- We are indebted to Borda likewise for many inge.
nious experiments and observations on the motion of fluids through different orifices. He prepared a theo ry of the motion, f fluids.different from that which had been given by. Bernoulli and D'Alembert, and he made new experiments on the vents contracta...:' In the year 1767, he published an excellent disser, tation in the Memoirs of.the Academy, entitled, life 'noires sztr les Roues Hydrauliqucs. In that. valuable paper he has shewn, that an undershot wheel.pro. duces a maximum effect when its velocity is! one-hay' that of the current, though in practice,the,velocity.is never more than three-eighths that ..of the He proved, after theory,.before Smeaton had determined it by experiment, that the effect of overshot wheels.increases with the SloWness of their motion • that they are capable of raising, through the height of the fall, a quantity of water equal to that by which they are driven ;, that under shot vertical wheels produce only three.eighths of this effect ;- that horizontal, wheels produce about one half of this effect with plain floatboards,•and a little more than one-half with curvilineal floatboards...
This memoir of Borda was followed by.another,.in 1768, on the construction of water-pumps. About this time his attention was directed to isoperimetrical problems, and he had the honour of obtaining the same results as Lagrange, though by a different me. thod.
The last work of our author, which appeared in the Memoirs of the Academy, was a dissertation on the Theory of Projectiles. The immense differences between the theory and the experimental results which bad been obtained on this subject, stimulated the ingenuity of•Borda. He found, that the range of a twenty-four pounder was diminished nine-tenths by the resistance of the air ; and that the diminution would be still greater when the flight of the ball was opposed by wind ; and. he has formed a table, shew. ing the results calculated for pieces of all calibres, for all angles of elevation, and for.various ranges and degrees of velocity. , — The success and utility of the labours of Borda brought him under the particular notice of M..Pras lin, the minister of marine, who was anxious to have the benefit of his talents in the French navy, The practice of the service,, however, opposed such a plan, and the officers of the navy naturally resisted a mea sure which might ultimately prove injurious to their own interests. But M. de Praslin had taken his re
solution : He considdred the brilliancy of Borda's ta lents as entitling him to. an exception from general usage, and he therefore appointed him sub-lieutenant in the navy.
Borda made his first appearance in his lion in the year 1768, • but, till the year. 1771, no events occurred which are deserving of -The prizes which were at this time offered, both in•Eng land and France, for the improvement of-chronome ters, to find the longitude at sea, naturally produced in both countries a great variety of inventions. The French government having determined• to try -the'ac curacy of some of. these timepieces, and of <,ther in struments which were subsidiary to the great objf.ct of finding the longitude, •the Academy of 'Scit•neta appointed Borda and Pingre as commissioners fey making these trials ; and they were ordered- to sail in 'the ,Flora frigate,r under the command of.Ver- ' dun cle.la- This voyage was performed in the,years 1771 and 1772, during which they touched at.various 'places: in .Europe, Africa, and America, and completelyi fulfilled. the objects. for which they out.. ' An account of this voyage was pub lished..' at :Paris in •1778, in .2 ;vols. 4to, entitled, Follagefait par ordre cht.Roy en 1771 et 1772, &c. A shorter acconnt.of the results obtained during the expeditionwill.be found in the Memoirs of the Aca demy for ,1773. .
The zeal and success.with which Borda had per. forded. his•part in this expedition, pointed him out as the fittest person to be employed in determining the position of the Canary Isles. With this view he was promoted. to the rank of lieutenant and in the :year,following he set sail in the frigate La Bous sole, having under his orders the Espiegle, command ed by M. de Puysegur. • During this interesting voyage he,determined the relative • and -absolute post tion.of the Canary Isles,,by means of several points taken on each, and on the coast of Africa.' He veri fied the height of the Peak of Teneriffe, and calcu lated tables for finding the position- of a ship at sea from-the apparent height of this mountain.. He ex amined the peak itself with great care, and brought home with him several mineralogical specimens.