SIMEON DENIS POISSON (17811840), French mathematician, was born at Pithiviers in the department of Loiret, on the 21st of June 1781. His father, Simeon Poisson, served as a common soldier in the Hanoverian wars; but, disgusted by the illtreatment he received from his patrician officers, he deserted. About the time of the birth of his son, Simeon Denis, he occupied a small administrative post at Pithiviers, and seems to have been at the head of the local government of the place during the revolutionary period. Poisson was first sent to an uncle, a surgeon at Fontainebleau, and began to take lessons in bleeding and blistering, but made little progress. Having given promise of mathematical talent he was sent to the Ecole Centrale of Fontainebleau, and was fortunate in having a kind and sympathetic teacher, M. Billy, who, when he speedily found that his pupil was becoming his master, devoted himself to the study of higher mathematics in order to follow and appreciate him, and predicted his future fame by the punning quotation from Lafontaine':
" Petit Poisson deviendra grand
Pourvu que Dieu lui prete vie."
In 1798 he entered the )r tole Polytechnique at Paris as first in his year, and immediately began to attract the notice of the professors of the school, who left him free to follow the studies of his predilection. In "Soo, less than two years after his entry, he published two memoirs, one on E. Bezout's method of elimination, the other on the number of integrals of an equation of finite differences. The latter of these memoirs was examined by S. F. Lacroix and A. M. Legendre, who recommended that it should be published in the Recueil des savants etrangers, an unparalleled honour for a youth of eighteen. This success at once procured for Poisson an entry into scientific circles. J. L. Lagrange, whose lectures on the theory of functions he attended at the )tole Polytechnique, early recognized his talent, and became his friend; while P. S. Laplace, in whose footsteps Poisson followed, regarded him almost as his son. The rest of his career, till his death on the 25th of April r84o, was almost entirely occupied in the composition and publication of his many works, and in discharging the duties of the numerous educational offices to which he was successively appointed. Immediately after finishing his course at the Ecole Polytechnique he was appointed repetiteur there, an office which he bad discharged as an amateur while still a pupil in the school; for it had been the custom of his comrades often to resort to his room after an unusually difficult lecture to hear him repeat and explain it. He was made professeur suppleant in 18o2, and full professor in succession to J. Fourier in 18o6. In 18o8 he became astronomer to the Bureau des Longitudes; and when the Faculte des Sciences was instituted in a809 he was appointed professeur de in mecanique rationelle. He further became member of the Institute in 1812, examiner at the military school at St Cyr in 1815, leaving examiner at the )/tole Polytechnique in 1816, councillor of the university in 182o, and geometer to the Bureau des Longitudes in succession to P. S. Laplace in 1827. His father, whose early experiences led him to hate aristocrats, bred him in the stern creed of the first republic. Throughout the empire Poisson faithfully adhered to the family principles, and refused to worship Napoleon. When the Bourbons were restored, his hatred against Napoleon led him to become a Legitimist—a conclusion which says more for the simplicity of his character than for the strength or logic of his political creed. He was faithful to the Bourbons during the Hundred Days; in fact, was
t This prediction is sometimes attributed to Laplace.with difficulty dissuaded from volunteering to fight in their cause. After the second restoration his fidelity was recognized by his elevation to the dignity of baron in 1825; but he never either took out his diploma or used the title. The revolution of July 183o threatened him with the loss of all his honours; but this disgrace to the government of Louis Philippe was adroitly averted by F. Arago, who, while his " revocation " was being plotted by the council of ministers, procured him an invitation to dine at the Palais Royale, where he was openly and effusively received by the citizen king, who " remembered" him. After this, of course, his degradation was impossible, 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 Ecole Polytechnique. 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'a deux choses—a faire des mathematiques et a les professeur; " 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 application 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. Next (perhaps in the opinion of some first) in importance stand the memoirs on celestial mechanics, in which he proved himself a worthy successor to P. S. Laplace. The most important of these are his memoirs " Sur les inegalites seculaires des moyens mouvements des planetes," " Sur la variation des constantes arbitraires daps les questions de mecanique," both published in the Journal of the hcole Polytechnique (18o9) ; " Sur la libration de la tune," in Connaiss. d. temps (1821), &c. ; and " Sur la mouvement de la terre autour de son centre de gravite," in Mem. d. l'acad. (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 wellknown correction of Laplace's
partial differential equation for the potential was first published In the Bulletin de in societe philomatique (1813). His two most important memoirs on the subject are " Sur ?'attraction des spheroides " (Connaiss. d. temps, 1829), and " Sur ?'attraction d'un ellipsoide homogene " (Mem. d. l'acad., 1835). In concluding our selection from his physical memoirs we may mention his memoir on the theory of waves (Mem. d. l'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 L. Dirichlet and B. Riemann on the same subject; these are to be found in the Journal of the ?cote Polytechnique from 1813 to 1823, and in the Memoirs de l'academie for 1823. In addition we may also mention his essay on the calculus of variations (Mem. d. l'acad., 1833), and his memoirs on the probability of the mean results of observations (Connaiss. d. temps, 1827, &e.).
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 mecanique (2 vols. 8vo, 1811 and 1833), which was long a standard work; Theorie nouvelle de l'action cappillaire (4to, 1831) ; Theorie mathematique de la chaleur (4to, 1835) Supplement to the same (4to, 1837) ; Recherches sur la probabilite des jugements en matibres criminelles, &c. (4to,1837), all published at Paris.
See F. Arago, Biographie de Poisson, read before the Academie des Sciences on the 16th of December 1850.
Poitou, and now the chief town of the department of Vienne, 61 m. S.S.W. of Tours on the railway to Bordeaux. Pop. (1906), town, 31,532; commune, 39,302. Poitiers is situated 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 ft. above the level of the streams by which it is surrounded on three sides. The town is picturesque; and its streets are interesting for their remains of ancient architecture, especially of the Romanesque period, and the memories of great historical events. Blossac park, named after the intendant of the " generality " of Poitiers (17511786), and situated on the south side of the town, and the botanical garden on the northeast, are the two principal promenades. Till 1857 Poitiers 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 3rd century, were laid bare in 1877; and in 1879 a burialplace and the tombs of a number of Christian martyrs were discovered on the heights to the southeast—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 ft. long, 16 ft. broad and 6 or 7 ft. high, around which used to be held the great fair of St Luke.
The cathedral of St Peter, begun in 1162 by Henry II. of England and Eleanor of Guienne on the ruins of a Roman basilica, and well advanced by the end of the 12th century, is a building in the Romanesque and Early Gothic style, the latter predominating. It consists of three naves almost equal in height and width, both of which decrease towards the west, thus enhancing the perspective. Its length is 308 ft., and the keystone of the central vaulted roof is 89 ft. above the pavement. There is no apse, and the exterior generally has a heavy appearance. The principal front, the width of which is excessive in proportion to its height, has unfinished sidetowers 105 and Ito ft. in height, begun in the 13th century. Most of the windows of the choir and the transepts preserve their stained glass of the 12th and 13th centuries; the end window, which is certainly the first in the order of time, contains the figures of Henry II. and Eleanor. The choir stalls, carved between 1235 and 1257, are among the oldest in France. The church of St Jean near the cathedral is the most ancient Christian monument in the country. Built as a baptistery in the first half of the 4th century, it was enlarged in the 7th century, since when it has suffered little structural alteration. It contains frescoes of the 12th century and a collection of tombs of the Merovingian period. The church of St Hilaire was erected at the close of the 4th century over the tomb of the celebrated bishop. At first an oratory, it was rebuilt on a larger scale by Clovis, and afterwards became, in the loth, nth and 12th centuries, a sumptuous collegiate church, of which the nave was flanked by triple aisles and surmounted by six cupolas. Great damage was done to it in the Wars of Religion and the French Revolution, and the facade was entirely rebuilt in the 19th century. The confessional or oratory under the choir contains the relics of St Hilary and a Christian sarcophagus of the 4th century. The church of St Radegonde, a ,great resort of pilgrims, commemorates the consort of Clotaire (d. 587), and preserves in its crypt the tomb of Radegonde, who founded at Poitiers the abbey of the Holy Cross, and two others reputed to be those of St Agnes and St Disciola. The choir and tower above the entrance are of the 11th century, while the nave (late 12th century) is in the Angevin style. In a recess in the nave known as the Chapelle du Pas de Dieu, there is a footprint which tradition asserts to be that of Christ, who appeared in a vision to St Radegonde. NotreDame la Grande, which dates from the close of the i ith century, and represents a collegiate church of one or two hundred years older, has a sculptured Romanesque facade rivalled in richness only by that of St Pierre of Angouleme. The first stone of the church of Montierneuf (Monasteriur Novum) was laid in 1077 by William VI., duke of Aquitaine and count of Poitiers, who is buried within its walls; and the choir (in the 13th century
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