M. Arago's Historical Eloge of Joseph Fourier. 7 



tionable method. From that instant the dignity of science 

 was vindicated ; but in such a case, we could not say with the 

 poet, 



Le temps nefait rien d, Vaffaire. 



Now, although the processes invented by Lagrange, simple in 

 their principle, and applicable to all cases, have theoretically 

 the merit of leading to the result with certainty, they would 

 require, on the other hand, calculations of a repulsive length. 

 It remained then to perfect the practical part of the question : it 

 was necessary to find means to shorten the process, without 

 rendering it less certain. Such was the principal object of the 

 researches of Fourier, and this object he attained in a great 

 measure. ' 



Descartes had already found, in the order according to which 

 the signs of the different terms of any numerical equation suc- 

 ceed each other, the means of deciding, for instance, how many 

 real and positive roots this equation may have. Fourier did 

 more : he discovered a method of determining how many posi- 

 tive roots of an equation are included between two given quan- 

 tities. Here certain calculations become necessary, but they 

 are very simple, and, whatever degree of precision be desired, 

 they lead without trouble to the required solutions. 



I am doubtful if it is possible to mention a single scientific 

 discovery of any importance, which has not raised discussions 

 about priority. Fourier's new method of resolving numerical 

 equations, forms a striking illustration of this general rule. It 

 is proper, after all, to acknowledge that the theorem which serves 

 as the basis of this method was first published by M. Budan ; 

 that, according to a rule formally sanctioned by the principal 

 academiesof Europe, and from which scientific historians could 

 not deviate without falling into uncertainty and confusion, M. 

 Budan ought to be considered as the investor. I assert, how- 

 ever, with equal confidence, that it would be impossible to deny 

 to Fourier the merit of having attained his object by his own 

 efforts. I even regret, that in order to establish rights which 

 no one thought of denying, he should have j udged it necessary 

 to have recourse to certificates of former pupils of the Poly- 

 technic School, or of professors of the University. Since our 



