MEMOIR OF LEGENDKE. 



14/j 



to tlie first class of tlio Institute, Marcli 3, 1806, a new memoir entitled, Analij- 

 sis of triangles traced on the surface of a spheroid^ in which he considers the tri- 

 ano-ies as no lons^er described on the sphere, hut on a spheroid. Ho inquires 

 find demonstrates the properties of the shortest lines traced on its surface ; extends 

 and thus generalizes the numerous applications of the theorem which bears his 

 name, and reviewing the principal operations offered l>y geodesy, gives the modt 

 complete analysis of them. 



He concludes that there can remain no doubt of the exactness of the calcu- 

 lation of the triangles from which the distance of the parallels between Dunkirk 

 and Montjouy, near Barcelona, has been computed, as well as the length of the 

 metre ; but he considers it beyond question that the results deduced from difi"er- 

 ent chains of triangles do not always exactly accord among them.selves, on 

 account of certain anomalies in the latitudes and azimuths which may be due 

 to local attractions. 



At this epoch, in 1805, M. Legendre had just published, in the sequel of his 

 new methods for the determination of the orbits of comets, an appendix on the 

 method of least squares. Here lie proposed that method which has generally 

 been adopted for deriving Irom the measures yielded by observation the most 

 exact results which they are susceptible of furnishing. M. de Laplace has since 

 demonstrated that it is the most adv^antageous of which we can make use in prac- 

 tice. M. Legendre, after having developed it, made an immediate application 

 of it to the measurement of the degrees of the meridian of France, and he con- 

 cluded, as in the geodesic memoir, that the anomalies in the latitudes ought not 

 to be attributed to the observations, and that they jiertain probably to local 

 attractions which act irregularly on the plumb-line. M. Gauss, in 1809, seems 

 to have thought, for the moment, that he had rights of priority to the invention 

 of the method of least squares ;* but, if it cannot be contested that so eminent 

 a savant may have had the same idea with M. Legendre, and may even have 

 applied it in his labors, it is certain that M. Legendre had, on his part, discov- 

 ered the method and was the first who published it. 



]\L Legendre continued henceforth to make part of the commission of weights 

 and measures ; but, though his labors of 1787 had rendered his co-operation 

 indispensable in the great enterprise which that commission was charged with 

 conducting to a successful issue, there was a period during which, as we have 

 said, he ceased to be officially attached to it : this was under the reign of terror. 

 Like most of the savants of his epoch, he was favorable to the ideas which 

 have become the basis of modern society ; but he remained a stranger to the 

 excesses which imbrued the Revolution in blood. Perhaps, indeed, his caustic 

 turn had not wholly spared its authors ; certain it is, that, during the violence of 

 the storm, he was forced to hide himself. It was one of the most happy inci- 

 dents of his life ; for, in the retreat which he found in Paris itself, he formed the 

 acquaintance of a young and engaging female, Marguerite-Claudine Coiihiny 

 whom he espoused shortly afterwards, and who constituted his happiness during 

 40 years. Much j'ounger than lier husband, she bore no inefficient part in his 

 great labors by the tranquillity, the assiduous attentions, the watchful solicitude, 

 with which she environed him, i)roving herself, in all circumstances, a model of 

 discretion, grace, and amiability. 



The revolutionary turbulence, however, had itself never interrupted the 

 labors of ]M. Legendre. In the year II of the republic, towards the end of 

 1793, he published a new memoir on ellqjtical transcendents, forming a quarto 



* la his work, entitled Theoria motus corporum ceiestium, M. Gauss expresses Limselt 

 with respect to this in the following manner : "This principle, which we have employed 

 since the year 1795, has been lately given by M. Legendre in his Noucdles M6lhodcs pour la 

 determination des orbitcs dts comite's : Paris, JS0(5. There will be found in that work several 

 consequences which the desire of being brief induces us to ouiit." (See the work enti- 

 tled M6tfiodes des moindres carres, MUmoires sur la combination des observations, by M. Ch. 

 F. Gauss, translated into French and published with authority of the author by M. J. 

 Bertrand, 1855, p. J 33.) 

 10 S(j7 



