148 MEMOIR 01? LEGENDRE. 



terLalanced by the leiigtli of the calcnlations and by other inconveniences. 

 They prefer employing the methods of Gibers and Gauss, which, while giving 

 perhaps a less certain approximation, furnish it in all cases more rapidly. In 

 ISOG JM. Legendre further published, in the memoirs of the Institute, a new 

 formula for reducing to true distances the apparent distances from the moon to 

 the sun or to a star.* Its ol)ject was to simplify and accelerate the labors of 

 practical astronomers. 



These last publications were in some sort excursions made by the indefatiga- 

 l)le author beyond the habitual sphere of his researches, and, seeing with what 

 i)romptness and facility M. Legendre thus passed from one subject to another, it 

 might be thought that lie was completely at liberty in the employment of his 

 time. He found means, however, in tho midst of his purely scientific labors, to 

 reconcile with the duties of the academician those of sevei'al important functions. 



Some time after the creation of the Polytechnic School, the former laureate of 

 the balistic competition was a})pointed examiner in mathematics for the graduat- 

 ing- students destined for the artillery, and he continued to fulfil these honorable 

 and delicate functions till 1815, when he voluntarily withdrew and was replaced 

 by ^I. de ]'rony. From the creation of the university, in ISOS, M. Legendre 

 was of its coimcil. At the death of Lagrange, in 1812, he \vas chosen to suc- 

 ceed him at the bureau of longitudes, in quality of geometer. He thus took 

 his place by the side of M. de Laplace, whom he had replaced in 1783, as adjunct 

 member of the Academy of Sciences, when the illustrious author of the Mcchan- 

 ique Celeste became an associate member. Thus, at an interval of 29 years, and 

 under circumstances assuredly very different, no one was found in France who, 

 by his scientific merit, could more naturally be called than M. Legendre to 

 replace M. de Laplace or M. de Lagrange. That he owed to his merit alone a 

 choice so honorable for himself and those Avho made it, may be gathered fiom 

 a slight anecdote which is related of him. Having, from the creation of the 

 legion of honor, been inscribed in the number of its chevaliers, though he failed 

 not to record this testimony to. his merit in the title-page of his works, his 

 natural modesty, we are told, long prevented him from attaching the red riband 

 to his T)utton-hole. M. Legendre continued, moreover, as has been already said, 

 to form part of the commission of weights and measures as long as it existed, 

 and more tliari once was a member of other commissions charged with objects of 

 importance. 



Yet independently of these numerous occupations and varied labors, all 

 impressed with a |)eculiar character of vigor and precision, by which he bore a 

 large part in the scientific movement of his epoch, M. Legendre had besides cer- 

 tain household gods, to which he sacrificed with ever renewed pleasure in tlie 

 silence of his closet. I mean the theory of numbers and the ell iptical functions. 

 To these he consecrated, during the latter 50 years of his life, all the leisure left 

 him by his daily occupations and more conspicuous labors. He has thus reared 

 two monuments which, by their extent, represent, no doubt, the better part of 

 his time, and which, though having had few readers and capable of having but 

 very few judges, Avill prove, perhaps, in the eye of posterity, two of his princi- 

 ])al titles to renown. 



The Theoru of numhcrs appeared in 1830, in two quarto volumes, after being 

 pr(!ceded at divers intervals by preliminary publications. ]\l. Legenth-e says, in 

 the advertisement : 



The woilc having received all the improvements whicii the author has been able to bestow 

 upon it, as well through his own labors as those of other geometers of which lie could avail 

 liimself, it has been thought proper to give it definitively the title of Tlieunj of numliers, in 

 place of that of an Essay on the subject which it has heretofore borne. 



The Essay on the theory (f numhcrs had passed through two editions, one in 

 1798, the other in 1808 ; this last had been followed by two supplements. The 



* Mimoirts, dc V Institute, t. vr, (printed January, JHUG, ) p. HO. 



