of anatomy and physics at Groningen, and chairs
of anatomy, botany, and physics at Basel. He
was a member of several academies, and took
numerous prizes in Paris. Daniel Bernoulli was
extremely versatile. His principal work is the
H yd rod !/ mi mica, in which he first developed the
kinetic theory of gases.
BERNOULLI, Jakob, .Jacql'es, or James ( ltJ54-1705) . A celebrated mathematician. He was born at Basel. Destined by his father for a chair of theology, he early showed his prefer- ence for science, and, after visiting France, Hol- land, and England, he was made professor of mathematics in the University of Basel (1087). He and his younger brother, .j'ohann (q.v. ), were among the first to understand and use the new method of Leibnitz. He solved the latter's prob- lem (1687) of the isochronous curve, propo.sed and solved the problem of the catenary, solved that of the brachistochrone proposed by Johann, contributed to the theory of isoperimetry, and, in general, was one of a famous group of prob- lem solvers, including his brother, Leibnitz, I'Hopital, and Huygens. The result of the dis- putes over these problems was a serious estrange- ment between his brother and himself. He was a voluminous writer, his principal works in- cluding: Conamen Novi Systematis Cometarum (Amsterdam, 1682), suggested by the apjiearance of the comet of 1680; Dissertatio de Uraritule .^theris (Amsterdam, 1683) : and his contribu- tions to the Acta Eriiditorum, in one of which (May, 1690) the word 'integral.' as applied to a difl'erential equation, is used for the first time, although Leibnitz had already used the symbol 5 The best known of his works. .Irs Coiijec- tandi (1713), published posthumously (by Nicolas Bernoulli), extended the doctrine of probabilities to moral, political, and economical subjects.
In connection with the effort to prove that the number of times an event can happen in n trials lies between definite limits, Bernoulli proved the celebrated proposition, according to which "it is always possible to increase the num- ber of trials till it becomes a certainty that the proportion of occurrences of the event will differ from ;), its probability on a single trial, by a quantity less than any assignable."
His works were published vmder the title Jacobi Bernoulli Basileensis Opera, in two vol- umes (Geneva, 1744). At his request, recalling the example of Archimedes (q.v.), a logarithmic spiral was engraved on his tomb, with the motto, Eadem Mutata Rcsiirgo : and this is still to be seen in the cloisters of the cathedral at Basel. Consult: Saalschiitz, Vorlesungen iiler die Ber- noulUschen ZaJilen. (Berlin, 1893) ; and Cantor, Geschichte der Mathematik (2d ed., Leipzig, 1898). ' 1 o.
BERNOULLI, Jakob, or .Jacques (1758- 89). He was l)orn at Basel. At the age of 21 he undertook the duties of the chair of experi- mental physics at Basel, his uncle Daniel having resigned the post on account of old age. A little later he became professor of mathematics at Saint Petersburg, and married a granddaughter of the great mathematician Euler. He was short- ly after drowned in the Neva. Several of his memoirs were published in the Nova Acta Aca- demiw Petroiiolciisis.
BERNOULLI, Joha.nx, ,,r Jean (1667-1748). He was born at Basel. He and his brother Jakob were the first two foreigners honored by an elec- tion to the academies of Paris and Berlin. At the age of 28 he was appointed professor of mathematics at Groningen, and on the death of his brother, ten years later, succeeded him in a similar chair at Basel. As a teacher of mathe- matics he had no superior in his day. Among his pu])ils was Euler, whom he encouraged in liis first efforts, and among his friends was Leib- nitz, wliose cause he always championed. Un- fortunately, he had a very jealous disposition, which showed itself not only in his relations with his brother, but even with his own son (Daniel). His Opera Omnia, in 4 vols., quarto, were pub- lished at Geneva in 1742; and his correspondence with Leibnitz, in 2 vols., at Lausanne in 1745. He proposed the problem of the brachistochrone and that of the minimum line between two points on a given surface; founded, jointly with his brother Jakob, the theory of isoperimeters, and was one of the pioneers in the work of con- structing an exponential and an integral calcu- lus, and to recognize completely the "legitimacy of the real results from calculations involving the imaginary.
BERNOULLI, .Johann, or Jean (1710-90). He was born at Basel, and was a brother of Daniel, and the third son of Nicolas Bernoulli. He occupied successively the chairs of eloquence and mathematics at Basel. The Academy of Science of Paris honored him three times for his contributions to the theory of lieat and light. He was also a member of the Berlin Academy. His two sons, Johann and .Jakob, were likewise famous men of science.
BERNOULLI, Johann, or .Jean (1744-1807). He was born at Basel. He received the degree of doctor of philosophy at the age of 13, and was made astronomer to the Academy of Berlin at the age of 19. His later works did not fulfill his youthful promise. His principal contribu- tions were: l{eciieil pour les astronomes (3 vols., Berlin, 1772-76, with a supplement in 1779) . and Lettres astronomiques ( 1781) .
BERNOULLI, Xici.aus, or Nicolas (1695- 1726). He was born at Basel, and, like several other members of his family, was a youthful prodigy. At the age of 8 he could speak German,. Dutch, French, and Latin: at 10 he took the degree of doctor of philosophy at Basel, and at 20 he received the degree of doctor of laws. He was professor of jurisprudence at Bern, and pro- fessor of mathematics at Saint^ Petersburg, where he died. He wrote a history of the problem of trajectories. His important papers were pub- lished in an edition of his father's works in 1742.
BERNOULLI, Nicolas (1087-1759). He was born at Basel. He was a friend of Newton and Halley, whom he visited in England; was a corresponding member of the principal acad- emies of Europe, aiul professor of mathematics at Padua, and of law and logic at Basel. He edited the Ars Conjectandi of his uncle Jakob. JJis own contributions relate chiefly to differen- tial equations.
BERNSTEIN, bern'stin, A.kon (1812-84). A German publicist and author. He was born at Danzig, of Jewish parentage. His admirable translation of the Song of Songs (published
