(Stephen), a celebrated French mathematician, member of the Academies of Sciences and the Marine, and examiner of the guards of the marine and of the elevens of artillery, was born at Nemours the 31st of March 1730. In the course of his studies he met with some books of geometry, which gave him a taste for that science; and the Eloges of Fontenelle, showed him the honours attendant on talents and the love Binomial, a quantity consisting of two terms or members, connected by either of the signs + and −.

See Algebra, def. 9. Encycl.

Impossible or Imaginary Binomial, is a binomial which has one of its terms an impossible or an imaginary quantity; as \(a + \sqrt{-b}\).

Binomial Curve, is a curve whose ordinate is expressed by a binomial quantity, as the curve whose ordinate is \(x^2 + bx + c\). Stirling, Method Diff. p. 58.

Binomial Line, or Surd, is that in which at least one of the parts is a surd. Euclid, in the tenth book of his Elements, enumerates five kinds of binomial lines or surds, viz:

1st binomial \(3 + \sqrt{5}\), 2nd binomial \(18 + 4\), 3rd binomial \(24 + \sqrt{18}\), 4th binomial \(4 + \sqrt{3}\), 5th binomial \(6 + 2\), 6th binomial \(6 + \sqrt{2}\).

Binomial Theorem. See Algebra, Chap. VII, Sect. iii. (Encycl. Vol. I); and Infinite Series, (Vol. XVII.) The reader who wishes for a fuller account of this famous theorem, may find it in Dr Hutton's Mathematical Tracts, Vol. I.

Bird-catching, is an art which, as it is practised by means of bird-lines, nets, decoys, &c., has been sufficiently explained in the Encyclopedia. But there is another method of catching birds alive, by means of a fusee or musket, which was invented by M. Vaillant during his travels in Africa, and is sufficiently ingenious to deserve a place here. It is as follows:

Put a smaller or larger quantity of powder into your fusee according as circumstances may require. Immediately above the powder place the end of a candle of sufficient thickness, ramming it well down; and then fill the barrel with water up to the mouth. When at a proper distance you fire a musket thus loaded at a bird, you will only blow it by watering and moistening its feathers; and if you be silent, you may easily lay hold of it before it have time to spoil its plumage by fluttering. Our author admits, that in his first attempts he often put too much powder, or too thick a piece of candle into his fusee, or fired at too short a distance; and when any one of these mistakes was committed, he generally found the candle entire in the animal's belly; but after a short apprenticeship he acquired sufficient skill to adjust matters so as that the water impelled by the powder went directly to the mark, whilst the tallow being lighter than the water fell short of it. If this method be indeed practicable (for not being sportmen we have not made trial of it), it may on many occasions aid the researches of the ornithologist.

Birds' Nests, in cookery. See Encycl. and Car and Button in this Suppl.

Blacklock (Dr Thomas) deserves, on so many accounts, to have the principal incidents of his life recorded in this work, that to omit such an article from our list of biographical sketches would be unpardonable negligence. We cannot, however, propose to write of him anything which has not been written before, by an author who has repeatedly appeared before the public, and on each appearance has gained possession of the public heart. We shall therefore content ourselves with inferring in this place a short abridgment of the elegant account of the life and writings of Dr Blacklock, which was prefixed to that edition of his works which was published in 1793; and if we thus lessen our own labour, we are conscious that we shall at the same time increase the pleasure of our readers.

Thomas Thomas Blacklock was in 1721 born at Aman, in the county of Dumfries in Scotland, but his parents were natives of the bordering county of Cumberland; so that, though a native of Scotland, his descent was English. His father was a bricklayer, and his mother the daughter of a considerable dealer in cattle. Both were respectable in their characters, and polite, tho' moving in an humble sphere, a considerable degree of knowledge and urbanity. Their son was not quite six months old when he lost his eye-sight in the small-pox, which rendered him as complete a stranger to the visible world as if he had been blind from the hour of his birth. It rendered him likewise incapable of learning any of the mechanical arts; and therefore his father kept him at home, and with the assistance of some friends fostered that inclination which, at a very early period, he showed for books. This was done by reading to him first the simple sort of publications which are commonly put into the hands of children, and then several of our best authors, such as Milton, Spencer, Prior, Pope, and Addison. His companions, whom his early gentleness and kindness of disposition, as well as their compassion for his misfortune, strongly attached to him, were very afflicious in their good offices, in reading to instruct and amuse him. By their assistance he acquired some knowledge of the Latin tongue, but he never was at a grammar school till at a more advanced period of life. Poetry was even then his favourite reading; and he found an enthusiastic delight in the works of the best English poets, and in those of his countryman Allan Ramsay. Even at an age so early as twelve he began to write poems, one of which is preserved in the collection that was published after his death, and is not perhaps inferior to any of the premature compositions of boys afflicted by the best education, which are only recalled into notice by the future fame of their authors.

He had attained the age of nineteen when his father was killed by the accidental fall of a malt kiln belonging to his son-in-law. This loss, heavy to any one at that early age, would have been, however, to a young man possessing the ordinary means of support, and the ordinary advantages of education, comparatively light; but to him—thus suddenly deprived of that support on which his youth had leaned—destitute almost of every resource which industry affords to those who have the blessings of sight—with a body feeble and delicate from nature, and a mind congenially susceptible—it was not surprising that this blow was doubly severe, and threw on his spirits that despondent gloom to which he then gave way in the following pathetic lines, and which sometimes overclouded them in the subsequent period of his life.

"Dejecting prospect! soon the hapless hour May come; perhaps this moment it impends, Which drives me forth to penury and cold, Naked, and beat by all the storms of heav'n, Friendless and guideless to explore my way; Till, on cold earth this poor unfelter'd head Reclining, vainly from the ruthless blast Reprie I beg, and in the shock expire."

He lived with his mother for about a year after his father's death, and began to be distinguished as a young man of uncommon parts and genius. There were at that time unafflicted by learning; the circumstances of his family affording him no better education than the flattery of Latin which his companions had taught him, and the perusal and recollection of the few English authors which they, or his father in the intervals of his professional labours, had read to him. Poetry, however, though it attains its highest perfection in a cultivated soul, grows perhaps as luxuriantly in a wild one. To poetry, as we have before mentioned, he was devoted from his earliest days; and about this time several of his poetical productions began to be handed about, which considerably enlarged the circle of his friends and acquaintance. Some of his compositions being shown to Dr Stevenson, an eminent physician of Edinburgh, who was accidentally at Dumfries on a professional visit, that gentleman formed the benevolent design of carrying him to the Scotch metropolis, and giving to his natural endowments the assistance of a classical education. He came to Edinburgh in the year 1741, and was enrolled a student of divinity in the university there, though at that time without any particular view of entering into the church. In that university he continued his studies under the patronage of Dr Stevenson till the year 1745, when he retired to Dumfries, and resided in the house of Mr MacMurdie, who had married his sister, during the whole time of the civil war, which then raged in the country, and particularly disturbed the tranquility of the metropolis. When peace was restored to the nation, he returned to the university, and pursued his studies for five years longer. During this last residence in Edinburgh, he obtained, among other literary acquaintance, that of the celebrated David Hume, who attached himself warmly to Mr Blacklock's interests, and was afterwards particularly useful to him in the publication of the 4th edition of his Poems, which came out by subscription in London in the year 1756. Previously to this, two editions in 8vo had been published at Edinburgh, the first in 1746, and the second in 1754.

In the course of his education at Edinburgh, he acquired a proficiency in the learned languages, and became more a master of the French tongue than was then common in that city. For this last acquisition he was chiefly indebted to the social intercourse to which he had the good fortune to be admitted in the house of Provost Alexander, who had married a native of France. At the university he attained a knowledge of the various branches of philosophy and theology, to which his course of study naturally led, and acquired at the same time a considerable fund of learning and information in those various departments of science and belles lettres, from which his want of sight did not absolutely preclude him.

In 1757, he began a course of study, with a view to give lectures in oratory to young gentlemen intended for the bar or the pulpit. On this occasion he wrote to Mr Hume, informed him of his plan, and requested his assistance in the prosecution of it. But Mr Hume doubting the probability of its success, he abandoned the project; and then, for the first time, adopted the decided intention of going into the church of Scotland. After applying closely for a considerable time to the study of theology, he passed the usual trials in the presbytery of Dumfries, and was by that presbytery licensed a preacher of the gospel in the year 1759. As a preacher he obtained high reputation, and was fond of composing The tenor of his occupations, as well as the bent of his mind and dispositions, during this period of his life, will appear in the following plain and unaltered account, contained in a letter from a gentleman, who was then his most intimate and constant companion, the Rev. Mr. Jamison, formerly minister of the Episcopal chapel at Dumfries, afterwards of the English congregation at Danzig, and who lately resided, and perhaps yet resides, at Newcastle upon Tyne.

"His manner of life (says that gentleman) was so uniform, that the history of it during one day, or one week, is the history of it during the seven years that our personal intercourse lasted. Reading, music, walking, conversing, and disputing on various topics, in theology, ethics, &c., employed almost every hour of our time. It was pleasant to hear him engaged in a dispute; for no man could keep his temper better than he always did on such occasions. I have known him frequently very warmly engaged for hours together, but never could observe one angry word to fall from him. Whatever his antagonist might say, he always kept his temper. 'Semper paratus et refellere sine pertinacia, et refellere sine iracundia.' He was, however, extremely sensible to what he thought ill usage, and equally so whether it regarded himself or his friends. But his resentment was always confined to a few satirical verses, which were generally burnt soon after.

"I have frequently admired with what readiness and rapidity he could sometimes make verses. I have known him dictate from thirty to forty verses and by no means bad ones, as fast as I could write them; but the moment he was at a loss for a rhyme or a verse to his liking, he flopped altogether, and could very seldom be induced to finish what he had begun with so much ardour."

This account sufficiently marks that eager sensibility, chafed at the same time with uncommon gentleness of temper, which characterized Dr. Blacklock, and which indeed it was impossible to be at all in his company without perceiving. In the science of mind, this is that division of it which perhaps one would peculiarly appropriate to poetry, at least to all those lighter species which rather depend on quickness of feeling, and the ready conception of pleasing images, than on the happy arrangement of parts, or the skilful construction of a whole, which are essential to the higher departments of the poetical art. The first kind of talent is like those warm and light foils which produce their annual crops in such abundance; the last, like that deeper and firmer mould on which the roots of eternal forests are fixed. Of the first we have seen many happy instances in that sex which is supposed less capable of study or thought; from the last is drawn that masculine sublimity of genius which could build an Iliad or a Paradise Lost.

Dr. Blacklock could never dictate till he flooded up; and as his blindness made walking about without assistance inconvenient or dangerous to him, he fell insensibly into a vibratory sort of motion of his body, which increased as he warmed with his subject, and was pleased with the conceptions of his mind. This motion at last became habitual to him; and though he could sometimes restrain it when on ceremony, or on any public appearance, such as preaching, he felt a certain uneasiness from the effort, and always returned to it when he could without impropriety. This appearance he describes in a short poem, in which he gives a ludicrous picture of himself; a picture indeed, of which, though the outlines are true, the general effect is greatly overcharged. Though his features were hurt by the disease which deprived him of sight, there was a certain placid expression in his countenance, which marked the benevolence of his heart, and was calculated to procure to him individual attachments and general regard.

In 1762 he married Miss Sarah Johnston, daughter of Mr. Joseph Johnston surgeon in Dumfries; a connection which formed the great solace and blessing of his future life, and gave him, with all the tenderness of a wife, all the zealous care of a guardian and a friend. This event took place a few days before his being ordained minister of the town and parish of Kirkgunzeon, in consequence of a presentation from the crown, obtained for him by the earl of Selkirk, a benevolent nobleman, whom Mr. Blacklock's situation and genius had interested in his behalf. But the inhabitants of the parish, whether from that violent aversion to patronage, which was then so universal in the southern parts of Scotland, from some political disputes which at that time subsisted between them and his noble patron, or from those prejudices which some of them might naturally enough entertain against a pastor deprived of sight, or perhaps from all these causes united, were so extremely disinclined to receive him as their minister, that after a legal dispute of nearly two years, it was thought expedient by his friends, as it had always been wished by himself, to compromise the matter, by resigning his right to the living, and accepting a moderate annuity in its stead. With this slender provision he removed in 1764 to Edinburgh; and to make up by his industry a more comfortable and decent subsistence, he adopted the plan of receiving a certain number of young gentlemen as boarders into his house, whose studies in languages and philosophy he might, if necessary, assist. In this situation he continued till the year 1787, when he found his time of life and state of health required a degree of quiet and repose which induced him to discontinue the receiving of boarders. In 1767 the degree of doctor in divinity was conferred on him by the university and Marischal college of Aberdeen.

In the occupation which he thus exercised for so many years of his life, no teacher was perhaps ever more agreeable to his pupils, nor master of a family to its inmates, than Dr. Blacklock. The gentleness of his manners, the benignity of his disposition, and that warm interest in the happiness of others which led him to constantly promote it, were qualities that could not fail to procure him the love and regard of the young people committed to his charge; while the society, which esteem and respect for his character and his genius often assembled at his house, afforded them an advantage rarely to be found in establishments of a similar kind.

In this mixed society he appeared to forget the privation of sight, and the melancholy which it might at other times produce in his mind. He entered, with the cheerful playfulness of a young man, into all the sprightly narrative, the sportful fancy, and the humorous jest that rose around him. Next to conversation, music was perhaps the source of his greatest delight; for he not only relished it highly, but was himself a tolerable performer on several instruments, particularly the flute. He generally carried in his pocket a small flageolet, on which he played his favourite tunes; and was not displeased when asked in company to play or to sing them; a natural feeling for a blind man, who thus adds a scene to the drama of his society.

Of the happinesses of others, however, we are incompetent judges. Companionship and sympathy bring forth those gay colours of mirth and cheerfulness which they put on for a while, to cover perhaps that sadness which we have no opportunity of witnessing. Of a blind man's condition we are particularly liable to form a mistaken estimate; we give him credit for all those gleams of delight which society affords him, without placing to their full account those dreary moments of darksome solitude to which the supposition of that society condemns him. Dr Blacklock had from nature a constitution delicate and nervous, and his mind, as is almost always the case, was in a great degree subject to the indisposition of his body. He frequently complained of a lowness and depression of spirits, which neither the attentions of his friends, nor the unceasing care of a most affectionate wife, were able entirely to remove. The imagination we are so apt to envy and admire serves but to irritate this disorder of the mind; and that fancy in whose creation we so much delight, can draw, from sources unknown to common men, subjects of disgust, disquietude, and affliction. Some of his later poems express a chagrin, though not of an ungentle sort, at the supposed failure of his imaginative powers, or at the satiety of modern times, which he deplored to please.

"Such were his efforts, such his cold reward, "Whom once thy partial tongue pronounced a bard; "Excursive, on the gentle gales of spring, "He rov'd, whilst favour imp'd his timid wing; "Exhausted genius now no more inspires, "But mourns abortive hopes, and faded fires; "The short-lived wreath, which once his temples grac'd, "Fades at the fickle breath of squamish taste; "Whilest darker days his fainting flames immure "In cheerless gloom and winter prematurity."

These lines are, however, no proof of "exhausted genius," or "faded fires." "Abortive hopes," indeed, must be the lot of all who, like Dr Blacklock, reach the period of old age. In early youth the heart of every one is a poet; it creates a scene of imagined happiness and delusive hopes; it clothes the world in the bright colours of its own fancy; it refines what is coarse, it exalts what is mean; it fees nothing but disinterestedness in friendship, it promises eternal fidelity in love. Even on the distresses of its situation it can throw a certain romantic shade of melancholy that leaves a man sad, but does not make him unhappy. But at a more advanced age, "the fairy visions fade," and he suffers most deeply who has indulged them the most.

About the time that these verses were written, Dr Blacklock was, for the first time, afflicted with what to him must have been peculiarly distressful. He became occasionally subject to deafness, which, though he seldom felt it in any great degree, was sufficient, in his situation, to whom the sense of hearing was almost the only channel of communication with the external world, to cause very lively uneasiness. Amidst these indispositions of body, however, and disquietudes of mind, the gentleness of his temper never forsook him, and he felt all that resignation and confidence in the Supreme Being which his earliest and his latest life equally acknowledged. In summer 1791 he was seized with a feverish disorder, which at first seemed of a slight, and never rose to a very violent kind; but a frame too little robust as his was not able to resist it, and after about a week's illness it carried him off on the 7th day of July 1791. His wife survives him, to feel, amidst the heavy affliction of his loss, that melancholy consolation which is derived from the remembrance of his virtues.

The writings of Dr Blacklock consisted principally of poems, which were published in 4to in the year 1793; and to that edition was added, An Essay on the Education of the Blind, translated from the French of M. Huy. But besides his avowed works, we have reason to believe that he was the author of many articles in the second edition of the Encyclopedia Britannica, though we cannot say with certainty what those articles were. If our memory does not deceive us, we have been informed that the preface to that edition was furnished by him; and we have elsewhere attributed to him, on the best authority, the article Blind, and the Notes to the article Music; but he undoubtedly contributed much more to the work, and was one of the principal guides of the proprietors.