FOURIER, JOSEPH, was born at Auxerre in 1768. He was the son of a tailor in that town, nod there received his education at a school directed by the Benedictines. Into this order he was about to enter, and had passed a part of his noviciate, when the Revolution com menced. He had applied himself very early to the mathematics, and had gained such reputation that in 1789 he was appointed professor in the school at which he had formerly studied. He had not confined himself to one branch of learning, as appears from his giving courses of history, rhetoric, and philosophy. Before this time, in 1787, he had sent to Paris a memoir on the theory of equatioris, to be presented to the Academy of Sciences. This memoir contained the first steps of the theory which was afterwards published : it was lost during the Revolution, but a sufficiently attested copy exists.
Fourier took some part in the civil troubles, at their commencement, and was a member of the Committee of Public Safety at Auxerre. Ha' was more than once the object of proscription, having been twice either saved or delivered from prison by his fellow-townsmen of Auxerre, once saved from the guillotine by the death of Robespierre, and once by the interference of the professors of the ?';cote Polytech nique. Having previously been a pupil of the &olio Normale, he was appointed a sub-professor of the Polytechnic School in 1794, and remained in that post till 1798. In the latter year Monge proposed to him to accompany the expedition to Egypt. His occupations in that country were various : he was secretary of the Institute which was formed at Cairo ; he superintended the commission which was employed in collecting materials for the great work on Egypt, and was employed in judicial and diplomatic capacities. At his return from Egypt he was appointed by the First Consul prefect of the department Isiire, which place he continued to fill till 1815, his situation having been preserved to him at the fall of Napoleon in 1814, by the high estimation in which he was held, aud the gratitude of those adherents of the old monarchy whom he had served. When Napoleon I, in 1815 passed through Grenoble (a town of Fourier's prefecture), Fourier, who had hesitated much, issued a moderate Bourboaist proclamation, and left the town by one gate as Napoleon entered it by another. Napoleon was extremely enraged at this step, and causing Fourier to be brought into hia presence, reminded him in strong terms of former benefits, and telling him that, after the proclamation, he could not remain at Grenoble, appointed him prefect of the department of the Ithritie. Fourier appears to have been softened by the matter, or subdued by the manner, of Napoleon's address to him, and went quietly to his new post. He resigned it however on the let of May, n consequence of his determination not to execute the orders of Carnet, which required him to make numerous arrests among the Bourbonites ; and he was in Paris when the news of the battle of Waterloo arrived. Here he remained for some time, entirely neglected, and with very moderate funds, until his former pupil, M. de Chabrol,
gave hint the superintendence of a bureau de statiatique: In 1816 he was chosen a member of the Institute, but Louis XVIII. refused to ratify the election ; and it was not till a year after that this king could be induced to allow it. On the death of Delambre he was chosen secretary of the Academy, and on that of Laplace president of the council of the Polytechnic School. Fourier died at Paris in May 1830.
The character of Fourier was in every point of view respectable. His appearance and manners were decidedly good, and hie address, united with the respect which he created, enabled him to manage the prejudices and passions of others to a remarkable extent, of which M. Cousin, in his notes to his 6loge of Fourier, gives several instances. He knew how, says M. Cousin, "prendre chacun par oh it 6tait prenable ; " and his own explanation of this faculty was "je prends l'epi dans son Bens, au lieu de le prendre it rebours." The influence of his conversation produced in one case at least abiding and remark able effects : it was he who first gave a taste for Egyptian antiquities to the Champolliona.
The writings of Fourier consist of papers in the `Memoirs' of the Academy of Sciences, the Annalee de Physique,' and the 'Recherches Statistiques our la Ville de Paris,' &c., as well as of two separate works, namely, the Th6orie de la Chaleur,' Paris, 1822, and the Analyse des Equations deternsiodes,' Paris, 1831. The last work is posthumous, and was completed under the inspection of 3r. Navier.
In the first of the two works, the object of which is the deduction of the mathematical laws of the propagation of heat through solids, Fourier extended the solution of partial differential equations, gave some remarkable views ou the solution of equations with an infinite number of terms, expressed the particular value of a function by means of a definite integral containing its general value (which is called Fourier's Theorem '), &c. This work is full of interesting details, and is cue of the highest productions of analysis of our day.
The latter of the two works contains an extension of Descartes' well-known rule of signs, by means of which the number of the real roots of an equation may be determioed. Considered with respect to results merely, the method of Fourier may perhaps be considered as superseded by the remarkable theorem of M. Sturm ; but there is nevertheless much in the course marked out by Fourier which it would be worth while to examine. The work also contains a method of solving equations by determination of the successive figures of the root, analogous to that proposed by Mr. Homer and others. Tho preface of M. Navier contains attestations as to the time at which the several parts of the work were written, which it will be worth the while of those to consult who think that "all which has been done by Fourier was virtually done by Mr. Horner long before."