BERNOULLI, JAmEs, a celebrated methemati cian, was the fifth son of Nicholas Bernoulli, mem ber of the grand council and of the chamber of fi nances of Bask in Switzerland, and was born at Basle on the 27th December 1651. James Ber noulli, the grandfather of the subject of this article, came originally from Antwerp, and established him self at Basle in 1622. He left behind him three children, the eldest of whom was Nicholas, who was born in 1623, and died in 1708 ; leaving a family of eleven children, among whom were James and John, two of the most illustrious mathematicians of the 18th century.
James Bernoulli was originally intended for the church, and, after haring taken his degrees in the university of Basle, he entered upon the study of divinity. His attachment to mathematics, however, gradually withdrew his attention from the study of theology. His favourite pursuit engrossed the whole of his time ; and without the aid of a master, and even without the assistance of books, which his fa ther carefully concealed, he made such rapid advanced in the science of geometry,* that before he was 18 years old, he resolved the problem of finding the Ju lian period, when the year of the solar cycle, the golden number, and the indiction, are given.
He began his travels in the year 1676 ; and when he passed through Geneva, he found out a method, different from that proposed by Cardan, of teaching a blind person to write, which he tried with great success upon a young girl, who had been blind from the age of two months. At Bourdeaux he compu ted universal tables for dialling, but they have never been given to the world. The attention of astrono mers was at this time occupied with 'the famous co met of 1680 ; and such was the enthusiasm with which Bernoulli was. inspired, that, on his return to Basle, he published a treatise on the subject, entitled, Neu erfiindene Auleitung teie man den lag' der Co meter!, 8jc. Bas. 1to, 1681. In this first production Bernoulli adopted the vortical system of Descartes, and maintained, that comets were the satellites of a large and invisible planet, which revolved round the sun in 4• years and 157 days, at the distance of 2583 semidiameters of the (rills magnzzs. Upon these prin ciples, lie predicted that the comet of 1680 would re turn on the 17th May 1719, and would be situated in the 12th degree of Libra ; but, alas ! his prediction, founded on such a theory, could not be otherwise than false, though, like Phaeton, to follow out the simile contained in his own device, tnmen, excielit ausis.
Soon after the publication of this work he left Basle, and visited Flanders and Holland on his way to England, where he was introduced to the most eminent philosophers of the times, and attended all their philosophical meetings in London. On his re turn to Basle in 1682, he commenced a course of public experiments on natural philosophy ; and, in the same year, he published, at Amsterdam, his Conamen novi systenzatis cometarum, pro mart eorum sub calming' revocando et apparitionibus predicendis, 8vo, Amstel. 1682; a work not altogether unworthy of his genius. In 1682, he published his disserta tion De Gravitate ./Etheris, which is not distinguish ed by any peculiar marks of its author. It treats principally of ether, that hypothetical substance by which Euler, his great successor in the career of geometrical discovery, endeavoured to explain the various phenomena of nature. After this work was composed, Bernoulli found, that many of the views which it contained had already been by Male branche, in his Recherche de la Verite ; and he de clares in his preface, that he had not read that cele brated work.
About this time he established at Basle a kind of experimental academy, where he made a number of ex periments on different points in physics. The profes sorship of mathematics at Heidelberg having become vacant in 1684, James Bernoulli was elected to that office, and, during the three years which he spent in that university, he devoted himself, with the utmost ardour, to the study of geometry. The paper of Leibnitz, entitled, Nova illethodus pro maximis et itonque tangentibus, quer nec fractas, nee irrationales quantitates moratur, et singulare pro illis calculis genus, with the application of the calculus to the solution of several physical and geometrical problems, appeared in the Leipsic acts for 1684, and were the first attempts of that great philosopher to employ the new calculus which he had invented. The attention of James Bernoulli was particularly attracted by this paper, and he and his brother John, who had been studying mathematics under him, were so delighted with these elements of the differential calculus, that they embraced it with avidity, and by extending its limits, and applying it with success to several curious problems, they, in the opinion" of Leibnitz himself, the discovery in a great mea sure their own.