801 



STURM, JACQUES CHARLES FRANCOIS. 



STURZ, HELFRICH PETER. 



802 



The principal works of Sturm are, ' Collegium Experimental sive 

 Curiosum, in quo primaris hujus seculi Inventa et Experimenta 

 Physico-mathematica An. 1672,' Niirnberg, 2 vole. 4to, 1676; 'Come- 

 tarum Hevelii et Petiti Hypotheses,' Altdorf, 4to, 1677; 'Mathesis 

 Euucleata,' 1 vol. 8vo; 'Mathesis Juvenilis,' 2 vols. 8vo, of which the 

 second contains a tract entitled ' Scientia Cosmica, sive Astronornica 

 Spherica, et Thoorica Tabulis comprehensa;' Niirnberg, 1684; ' Physicsc 

 Conciliatricis Conamina, Niirnberg, 1685, being a collection of the 

 principal dissertations before published on the different systems of 

 philosophy. Sturm also published a translation into Latin of the 

 1 Hydraulic Architecture ' of Bockler ; a German translation of Archi- 

 medes; and a collection of letters to Dr. Henry More of Cambridge, 

 on the weight and elasticity of the air. In 1684 he published a second 

 part of the collection of discoveries made up to that time; and 

 editions of both parts, together with the letters to Dr. More, 

 were published in 1701 and 1715 ; these contain many curious 

 experiments. 



STURM, JACQUES CHARLES FRANCOIS, the discoverer of 

 the celebrated thi orem which bears his name, was born at Geneva in 

 September 1803, of a family which had quitted Strasbourg in the 

 middle of the last century. After completing his school education 

 and his classical studies at the college with remarkable success, he 

 became in his fiftt enth year a student of the university of his native 

 city, where he made rapid progress in the study of mathematics and 

 philosophy. The sudden death of his father, leaving his mother and 

 four children, of whom Charles was the eldest, without any adequate 

 maintenance, 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 as tutor to 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 French metropolis. Sturm had already become favour- 

 ably known to mathematicians by several articles in the 'Annales des 

 Mathdmatiques ' of M. Gergonne, published at Nimes, 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, an eminent teacher of mathematics at Paris, 

 made them known to Ampere, Fourier, Arago, and other eminent 

 members of th'e Institute of Sciences, who recommended them to 

 pupils as a means of support. Sturm afterwards obtained employment 

 upon the ' Bulletin Universelle,' under Baron de Fdrussac, and was in 

 fact a subordinate in the office of that journal when he published his 

 theorem. The joint labours of Sturm and his friend were shortly after 

 rewarded by a distinction of no ordinary importance, when the 

 Academy of Sciences of the Institute awarded to them, on June llth, 

 1827, the great prize of mathematics proposed for the best essay 

 on the compression of liquids. Their ^memoir was inserted in the 

 ' Memoires par divers Savants ' (' Savants Etrangers '), vol. v., published, 

 agreeably to the very inconvenient usage of the Academy, eleven years 

 afterwards, in 1838. 



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 Lagrange, 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, encouraged, as he 

 himself assures us, by the instructions and advice of this eminent 

 master. The result was the discovery of the theorem which will be 

 for ever associated with his name, and which conquered the difficulty 

 that had embarrassed all his predecessors, and thus permanently 

 extended the dominion of analysis. 



The memoir which contained this important theorem was presented 

 to the Academy on the 23rd of May 1829, supplementary papers being 

 read at the two following meetings ; and rapidly conducted its 

 author to fortune and public honours. His connection with the 

 ' Bulletin Universel ' enabled him to give an immediate account of 

 his method to the world (' Bull. Univ. des Sciences Math. Phys. et 

 Chim.,' vol. xi. p .419, art. 271, 272, 273). The paper itself was n.it 

 published till the year 1835, in the ' Me"moires des Savants Etrangers,' 

 vol. vi., where it appears without a date. 



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

 cipal scientific societies of Europe : 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, re'pe'titeur at the Ecole Polytechnique in 

 1838, and in 1840 he was appointed to succeed Poisson in the chair of 

 Mechanics in the same school. In 1840 also, he was elected a foreign 

 member of the Royal Society of London, and received the Copley 

 Medal, " for his valuable mathematical labours in the solution of a 

 problem which has baffled some of the greatest mathematicians that 

 the world has produced." The first announcement of the theorem in 

 the English language was not made until 1835, when Professor J. R. 

 Young, of Belfast, inserted the substance of Sturm's memoir in his 



BIOG. DiV. VOL. V. 



work entitled ' The General Theory and Solution of Algebraical 

 Equations,' published in that year. The first intimation of it had 

 reached him in the mouth of May, when his own work was in great 

 part printed, and disregarding a disparaging comment of Lacroix, he 

 thought the discovery of sufficient importance to justify the destruc- 

 tion of many pages of his manuscript prepared for the printer, and 

 the suspension of the work until the volume of the 'Savants Etrangers 1 

 should be published. Thia he received in July, and his own work 

 was published in August. To the appreciation and zeal of this 

 analyst, whose recognition and promulgation of the value of Sturm's 

 labours were thus both immediate and simultaneous, British mathema- 

 ticians, as well as M. Sturm himself, were greatly indebted. In the 

 preface to his ' Mathematical Dissertations ' (one of which is devoted 

 to the theorem) dated November 25, 1840 only five days before the 

 presentation of the Copley medal he adverts to Sturm's discovery as 

 at that time exciting considerable interest among analysts, as well in 

 this country as on the continent ; and he then expresses his own 

 estimation of it in the following terms : " I believe that I have already 

 contributed somewhat to extend the knowledge of this important 

 theorem among British analysts; and although it has been since dis- 

 paraged and undervalued ha certain quarters, I have alway a entertained 

 the conviction that it must eventually supersede every other method 

 at present known for effecting the complete analysis of a numerical 

 equation." In Professor Young's subsequent introductory volume on 

 1 The Analysis and Solution of Cubic and Biquadratic Equations,' pub- 

 lished at the beginning of 1842, he invited the attention of the young 

 analyst to Sturm's method ; and the second edition of his former 

 work on equations, entitled ' The Theory and Solution of Algebraical 

 Equations of the t'igher Orders,' which appeared early in the follow- 

 ing year, is chiefly devoted to the analysis and developments of that 

 method and the previous theories of Budan and Fourier. 



In France it was not without some difficulty that the substantial 

 rewards of his scientific achievements 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. 

 Liouville. Two of these memoirs, relating to the discussion of 

 differential and partial differential equations, such as present them- 

 selves so commonly in the solution of the more important problems 

 of mathematical physics, possessed a merit so extraordinary that M. 

 Liouville a most competent judge declared, at a time when he was 

 himself a competitor with Sturm for a place in the Academy, " that 

 impartial posterity would place them by the side of the finest memoirs 

 of Lagrange." 



The first of these two memoirs was presented in 1833 to the con- 

 cours for the great prize of mathematics, to be awarded by the 

 Academy in 1834 for the most important discovery in that science 

 made known within the preceding three years. The academy con- 

 ferred the prize on Sturm not for the memoir which he had 

 submitted to the judgment of the commission, but for that which 

 contained his celebrated theorem and which had been presented in 

 1829. Other memoirs relate to optics, mechanics, pure analysis, and 

 analytical geometry, and embrace the most difficult questions which 

 have been treated in those several branches of science. One of the 

 latest of these was a communication to the academy on the theory of 

 vision, and is remarkable both for the geometrical and analytical 

 elegance with which many questions subsidiary to the theory are 

 treated in it. It confirms generally, with one important exception 

 relating to the asserted muscularity of the crystalline lens and the 

 changes attributed to its action, the views of the late Dr. Thomas 

 Young [YOUNG, THOMAS] in his well-known memoir on this subject : 

 Dr. Young himself, it must be remembered, once relinquished his 

 belief in the muscularity of the lens, though he finally resumed it. 



Sturm visited England in 1841, and gave the mathematicians with 

 whom he conversed a high impression, as well of the extent of his 

 knowledge as of his inventive power. 



The health of M. Sturm, which had previously been remarkably 

 vigorous, began to decline in 1851, probably in consequence of his 

 laborious public employments and the unremitting severity of his 

 studies. He died on the 18th of December 1855, to the deep regret 

 of a large circle of friends and pupils, to whom he appears to have 

 been singularly endeared by the modesty, truthfulness, and simplicity 

 of his character. 



STURZ, HELFRICH PETER, born Feb. 16th, 1740, at Darm- 

 stadt, was, although in a subordinate class of literature, a first-rate 

 writer, and almost the first who distinguished himself by an elegant 

 and graceful prose style in German, and by his playful humour. 

 After filling the post of private secretary, first to Baron von Widmann 

 at Munich, and next to the chancellor Von Eyben at Gliickstadt, he 

 went, in 1762, to Copenhagen, where he resided some time in a similar 

 capacity with the minister Bernstorf, who obtained for him appoint- 

 ments of very considerable value. In 1768 he was made Danish 

 ' Legationsrath,' and visited France and England in the suite of 

 Christian VII. From this journey originated his ' Briefe eines 

 Reisenden/ which contain many interesting details, and various anec- 

 dotes relative to the eminent literary characters and others to whom 



