that kind of notation in which unity or 1 and 0 only are used. This was the invention of Leibnitz, who shows it to be very expeditions in discovering the properties of numbers and in constructing tables; and M. Dangecourt, in the History of the Royal Academy of Sciences, gives a specimen of it concerning arithmetical progressions, where he shows, that because in binary arithmetic only two characters are used, therefore the laws of progression may be more easily discovered by it than by common arithmetic. All the characters used in binary arithmetic are 0 and 1; and the cipher multiplies every thing by two, as in the common arithmetic by 10. Thus 1 is one; 10, two; 11, three; 100, four; 101, five; 110, six; 111, seven; 1000, eight; 1001, nine; 1100, ten; which is founded on the same principles with common arithmetic. Hence appears the reason of the celebrated property of the duplicate geometrical proportion in whole numbers, namely, that one number of each degree being taken, we may thence compose all the other whole numbers above the double of the highest degree. For example, 111 being the sum of 4, 2, and 1, or, analytically, of 100 = 4, 10 = 2, and 1 = 1, or 7 in all, this property may serve assayers to weigh all kinds of masses with a little weight; and may be used in coins, to give several values with small pieces. The binary method of expressing numbers once established, all the operations will be easy; in multiplication, particularly, there will be no need for a table, or getting anything by heart. But the inventor does not recommend it for common use, because of the great number of figures required to express a number; adding, that if the common progression were from 12 to 12, or from 16 to 16, it would be still more expeditions; and that its use consists chiefly in discovering the properties of numbers, in constructing tables, and the like. What makes the binary arithmetic the more remark- able is, that it appears to have been the same with that used four thousand years ago among the Chinese, and left as an enigma by Fohi, the founder of their empire as well as of their sciences.

**Binary Measure**, in *Music*, is a measure which is beaten equally, or where the time of rising is equal to that of falling. This is usually called *common time*.

**Binary Number** is that which is composed of two units.

**Bingen**, a town in the grand duchy of Hesse-Darmstadt, province of Rhenish Hesse, and fifteen miles west of Mentz. It is pleasantly situated on the left bank of the Rhine, where that river receives the Nahe. It has a considerable trade in wine, grain, and cattle, and manufactures leather and tobacco. Pop. 4500.

**Bingham, Joseph**, a learned scholar and divine, born at Wakefield in Yorkshire, in September 1668; educated at University College, Oxford; and afterwards, by John Radcliffe, M.D., presented to the rectory of Headbournworthy, near Winchester. In this country retirement he began his laborious and valuable work entitled *Origines Ecclesiasticae*, or Antiquities of the Christian Church, the first volume of which appeared in 1798. It was completed by the publication of the tenth volume in 1722. Notwithstanding his learning and merit, Bingham received no higher preferment than that of Headbournworthy till the year 1712, when he was collated to the rectory of Havant, near Portsmouth, by Sir Jonathan Trelawney, bishop of Winchester. He died August 17, 1723, in his fifty-fifth year.

**Bingham**, a market-town in the hundred of that name, in the county of Nottingham, 123 miles from London, and 8½ from Nottingham. It is situated in the fertile vale of Belvoir, and consists of two parallel well-paved streets, with a fine Gothic church, and a good market-place, in which a market is held on Thursday. Pop. of parish in 1851, 2054.

**Bingley**, a market-town in the west riding of Yorkshire, on the river Aire, 31 miles W.S.W. of York. The inhabitants in 1851 amounted to 5019, principally engaged in manufactures of worsted, cotton, and paper, which have been much improved during the last ten years. The town is well built and flourishing, and has a neat church, grammar-school, and several charities.

**Bink, Jacob**, a German engraver, who also designed well; born about 1500. Bartsch describes 98 prints by him. He seems to have died about 1550.

**Binomial**, in *Algebra*, a root consisting of two factors connected by the sign plus or minus. Thus $a + b$ and $8 - 3$ are binomials, consisting of the sums and differences of these quantities. See *Algebra*.

**Bintang**, one of the Dutch East India islands, S.E. of Singapore, in Lat. 1° 5° N. Long. 104° 30° E. It is about 24 miles in length by 12 in breadth, and is surrounded by numerous rocky islets, which render the navigation dangerous. Its principal exports are pepper, rice, and particularly gambier, from its chief town Rhio on the S.W. coast. Pop. 15,000.

**Biography** (*βίον*, life, and γραφεῖν, a writing), the history of a life. Of this species of literary composition examples are preserved in the earliest records of antiquity. In Sacred Scripture we have the history of the lives of Abraham, Joseph, David, &c. In the first rank in Grecian literature stand the *Parallel Lives* of Plutarch, which comprise the biographies of forty-six of the most celebrated Greeks and Romans who flourished prior to his own time. The *Lives of the Philosophers* by Diogenes Laertius, the *Lives of Philosophers and Sophists* by Eunapius, and the *Lives of the Sophists* by Philostratus, are the other principal works of this class in the Greek language. Among Roman writers of biography the principal are Cornelius Nepos and Suetonius. Besides these there are other writers whose works, though in a certain degree biographical, more strictly belong to the province of history; as, for example, Sallust's Biography account of the conspiracy of Catiline, the *Commentaries* of Julius Caesar, and Quintus Curtius's account of the expedition of Alexander.

In all civilized countries biography has always formed a favourite subject of study. France has been especially prolific in biographical publications, and our own country can show a goodly array of volumes in this department of literature; and, indeed, the same may be said of Italy, Germany, and Spain. To enumerate even the principal works of this class, whether single lives or biographical collections and dictionaries, in any of these languages, would far exceed our limits. We shall therefore content ourselves with a few general reflections on the uses and peculiarities of biographical composition.

It is pleasant no less than instructive to be, as it were, introduced to the companionship of men who have been distinguished in the sphere which they occupied. If they be great and good men, we love to be made acquainted with the motives of their actions, to follow them in their wanderings, to mark the difficulties and the opposition they had to encounter in their honourable struggles through life, the energy and skill by which these were overcome, and the courage that animated them to persevere in their career of usefulness and honour.

If the author honestly exhibit the failings as well as the excellences of his subject, the reader will be warned of the quicksands and dangers that beset the path of life; and should he succeed in portraying aright the attractive lineaments of a virtuous character, he will insensibly arouse in the mind of the reader aspirations after the excellences which he is led to admire. The mind has a tendency to assimilate to the character of those with whom we associate; and to peruse the memoirs of wise and good men is living for the time in their company.

Every man, whatever be his sphere in life, has an influence for good or for evil on the society around him; and he who gives to the world the history of an exemplary life, reproduces in a certain degree the influence which had been extinguished by the hand of death. The biographer not only revives the lost influence, but by the circulation of his narrative he becomes the medium of more extended usefulness, and in some degree a benefactor of mankind.

Where personal character and habits form the principal subject of interest, a stranger stands at too great a distance to give to his portrait a faithful outline or correct colouring; a true picture can only be drawn by one whose friendly intercourse gave opportunity of marking the peculiar characteristics of his subject.

Autobiography, or memoirs of one's self, is preferable to biography only when the writer has something to communicate, by way of confession or explanation; of which no other person is cognizant. But it is almost impossible, nor is it perhaps desirable, that an autobiographer should disclose with unflinching impartiality the whole particulars of his life, and unveil the real motives of his actions.

"Thus conscience does make cowards of us all."

Nevertheless, in autobiography concealment itself is a species of disclosure. The moment a man begins to speak of himself, however cautious his mode of expression, the discerning reader will have little difficulty in appreciating his real character and the quality of his actions. What reader is blind to the bad temper, meanness, and impracticability of Rousseau, notwithstanding his cunning attempts to disguise them? The autobiographer always betrays himself when he least suspects it; he exhibits his greatest weakness when he flatters himself that he is putting forth his strength. The task of the autobiographer is not only delicate but difficult. How frequently does the consciousness of sitting for one's portrait to another alter at once the whole demeanour; but still more marked is the change when a man becomes the limner of his own mental likeness. In short, the obstacles to a successful execution of this experiment are almost insuperable.

Of autobiographies which interest principally as histories of the mind, the examples are rare; but those which are intended to amuse or instruct, as delineations of the times in which the writer lived, are innumerable. Of biography of all kinds the same may be said. The unparalleled increase of this department of literature in our own time may be regarded as one of the most characteristic features of the age; and, as must therefore be the case, the number of obscure or unimportant lives thus chronicled forms an enormous proportion to the histories that are truly deserving of record.