BERNOULLI. 



485 



Bernoulli, Ruler. From this solution he afterwards deduced 

 Daniel. t h e lateral vibrations of an elastic rod fixed at one 



v v~-' extremity; ar 1 investigated the vibrations of a co- 

 lumn of air impelled with different degrees of force 

 and velocity : and the results of his researches wen- 

 found to accord with the most accurate experiments. 

 His memoirs on these subjects will be found in the 

 Mem. Acad. Par. 1762, p. 442. Comment. Petrop. 

 torn. iii. p. 13, 62. ; torn; xiii. p. 105, 1G7. A'or. 

 Com. Petrop. torn. xv. p. 862. ; torn. xvi. p. 257- 



In the year 1716, Bernoulli discovered a new prin- 

 ciple in dynamics, called the Conservation of the mo- 

 mentum of rotatory motion, of which he published 

 an account in the memoirs of the academy of Berlin 

 for 1716. The same discovery was made nearly 

 about the same time by Euler and the Chevalier 

 d'Arcy. 



The only separate work of any magnitude which 

 was published by Bernoulli, appeared in 1738, under 

 the title of Hydrodynamica, sen de viribus et mclibus 

 Fluidorum commcnlarii. The theory of the motion 

 of fluids having hitherto been treated in a vague and 

 unphilosophical manner, it was reserved for Bernoulli 

 to lay the foundation of a new theory, more conform- 

 able to experience. He supposed, that the surface 

 of a fluid, discharging itself through an orifice, al- 

 ways continued horizontal ; and that all the points of 

 the elementary horizontal strata, into which the fluid 

 mass is conceived to be divided, descend vertically, 

 with velocities inversely proportional to the horizon- 

 tal breadth of the strata to which they belong. By 

 employing the principle of the conservation of living 

 forces, he determined the motion of the strata with 

 such elegance and address, that the Abbe Bossut 

 pronounces the work which contains them to be one 

 of the finest specimens of mathematical genius. A 

 more direct theory, however, was afterwards given 

 by Maclaurin and John Bernoulli ; but it is to D'A- 

 lembert that we are indebted for a complete theory 

 of the equilibrium and the motion of fluid bodies. 



The curious and important subject of probabilities 

 occupied much of Bernoulli's attention. After lay- 

 ing down a new principle instead of that which was 

 employed by Fermat, Pascal, Huygens, and James 

 Bernoulli, he applied it to the subject of innoculation, 

 to the observations of practical astronomy, to the ir- 

 regularities in the motion of time-pieces, and to some 

 subjects of political economy. 



Bernoulli had the high honour of gaining ten aca- 

 demical prizes, which he disputed with the most il- 

 lustrious geometers of Europe. At the age of 24 

 he carried off the prize for the best construction of 

 a clepsydra for measuring time at sea ; and in 1754, he 

 divided the prize with his father for the best expla- 

 nation of the variation in the inclinations of the pla- 

 netary orbits. His father could not conceal the mor- 

 tification which he felt at being thus brought down 

 to a level with his son. The love of glory was the 

 ruling principle in his heart ; and all the feelings of a 

 father and a man were instantly extinguished when 

 they came in competition with his reputation as a 

 philosopher. The reproaches with which be loaded 

 his son might have found some palliation in the irri- 

 tability of his temper, when the judgment of the 

 academy was first pronounced, but no apology can 



be offered for the permanency of a resentment so un- 

 natural and unmanly. Never, perhaps, was there a 

 case in the rivalry of talents that afforded such an 

 opportunity for the finest exhibition of feeling, and 

 for the noblest display of character ; and never, per- 

 haps, was there a case in which genius appeared in 

 such an offensive and mortifying form. While the 

 exultation of youthful genius ought to have been 

 tempered in the one by filial regard, a paternal pride- 

 ought to have animated the other, and the father 

 ought to have gloried in having transmitted to his 

 son the full inheritance of his genius, without having 

 impaired or resigned the original possession. 



In 1740, Bernoulli divided the prize on the sub- 

 ject of tides with Euler and Maclaurin ; and in this 

 and the preceding dissertation he supported the New- 

 tonian theory, which his father and his uncle had uni- 

 formly endeavoured to overturn. He carried of! also 

 the prize which was offered in 17-1-3, for the best 

 treatise on the mariner's needle. In 1747, he divided 

 with an anonymous author, the prize for finding 

 the time at sea when the horizon is invisible. His 

 dissertation on currents gained the double prize in 

 1751 ; and in 1753, he was rewarded with the prize 

 for the best method for supplying the action of the 

 wind in large vessels. The last reward which he 

 gained, was the prize for diminishing the rolling and 

 the pitching of vessels, without injuring their other 

 qualities. In the year 1748, he succeeded his father in 

 the Academy of Sciences ; and such was the extent of 

 his fame, that he was elected a member of the Royal 

 Society of Loudon, of the Institute of Bologne, and 

 of the Academies of Petersburgh, Berlin, Turin, and 

 Manheim. 



Though Bernoulli possessed a delicate constitution,. 

 yet the regularity of his life, and the serenity of his 

 temper, exempted him from those diseases to which 

 he might otherwise have been subject. During a 

 long life of 83 years, he retained the complete use of 

 all his faculties, and the last of his works exhibits the 

 same profound genius which marked his earlier pro- 

 ductions. For some years before he died, he withdrew 

 himself from the fatigues of society, and associated 

 only with a few select friends, with whom he had 

 been long connected. The attack of an asthma, how- 

 ever, began to impair his strength, and at last carried 

 him off on the morning of the 17th of March 1782, 

 when he was found dead in his bed. 



Daniel Bernoulli was distinguished in private life 

 l>y his simple and unassuming manners, which were 

 neither marked by false diffidence, nor affected auste- 

 rity. He was charitable and humane without osten- 

 tation ; and though his affairs were managed with 

 that laudable economy which shuns the expenses of 

 an idle vanity, he was never guilty of that avarice 

 which some of his enemies have endeavoured to fix 

 upon his name. Actuated by a love of peace, or 

 warned perhaps by the fatal example whicli was ex- 

 hibited in the conduct of his father and his uncle, his 

 life was never embittered by those malignant dissen- 

 sions which generally rage among men of genius. The 

 humour which is occasionally displayed in some of 

 his controversial writings, is a proof that the tran- 

 quillity which he enjoyed, was more the offspring of 

 reason than of insensibility.. Possessed of such qua* 



Bernoulli, 

 Daniel. 



