4 Remarks on M. Delamlre's [July, 



not fail to apply it to this question ; and when he informed Fuler 

 in 1756 that he had succeeded in extending his fine theorem to any 

 system whatever of bodies, he made hi in acquainted with the 

 method of using it to resolve all the problems in dynamics. (See 

 the Melanges de Turin, t. iv. p. 166.) We see likewise, by his 

 prize essay on the Libration of the Moon, that in 1764 he had 

 already perceived that this pretended principle of least action was 

 only a consequence of the principle of virtual velocities. But it 

 was only in his Mechanique Analytiqne that he demonstrated this 

 consequence; and it is there only that he says, without giving any 

 account of the way by which he was led to the discovery, that he 

 regards the principle of the least action, not as a metaphysical 

 principle, but as a simple and general result of the laws of mecha- 

 nics. (P. 189.) 



I shall point out still two slight inaccuracies in the biographical 

 account of Lagrange. 



It is said that the concert of praises of which Lagrange was the 

 object was interrupted only one single time. It would have been 

 better to have said, by one single man ; for Fontaine attacked 

 Lagrange in the Memoirs of the Academy two different times : in 

 1767j on the method of variations; and in 17<>H, on the solution 

 of the problem of tautochrones. Lagrange made two separate 

 answers. He answered the first attack in the fourth volume of the 

 Melanges de Turin, and the second in the Berlin Memoirs for 



1770. 



It is stated likewise that the lectures ot Lagrange at the Poly- 

 technic School, published under the well-known title of a Theory 

 of Functions, are the developement of the ideas contained in two 

 memoirs published in 177-- But he only wrote one memoir on 

 that subject. It is to be found in the Berlin Memoirs for 1 77—* It 

 may be proper on this occasion to mention, that Arbogast, in a 

 paper sent to the Paris Academy in 1JS9, anticipated Lagrange in 

 the application of geometry to the principal idea of this paper of 



1772. 



After these observations, for the most part of little importance, 

 we will proceed to the supplement which we promised, and state 

 faithfully what a long intimacy enabled us to collect from the con- 

 versation of this great mathematician. 



A striking expression of his is noticed in the biographical account. 

 ■• Had I been possessed of a fortune," says Lagrange, " in all 

 probability I should not have devoted myself to mathematics." He 

 must have regarded such an obstacle as a real advantage ; for I 

 remember one day when a young man was presented to him, who 

 devoted himself to mathematics with peculiar ardour, his first 

 question was, " Are you possessed of a fortune ? " and when the 

 answer was not a denial, " So much the worse," replied Lagrange, 

 " the want of fortune, and of the consequence which it gives in 

 the world, is a constant stimulus for which nothing can be substi- 



