68 Lagrange' s Memoirs. 



instruments, the size and position of their holes, and the velocity 

 of the sound in general. It is probable in effect, that in these in- 

 struments particularly, the air should no longer be considered as di- 

 vided into straight lines ; at least, however, the solution explains the 

 famous experiments of Tartinl, if we admit that this celebrated Pro- 

 fessor could have been deceived in putting the octave in the place 

 of the real sound which he heard. 



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

 object of his most profound meditations. D'Alembert did not coin- 

 cide. In his private letters, as in his printed memoirs, he proposed 

 numerous objections, to which Lagrange has since answered but 

 which can at least leave this doubt ; . . . How in a science to which 

 we grant universally the merit of exactness, can it be that men of 

 the first order are divided against themselves, and for a long time 

 dispute ? The reason is, that in problems of this kind, the solutions 

 of which cannot be submitted to the proof of a direct experiment, 

 besides the part of the calculus which is subjected to rigorous laws, 

 and upon which it is not possible to have two opinions, there is al- 

 ways a metaphysical part which leaves doubt and obscurity. The 

 reason is, that in the calculations themselves, geometers are often 

 content \\\\\\ pointing out the steps of demonstrations, while they sup- 

 press developments that are not always so superjluous as they have 

 been thought ; while the care of filling up their gaps require a labor 

 which the author only has courage to undertake, and while, in fine, 

 he himself led on by his subjects, and by the habit which he has ac- 

 quired, permits himself to pass over intermediate ideas, and antici- 

 pates his resulting equation, instead of arriving at it, step by step, with 

 an attention that would escape all mistake. It is that very great 

 geniuses cannot be made to harmonize together at first, for want of 

 being read with sufficient attention to be well understood. 



The first answer of Euler was to cause Lagrange to be associated 

 with the Academy of Berlin. Upon announcing to him this nom- 

 ination, on the '2nd of Oct. 1759, he said to him : "voire solution 

 du probleme des isoyerimetres ne laisse rien a desire etje me rejou- 

 is que ce sujets, dontje m^etais presque seul occupe depuis les prem- 

 ieres tentatives, ait ete porte par vous au plus haut degre de perfec- 

 tion, U importance de la matiere m'a excite a en tracer a Vaide de 

 vos lumieres, une solution analytique a laquelleje ne donnerai au- 

 cune pnblicite jusqu a ce que vous-meme ayer publie la suite de vos 

 recherches pour ne vous enlever aucune partie de la gloire qui vous 

 est dueJ'^ 



