L E G L E G 413 latere, and the title is now almost quite honorary. It still attaches to the sees of Seville, Toledo, Aries, Ilheims, Lyons, Gran, Prague, Gnesen-Posen, Cologne, Salzburg, among others. The commission of the leyatus delegates (generally a member of the local clergy) is of a limited nature, and relates only to some definite piece of work. The nuncius apostolicus (who has the privilege of red apparel, a white horse, and golden spurs) possesses ordinary jurisdiction within the province to which he has been sent, bat his powers otherwise are restricted by the terms of his mandate. The legatus a latere (almost invariably a cardinal, though the power can be conferred on other prelates) is in the fullest sense the plenipotentiary representative of the pops, and possesses the high prerogative implied in the words of Gregory VII., " nostra vies qune corrigenda sunt corrtgat, quee statuend^ constituat." He has the power of suspending all the bishops in his province, and no judicial cases are reserved from his judgment. Without special mandate, however, he cannot depose bishops or unite or separate bishoprics. At present leyati a latere are not s.>nt by the holy see, but diplomatic relations, where they exist, are maintained by means of nuncios, inter- nuncios, and other agents. According to the congress of Vienna, the diplomatic rank of a papal nuncio corresponds t > that of an ambassador. The pope at present has nuncios at the courts of Bivaria, Austria-Hungary, Belgium, Chili, Spain, France, and Portugal. Inferior in rank and less numerous are the internuncios (Holland, Brazil). LEGENDRE, ADRIEN MARIE (1752-1833), French mathematician, a contemporary of Laplace and Lagrange, with whom he deserves to be ranked, 1 was born at Paris (or, according to some accounts, at Toulouse) in 1752. He was brought up at Paris, where he completed his studies at the College Mazarin. His first published writings consist of some articles forming part of the Traite de Mecanique (1774) uf the Abbe Marie, who was his professor ; Legendre s name, however, is not mentioned. Soon afterwards he was appointed professor of mathematics in the Ecole Militaire at Paris, and ho was afterwards professor in the cole Xormale. In 1782 he received the prize from the Berlin Academy for his "Dissertation sur la question de balistique," a memoir relating to the paths of projectiles in resisting media. He also, about this time, wrote his "Recherches sur la figure des planetes," published in the Memoires of the French Academy, of which he was elected a member in succession to D Alembert in 1783. He was also appointed a commissioner for connecting geodetically Paris and Greenwich, his colleagues being Mechain and Cassini ; General Roy conducted the operations on behalf of England. The French observations were published in 1792 (Expose des operations faites en France in 1787 j/our lajonction des obser- vatoires de Paris et de Greenwich). During the Revolution, when the decimal system had been decreed, he was one of the three members of the council established to introduce the new system, and he was also a member of the commission appointed to determine the length of the metre, for which purpose the calculations, &c., connected with the arc of the meridian from Barcelona to Dunkirk were revised. He was also associated with Prony in the formation of the great French tables of logarithms of numbers, sines, and tangents, and natural sines, called the Tallies du Cadastre,in which the quadrant was divided centesimally ; these tables have never been published (see LOGARITHMS). He also served on other public commissions. He was examiner in the Ecole Poly technique, but held few important state offices, and he 1 Besides Laplace and Lngrange, with whom it is most natural to associate Legendre, the names of Poisson, Cauchy, Fourier, and Monge should be mentioned as contemporaries. The number of French mathe maticians of the highest rank who were living at the same time, at the beginning of the century, has often been the subject of remark. seems never to have been much noticed by the different Governments ; it has indeed been generally remarked that the offices he held were not such as his reputation entitled him to. Not many facts with regard to his personal life seem to have been published, but in a letter to Jacobi of June 30, 1832, he writes " Je me suis marie" a la suite d une revolution sanglante qui avait detruit ma petite fortune ; nous avous eu de grands embarras et des moments bien difficiles a passer, mais ma femme m a aide puissam- ment a restaurer progressivement mes affaires et a me donner cette tranquillity d esprit ndcessaire pour me livrer h, mes travaux accoutume s et pour composer de nouveaux ouvrages qui ont ajoute" de plus en plus a ma reputation, de maniere a me procurer bientot une existence honorable et une petite fortune dont les debris, apres de nouvelles revolutions qui m ont cause de grandes pertes, suffisent en core pour pourvoir aux besoins de ma vieillesse, et suffiront pour pourvoir a ceux de ma femme bien-aimee quand je n y serai plus." He died at Paris on January 10, 1833, in his eighty -first year, and the discourse at his grave was pronounced by Poisson. He was engaged in mathematical investigations almost up to the time of his death. The last of the three supplements to his Traite des Functions Elliptirjues was published in 1832, and Poisson in his funeral oration remarked " M. Legendre a eu cela de commun avec la plupart des ge"oinetres qui 1 ont precede, que ses travaux n ont fini qu avec sa vie. Le dernier volume de nos memoires renferme encore un me"moire de lui, sur une question difficile de la theorie des nombres ; et peu de temps avant la maladie qui 1 a conduit au tombeau, il se procura les observations les plus re"centes des cometes a courtes periodes, dont il allait se servir pour appliquer ct perfectionner ses m6thodes." Legendre was the author of separate works on elliptic functions, the integral calculus, the theory of numbers, and the elements of geometry, besides numerous papers which were published chiefly in the Memoires of the French Academy ; and it will be convenient, in giving an account of his writings, to consider them under the dif ferent subjects which are especially associated with his name. Elliptic Functions. This is the subject with which Legendre s name will always be most closely connected, and his researches upon it extend over a period of more than forty years. His first published writings upon the subject consist of two papers in the Memoires of the French Academy for 1786 upon elliptic arcs. In 1792 lie pre sented to the Academy a memoir on elliptic transcendents. The contents of these memoirs are included in the first volume of his Exerciccs de Calcul Integral (1811). The third volume (1816) con tains the very elaborate and now well-known tables of the elli| tic- integrals which were calculated by Legendre himself, with an account of the mode of their construction. In 1827 appeared the Traite drs fonclions clliptiqucs (2 vols., the first dated 1825, the second 1826) ; a great part of the first volume agrees very closely with the contents of the Exerciccs; the tables, &c., are given in the second volume. Three supplements, relating to the researches of Abel and Jacobi, were published in 1828-32, and form a third volume. Legendre had pursued the subject which would now be called elliptic integrals alone from 1786 to 1827, the results of his labours having been almost entirely neglected by his contemporaries, but his work had scarcely appeared in 1827 when the discoveries which were independ ently made by the two young and as yet unknown mathematicians Abel and Jacobi placed the subject on a new basis, and revolution ized it completely. The readiness with which Legendre, who was then seventy-six years of age, welcomed these important researches, that quite overshadowed his own, and included them in successive supplements to his work, does the highest honour to him. The sudden occurrence, near the close of his long life, of these great discoveries relating to a subject which Legendre had so completely made his own and apparently exhausted, and their ready acceptance by him, form one of the most striking episodes in the history of mathematics. A very full account of the contents of Legendre s work and of the results obtained by Abel and Jacobi has been given in the article INFINITESIMAL CALCULVS, vol. xiii. pp. 62-72. See also Leslie Ellis s report "On the Recent Progress of Analysis," in the Report of the British Association for 1846 (pp. 44 sq.). Eukrian Integrals and Integral Calculus. The Exerciccs de Calcul Integral consist of three volumes, a great portion of the first and the whole of the third being devoted to elliptic functions. The
