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by the name of the moral probability, which estimates a 

 loss or gain, not absolutely, but by its proportion to the 

 fortune of the person who stands the risk. His paper on 

 inoculation, published in 1760, was one of the first in whicl 

 a science whose practical utility is great, though difficult for 

 the world at large to see, is applied to a question of sta- 

 tistics. On this subject he added to the methods which 

 had begun to appear for the evasion of the difficulties arising 

 from the necessary introduction of very large numbers intc 

 questions of combinations. 



Daniel Bernoulli gained or divided the prize of the Aca- 

 demy of Sciences ten times; once (in 1734) in company 

 with his father, on the question of the physical cause of the 

 smallness of the planetary inclinations, by which, as before 

 remarked, he excited jealousy in a quarter from whence 

 admiration should have been most certain. His memoir 

 has been considered the better of the two ; and Condorcet 

 observes, that he knew this, and showed that he knew it, 

 which was not quite decorous. In 1740 he shared with 

 Kuler and Maclaurin the prize for a dissertation on the 

 tides ; and their three memoirs, which are all celebrated, 

 contain all that was done on the theory of that subject be- 

 tween the writings of Newton and Laplace. 



In 1748 he succeeded his father as member of the Aca- 

 demy of Sciences, in which he was succeeded by his brother 

 John ; so that for more than ninety years the foreign list of 

 that body always contained a Bernoulli. 



Daniel Bernoulli was found dead in his bed by his ser- 

 vant, March 17, 1782, having in his latter years bsen subject 

 to asthma. He was never married, the only engagement 

 of th;it sort which he ever contemplated having been broken 

 off by him on the discovery that his intended wife was ava- 

 ricious. In religion he was said by the clergy of his town 

 to be a freethinker, a rumour which he never took any 

 st-'ps either to prove or disprove. But his conduct and 

 talents had gained him so much respect among his fellow- 

 citizens, that to take off the hat to Daniel Bernoulli was 

 one of the first lessons inculcated upon the children of Basle. 

 The following anecdotes were related by himself, and he 

 asserted that his self-love was more flattered by the inci- 

 dents they contain than by all his prizes. When he was a 

 young man on his travels, he talked with a stranger whose 

 curiosity was excited by his conversation, and who asked 

 his name. 'I am Daniel Bernoulli,' answered he. The 

 stranger, thinking from his youthful looks that he could not 

 be so celebrated a man, and wishing to answer the supposed 

 hoax by one still better, replied, ' And I am Isaac Newton.' 

 The other is as follows : Koenig, then well known as a 

 mathematician, was dining with him, and talking with some 

 pride of a very difficult question, which it had taken him a 

 long time to solve; Bernoulli went on attending to his 

 guests, and before they rose from table furnished Koenig 

 with a solution of his question. (See the eloge of Daniel 

 Bernoulli by Condorcet.) 



JOHN BERNOULLI H., third son of John Bernoulli I., born 

 at Basle, May 18, 1710, died there July 17, 1790. He 

 studied law and mathematics, and was successively professor 

 of eloquence and of mathematics. Three of his memoirs 

 gained the prize of the Academy of Sciences. 



JOHN BERNOULLI III., his son, born at Basle, November 

 4, 1744, died at Berlin, July 13, 1807. At nineteen years 

 of age he became a member of the academy of Berlin, 

 lie devoted himself particularly to astronomy, and his 

 numerous observations are in the Berlin Memoirs and 

 l'-phemeride$. He gave an edition of the algebra of Euler : 

 his Lf.ttres sur differents sujets, $~c., 1777 1779, contain 

 much information on the state of observatories. There is 

 a list of his works in the Biographie Uniaerselle. 



JAMKS BERNOULLI II., second son of John Bernoulli 

 II., born at Basle, October 17, 1759, was the deputy of his 

 uncle Daniel in his professorship, when the latter became 

 infirm, but did not succeed him, owing to candidates being 

 then chosen by lot. He was afterwards professor of mathe- 

 matics at Petersburg, and married a grand- daughter of 

 Euler. His memoirs in tha Petersburg transactions had 

 begun to show that he had the talent of his predecessors, but 

 )>' died of apoplexy while bathing in the Neva, July 3, 1 789. 

 His ehge is in the Nov. Act. Petropol. vol. vii. (Biog. Univ.) 

 NICOLAS BERNOULLI I., nephew of the two first Ber- 

 noullis, was born at Basle, October 10, 1687, died there 

 November 29, 1719. He was professor of mathematics and 

 of logic at Padua, afterwards of law at Basle. There are 

 some of his writings among those of John Bernoulli. 



In concluding this article we shall remark that the two 

 elder Bernoullis lived during the time while the mathe- 

 matics were in a state of growth towards the power which 

 was required for physical analysis. No two men contributed 

 more to this work; and it is the integral calculus, as received 

 from their hands, which became the instrument of their 

 successors. They are of the age of Newton and Leibnitz : 

 Daniel Bernoulli, on the other hand, is the contemporary 

 of Clairaut, Euler, and D'Alembert; and in the hands of 

 these four, the new calculus was applied to investigation of 

 material phenomena. The circumstances of the times re- 

 quired such men, and there is no question that they must 

 have appeared ; but that they should all three have come 

 from one family was not to be looked for, and furnishes an 

 instance of consanguinity of talent of one kind, which must 

 excite the curiosity even of those who care little for the sub- 

 jects on which it was employed. 



BERNSTORF, JOHANN HARTWIG ERNST, 

 COUNT VON, a younger son of Joachim Engelke, Baron 

 Von Bernstorf, chamberlain to the elector of Hanover, was 

 born at Hanover, May 13, 1712. His education was con- 

 ducted by the learned Keyssler, and in his company he tra- 

 velled through the principal states of Europe. Huving 

 visited Denmark, he obtained from Christian VI., in 1732, 

 the appointment of minister at the court of Augustus IT., 

 elector of Saxony and king of Poland. In 1737 he became 

 envoy from Denmark to the Germanic diet at Ratisbon, and 

 from 1 744 to 1750 resided in France as Danish ambassador. 

 [n 1751 Frederic V. appointed him minister for foreign 

 affairs, which office he filled till the ascendancy of Struensee 

 in 1770, when he was dismissed, and retired to Hamburg, 

 where he died, February 1 8, 1 772. He was created a count 

 in 1767 by Christian VII., whom he accompanied on his 

 travels in 1768. 



The principal event of his ministry was the accommoda- 

 tion of the differences between Denmark and Russia on the 

 subject of Holstein-Gottorp. In 1 762 war was threatened 

 >y Peter III. of Russia, but his death having averted the 

 irescnt danger, a treaty was negotiated by Bernstorf, which 

 was finally concluded in 1773, by which Russia resigned all 

 >re tensions to Holstein, and received in exchange Oldenburg. 

 tt was by Bernstorf's advice that Frederic V. purchased the 

 >roperty of the Danish West India Company, and opened 

 he trade in 1 754. The claims of Denmark on the city of 

 [lamburg were finally adjusted during his administration. 

 'n 1768 Denmark formally resigned her claim of suze- 

 rainete over Hamburg, Hamburg remitting in return a 

 tart of the debt due to her from Denmark. The main ob- 

 ect of his policy was the preservation of peace, in conjunc- 

 ion with which he directed all his efforts to the promotion 

 if commerce and manufactures, and the encouragement of 

 iterature. He bears the character of an able and upright 

 minister, and his exertions for the abolition of feudal slavery 

 ellect the highest honour both on his wisdom and huma- 

 nity. (A fuller account of his life and administration may 

 >e found in the third volume of Materialien zur Statislike 

 der Danischen Staaten.) 



BERNSTORF, ANDREW PETER, COUNT VON, 

 nephew of the preceding, was born at Gartow, in Liine- 

 >urg, August 28, 1735. He became minister for foreign 

 affairs in Denmark, in 1773, which office he held during the 

 'reater part of the remainder of his life. He died July 21, 

 797. (Sammlung von Bildnissen verdienstvoller Dd- 

 icn.) 



BE'ROE, in zoology, a genus of marine animals esta- 

 lished by Miiller, and placed by Lamarck under the second 

 ivision of the first section of his first order of Radiaria, or 

 adiated animals. Cuvier arranges the genus under his Aca- 

 ephte, which form his third class of zoophytes. It belongs to 

 he Cilingrada of De Blainville, and to the Ctenophorce of 

 Sschscholtz. In Lepon's arrangement the Beriiidac form the 

 rst family of the first division of Acalephans. The species, 

 hich are gelatinous, transparent, and either oval or globular, 

 loat in the ocean, where they are widely diffused. Lamarck 

 ays that they are very phosphoric, and that they shine at 

 light like lamps suspended in the sea, their brilliancy be- 

 oming vivid in proportion to the rapidity of their motions, 

 'heir breathing is carried on by means of cilia, which ex- 

 end longitudinally and at equal distances along the surface 

 rom the mouth to the inferior opening. Fabricius observed 

 ninute crustaceans in the digestive organs, and that when 

 ne of these animals was broken to pieces those pieces still 

 ontinued to live and swim about by the action of the cilia, 



