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 borders as of the “Bernician type,” which is the most satisfactory way in which the term may now be used (Report of the Brit. Sub-committee on Classification and Nomenclature, 2nd ed., Cambridge, 1888). “Demetian” was the corresponding designation proposed by Woodward for the Upper Carboniferous rocks.  BERNINI, GIOVANNI LORENZO (1598–1680), Italian artist, was born at Naples. He was more celebrated as an architect and a sculptor than as a painter. At a very early age his great skill in modelling introduced him to court favour at Rome, and he was specially patronized by Maffeo Barberini, afterwards Pope Urban VIII., whose palace he designed. None of his sculptured groups at all come up to the promised excellence of his first effort, the Apollo and Daphne, nor are any of his paintings of particular merit. His busts were in so much request that Charles I. of England, being unable to have a personal interview with Bernini, sent him three portraits by Vandyck, from which the artist was enabled to complete his model. His architectural designs, including the great colonnade of St Peter’s, brought him perhaps his greatest celebrity. Louis XIV., when he contemplated the restoration of the Louvre, sent for Bernini, but did not adopt his designs. The artist’s progress through France was a triumphal procession, and he was most liberally rewarded by the great monarch. He left a fortune of over £100,000.  BERNIS, FRANÇOIS JOACHIM DE PIERRE DE (1715–1794), French cardinal and statesman, was born at St Marcel-d’Ardèche on the 22nd of May 1715. He was of a noble but impoverished family, and, being a younger son, was intended for the church. He was educated at the Louis-le-Grand college and the seminary of Saint-Sulpice, Paris, but did not take orders till 1755. He became known as one of the most expert epigrammatists in the gay society of Louis XV.’s court, and by his verses won the friendship of Madame de Pompadour, the royal mistress, who obtained for him an apartment, furnished at her expense, in the Tuileries, and a yearly pension of 1500 livres (about £60). In 1751 he was appointed to the French embassy at Venice, where he acted, to the satisfaction of both parties, as mediator between the republic and Pope Benedict XIV. During his stay in Venice he received subdeacon’s orders, and on his return to France in 1755 was made a papal councillor of state. He took an important part in the delicate negotiations between France and Austria which preceded the Seven Years’ War. He regarded the alliance purely as a temporary expedient, and did not propose to employ the whole forces of France in a general war. But he was overruled by his colleagues. He became secretary for foreign affairs on the 27th of June 1757, but owing to his attempts to counteract the spendthrift policy of the marquise de Pompadour and her creatures, he fell into disgrace and was in December 1758 banished to Soissons by Louis XV., where he remained in retirement for six years. In the previous November he had been created cardinal by Clement XIII. On the death of the royal mistress in 1764, Bernis was recalled and once more offered the seals of office, but declined them, and was appointed archbishop of Albi. His occupancy of the see was not of long duration. In 1769 he went to Rome to assist at the conclave which resulted in the election of Clement XIV., and the talent which he displayed on that occasion procured him the appointment of ambassador in Rome, where he spent the remainder of his life. He was partly instrumental in bringing about the suppression of the Jesuits, and acted with greater moderation than is generally allowed. He lost his influence under Pius VI., who was friendly to the Jesuits, and the French Revolution, to which he was hostile, reduced him almost to penury; the court of Spain, however, mindful of the support he had given to their ambassador in obtaining the condemnation of the Jesuits, came to his relief with a handsome pension. He died at Rome on the 3rd of November 1794, and was buried in the church of S. Luigi de’ Francesi. In 1803 his remains were transferred to the cathedral at Nîmes. His poems, the longest of which is La Religion vengée (Parma, 1794), have no merit; they were collected and published after his death (Paris, 1797, &c.); his Mémoires et lettres 1715–58 (2 vols., Paris, 1878) are still interesting to the historian.

 BERNKASTEL, a town of Germany, in the Prussian Rhine province, on the Mosel, in a deep and romantic valley, connected by a branch to Wengerohr with the main Trier-Coblenz railway. Pop. 2300. It has some unimportant manufactures; the chief industry is in wine, of which Berncastler Doctor enjoys great repute. Above the town lie the ruins of the castle Landshut. Bernkastel originally belonged to the chapter of Trier, and received its name from one of the provosts of the cathedral, Adalbero of Luxemburg (hence Adalberonis castellum).  BERNOULLI, or, the name of an illustrious family in the annals of science, who came originally from Antwerp. Driven from their country during the oppressive government of Spain for their attachment to the Reformed religion, the Bernoullis sought first an asylum at Frankfort (1583), and afterwards at Basel, where they ultimately obtained the highest distinctions. In the course of a century eight of its members successfully cultivated various branches of mathematics, and contributed powerfully to the advance of science. The most celebrated were Jacques (James), Jean (John) and Daniel, the first, second and fourth as dealt with below; but, for the sake of perspicuity they may be considered as nearly as possible in the order of family succession. A complete summary of the great developments of mathematical learning, which the members of this family effected, lies outside the scope of this notice. More detailed accounts are to be found in the various mathematical articles.

I. (1654–1705), mathematician, was born at Basel on the 27th of December 1654. He was educated at the public school of Basel, and also received private instruction from the learned Hoffmann, then professor of Greek. At the conclusion of his philosophical studies at the university, some geometrical figures, which fell in his way, excited in him a passion for mathematical pursuits, and in spite of the opposition of his father, who wished him to be a clergyman, he applied himself in secret to his favourite science. In 1676 he visited Geneva on his way to France, and subsequently travelled to England and Holland. While at Geneva he taught a blind girl several branches of science, and also how to write; and this led him to publish A Method of Teaching Mathematics to the Blind. At Bordeaux his Universal Tables on Dialling were constructed; and in London he was admitted to the meetings of Robert Boyle, Robert Hooke and other learned and scientific men. On his final return to Basel in 1682, he devoted himself to physical and mathematical investigations, and opened a public seminary for experimental physics. In the same year he published his essay on comets, Conamen Novi Systematis Cometarum, which was occasioned by the appearance of the comet of 1680. This essay, and his next publication, entitled De Gravitate Aetheris, were deeply tinged with the philosophy of René Descartes, but they contain truths not unworthy of the philosophy of Sir Isaac Newton’s Principia.

Jacques Bernoulli cannot be strictly called an independent discoverer; but, from his extensive and successful application of the calculus and other mathematical methods, he is deserving of a place by the side of Newton and Leibnitz. As an additional claim to remembrance, he was the first to solve Leibnitz’s problem of the isochronous curve (Acta Eruditorum, 1690). He proposed the problem of the (q.v.) or curve formed by a chain suspended by its two extremities, accepted Leibnitz’s construction of the curve and solved more complicated problems relating to it. He determined the “elastic curve,” which is formed by an elastic plate or rod fixed at one end and bent by a weight applied to the other, and which he showed to be the same as the curvature of an impervious sail filled with a liquid (lintearia). In his investigations respecting cycloidal lines and various spiral curves, his attention was directed to the loxodromic and logarithmic spirals, in the last of which he took particular interest from its remarkable property of reproducing itself under a variety of conditions.