BERNOULLI or BERNOUILLI, the name of a Swiss family of scientists and mathematicians who made their home in Basle.
(1) JACQUES BERNOULLI (1654-1705), mathematician, after concluding his studies at the University of Basle, travelled in Eng land, France and Holland. He constructed his Universal Tables on Dialling at Bordeaux and returned in 1682 to Basle, where he opened a public seminary for experimental physics. In 1687 he became professor of mathematics in the university and later its rector. Jacques Bernoulli was the first to solve Leibnitz's prob lem of the isochronous curve. He proposed the problem of the catenary (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. In 1696 he offered a reward for the solu tion of the problem of isoperimetrical figures, which led to a quarrel with his brother Jean whose solution he declined.
Jacques Bernoulli's mathematical works are: Ars Conjectandi; opus posthumum: accedunt tractatus de Seriebus Infinitis, et epistola (Gallice scripta) de Ludo Pilae Reticularis (Basiliae, I 7 1 3) ; Jacobi Bernoulli Basiliensis Opera (Genevae, i7 44) (2) JEAN BERNOULLI (166 7-1 7 48 ), studied under his brother Jacques at Basle and then worked under the marquis de l'Hopital in Paris. He spent ten years as professor of mathematics at Groningen, and in 1705 succeeded his brother Jacques in the chair of mathematics at the university of Basle. Like his brother he was a great mathematician. Among his independent discoveries were the exponential calculus, and the line of swiftest descent, which he was the first to determine, pointing out at the same time the relation which this curve hears to the path described by a ray of light passing through strata of variable density.
Jean Bernoulli's writings were collected and published under the title of Johannis Bernoulli Operi Omnia (Lausan. et Genev.); his correspondence with Leibnitz appeared under the title of Gul. Leibnitii et Johannis Bernoulli Commerciurn Philosoplticum et Mathematicum (Lausan. et Genev., (3) NICOLAS BERNOULLI (1695-1726), eldest son of the pre ceding, was for three years professor of jurisprudence of Berne. He and his brother Daniel were appointed professors of mathe matics in the Academy of St. Petersburg, but within eight months of the appointment Nicolas died. Some of his mathematical papers are published in his father's works.
(4) DANIEL BERNOULLI (I 700—I 782 ), younger brother of the preceding, spent seven or eight years at St. Petersburg as pro fessor of mathematics and then returned to Basle, where in he became professor of anatomy and botany and afterwards of experimental and speculative philosophy. His most important work is his Hydrodynamica (1738), in which the equilibrium, the pressure, the reaction and varied velocities of fluids are considered both theoretically and practically. One of these problems deals with an ingenious mode of propelling vessels by the reaction of water ejected from the stern. Daniel Bernoulli gained or shared no less than ten prizes of the Academy of Sciences of Paris. The first, for a memoir on the construction of a clepsydra for measur ing time exactly at sea, he gained at the age of 24 ; the second, for one on the physical cause of the inclination of the planetary or bits, he divided with his father; and the third, for a communi cation on the tides, he shared with Euler, Colin Maclaurin and another competitor. The problem of vibrating cords, which had been some time before resolved by Brook Taylor (1685-1731 ) and d'Alembert, became the subject of a discussion between Bernoulli and his friend Euler. In one of his early investigations he gave a demonstration of the problem of the parallelogram of forces. His labours in the decline of life were chiefly directed to the doctrine of probabilities in reference to practical purposes, and in particular to economic subjects.