be produced by the continued multiplication of this series m × (m−1) × (m−2) × (m−3)... &c.”
The binomial theorem was thus discovered as a development of John Wallis’s investigations in the method of interpolation. Newton gave no proof, and it was in the Ars Conjectandi (1713) that James Bernoulli’s proof for positive integral values of the exponent was first published, although Bernoulli must have discovered it many years previously. A rigorous demonstration was wanting for many years, Leonhard Euler’s proof for negative and fractional values being faulty, and was finally given by Niels Heinrik Abel.
The multi- (or poly-) nomial theorem has for its object the expansion of any power of a multinomial and was discussed in 1697 by Abraham Demoivre (see Combinatorial Analysis).
References.—For the history of the binomial theorem, see John Collins, Commercium Epistolicum (1712); S. P. Rigaud, The Correspondence of Scientific Men of the 17th Century (1841); M. Cantor, Geschichte der Mathematik (1894–1901).
BINTURONG (Arctictis binturong), the single species of the viverrine genus Arctictis, ranging from Nepal through the Malay Peninsula to Sumatra and Java. This animal, also called the bear-cat, is allied to the palm-civets, or paradoxures, but differs from the rest of the family (Viverridae) by its tufted ears and long, bushy, prehensile tail, which is thick at the root and almost equals in length the head and body together (from 28 to 33 inches). The fur is long and coarse, of a dull black hue with a grey wash on the head and fore-limbs. In habits the binturong is nocturnal and arboreal, inhabiting forests, and living on small vertebrates, worms, insects and fruits. It is said to be naturally fierce, but when taken young is easily tamed and becomes gentle and playful.
BINYON, LAURENCE (1869–), English poet, born at Lancaster on the 10th of August 1869, was educated at St Paul’s school, London, and Trinity College, Oxford, where he won the Newdigate prize in 1890 for his Persephone. He entered the department of printed books at the British Museum in 1893, and was transferred to the department of prints and drawings in 1895, the Catalogue of English Drawings in the British Museum (1898, &c.) being by him. As a poet he is represented by Lyric Poems (1894), Poems (Oxford, 1895), London Visions (2 vols., 1895–1898), The Praise of Life (1896), Porphyrion and other Poems (1898), Odes (1900), The Death of Adam (1903), Penthesilea (1905), Dream come true (1905), Paris and Oenone (1906), a one-act tragedy, and Attila, a poetical drama (1907); as an art critic by monographs on the 17th-century Dutch etchers, on John Crome and John Sell Cotman, contributed to the Portfolio, &c. In 1906 he published the first volume of a series of reproductions from William Blake, with a critical introduction.
See also R. A. Streatfeild, Two Poets of the New Century (1901), and W. Archer, Poets of the Younger Generation (1902).
BIO-BIO, a river of southern Chile, rising in the Pino Hachado pass across the Andes, 38° 45′ S. lat., and flowing in a general north-westerly direction to the Pacific at Concepción, where it is 2 m. wide and forms an excellent harbour. It has a total length of about 225 m., nearly one half of which is navigable.
BIO-BIO, an inland province of southern Chile, bounded N., W. and S. respectively by the provinces of Concepción, Arauco and Malleco, and E. by Argentina. It has an area of 5246 sq. m. of well-wooded and mountainous country, and exports timber to a large extent. The great trunk railway from Santiago S. to Puerto Montt crosses the western part of the province and also connects it with the port of Concepción. The capital, Los Angeles (est. pop. 7777 in 1902) lies 15½ m. E. of this railway and is connected with it by a branch line.
BIOGENESIS (from the Gr. βίος, life, and γένεσις, generation, birth), a biological term for the theory according to which each living organism, however simple, arises by a process of budding, fission, spore-formation of sexual reproduction from a parent organism. Under the heading of Abiogenesis (q.v.) is discussed the series of steps by which the modern acceptance of biogenesis and rejection of abiogenesis has been brought about. No biological generalization rests on a wider series of observations, or has been subjected to a more critical scrutiny than that every living organism has come into existence from a living portion or portions of a pre-existing organism. In the articles Reproduction and Heredity the details of the relations between parent and offspring are discussed. There remains for treatment here a curious collateral issue of the theory. It is within common observation that parent and offspring are alike: that the new organism resembles that from which it has come into existence: in fine, biogenesis is homogenesis. Every organism takes origin from a parent organism of the same kind. The conception of homogenesis, however, does not imply an absolute similarity between parent and organism. In the first place, the normal life-cycle of plants and animals exhibits what is known as alternation of generations, so that any individual in the chain may resemble its grand-parent and its grand-child, and differ markedly from its parent and child. Next, any organism may pass through a series of free-living larval stages, so that the new organism at first resembles its parent only very remotely, corresponding to an early stage in the life-history of that parent. (See Embryology, Larval Forms and Reproduction.) Finally, the conception of homogenesis does not exclude the differences between parent and offspring that continually occur, forming the material for the slow alteration of stocks in the course of evolution (see Variation and Selection). Homogenesis means simply that such organism comes into existence directly from a parent organism of the same race, and hence of the same species, sub-species, genus and so forth.
From time to time there have been observers who have maintained a belief in the opposite theory, to which the name heterogenesis has been given. According to the latter theory, the offspring of a given organism may be utterly different from itself, so that a known animal may give rise to another known animal of a different race, species, genus, or even family, or to a plant, or vice versa. The most extreme cases of this belief is the well-known fable of the “barnacle-geese,” an illustrated account of which was printed in an early volume of the Royal Society of London. Buds of a particular tree growing near the sea were described as producing barnacles, and these, falling into the water, were supposed to develop into geese. The whole story was an imaginary embroidery of the facts that barnacles attach themselves to submerged timber and that a species of goose is known as the bernicle goose. In modern times the exponents of heterogenesis have limited themselves to cases of microscopic animals and plants, and in most cases, the observations that they have brought forward have been explained by minuter observation as cases of parasitism. No serious observer, acquainted with modern microscopic technical methods, has been able to confirm the explanation of their observations given by the few modern believers in heterogenesis. (P. C. M.)
BIOGRAPHY (from the Gr. βίος, life, and γράφη, writing), that form of history which is applied, not to races or masses of men, but to an individual. The earliest use of the word βιογραφία is attributed to Damascius, a Greek writer of the beginning of the 6th century, and in Latin biographia was used, but in English no earlier employment of the word, “biography” has been traced than that of Dryden in 1683, who uses it to describe the literary work of Plutarch, “the history of particular men’s lives.” It is obvious that this definition is necessary, for biography is not the record of “life” in general, but of the life of a single person. The idea of the distinction between this and history is a modern thing; we speak of “antique biography,” but it is doubtful whether any writer of antiquity, even Plutarch, clearly perceived its possible existence as an independent branch of literature. All of them, and Plutarch certainly, considered the writing of a man’s life as an opportunity for celebrating, in his person, certain definite moral qualities. It was in these, and not in the individual characteristics of the man, that his interest as a subject of biography resided.
The true conception of biography, therefore, as the faithful portrait of a soul in its adventures through life, is very modern.