24 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



the marvellous power of analysis, in unravelling intri- 

 cate consequences of admitted or assumed laws, could 

 supply deficiencies of primary conceptions of the laws 

 of nature, or could teach men fundamental truths in 

 natural science. 



(93.) To add to the remarkable list of Laplace's endow- 



His Systeme me nts one more ; he was a perspicuous and elegant 



1 e ' writer. His Systeme du Monde contains a popular 



exposition of astronomy in theory and practice en- 

 tirely original in its plan and execution, and though 

 frequently imitated, it is still perhaps the first of its 

 class. 



Laplace was born in Normandy 23d March 1749, (94.) 

 and died the 5th May 1827, leaving in the Academy -Date of 

 he had so long honoured no one within many degrees 

 of his ability in the same peculiar walk of science. 



3. LEGENDRE. IVORY. Theory of Integration; Elliptic Transcendants (Abel, Jacobi). 

 The Attraction of Spheroids, and Theory of the Earth's Figure. Atmospherical Refractions. 



(95.) 

 Legendre. 



(96.) 

 Distin- 

 guished as 

 an able 

 mathe- 

 matician. 



(97.) 

 His re- 

 searches on 

 Elliptic 

 Functions. 



ADRIEN MARIE LEGENDRE was born in France in 

 1752, and died in 1833 (10th January); he was 

 consequently three years younger than Laplace, and 

 survived him by nearly six years. He formed, there- 

 fore, an integral part of that constellation of mathe- 

 matical talent of which Paris was for more than 

 two generations the main centre. Like his illustrious 

 compeers Lagrange and Laplace, he laboured with 

 enthusiasm all the days of his life, and like them was 

 engaged in editing and improving his works down 

 almost to the day of his death, at the ripe age of four- 

 score. 



The mathematical career of Legendre was less 

 splendid than that of the other two whom we have 

 just mentioned. He did not possess the wonderful 

 powers of generalization of Lagrange, and he wanted 

 the flexibility of mind, and the general physical 

 knowledge, of Laplace. Legendre was very strictly a 

 mathematician ; and he has been exceeded by none 

 in the unquenchable zeal with which he pursued sub- 

 jects of a dry and even repulsive character, often 

 till he had hunted them down by sheer force of ap- 

 plication, or, to adopt the metaphor applied to him by 

 Lagrange, until he carried, sword in hand, the strong- 

 hold which he besieged. 



No more striking proof can be given of these state- 

 ments than the unflinching pertinacity with which, 

 during nearly fifty years (1786-1833), he studied and 

 improved the theory of Integration, applicable to those 

 cases frequently occurring, which involve the higher 

 powers of the independent variable, and which do not 

 usually admit of finite expression. Two large works, 

 the Exercises du Calcul Integral (1811), and the 

 TraitS des Fonctions Elliptiques (1827-32), the lat- 

 ter in good measure a republication of the materials of 

 the former, bear testimony to his diligence ; and these 

 works were almost entirely original, and contained 

 tables of most laboured construction, calculated by 

 himself. Hardly any mathematician entered into 

 competition or co-operation with him until his 

 labours were drawing to a close, when, with a libe- 

 rality worthy of all commendation, he welcomed the 



analytical discoveries of Abel and Jacobi, which 

 were to give an unlooked-for extension to his own. 

 These methods of integration, and their reference to 

 certain properties of the Lemniscate and the Ellipse, 

 originated in the early part of the last century 

 with Fagnano and Euler. Legendre took up the 

 subject exactly where Euler left it, and finally re- 

 duced the large class of expressions to which his 

 methods are applicable to three standard forms or in- 

 tegrals in which the independent variable is always 

 expressed by a circular function, nd to which a 

 numerical approximation may always be made by 

 means of the tables calculated by himself. 



ABEL, who succeeded in generalizing Legendre's (98.) 

 methods to a far greater extent, was a native of Abel's dis- 

 Norway, born in 1802 (25th August), 1 and died 1^^ 

 at the premature age of twenty-six (1829, 2 6th subject; his 

 April). His principal memoir was presented to the personal; 

 Institute when he was only twenty-four years old ; histor y- 

 and, to use the language of Mr Leslie Ellis, " when 

 the resources of the integral calculus were appar- 

 ently exhausted, Abel was enabled to pass into 

 new fields of research by bringing it into intimate 

 connection with a new branch of analysis, namely 

 the Theory of Equations. The manner in which 

 this was done shows that he was not unworthy to 

 follow in the path of Euler and of Lagrange." 2 

 Legendre's eulogy of Abel was concise : " Quelle 

 tete celle du jeune Norvegien!" It is less agreeable 

 to add that the life of Abel was perhaps shortened by 

 poverty and care. Though ultimately befriended by 

 Legendre, Poisson, and others, his firstvisit to Paris(in 

 1826) occasioned nothing but disappointment, and his 

 great memoir (no unusual lot, for the same happened 

 to Fresnel) lay hopelessly lost amidst the papers of the 

 Institute for fifteen years. Much, however, to their 

 credit, the geometers above mentioned at length ad- 

 dressed the King of Sweden on behalf of the rare genius 

 his dominions contained ; but in vain. Abel died ne- 

 glected, unable even to print his researches, which were 

 tardily given to the world in a collected form, at the 

 expense of the government which refused to support 



1 There is some discrepancy, as to the year of his birth, but I believe this to be correct. 

 Report on the recent progress of Analysis. British Association Report for 1846. 



