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BERNOULLI. 



BERNOULLI. 



if done within the year. James Bernoulli replied, " I recommend my 

 brother to look again at his lost solution, and to eay whether he still 

 thinks it rijjht; and I declare that when I shall have published mine, 

 pretexts of precipitation will not bo listened to." John Bernoulli 

 answered, that he would not revise his solution, and that his time was 

 better employed in making new discoveries. James Bernoulli replied, 

 that if in three minutes he had solved the whole mystery, surely six 

 minutes more would not much diminish the number of his new dis- 

 coveries. After some further communications, in the course of which 

 John Bernoulli sent the demonstration of his solution to Leibnitz (who 

 declined giving any positive opinion), and declared that he would say 

 no more on the subject, James Bernoulli published his own solutions, 

 with those of other problems, without demonstrations, in the Leipzig 

 Acts for June 1700. He also printed at Basel a letter to his brother, 

 in which he invites him to publish his method, and sends his own 

 solution, without demonstration. John Bernoulli, though now in 

 possession of the true result, could not see where he was wrong ; 

 perhaps would not, for a material part of this letter was suppressed at 

 his desire in the posthumous edition of his brother's works. (It was 

 reprinted whole in 1792, as already mentioned.) John Bernoulli 

 replied by sending his own demonstration under cover to the Academy 

 of Sciences at Paris, to be opened so soon as his brother should send 

 his. On this, James Bernoulli (March 1701) published his own solution 

 nt Basel, and also in the Leipzig Acts with the demonstration. De 

 1'Hopital and Leibnitz immediately admitted its correctness, and made 

 John Bernoulli acquainted with their opinion. But no more was heard 

 from the latter : ho continued obstinately silent as long as his brother 

 was alive ; nor was it till 1706, after the death of James Bernoulli, 

 that he published an incorrect solution in the memoirs of the academy. 

 The inference is obvious, that he suspected the incorrectness of his 

 own method, and was afraid to expose it to the searching eye of his 

 brother ; but that when the latter was dead, he did not fear tbat any 

 other person in Europe would be able to expose him. As late as 

 1718 he published a correct solution, and admitted that he had been 

 mistaken ; but he had not the fairness to add, that his new solution 

 was only that of his brother in another shape. 



After the preceding account, which is now undisputed, the reader 

 will not be surprised to be told that after the deaths of Leibnitz and 

 De 1'Hopital, their bosom friend John Bernoulli endeavoured to rob 

 them both. He claimed to be a contemporaneous inventor of a 

 method of the former (that which was called the differentiatio de 

 curva in curvam), of which he had said in admiration, when it was 

 first produced, that "the god of geometry had admitted Leibnitz 

 farther into his sanctuary than himself." And here too, if either of 

 the brothers can be said to have invented that method as well as 

 Leibnitz, it was James Bernoulli. He also advanced an absurd pre- 

 tension to be the author of all that was new in the ' Analyse,' &c., of 

 De 1'Hopital, a claim which merits no refutation. He was jealous of 

 his own eon, Daniel Bernoulli, who divided with him the prize of the 

 Academy of Sciences in 1734, and was displeased that he turned New- 

 tonian. The following anecdote is related by Condorcet, we know not 

 on what authority, but we believe it : " One day he proposed to his 

 son Daniel, then a youth, a little problem to try his strength ; the boy 

 took it with him, solved it, and came back expecting some praise from 

 his father. You ought to have done it on the spot, was all the observa- 

 tion made, and with a tone and gesture which his son remembered to 

 the latest day of bis life." The only instance which has ever fallen 

 within our reading, in which John Bernoulli showed himself free from 

 petty feeling, was in his treatment of Euler, when the latter was his 

 pupil at Basel. Observing his talent for mathematics, he encouraged 

 it, and gave him private lessons, in addition to those of the public 

 course. 



In thus displaying a character which appears to have no one amiable 

 point about it, we depart from the common practice, which is never to 

 admit, if by any softening it can be helped, that great intellect is not 

 accompanied by greatness of mind in other respects. But it is not 

 good to substitute falsehood (and coloured truth is falsehood) for 

 truth, and it is not good for the living to know that literary or scien- 

 tific reputation covers moral obliquity as soon as the grave has covered 

 the body. D'Alembert, who, in the form of an cloge, has written an 

 excellent account of the mathematical character of John Bernoulli, has 

 dexterously evaded the difficulty : " Bernoulli was only known to me 

 by his works ; I owe to them almost entirely the little progress I 

 have made in geometry. Not having had any kind of acquaintance 

 with him, I am ignorant of the unintei-esting details of his private life." 

 Speaking of the celebrated dispute above related, he says, " This alter- 

 cation produced several pieces in which bitterness seems to have taken 

 the place of emulation ; but as one of the two must have been in the 

 wrong, one of the two must have been in a passion." He only forgets 

 to state, what he himself knew as well as any body, that the " one of the 

 two " was the subject of the eloge, and hisprotegS for the time being. 



In concluding what we mean to say on the two brothers, who stood 

 at the head of their family, we may observe that it is clear that both 

 one and the other had pushed their researches in the infinitesimal 

 analysis far beyond the view of any other men of their time. Newton 

 had .abandoned the sciences, and Leibnitz, the other inventor, though 

 he could decide between the right and the wrong, would not commit 

 himself by an opinion on the solution of John Bernoulli only, but 



contented himself with stating that it seemed to him to be correct, 

 but that he could not give it sufficient attention to speak positively. 

 Of the two brothers, the elder was certainly the deeper and the more 

 correct ; the younger the quicker and the more elegant. The works 

 of John Bernoulli, who lived much longer than his brother, contain an 

 immense mass of discovery ; but there is no particular on which we 

 could dwell for the benefit of the general reader : the mathematician 

 should consult the 6loge of D'Alembert already alluded to. 



NICOLAS BERNOULLI II. (to distinguish him from his cousin of the 

 same name), the eldest son of John Bernoulli, was born on the 27th 

 of January 1695, at Qroningen. He came to Basel with his father in 

 1705, and studied at the university, -where he formed an intimate 

 friendship with the afterwards celebrated Euler. In 1725 he was 

 invited to St. Petersburg by the Empress Catherine, with bis brother 

 Daniel. But he had hardly time to do more than show that he had 

 the talents of his family, when he died, on the 26th of July 1726, at 

 St. Petersburg. For his eloge see ' Comm. Acad. Petrop.,' v. ii., and 

 for some memoirs of his, see voL i. There are some of his memoirs in 

 his father's works. (See the ' Biographic Universelle.') 



DANIEL BERNOULLI, the second son of John, was born at Groningen, 

 February 9, 1700. His father at first intended that he should apply 

 himself to trade, but his objections to that course of life prevailed, 

 and he was allowed to study medicine. He had received some 

 instruction in mathematics from his father; we have already seen 

 how. After passing some years in Italy, professedly employed upon 

 medicine, but really upon mathematics, he returned to Basel. He 

 could not at this time have been actually known as a mathematician 

 by any decided effort of his own ; but it was sufficient that he was a 

 Bernoulli, for we are told that before he was twenty-four years old he 

 had refused the presidency of the Academy of Sciences at Genoa. The 

 following year he and his brother Nicolas were invited to St. Peters- 

 burg, as already mentioned. He appears not to have been well satis- 

 fied with the half savage court of Russia, and had made up his mind 

 to quit it ; but the empress, who wished him to remaiu, increased his 

 salary, and gave him full liberty to retire on the half of it whenever he 

 pleased. Thus obliged in honour to remain, he continued at St. Peters- 

 burg till 1733, when the state of his health compelled him to return to 

 his country. Here he obtained, first a chair of medicine, and after- 

 wards of natural philosophy, to which was subsequently added one of 

 metaphysics. 



He had published, in 1724, his first work, entitled ' Exercitationes 

 Mathematics,' in the title-page of which he styled himself ' son of 

 John Bernoulli,' which title he always afterwards continued. His 

 succeeding essays on mechanics were the first in which motion is 

 decomposed into that of translation and rotation. He afterwards 

 entered into the theory of compound oscillations, and is the first who 

 applied mathematics to a species of considerations which have since 

 become of the greatest utility and singularly extensive application. 

 His ' Hydrodynamique,' published in 1738, is the first work in which 

 the motions of fluids are reduced to a question of mathematics. It is 

 in one point like the subsequent work of Lagrange (the 'Me"canique 

 Analytique') : in that work the whole question is reduced to the 

 results of one principle , which, in the work of Daniel Bernoulli, is 

 called the ' conservation of vis viva.' 



In the theory of probabilities he introduced what is known 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 which a science whose practical utility is great, though 

 difficult for the world at large to see, is applied to a question of 

 statistics. 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 into questions of combinations. 



Daniel Bernoulli gained or divided the prize of the Academy 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 inclina- 

 tions, 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 Euler 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 

 between the writings of Newton and Laplace. 



In 1748 he succeeded his father as member of the Academy of 

 Sciences, in which he was succeeded by his brother John ; so that for 

 more than ninety years the foreigu list of that body always contained 

 a Bernoulli. 



Daniel Bernoulli was found dead in his bed by his servant, March 17, 

 1782, having in his latter years been subject to asthma. He was 

 never married, the only engagement of that sort which he ever con- 

 templated having been broken off by him on the discovery that his 

 intended wife was avaricious. In religion he was said by the clergy 

 of his town to be a freethinker, a rumour which he never took any 

 steps 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 Basel. 





