abbot of Richenou, in the diocese of Constance, who flourished about the year 1008, is celebrated as a poet, rhetor, musician, philosopher, and divine. He was the author of several treatises on music, particularly of one De Instrumentis Musicalibus, beginning with the words Musicae non est content! which he dedicated to Arrabon, Archbishop of Mentz. He also wrote De Mensura Monochordi. But the most celebrated of his works is a treatise De Musica seu Toni, which he wrote and dedicated to Pellegrino archbishop of Cologne, beginning Vero mandi iift advene et peregrina. This latter tract is part of the Balioi manuscript, and follows the Enchiridion of Ordo: it contains a summary of the doctrines delivered by Boetius, an explanation of the ecclesiastical tones, intermixed with frequent exhortations to piety, and the application of music to religious purposes. He was highly favoured by the emperor Henry II. for his great learning and piety; and succeeded so well in his endeavours to promote learning, that his abbey of Richenou was as famous in his time as those of St Gaul and Cluny, then the most celebrated in France. He died in 1048; and was interred in the church of his monastery, which but a short time before he had dedicated to St Mark.

BERNOULLI (James), a celebrated mathematician, born at Basle the 27th of December 1654. Having taken his degrees in the university of Basle, he applied himself to divinity, not so much from inclination as complaisance to his father. He gave very early proofs of his genius for mathematics, and soon became a geometrician, without any affluence from matters, and at first almost without books: for he was not allowed to have any books of this kind; and if one fell by chance into his hands, he was obliged to conceal it, that he might not incur the reprimands of his father, who disdained him for other studies. This severity made him choose for his device, Phaeton driving the chariot of the sun, with these words, Invito patre sidera verfe, "I traverse the stars against my father's inclination:" This had a particular reference to astronomy, the part of mathematics to which he at first applied himself. But the precautions of his father did not avail, for he pursued his favourite study with great application. In 1656 he began his travels. When he was at Geneva, BER

Bernouilli, he fell upon a method to teach a young girl to write, though she had lost her sight when she was but two months old. At Bourdeaux he composed universal gnomonic tables, but they were never published. He returned from France to his own country in 1680. About this time there appeared a comet, the return of which he foretold; and wrote a small treatise upon it, which he afterwards translated into Latin. He went soon after to Holland, where he applied himself to the study of the new philosophy. After having visited Flanders and Brabant, he went to Calais, and passed over from thence to England. At London he contracted an acquaintance with all the most eminent men in the several sciences; and had the honour of being frequently present at the philosophical societies held at the house of the famous Mr Boyle. He returned to his native country in 1682; and he exhibited at Basil a course of experiments in natural philosophy and mechanics, which consisted of a variety of new discoveries. In 1682, he published his essay of a new system of comets; and the year following, his dissertation on the weight of air. Mr Leibnitz, about this time, having published in the Acta Eruditorum at Leipzig some essay of his new Calculus differentialis, or infinitesimis petitis, but concealed the art and method of it; Mr Bernouilli, and one of his brothers, discovered, by the little which they saw, the beauty and extent of it: they endeavoured to unravel the secret; which they did with such success, that Mr Leibnitz declared, that the invention belonged to them as much as to himself. In 1687, the professorship of mathematics at Basil being vacant, Mr Bernouilli was appointed his successor. He discharged this trust with universal applause; and his reputation drew a great number of foreigners from all parts to hear his lectures. He had an admirable talent in teaching, and adapting himself to the different genius and capacity of his scholars. In 1699, he was admitted into the academy of sciences at Paris as a foreign member, and in 1701 the same honour was conferred upon him by the academy of Berlin. He wrote several pieces in the Acta Eruditorum of Leipzig, the Journal des Sciences, and the Histoire de l'Academie des Sciences. His assiduous application to his studies brought upon him the gout, and by degrees a flow fever, of which he died the 16th of August 1705, in the 58th year of his age.—Archimedes having found out the proportion of a sphere to a cylinder circumscribed about it, ordered it to be engraved upon his monument. In imitation of him, Mr Bernouilli appointed, that a spiral logarithmical curve should be inscribed upon his tomb, with these words, Eadem mutata resurgo; in allusion to the hopes of the resurrection, which are represented in some measure by the properties of the curve which he had the honour of discovering.