Bernoulli, Or Bernouilli, a celebrated family of mathematicians and savants, originally of Antwerp, driven thence by Alva, settled first in Frankfort, and in 1022 in Basel, Switzerland. I. James, born in Basel, Dec. 25, 1654, died there, Aug. 16, 1705. He was destined by his father for the ministry, but accident having thrown some geometrical books in his way, he took for his device Phaethon driving the chariot of the sun, with the motto, Invito patre, sidera verso, and devoted himself to the study of mathematics. In 1676 he visited Geneva, where he taught a blind girl to write, and thence travelled into France, where he constructed gnomical tables, and returned home in 1080. The appearance of a comet in that year led to his publishing an essay entitled Conamen novi Systematis Cometarum, in which he contended that the orbits of comets might be calculated. He again travelled in various countries, and at London made the acquaintance of Bayle. After his return to Basel in 1082 he tried experiments in physical and mechanical science which attracted much attention.

In 1687 he was appointed professor of mathematics in the university of Basel, and engaged in profound mathematical investigations, particularly in the development of the theory of the differential and integral calculus which had been devised by Leibnitz. In 1699 he was chosen member of the French academy, the first foreigner ever elected, and in 1701 became member of the Berlin academy. He directed that the logarithmic spiral, of which he had demonstrated the properties, should be engraved upon his tombstone with the motto: Eadem mutata resurgo. After his death his treatise entitled Ars Conjectandi was published (1713). It was one of the earliest works on the theory of probabilities. His collected works were published at Geneva in 1744 (2 vols. 4to). II. John, brother of the preceding, born July 27, 1667, died Jan. 1, 1748. He was educated at the university of Basel, studied medicine, and in 1690 published a dissertation on effervescence and fermentation. But he soon turned his attention to mathematics. In 1690 he went to Geneva, and travelled in France, where he made the acquaintance of Male-branche, De l'Hopital, and other men of science.

He returned to Basel in 1692, and was appointed in 1695 professor of mathematics at Groningen. In 1696 he proposed for solution the following problem: "To find the curve on which a material point will fall from one given.point to another in the least possible time." It was solved by his brother James and others, and James proposed in return another problem in regard to the solution of which there was a long controversy between the two brothers. John exhibited unreasonable jealousy of his brother, and was not equal to him as a mathematician. He, however, succeeded him as professor of mathematics at Basel, and remained in that position till his death. He was also jealous of his son Daniel, and had controversies with many of the scientific men of his day; but he was the instructor of Euler and the friend of Leibnitz, with whom he carried on a long correspondence, published at Lausanne and Geneva (2 vols., 1745). He aided with his brother in the development of the calculus, investigated many curious questions in physics, and contributed greatly to the advancement of mathematical science.

He addressed many papers to the different scientific bodies of Europe, which were collected by Cramer (4 vols. 4to, Lausanne and Geneva, 1742), and was a member of the academies of Paris, Berlin, and St. Petersburg, of the royal society of London, and of the institute of Bologna. His works were published at Geneva in 1742 (1 vol. 4to). HI. Daniel, second son of the preceding, born in Groningen, Feb. 9, 1700, died in Basel, March 17, 1782. He received instruction from his" father in mathematics, and studied medicine for some years in Italy. While there he distinguished himself by a paper upon a question of geometry, and at the age of 24 was offered the presidency of an academy of sciences which had just been founded at Genoa. The following year he was appointed professor of mathematics at St. Petersburg, where he remained till 1733, when he was appointed first professor of botany and anatomy, and afterward of natural philosophy and metaphysics, in the university of Basel. In 1748 he succeeded his father as member of the academy of sciences at Paris, and ten times obtained the prizes of that body.

He made many new and ingenious applications of mathematical science in mechanics, astronomy, and hydraulics, and in 1760 wrote a paper on inoculation in which he introduced a new principle into the theory of probabilities. He resigned his professorship in 1777, suffered much from asthma during the latter part of his life, and was finally found one morning by his servant dead in his bed. Among his works are: Exer-citationes qucedam Mathematices (4to, Venice, 1724); Hydronamica, seu de Viribus et Motibus Fluidorum (4to, Strasburg, 1738); and a work on the physical cause of the inclination of the axes and orbits of planets with reference to the solar equator. IV. Nicholas, elder brother of the preceding, born in Basel, Jan. 27, 1695, died in St. Petersburg, July 26,1726. He travelled in France and Italy, and was then appointed professor at St. Petersburg with his brother. V. John, brother of the preceding, born in Basel, May 18, 1710, died July 17, 1790. He studied law and mathematics, in 1743 was appointed professor of eloquence at Basel, and in 1748 succeeded his father as professor of mathematics there. He was a member of the academy of sciences of Berlin and of Paris, and received three prizes from the French academy.

VI. John, son of the preceding, born in Basel, Nov. 4, 1744, died July 13, 1807. He studied at Basel and Neufchatel, devoting himself especially to astronomy, mathematics, and philosophy. At the age of 19 he was appointed astronomer of the Berlin academy, and afterward director of the mathematical class. He published Reeueil pour les astronomes (3 vols., Berlin, 1772-'6), Lettres astrononiiques (1781), and 6 vols, of his own travels, besides a collection of travels in 15 vols. VII. James, brother of the preceding, born in Basel, Oct. 17, 1759, died in St. Petersburg, July 13, 1789. When his uncle Daniel became infirm, he assumed at the age of 21 his duties as professor of natural philosophy, but was not chosen his successor, the appointment being made by lot. At the age of 29 he was appointed professor of mathematics in St. Petersburg, and married there a granddaughter of Euler. Two months afterward he died of apoplexy while bathing in the Neva. VIII. Nicholas, nephew of the first James and John, born in Basel, Oct. 10, 1687, died Nov. 29, 1759. He edited the Ars Conjectandi of his uncle James, and solved several of the geometrical problems proposed by his uncle John. He was professor , of mathematics at Padua from 1716 to 1722, in the chair once filled by Galileo, and was afterward professor first of logic and then of law at Basel. He was a member of the Berlin academy of the royal society of London, and of the institute of Bologna. IX. Jerome, of the same family, born in Basel in 1745, died in 1829. He was distinguished as a naturalist and a mineralogist, and was for a time president of the council of his native canton.

X. Christopher, a technologist, of the same family, horn in Basel, March 15, 1782, died there, Feb. 6, 1863. He studied at Neuichatel and afterward at Gottingen, where he devoted himself chiefly to the natural sciences. In 1802 he became professor at Halle, where he remained two years. He then spent some time in travelling, and in 1806 opened a private school at Basel, which he gave up in 1817 and became professor of natural history in the uni-versity, retiring in 1861. He published a number of works upon subjects connected with rational technology, among which are: Ucber den nachtheiligen Einfluss der Zunftverfassung auf die Industrie (Basel, 1822); Handbuch der Technologie (2 vols., 1833-'4; 2d ed., 1840); Handbuch der industriellen Pliysik, Mechanih und Hydraulik (2 vols., Stuttgart, 1834-'5).