P I P O I 281 diploma or used the title. The revolution of July 1830 threatened him with the loss of all his honours ; but this disgrace to the Government of Louis Philippe was adroitly averted by Arago, who, while his " revocation " was being plotted by the council of ministers, procured him an invita tion to dine at the Palais Koyale, where he was openly and effusively received by the citizen king, who " remembered " him. After this, of course, his degradation was impossible; he was left in undisturbed possession of all his well-earned appointments ; and seven years later he was made a peer of France, not for political reasons, but as a representative of French science. As a teacher of mathematics Poisson is said to have been more than ordinarily successful, as might have been expected from his early promise as a repetiteur at the Polytechnic School. As a scientific worker his activity has rarely if ever been equalled. Notwithstanding his many official duties, he found time to publish more than three hundred works, several of them extensive treatises, and many of them memoirs dealing with the most abstruse branches of pure and applied mathematics. There are two remarks of his, or perhaps two versions of the same remark, that explain how he accomplished so much : one, " La vie n est bonne qu ; deux choses a faire des mathematiques et a les professer ;" the other, " La vie c est le travail." A list of Poisson s works, drawn up by himself, is given at the end of Arago s biography. A lengthened analysis of them would be out of place here, and all that is possible is a brief mention of the more important. There are few branches of mathematics to which he did not contribute something, but it was in the applica tion of mathematics to physical subjects that his greatest services to science were performed. Perhaps the most original, and certainly the most permanent in their influence, were his memoirs on the theory of electricity and magnetism, which virtually created a new branch of mathematical physics. They have been already repeatedly referred to in the articles ELECTRICITY and MAGNETISM (q.v.}. Next (perhaps in the opinion of some first) in importance stand the memoirs on celestial mechanics, in which he proved him self a worthy successor to Laplace. The most important of these are his memoirs "Sur les inegalites seculaires des moyens mouve- ments des planetes, " Sur la variation des constantes arbitraires dans les questions de mecanique," both published in the Journal of the Polytechnic School, 1809; " Sur la libration de la June," in Connaiss. d. Temps, 1821, &c. ; and "Sur la mouvement de la terre autour de son centre de gravite," in Mem. d. VAcad., 1827, &c. In the first of these memoirs Poisson discusses the famous question of the stability of the planetary orbits, which had already been settled by Lagrange to the first degree of approximation for the disturbing forces. Poisson showed that the result could be extended to a second approximation, and thus made an important advance in the planetary theory. The memoir is remarkable inasmuch as it roused Lagrange, after an interval of inactivity, to compose in his old age one of the greatest of his memoirs, viz., that "Sur la theorie des variations des elements des planetes, et en particulier des variations des grands axes de leurs orbites." So highly did he think of Poisson s memoir that he made a copy of it with his own hand, which was found among his papers after his death. Poisson made important contributions to the theory of attraction. His well-known correction of Laplace s partial differential equation for the potential was first published in the Bulletin de la Societe Philomatiquc, 1813. His two most important memoirs on the subject are " Sur 1 attraction des spheroides" (Connaiss. d. Temps, 1829), and "Sur 1 attraction d un ellipsoide liomogene (Mem. d. I Acad., 1835). In concluding our selection from his physical memoirs we may mention his memoir on the theory of waves (Mem. d. I Acad., 1825). In pure mathematics, his most important works were his series of memoirs on definite integrals, and his discussion of Fourier s series, which paved the way for the classical researches of Dirichlet and Riemann on the same subject; these are to be found in the Journal of the Polytechnic School from 1813 to 1823, and in the Memoirs of the Academy for 1823. In addition we may also mention his essay on the calculus of variations (Mem. d. I Acad., 1833), and his memoirs on the probability of the mean results of observations (Connaiss. d. Temps, 1827, &c. ). Besides his many memoirs Poisson published a number of treatises, most of which were intended to form part of a great work on mathematical physics, which he did not live to complete. Among these may be mentioned his Traite de Mtcaniquc, 2 vols. 8vo, 1811 and 1833, which was long a standard work; Theorie Nouvelle de I Action Capillairc, 4to, 1831 ; Theorie Mathcmatique de la Chaleur, 4to, 1835; Supplement to the same, 4to, 1837; Rcchcrchcs sur la probabilite des jugements en matures criminelles, &c. 4to, 1837, all published at Paris. Enough has been said to establish Poisson s fertility as a writer on mathematical subjects, and the question naturally suggests itself, What is his rank among the mathematicians of all ages 1 Since his own age was more productive of great mathematicians than any other the world has yet seen, it is natural to compare him with his contemporaries, chief among whom were Lagrange and Laplace. In so doing we see at once that, although we cannot seat him alongside of these mighty sovereigns, yet it is impossible to deny him the nearest rank to them in the temple of mathematical fame. In confirmation of this judgment, we cannot do better than quote one of them " I am old," said Lagrange to Poisson one day ; " during my long intervals of sleeplessness I divert myself by making numerical approximations. Keep this one ; it may interest you. Huygens was thirteen years older than Newton, I am thirteen years older than Laplace ; D Alembert was thirty-two years older than Laplace, Laplace is thirty-two years older than you." Arago, who gives this story, justly remarks that no more delicate way could be conceived of intimating to Poisson his admission into the inner circle of the fraternity of mathematical genius. (G. CH.) POITIERS, a town of France, formerly the capital of Poitou, and now the chief town of the department of Vienne, lies 206 miles south-west of Paris on the railway to Bordeaux, at the junction of the Boivre with the Clain (a tributary of the Loire by the Vienne), and occupies the slopes and summit of a plateau which rises 130 feet above the level of the streams by which it is surrounded on three sides. The town is picturesque ; and its narrow, ill-paved, irregular, and deserted streets with their ill- built houses are interesting for certain remains of ancient architecture and the memories of great historical events. Blossac park, named after the intendant of the "gene rality" of Poitiers (1751-1786), and situated on the south side of the town, and the botanic garden on the north-east, are the two principal promenades. Besides being the see of a bishopric, which comprises the depart ments of Vienne and Deux-Sevres, Poitiers possesses a court of appeal, national faculties of law, literature, and science, a free faculty of Catholic theology, a school of artillery, and numerous learned societies, of which the most celebrated is that of the " Antiquaires de 1 Ouest " dating from 1834. Though not strictly a commercial or industrial town, it is the centre from which railways branch out to Tours, Angers, Niort, Angouleme, Limoges, and prospectively to Chateauroux and Nantes. L T p till 1857 it contained the ruins of a Roman amphitheatre more extensive than that of Nimes ; remains of Roman baths, constructed in the 1st and demolished in the 3d century, were laid bare in 1877 ; and in 1879 a pagan burial place and the tombs of a number of Christian martyrs were discovered on the heights to the south-east the names of some of the Christians being preserved in paintings and inscriptions. Not far from these tombs is a huge dolmen (the "Pierre Levee"), 22 feet long, 16 feet broad, and 6 or 7 feet high, around which used to be held the great fair of St Luke. The cathedral of St Peter, begun in 1162 by Eleanor of Guienne on the ruins of a Roman basilica, and well advanced at the time of her death in 1204, is a building after the Plantagenet or Angevin style. Its length is 308 feet, its width 128, and the keystone of the central vaulted roof is 89 feet above the pavement. There is no apse, and the exterior generally has a heavy appearance. The principal front has unfinished side-towers 105 and 110
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