246 Biography of M. Le Comte Lagrange. 



came to the same conclusion ; he perceived the necessity of 

 a demonstration independent of geometry and of analysis. 



In an appendix to the volume having for its title du 

 Mouvement des projectiles dans un milieu non resistant, he 

 seemed wholly to distrust the resources of analysis, and 

 finishes by saying Si mon principe {it is that which Lagrange 

 has since named the principle of the last action) nest pas 

 suffisamment demontre, comme cependant it est conforme 

 a la verite, je ne doute pasqu'au moyen des principes d'une 

 saine metaphyssique on ne puisse lui donner la plus grande 

 evidence, et j'en laisse le soin a ceux qui font leur etat de 

 la metaphysique. 



This appeal, to which metaphysicians did not answer, 

 was understood by Lagrange who excited their jealousy. 



In a short time the young man found the solution of 

 which Euler had despaired. He found it by analysis ; and in 

 giving an account of the way in which he had been led to this 

 discovery, he said positively, to answer the doubts of Euler, 

 that he viewed it, not as a metaphysical principle, but as a 

 necessary result of the laws of mechanics, as a simple 

 corollary of a more general law, which he afterwards made 

 the base of his Mecanique Analytique. (See this work, 

 page 246 of the second edition, or 189 of the first.) 



This noble spirit that excited him to triumph over diffi- 

 culties regarded as insurmountable, and to rectify or com- 

 plete theories still imperfect, appeared to have constantly 

 directed Lagrange in the choice of his subject. 



D'Alembert had thought it impossible to submit to the 

 calculus the motions of a fluid contained in a vessel, if this 

 vessel had not a certain figure. Lagrange demonstrated 

 on the contrary, that there would be no difl^iculty except in 

 the case when the fluid is divided into many portions. Yet 

 then we can determine the places where the fluid ought to 

 be divided into many portions, of which we can determine 

 the motions as if they were isolated. 



D'Alembert had thought, that in a fluid mass such as the 

 earth might have been originally, it was not necessary that 

 the diff*erent layers should be on a level : Lagrange shews 

 that the equations of D'Alembert were themselves only 

 those of strata on a level. 



In opposing D'Alembert with all the respect due to a 



