MEMOIR OF LEGENDRE. 145 



to tlic first class of tlie Institute, Marcli 3, 1806, a new memoir entitled, Analy- 

 sis of triangles traced on the surface of a spheroid, in wliicli he considers the tri- 

 ano-les as no longer described on the sphere, but on a spheroid. He inquires 

 and 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 by geodesy, gives the most 

 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 differ- 

 ent chains of triangles do not always exactly accord among themselves, 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 he proposed that method which has generally 

 been adopted for deriving from 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 advantageous 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 pertain prol)al)ly 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. 



51. 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 sffvants 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 Avhich he found in Paris itself, he formed the 

 acquaintance of a young and engaging female, Marguerite-Claudinc Couhin,. 

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

 40 years. Much j'ounger than her husband, she bore no inefficient ])art in his 

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

 with which she environed him, proving 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 elliptical transcendents, forming a quarto. 



* la his work, entitled Theoria motus corpurum celestium, M. Gauss expresses himself 

 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 Noiivclles Mtthodcs pour la 

 determination des orbitcs dts coiueie.s : Paris, 18U(). There will be found in that work several 

 consequences which the desire of being brief induces us to omit." (St^e the work enti- 

 tled Mithodes dcs iiioindres carres. Mt-iiioircs sur Id combination dcs obscreatiuns, by M. Ch. 

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

 Bertrand, 1H55, p. 133.) 

 10 S 



