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 sub sequently 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 Boyle,
Hooke, Stillingfle3t, 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 appear ance of the cornet of 1630. This essay, and his next publication, entitled De Gravitate Athens, were deeply tinged with the philosophy of Descartes, but they contain truths not unworthy of the philosophy of the Principia.
James Bernoulli cannot be strictly called an independent discoverer ; but, from his extensive and successful applica tion of the calculus, he is well 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, and to determine the catenary, or curve formed by a chain suspended by its two extremi ties, which he also showed to be the same as the curva ture of a sail filled with wind. This led him on to another curve, which, being forni3d by an elastic plate or rod fixed at one end and bant by a weight applied to the other, he called the elastic curve, and which he showed to be the same as the curvature of an impervious sail filled with a liquid. In his investigations respecting cycloidal lines and various spiral curves, his attention was directed to the loxo- droinic and logarithmic spirals, in the last of which he took particular interest from its remarkable property of repro ducing itself under a great variety of conditions.
In 1696 he proposed the famous problem of isoperimetrical figures, and offered a reward for its solution. This problem engaged the attention of British as well as Continental mathematicians ; and its proposal gave rise to a painful quarrel between the brothers. John offered a solution of the problem ; his brother pronounced it to be wrong. John then amended his solution, and again offered it, and claimed the reward. James still declared it to be no solution, and soon after published his own. In 1701 he published also the demonstration of his solu tion, which was accepted by De 1 Hopital and Leibnitz. John, however, held his peace for several years, and then dishonestly published, after the death of James, another incorrect solution; and not until 1718 did he admit that he had been in error. Even then he set forth as his own his brother s solution purposely disguised.
In 1687 the mathematical chair of the University of Basel was conferred upon James ; and in the discharge of its duties he was so successful as to attract students from other countries. Some of his pupils became afterwards pro fessors in the universities of Germany. He was once made rector of his university, and had other distinctions bestowed on him. He and his brother John were the first two foreign associates of the Academy of Sciences at Paris ; and, at the request of Leibnitz, they were both received as members of the Academy of Berlin. In 1684 he had been offered a professorship at Heidelberg ; but his marriage with a lady of his native city led him to decline the invitation. Intense application brought on infirmities and a slow fever, of which he died on the 16th of August 1705, with the resignation of a Christian and the firmness of a philosopher. Like another Archimedes, he requested that, as a monument of his labours and an emblem of his hope of a resurrection, the logarithmic spiral should be engraven on his tombstone, with these words, Eadem mutata resurgo.
James Bernoulli wrote elegant verses in Latin, German, and French ; but although these were held in high estima tion in his own time, it is on his mathematical works that his fame now rests. These are (1.) Jacoli Bernoulli Basiliensis Opera, Genevae, 1744, 2 torn. 4to ; (2.) Ar Conjectandi, opus posthumum : accedunt tractatus de Serie- bus Inftnitis, et epistola (Gallice scripta] de Ludo Piles Reticularis, Basiliae, 1713, 1 torn. 4to.
born at Basel on the 7th August 1667. His education was begun at six years of age ; and after finishing his literary studies he was sent to Neufchatel to learn commerce and acquire the French language. But at the end of a year he renounced the pursuits of commerce, returned to the Uni versity of Basel, and was admitted to the degree of bachelor in philosophy, and a year later, at the age of 18, to that of master of arts. In his studies he was aided by his elder brother James. Chemistry, as well as mathematics, seems to have been the object of his early attention ; and in the year 1690 he published a dissertation on effervescence and fermentation. The same year he went to Geneva, where he gave instruction in the differential calculus to Fatio de Duiller, and afterwards proceeded to Paris, where he en joyed the society of Malebranche, Cassini, De Lahire, and Varignon. With the Marquis de 1 Hopital he spent four months at his country house in the study of the higher geometry and the resources of the new calculus. His inde pendent discoveries in mathematics are numerous and important. Among these were the exponential calculus, and the curve called by him the linea brackistochrona, or line of swiftest descent, which he was the first to deter mine, pointing out at the same time the beautiful relation which this curve bears to the path described by a ray or particle of light passing through strata of variable density, such as our atmosphere. On his return to his native city he studied medicine, and in 1694 took the degree of M.D. At this period he married into one of the oldest families in Basel ; and although he had declined a professorship in Germany, he now accepted an invitation to the chair of mathematics at Groningen (Commercium Philosophicum, epist. xL and xii.) There, in addition to the learned lectures by which he endeavoured to revive mathematical science in the university, he gave a public course of experi mental physics. During a residence of ten years in Gron ingen, his controversies were almost as numerous as his discoveries. His dissertation on an electrical appearance of the barometer first observed by Picard, and discussed by John Bernoulli under the name of mercurial phosphorus, or mercury shining in vacuo (Diss. Physica de Mercuric lucente in vacuo}, procured him the notice of royalty, and engaged him in controversy. Through Leibnitz he re ceived from the king of Prussia a gold medal for his sup posed discoveries ; but Hartsoeker and some of the French academicians disputed the fact. The family quarrel about the problem of isoperimetrical figures above mentioned began about this time. In his dispute with his brother, in his controversies with the English and Scotch mathe maticians, and in his harsh and jealous bearing to his son Daniel, he showed a temper mean, unfair, and violent. He had declined, during his residence at Groningen, an invitation to Utrecht, but accepted in 1705 the mathe matical chair in the university of his native city, vacant by the death of his brother James ; and here he remained till his death. His inaugural discourse was on the " new
analysis," which he so successfully applied in investigating