66 Lagrange's Memoifs. 



tive to his lessons. He selected some of them whom he made his 

 friends. 



From this association sprang the Academy of Turin, which pub- 

 lished in 1759 a first volume, under the title of Actes de la societe 

 privee. We therein see Lagrange directing the physical researches 

 of doctor Cigna, and the works of the Marquis de Saluces. He 

 furnished to Foncenex the analytical part of his memoirs, at the 

 same time leaving to him the care of developing the arguments on 

 which his formulas rested. In effect, we notice already in these 

 memoirs this pure analytical step which afterwards characterised the 

 great productions of Lagrange. He had found a new theory of the 

 lever. It constituted the third part of a memoir that had much suc- 

 cess. Foncenex in return, was put at the head of the navy which 

 the king of Sardinia was then forming. The two first parts seem of 

 the same style and from the same hand. Are they alike from La- 

 grange ? He has not positively claimed them. What however, can 

 direct our conjectures upon the real author, is, that Foncenex soon 

 ceased to enrich the collections of the new Academy, and that Mon- 

 tucla, ignorant of what has been revealed to us by Lagrange at his 

 last moments is astonished that Foncenex, after being so favorably 

 announced, broke off researches that could have obtained for him a 

 great name. 



Lagrange abandoning to his friend isolated solutions, published 

 at the same time under his own name some theories which he prom- 

 ised to follow out and develope. Thus after having given new 

 methods for maxima and minima of every kind, after having shewn 

 the insufficiency of the the known formulas, he announced that he 

 would treat this subject, which otherwise appeared to him interest- 

 ing, in a work which he was preparing, and in which, too, are seen 

 deduced from the same principles all the mechanics of bodies, 

 whether solid, or fluids. Thus, at twenty three years he had al- 

 ready laid the foundation of great works which have since caused 

 the wonder of savans. 



In the same volume, he brings back to the differential calculus, 

 the theory of recurring series, and the doctrine of chances, which, 

 until now, had been treated only by indirect methods, and w'hich he 

 establishes upon the most natural and the most general principles. 



Newton had undertaken to submit to the calculus the motions of 

 fluids : he had made researches on the propagation of sound. His 

 principles were insufficient and even defective ; and his suppositions 



