148 MEMOIR OF LEGENDRE. 



tcrbalanced by the length of the calculations and by other inconveniences. 

 They prefer employiiig the methods of Olbers and Gauss, which, while giving 

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

 1S06 j\I. Legendre further published, in the memoirs of the Institute, a new 

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

 the sun or to a star.* Its object was to simplify and accelerate the labors of 

 practical astronomers. 



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

 ble author beyond the habitual sphere of his researches, and, seeing with what 

 promptness and iacility iM. Legendre thus passed from one subject to another, it 

 might be thought that he was completely at liV>ei1y in the employment of his 

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

 reconcile with the duties of the academician those of several important functions. 



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

 the balistic competition was appointed 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 M. de Prony. From the creation of the university, in 1808, M. Legendre 

 was of its council. At the death of Lagrange, in 1812, he was 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 Mechan- 

 ■iijue Celeste became an associate member. Thus, at an interval of 29 3'ears, and 

 under circumstances assuredly very ditferent, 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. Tliat he owed to his merit alone a 

 choice so honorable for himself and those who made it, may be gathered from 

 a slight anecdote wdiich 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 

 natm-al modesty, we are told, long prevented him from attaching the red riband 

 to his button-hole. M. Legendre continued, moreover, as has been ah-eady said, 

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

 and more than 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 peculiar 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 w'hich he sacrificed with ever renewed pleasure in the 

 silence of his closet. I mean the theonj of numhcrs and the elliptical 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, will prove, perhaps, in the eye of posterity, two of his princi- 

 pal titles to renown. 



The Theory of numbers appeared in 1830, in two quarto volumes, after being 

 preceded at divers intervals by preliminary publications. M. Legendre says, in 

 the advertisement : 



The work having received all the improvements which the author has been able to bestow 

 upon it, as well through his own labors as those of other geometers of which he coul<] avail 

 himself, it has been thought proper to give it definitively the title of Theory of numbers, ia 

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



The Essay on the theory of numbers had passed through two editions, one iu 

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



*M6moires, de V Institute, t, VI, (printed January, 180G,) p. 30. 



