ransome of Ipswich, where he soon became chief engineer, and ultimately a partner. Meanwhile, the subject of the employment of criminals had been much in his thoughts; and the result was his introduction of the treadmill about 1818. In 1826 he removed to London, where he gained a very large practice as a civil engineer. Among his works were the Oxford canal, the Birmingham & Liverpool Junction Canal, the improvement of the river Severn, the Bute docks at Cardiff, the Black Sluice drainage and its outfall sluice at Boston harbour, the Middlesborough docks and coal drops in the Tees, and the South-Eastern railway, of which he was chief engineer. The Hanoverian government consulted him about the harbour and docks at Harburg; the water-works of the city of Berlin were constructed under his immediate superintendence; he was asked to report on the construction of the Paris & Lyons railway; and he was consulting engineer for the line from Boulogne to Amiens. Among his later works were two floating landing stages at Liverpool, and the bridge for carrying the London turnpike across the Medway at Rochester. In 1851, when he was president of the Institution of Civil Engineers, he was knighted for his services in connexion with the buildings erected in Hyde Park for the exhibition of that year.He retired from active work in 1858, and died on the 13th of October 1861 at his house on Clapham Common, London. His son, Joseph Cubitt (1811-1872), was trained under him, and was engineer of various railways, including the Great Northern, London, Chatham & Dover, and part of the London & South-Western.
CUCHULINN(Cūchúlinn; pronounced “Coohoollin”), the chief warrior in the Conchobar-Cuchulinn or older heroic (Ulster) cycle of Ireland. The story of his origin is very obscure. The god Lug is represented as having been swallowed in a draught of wine by his mother Dechtire, sister of Conchobar, who was king of Ulster. But it is not unlikely that this story was invented to supersede the account of the incestuous union of Conchobar with his sister, which seems to be hinted at on various occasions. Usually, however, he is styled son of Sualdam, an Ulster warrior who plays a very inferior part in the cycle. His earliest name was Setanta, and he was brought up at Dun Imbrith (Louth). When he was six years of age he announced his intention of going to Conchobar’s court at Emain Macha (Navan Rath near Armagh) to play with the boys there. He defeats all the boys in marvellous fashion and is received as one of their number. Shortly after he kills Culann, the smith’s hound, a huge watch-dog. The smith laments that all his property is of no value now that his watchman is slain, whereupon the young hero offers to guard his domains until a whelp of the hound’s has grown. From this the boy received the name of Cū Chulinn or Culann’s Hound. The next year Cuchulinn receives arms, makes his first foray, and slays the three sons of Necht, redoubtable hereditary foes of the Ulstermen, in the plain of Meath. The men of Ulster decide that Cuchulinn must marry, as all the women of Ireland are in love with him. Chosen envoys fail to find a bride worthy of him after a year’s search, but the hero goes straight to Emer, the daughter of Forgall the Wily, at Lusk (county Dublin). The lady is promised to him if he will go to learn chivalry of Domnall the Soldierly and the amazon Scathach in Alba. After enduring great hardships he goes through the course and leaves a son Connlaech behind in Scotland by another amazon, Aife. On his return he carries off and weds Emer. He is represented as living at Dun Delgan (Dundalk). The greatest of all the hero’s achievements was the defence of the frontier of Ulster against the forces of Medb, queen of Connaught, who had come to carry off the famous Brown Bull of Cualnge (Cooley). The men of Ulster were all suffering from a strange debility, and Cuchulinn had to undertake the defence single-handed from November to February. This was when he was seventeen years of age. The cycle contains a large number of episodes, such as the gaining of the champion’s portion and the tragical death by the warrior’s hand of his own son Connlaech. When he was twenty-seven he met with his end at the hands of Lugaid, son of Cūrōi MacDaire, the famous Munster warrior, and the children of Calatīn Dāna, in revenge for their father’s death (seeCelt:Irish Literature).
Medieval Christian synchronists make Cuchulinn’s death take place about the beginning of the Christian era. It is not necessary to regard Cuchulinn as a form of the solar hero, as some writers have done. Most, if not all, of his wonderful attributes may be ascribed to the Irish predilection for the grotesque. It is true that Cuchulinn seems to stand in a special relation to the Tuatha De Danann leader, the god Lug, but in primitive societies there is always a tendency to ascribe a divine parentage to men who stand out pre-eminently in prowess beyond their fellows.