480 



BERNOULLI. 



Bernoulli, 



scmidiameters of the orbis magnits. Upon these prin- 

 ciples, he predicted that the comet of 1680 would re- 

 turn on the 17th May 1719, and would be situated in 

 the 12th degree of Libra ; but, alas ! his prediction, 

 founded on such a theory, could not be otherwise 

 than false, though, like Phaeton, to follow out the 

 simile contained in his own device, 



Afngnis, tnmcn, cxci'! ; t ausis. 



Soon after the publication of this work he left 

 Basle, and visited Flanders and Holland on his way 

 to England, where he was introduced to the most 

 eminent philosophers of the times, and attended all 

 their philosophical meetings in London. On his re- 

 turn to Basle in 1G82, he commenced a course of 

 public experiments on natural philosophy ; and, in 

 i the same year, he published, at Amsterdam, his 

 Conamen wow systemalis oomelarum, pro motu eorum 

 sub calcttlum rcvocat/do et apparitionibus predicendis, 

 8vo, Amstel. 1682 ; a work not altogether unworthy 

 of his genius. In 1682, he published his disserta- 

 tion De Gravitate Jlitheris, which is not distinguish- 

 ed by any peculiar marks of its author. It treats 

 principally of ether, that hypothetical substance by 

 which Euler, his great successor in the career of 

 geometrical discovery, endeavoured to explain the 

 various phenomena of nature. After this work was 

 composed, Bernoulli found, that many of the views 

 which it contained had already been given by Male- 

 branche, in his Recherche de la Vcriie ; and he de- 

 clares in his preface, that he had not read that cele- 

 brated work. 



About this time he established at Basle a kind of 

 experimental academy, where he made a number of ex- 

 periments on different points in physics. The profes- 

 sorship of mathematics at Heidelberg having become 

 vacant in 1684, James Bernoulli was elected to that 

 office, and, during the three years which he spent in 

 that university, he devoted himself, with the utmost 

 ardour, to the -study of geometry. The paper of 

 Leibnitz, entitled, A ova Methodus pro maximis et 

 minimis, ilcmque tangentibus, quce nee Jr act as, nee 

 irrationalcs quantitatcs moratur, et singulare pro Mis 

 cakulis genus, with the application of the calculus 

 to the solution of several physical and geometrical 

 problems, appeared in the Leipsic acts for 1684, and 

 were the first attempts of that great philosopher to 

 employ the new calculus which he had invented. 

 The attention of James Bernoulli was particularly 

 attracted by this paper, and he and his brother John, 

 who had been studying mathematics under him, were 

 so delighted with these elements of the differential 

 calculus, that they embraced it with avidity, and by 

 extending its limits, and applying it with success to 

 several curious problems, they, in he opinion" of 

 Leibnitz himself, made the discovery in a great mea- 

 sure their own. 



Before James Bernoulli entered upon this brilliant 

 career of discovery, he was elected, in 1687, to the 

 professorship of mathematics at Basle, an office 

 which he filled with distinguished reputation during 

 the whole of his life. He succeeded Peter Meger- 

 lin, who is known to astronomers as a zealous de- 

 fender of the Copernican system. 



Iu 1690 James Bernoulli solved the problem of 



the isochronous curve, of which Huygens and Leib- Bernoulli, 

 nitz had already obtained a solution ; and on this OC- Jam - 

 casion he proposed the celebrated problem of the """""^ ' " 

 catenarian curve, which Galileo had tried in vain. 

 Huygens, Leibnitz, and John Bernoulli soon obtain- 

 ed a solution ; but this solution was extended by 

 James Bernoulli to cases, in which the weight of the 

 chain varies in different parts of its length, according 

 to a given law. This able mathematician determined 

 also the curvature of a bcr.ded bow, and that of an elas- 

 tic rod, fixed at one end, and loaded at the other with 

 a given weight. He found likewise, that the form of a 

 sail, swollen by the action of the wind, is the common 

 catenarian curve when the wind docs not escape ; but 

 that it is one of the curves called Lintrat ice, when the 

 sail is supposed perfectly flexible, and expanded with 

 a fluid pressing in every direction. John Bernoulli 

 published a solution of the same problem in the Jour- 

 nal des Scavans for 1692 ; but it appears unquestion- 

 able, that he had received hints from his brother, 

 who communicated to him, by letter, his opinion 

 upon that subject. 



The theory r of curves, produced by the revolution 

 of one curve upon another, now occupied the atten- 

 tion of James ; and in this rich and untrodden field 

 he made many interesting discoveries. He found, 

 that the logarithmic spiral was its own evolutc, anti- 

 evolute, caustic, and pericaustic ; and that the cy- 

 cloid had a property analagous to it. The discovery 

 of this constant reproduction of the logarithmic spi- 

 ral was a source of such pleasure to Bernoulli, that, 

 in imitation of Archimedes, he requested that a lo- 

 garithmic spiral should be engraven on his tomb, 

 with the motto of Eadem mutata rcsurgn, a beauti- 

 ful and happy allusion to the future hopes of the 

 Christian. Besides these discoveries, James Ber- 

 noulli solved the problem of the paracentric isochro- 

 nal curve, proposed by Leibnitz in 1689, and also 

 the problem of the curve of quickest descent, which 

 his brother John had proposed in 1697. 



About this time began that famous dispute upon 

 isoperimetrical problems, between James and John 

 Bernoulli, in which their talents were displayed to 

 greater advantage than their dispositions. " These 

 illustrious characters," as the writer of this article 

 has elsewhere observed, " connected by the strongest 

 ties of affinity, were, at the commencement of their 

 distinguished career, united by the warmest affection. 

 John was initiated by his elder brother into the ma- 

 thematical sciences ; and a generous emulation, soft- 

 ened by friendship in the one, and gratitude in the 

 other, continued for some years to direct their stu- 

 dies, and accelerate their progress. There are few 

 men, however, who can support, at the same time, 

 the character of a rival and a friend. The success 

 of the one party is apt to awaken the envy of the 

 other ; and success itself is often the parent of pre- 

 sumption. A foundation is thus laid for future dis- 

 sensions ; and it is a melancholy fact in the history of 

 learning, that the most ardent friendships have been 

 sacrificed on the altar of literary ambition. Such was 

 the case between the two Bernoullis. As soon as 

 John was settled professor of mathematics at Gro- 

 ningen, all friendly intercourse between the two bro- 

 thers was at an end. Regarding John as the aggres- 



