Euler. From this solution he afterwards deduced the lateral vibrations of an elastic rod fixed at one 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 were found to accord with the most accurate experiments. His memoirs on these subjects will be found in the Menz. Acad. Par. 1762, p.412. Comment. Petrop. tom. iii. p. 13, 62. ; tom: xiii. p. 105, 167. Nor. Cann. Petrop. torn. xv. p. 362. ; tom. xvi. p. 257.
In the year 1746, Bernoulli discovered a new prin ciple in dynamics, called the Conservation of the mo ment:on (21 rotatory motion, of which he published an account in the memoirs of the academy of Berlin for 1746. 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 Hydrodynandea, see de viribus et milks Flnidorum comnzcntarii. 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 Bossirt pronounces the work which contains them to be one of the finest specimens of 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 conceal the mor tification which he felt at being thus brought down to a 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 tle 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 afforded such ail 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 off also the prize which was offered in 1743, 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 dis'sertation 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 London, of the Institute of Bologne, and of the Academies of Petersburgh, Berlin, Turin, and Manhcim.