BORDA (Joni; CHARLES), w Mathematician and Nautical Astronomer, celebrated for his improve- • meats in the theory of Hydraulics and Pneumatics,, and in the construction of instruments for observa tion. He was born at Drax, the 4th of May 1733, and waseriginallyclestined for the bar, but abandon ed the pursuit of the law in favour of a military life which he considered as better calculated to afford. him opportunities for the cultivation of his mathe matical talents, and, for the application of the results . of his studies to practice. His acquirements in science had very early attracted the attention of D'Alembert, who predicted his future eminence, and warmly recommended his turning his thoughts to the occupation of a place in the Academy. He obtained a commission in the Light Cavalry, and was appointed Teacher of Mathematics to the corps ; and, in 1756, he presented to the Academy a Sciences (A.) A Memoir on the Paths 9f Bombs, which was ordered to be printed in the collection of the Swans Etrangers, but which has not excited much attention. He was elected in the same year ' a member of the Academy ; and in the next he was present at the battle of Hastinbcck, in the capacity of Aide-de-Camp to the celebrated General Maillebois, to whom he looked up as a great master in the art of War.
He was afterwards admitted into the corps of Engineers, without the usual form of examination into his qualifications ; and, being stationed at a sea port, the occurrences of the place naturally directed his attention anew to the phenomena of the resist ance of fluids. He published, in 1763, a detailed memoir on this subject (B. Mtn. Ac. Par. 1768, p. 858), in which he relates a variety of experiments, showing, that the resistance of the air is actually pro portional to the square of the velocity, as had com monly been supposed from theoreti41 considerations. He also determines, by other experiments, the mag nitude of the resistance to the motion of a sphere, and proves, that nothing can be more erroneous the* the supposition, that the resistance to an oblique surface decreases as the square of the sine of the angle of incidence. He also finds, that the resist ance to the motion of a cube, in the directions of the diagonal of its base and of one of the sides, are as 21 to 16, while the calculations of former theorists had made the resistance greatest in the direction of the side.
In 1766, he published an Essay on the discharge of fluids through the orifices of vessels (C. Mini. Ac. Para 766, p. 579), in which he first states the objections to considering the different strata of a fluid as descending in all cases very nearly in parallel directions; he examines the contraction of the jet after its from the orifice, and determines some of the effects of abrupt changes in the velocity of the fluid passing through pipes or apertures of different forms, He contributed, in 1767, to the publications of the Academy, an important Memoir on Water Wheels (D. p. 270), which has escaped the notice of his able
Biographer M. Lacroix. He observes, in this paper, that the simple hypothesis of a resistance varying as the square of the velocity, which is so near the truth in common cases, where a number of particles, pro portional to the velocity, strikes, in a given time, upon a small exposed surface with a force also pro tional to the velocity, is totally inapplicable to the action of a confined stream upon the floatboards of a wheel, since, in 'this instance, the number of par ticles concerned cannot vary materially with the velocity, the whole stream being supposed to operate in all cases upon the successive floatboards; so that the analogy would require us to iuppose the force in this case nearly proportional to the simple relative velocity ; a conclusion which agrees remarkably well with the experiments of some practical authors.
The same volume contains a continuation of M. Borda's researches relating to the resistance of oblique surfaces (E. Mem. Ac. Par. 1767, p. 495), with a statement of experiments still more con clusively confuting the received hypothesis, respect ing oblique impulse, than his former investigations had done. We also find in it an Essay on isoperi metrical problems (F. p. 551), in which it is shown, that Euler's method of treating them, which had been in great measure abandoned by its equally pro found and candid author, in favour of the more ge neral and more elegant calculations of Lagrange, was still capable of affording all the results that had been derived from the method of variations ; and he even pointed out some deficiencies in the first Me moir of Lagrange, which contained the detail of his ingenious invention. These investigations of M. Borda afford collateral evidence of the strict truth of the demonstrations of both his great predecessors ; and though they have been little employed by later Mathematicians, yet it must be admitted to be of some importance, in enabling us to appreciate the value of a new mode of calculation, to determine whether its results are or are not such, as might be obtained, with almost equal convenience, by methods before in use.