142 JOSEPH FOURIER. 



discovered a metliod for dcterininmg what number of the equally posi- 

 tive roots of every equation may be found included between two given 

 quantities. Here certain calculations become necessary, but they are 

 very simple, and whatever be the precision desired, they lead without 

 any trouble to the solutions sought for. 



I doubt whether it were possible to cite a single scientific discovery 

 of any importance which has not excited discussions of priority. The 

 new method of Fourier for solving numerical equations is in this respect 

 amply comprised within the common law. We ought, however, to ac- 

 knowledge that the theorem which serves as the basis of this method 

 was lirst published by M. Budan ; that according to a rule which the 

 principal academies of Europe have solemnly sanctioned, and from which 

 the historian of the sciences dares not deviate without falling into arbi- 

 trary assumptions and confusion, M. Budan ought to be considered as 

 the inventor. I will assert with equal assurance that it would be im- 

 possible to refuse to Fourier the merit of having attained the same ob- 

 ject by his own eflbrts. I even regret that, in order to establish rights 

 which nobody has contested, he deemed it necessary to have recourse 

 to the certificates of early pupils of the Polytechnic School or profes- 

 sors of the University. Since our colleague had the modesty to suppose 

 that his simple declaration would not be sufiieieut, why (and the argu- 

 ment would have had much weight) did he not remarii in M'hat respect 

 his demonstration differed from that of his competitor? — an admirable 

 demonstration, in effect, and oue so impregnated with the elements of 

 the question, that a young geometer, M. Sturm, has just emi)loyed it to 

 establish the truth of the beautiful theorem by the aid of which he de- 

 termines not the simple limits, but the exact number of roots of any 

 equation whatever which are comi)rised between two given quantities. 



We had just left Fourier at Paris, submitting to the Academy of Sci- 

 ences the analytical memoir of which 1 have just given a general view. 

 Upon his return to Auxerre, the young geometer found the town, tJbe 

 surrounding country', and even the school to which he belonged, occu- 

 pied intensely with the great questions relative to the dignity of human 

 nature, philosophy, and politics, which were then discussed by the ora- 

 tors of the different parties of the National Assembly. Fourier aban- 

 doned himself also to this movement of the human mind. He embraced 

 with enthusiasm the principles. of the Eevolution, and he ardently asso- 

 ciated himself with everything grand, just, and generous which the pop- 

 ular impulse olfered. His i)atriotism made him accept the most difticult 

 missions. AVe may assert, that never, even when his life was at stake, 

 did he truckh^ to the base, covetous, and sanguinary passions which dis- 

 played themselves on all sides. 



A member of the popular society of Auxerre, Fourier exercised there 

 an almost irresistible ascendency. One day — all Burgundy has pre- 

 served the remembrance of it — on the occasion of a levy of three hun- 

 dred thousand men, he made the words honor, country, glory, ring so 



