will be for ever associated with his name, and which conquered 

 the difficulty which had embarrassed all his predecessors, and thus 

 permanently extended the dominion of analysis ; a rare good for- 

 tune, which though frequently denied to the most illustrious cul- 

 tivators of the sciences, is always reserved to those only who are 

 enabled, by the extent and accuracy of their knowledge and the 

 clearness of their views, to follow out the glimmerings of light which 

 escape the observation of ordinary eyes. 



The memoir which contained this important theorem was pre- 

 sented to the Academy on the 25th of May, 1829, and rapidly con- 

 ducted its author to fortune and public honours. The connexion 

 of its author with the ' Bulletin Universel ' enabled him to give an 

 immediate account of his method to the world ; the paper itself 

 was not published till some years afterwards, in the " Memoires des 

 Savans Etrangers." 



In the course of a few years he was chosen a member of the 

 principal scientific societies of Europe : the Copley Medal was given 

 to him by this Society : he was elected a member of the Academy, 

 as the successor of Ampere, in 1836 : in the same year he was made 

 Professor of Mathematics, upon the special recommendation of Arago, 

 at the College Rollin, Repe'titeur at the Ecole Polytechnique in 

 1838, and in 1840 he was deemed worthy to succeed to the chair of 

 Mechanics at the same school, which had been so long honoured by 

 the occupation of Poisson, the most illustrious of the successors of 

 La Place. It was not without some difficulty that the substantial 

 rewards of his scientific achievement were obtained: he was a 

 foreigner, and naturally placed at a disadvantage in a contest with 

 native competitors. It is right to notice this, both for the honour of 

 France and as a proof of the very high reputation which Sturm had 

 attained. 



The subsequent memoirs of Sturm, whether first presented to the 

 Academy or not, were chiefly printed in the Journal of M. Liouyille, 

 an analyst of congenial tastes and pursuits with his own, with whom 

 he lived on terms of the most affectionate friendship. Two of these 

 memoirs, relating to the discussion of differential and partial differ- 

 ential equations, such as present themselves so commonly in the 

 solution of the more important problems of mathematical physics, 

 possessed a merit so extraordinary, that M. Liouville a most compe- 



