201 



The sudden death of his father, leaving his mother arid four 

 children, of whom Charles was the eldest, without any adequate main- 

 tenance, compelled him, before the close of his seventeenth year, 

 to resort to private tuition for the support of himself and his family ; 

 and three years afterwards he was recommended to the Due de 

 Broglie, as tutor to the brother of Madame de Broglie, the son of 

 Madame de Stael. At the close of the year 1823, he accompanied his 

 pupil to Paris, and though he shortly afterwards returned to Geneva, 

 he found no sufficient occupation there, and he finally resolved, in 

 company with his intimate friend and school-fellow, M. Colladon, 

 the present distinguished Professor of Physics at Geneva, to seek his 

 fortune in the great city, which was then, and had long been, the 

 undisputed metropolis of European science. Sturm had already be- 

 come very favourably known to mathematicians by several articles in 

 the ' Annales de Mathematiques ' of M. Gergonne, on different 

 branches of analysis and geometry, and the strong recommendations 

 which he and his companion bore with them from Lhuillier, and the 

 kind offices of M. Gerono, made them known to Ampere, Fourier, 

 Arago, and other eminent members of the Institute, who recom- 

 mended them to pupils as a means of support. Sturm afterwards 

 obtained employment upon the 'Bulletin Universel,' under Baron 

 Ferussac, and was, in fact, a subordinate in the office of that journal 

 when he published his well-known Theorem. He and his friend 

 speedily began to feel the influence of breathing in an atmosphere of 

 science, and their joint labours were rewarded by a distinction of no 

 ordinary importance, when the Academy of Sciences awarded to them 

 the great prize of mathematics proposed for the best Essay on the 

 Compression of Liquids. 



The determination of the number of real roots of a numerical 

 equation which are included between given limits, is a problem 

 which had occupied the attention of the greatest analysts of the past 

 age, of Waring, of La Grange, and more especially of Fourier, who 

 of all other analysts had made the nearest approaches to its practical, 

 though he had failed in its theoretical, solution : the attention of 

 Sturm had been for some time directed to this class of researches, 

 which he pursued with remarkable continuity and diligence, encou- 

 raged, as he himself assures us, by the instructions and advice of this 

 eminent master. The result was the discovery of the theorem which 



VOL. VIII. Y 



