244 Biogra'phy of M. Le Comte Lagrange. 



line, he reduced this problem to that of vibrating cords, 

 about which the greatest geometers were divided ; he 

 sBowed that their calculations were insufficient to decide 

 the question ; he undertook a general solution by an 

 analysis new as it was interesting, since it permits of resolv- 

 ing at once an indefinite number of equations, and since it 

 extends even to discontinued functions : he established 

 more firmly the theory of the mixture of the simple and 

 regular vibrations of D. Bernouilli : he shows the limits 

 between which this theory is exact, and beyond which it is 

 defective; then he arrives at the construction given by 

 Euler, a true construction, although the author had arrived 

 at it only by calculations which were not sufficiently 

 rigorous : he answers objections raised by D'Alembert ; 

 he demonstrates that whatever figure we give to the cord, 

 the duration of oscillations will be always the same, a truth 

 of which for experiment D'Alembert had judged the demon- 

 stration very difficult or even impossible ; he passes to the 

 propagation of sound ; treats of simple and compound 

 echoes, of the mixture of sounds, of the possibility that 

 they spread in the same space without disturbing one 

 another, and demonstrates rigorously the generation of 

 harmonical sounds ; he announces lastly, that his object is 

 to destroy the prejudices of those who still doubt if mathe- 

 matics could ever shed true light on physics. 



Euler felt the worth of the new method, and selected it 

 for the object of his profound meditations. D'Alembert 

 did not coincide. In his private letters, as in his printed 

 memoirs, he proposed numerous objections, to which La- 

 grange has since answered, but which can at least leave 

 this doubt ; . . How, in a science to which we grant univer- 

 sally the merit of exactness, can it be that men of the first 

 order are divided among themselves, and for a long time 

 dispute ? 



The first answer of Euler was to cause Lagrange to be 

 associated with the Academy of Berlin. Upon announcing 

 to him this nomination, on the 2nd of Oct., 1759, he said 

 to him : *' voire solution duprobleme des isoperimetres ne laisse 

 rien a desire et je me rejouis que ce sujets, dont je metais 

 presque seul occupe depuis Ics premieres tentatives, ait tte porte 

 par vous au plus haut degrt de perfection. L' importance de 



