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 plusieurs points de l’astronomie égyptienne (1823); Recherches sur l’ancienne astronomie chinoise (1840); Études sur l’astronomie indienne et sur l’astronomie chinoise (1862); Essai sur l’histoire générale des sciences pendant la Révolution (1803); Discours sur Montaigne (1812); Lettres sur l’approvisionnement de Paris et sur le commerce des grains (1835); Mélanges scientifiques et littéraires (1858).

His son, (1803–1850), after amassing a competence from railway engineering, turned to the study of Chinese subjects, and published Causes de l’abolition de l’esclavage ancien en occident (1840); Dictionnaire des noms anciens et modernes des villes et des arrondissements compris dans l’empire chinois (1842); Essai sur l’histoire de l’instruction publique en Chine et de la corporation des lettres (1847); Mémoire sur les colonies militaires et agricoles des chinois (1850).  BIOTITE, an important rock-forming mineral belonging to the group of s (q.v.). The name was given by J. F. L. Hausmann in 1847 in honour of the French physicist, J. B. Biot, who in 1816 found the magnesia-micas to be optically uniaxial or nearly so. The magnesia-micas are now referred to the species biotite and phlogopite, which differ in that the former contains a considerable but widely varying amount of iron. Biotite is an orthosilicate of aluminium, magnesium, ferrous and ferric iron, potassium and basic hydrogen, with small amounts of calcium, sodium, lithium, fluorine, titanium, &c., and ranges in composition between (H, K)2(Mg, Fe)4(Al, Fe)2(SiO4)4 and (H, K)2(Mg, Fe)2Al2(SiO4)3.

Like the other micas, it is monoclinic with pseudo-hexagonal symmetry (figs. 1, 2) and possesses a perfect cleavage in one direction (c). Biotite is, however, readily distinguished by its darker colour, strong pleochroism, and small optic axial angle. The colour is usually dark-green or brown; thick crystals are often deep-black and opaque. The absorption of light-rays vibrating parallel to the cleavage is much greater than of rays vibrating in a direction perpendicular thereto, and in dark-coloured crystals the former are almost completely absorbed. The angle between the optic axes is usually very small, the crystals being often practically uniaxial; an axial angle of 50° has, however, been recorded in a dark-coloured biotite. The specific gravity of biotite is, as a rule, higher than that of other micas, varying from 2·7 to 3·1 according to the amount of iron present. The hardness is 2 to 3.

Several varieties of biotite are distinguished. By G. Tschermak it is divided into two classes, meroxene and anomite; in the former the plane of the optic axis coincides with the plane of symmetry, whilst in the latter it is perpendicular thereto. Meroxene includes nearly all ordinary biotite, and is the name given by A. Breithaupt in 1841 to the Vesuvian crystals; on the other hand, anomite (named from , “contrary to law”) is of rare occurrence. Haughtonite and siderophyllite are black varieties rich in ferrous iron, and lepidomelane (from , a scale, and  , black) is a variety rich in ferric iron. In barytobiotite and manganophyllite the magnesia is partly replaced by baryta and manganous oxide respectively. Rubellane, hydrobiotite, pseudobiotite, and others are altered forms of biotite, which is a mineral particularly liable to decomposition with the production of chlorites and vermiculites.

Biotite is a common constituent of igneous and crystalline rocks; in granite, gneiss and mica-schist it is often associated with muscovite (white mica), the two kinds having sometimes grown in parallel position. In volcanic rocks, and in nearly all other kinds of igneous rocks with the exception of granite, biotite occurs to the exclusion of the muscovite. In the dyke-rocks known as mica-traps or mica-lamprophyres biotite is especially abundant. It is also one of the most characteristic products of contact-metamorphism, being developed in sedimentary and other rocks at their contact with granite masses. In the ejected blocks of crystalline limestone of Monte Somma, Vesuvius, the most perfectly developed crystals of biotite (figs. 1, 2), or indeed of any of the micas, are found in abundance, associated with brilliant crystals of augite, olivine, humite, &c.

Although biotite (black mica) is much more common and widely distributed than white mica, yet it is of far less economic importance. The small size of the sheets, their dark colour and want of transparency render the material of little value. Large, cleavable masses yielding fine smoky-black and green sheets, sufficiently elastic for industrial purposes, are, however, found in Renfrew county, Ontario.  BIPARTITE (from the Lat. bi-, two, and partire, to divide). In a general sense, the word means having two corresponding parts or in duplicate. In geometry, a bipartite curve consists of two distinct branches (see, figs. 3, 5). In botany, the word is applied to leaves divided into two parts near the base. A bipartient factor is a number whose square exactly divides another number. In zoology, the Bipartiti was a name given by P. A. Latreille to a group of carnivorous Coleoptera.  BIPONT EDITIONS, the name of a famous series of editions, in 50 volumes, of Greek and Latin classical authors, so called from Bipontium, the modern Latin name of Zweibrücken or Deux-Ponts in Bavaria, where they were first issued in 1779. Their place of publication was afterwards transferred to Strassburg.

 BIQUADRATIC (from the Lat. bi-, bis, twice, and quadratus, squared). In mathematics, the biquadratic power or root of a quantity is its fourth power or root (see ); a biquadratic equation is an equation in which the highest power of the unknown is the fourth (see : Biquadratic).  BIQUINTILE (from Lat. prefix bi-, twice, quintilis, fifth), the aspect of two planets which are distant from each other twice the fifth part of a great circle, i.e. 144°. It was one of the new aspects introduced by Kepler.  <section begin="Birbhum" />BIRBHUM, a district of British India in the Burdwan division of Bengal, situated in the Gangetic plain and partly on the hills, being bounded on the south by the river Ajai. The administrative headquarters are at Suri, which is the only town in the district. The area comprises 1752 sq. m. The eastern portion of the district is the ordinary alluvial plain of the Gangetic delta; the western part consists of undulating beds of laterite resting on a rock basis, and covered with small scrub jungle. The Ajai, Bakheswar and Mor or Maurakshi, are the principal rivers of the district, but they are merely hill streams and only navigable in the rains. In 1901 the population was 902,280, showing an increase of 13% in the decade. The principal industry is the spinning and weaving of silk, chiefly from tussur or jungle silkworms. There are also several lac factories. The loop-line of the East Indian railway runs through the district, with a junction at Nalhati for Murshidabad.

History.—Birbhum in the early part of the 13th century was a Hindu state, with its capital at Rajnagar or Nagar. In the course of the century it was conquered by the Pathans and formed part of the Pathan kingdom of Bengal. At the beginning of the 18th century it appears as a kind of military fief held under the nawab of Murshidabad by one Asadullah Pathan, whose family had probably been its chieftains since the fall of the Pathan dynasty of Bengal in 1600. It passed into British possession in 1765, but the East India Company did not assume its direct government until 1787, when that course became necessary. In the interval it had been a prey to armed bands from the highlands of Chota Nagpur, with whom the raja was unable to cope, and who practically brought the trade of the Company in the district to a standstill. The two border principalities of Birbhum and Bankura were accordingly united into a district under a British collector, being, however, separated again in 1793. By 1789, after<section end="Birbhum" />