(B.)

The _Mecanique Celeste_.--This stupendous monument of intellectual research consists, as stated by the author, of five quarto volumes. The subject-matter is divided into sixteen books, and each book again is subdivided into several chapters. Vol. I. contains the first and second books of the work; Vol. II. contains the third, fourth, and fifth books; Vol. III. contains the sixth and seventh books; Vol. IV. contains the eighth, ninth, and tenth books; and, finally, Vol. V. contains the remaining six books. In the first book the author treats of the general laws of equilibrium and motion. In the second book he treats of the law of gravitation, and the movements of the centres of gravity of the celestial bodies. In the third book he investigates the subject of the figures of the celestial bodies. In the fourth book he considers the oscillations of the ocean and the atmosphere, arising from the disturbing action of the celestial bodies. The fifth book is devoted to the investigation of the movements of the celestial bodies around their centres of gravity. In this book the author gives a solution of the great problems of the precession of the equinoxes and the libration of the moon, and determines the conditions upon which the stability of Saturn's ring depends. The sixth book is devoted to the theory of the planetary movements; the seventh, to the lunar theory; the eighth, to the theory of the satellites of Jupiter, Saturn, and Ura.n.u.s; and the ninth, to the theory of comets. In the tenth book the author investigates various subjects relating to the system of the universe.

Among these may be mentioned the theory of astronomical refractions; the determination of heights by the barometer; the investigation of the effects produced on the movements of the planets and comets by a resisting medium; and the determination of the values of the ma.s.ses of the planets and satellites. In the six books forming the fifth volume of the work, the author, besides presenting his readers with an historical exposition of the labours of Newton and his successors on the theory of gravitation, gives an account of various researches relative to the system of the universe, which had occupied his attention subsequently to the publication of the previous volumes. In the eleventh book he considers the subjects of the figure and rotation of the earth. In the twelfth book he investigates the attraction and repulsion of spheres, and the laws of equilibrium and motion of elastic fluids. The thirteenth book is devoted to researches on the oscillations of the fluids which cover the surfaces of the planets; the fourteenth, to the subject of the movements of the celestial bodies around their centres of gravity; the fifteenth, to the movements of the planets and comets; and the sixteenth, to the movements of the satellites. The author published a supplement to the third volume, containing the results of certain researches on the planetary theory, and a supplement to the tenth book, in which he investigates very fully the theory of capillary attraction.

There was also published a posthumous supplement to the fifth volume, the ma.n.u.script of which was found among his papers after his death.

JOSEPH FOURIER.

BIOGRAPHY READ AT A PUBLIC a.s.sEMBLY OF THE ACADEMY OF SCIENCES, ON THE 18TH OF NOVEMBER, 1833.

Gentlemen,--In former times one academician differed from another only in the number, the nature, and the brilliancy of his discoveries. Their lives, thrown in some respects into the same mould, consisted of events little worthy of remark. A boyhood more or less studious; progress sometimes slow, sometimes rapid; inclinations thwarted by capricious or shortsighted parents; inadequacy of means, the privations which it introduces in its train; thirty years of a laborious professorship and difficult studies,--such were the elements from which the admirable talents of the early secretaries of the Academy were enabled to execute those portraits, so piquant, so lively, and so varied, which form one of the princ.i.p.al ornaments of your learned collections.

In the present day, biographies are less confined in their object. The convulsions which France has experienced in emanc.i.p.ating herself from the swaddling-clothes of routine, of superst.i.tion and of privilege, have cast into the storms of political life citizens of all ages, of all conditions, and of all characters. Thus has the Academy of Sciences figured during forty years in the devouring arena, wherein might and right have alternately seized the supreme power by a glorious sacrifice of combatants and victims!

Recall to mind, for example, the immortal National a.s.sembly. You will find at its head a modest academician, a patern of all the private virtues, the unfortunate Bailly, who, in the different phases of his political life, knew how to reconcile a pa.s.sionate affection for his country with a moderation which his most cruel enemies themselves have been compelled to admire.

When, at a later period, coalesced Europe launched against France a million of soldiers; when it became necessary to organize for the crisis fourteen armies, it was the ingenious author of the _Essai sur les Machines_ and of the _Geometrie des Positions_ who directed this gigantic operation. It was, again, Carnot, our honourable colleague, who presided over the incomparable campaign of seventeen months, during which French troops, novices in the profession of arms, gained eight pitched battles, were victorious in one hundred and forty combats, occupied one hundred and sixteen fortified places and two hundred and thirty forts or redoubts, enriched our a.r.s.enals with four thousand cannon and seventy thousand muskets, took a hundred thousand prisoners, and adorned the dome of the Invalides with ninety flags. During the same time the Chaptals, the Fourcroys, the Monges, the Berthollets rushed also to the defence of French independence, some of them extracting from our soil, by prodigies of industry, the very last atoms of saltpetre which it contained; others transforming, by the aid of new and rapid methods, the bells of the towns, villages, and smallest hamlets into a formidable artillery, which our enemies supposed, as indeed they had a right to suppose, we were deprived of. At the voice of his country in danger, another academician, the young and learned Meunier, readily renounced the seductive pursuits of the laboratory; he went to distinguish himself upon the ramparts of Konigstein, to contribute as a hero to the long defence of Mayence, and met his death, at the age of forty years only, after having attained the highest position in a garrison wherein shone the Aubert-Dubayets, the Beaupuys, the Haxos, the Klebers.

How could I forget here the last secretary of the original Academy?

Follow him into a celebrated a.s.sembly, into that Convention, the sanguinary delirium of which we might almost be inclined to pardon, when we call to mind how gloriously terrible it was to the enemies of our independence, and you will always see the ill.u.s.trious Condorcet occupied exclusively with the great interests of reason and humanity. You will hear him denounce the shameful brigandage which for two centuries laid waste the African continent by a system of corruption; demand in a tone of profound conviction that the Code be purified of the frightful stain of capital punishment, which renders the error of the judge for ever irreparable. He is the official organ of the a.s.sembly on every occasion when it is necessary to address soldiers, citizens, political parties, or foreign nations in language worthy of France; he is not the tactician of any party, he incessantly entreats all of them to occupy their attention less with their own interests and a little more with public matters; he replies, finally, to unjust reproaches of weakness by acts which leave him the only alternative of the poison cup or the scaffold.

The French Revolution thus threw the learned geometer, whose discoveries I am about to celebrate, far away from the route which destiny appeared to have traced out for him. In ordinary times it would be about Dom[40]

Joseph Fourier that the secretary of the Academy would have deemed it his duty to have occupied your attention. It would be the tranquil, the retired life of a Benedictine which he would have unfolded to you. The life of our colleague, on the contrary, will be agitated and full of perils; it will pa.s.s into the fierce contentions of the forum and amid the hazards of war; it will be a prey to all the anxieties which accompany a difficult administration. We shall find this life intimately a.s.sociated with the great events of our age. Let us hasten to add, that it will be always worthy and honourable, and that the personal qualities of the man of science will enhance the brilliancy of his discoveries.

FOOTNOTE:

[40] An abbreviation of Dominus, equivalent to the English prefix Reverend.--_Translator_.

BIRTH OF FOURIER.--HIS YOUTH.

Fourier was born at Auxerre on the 21st of March, 1768. His father, like that of the ill.u.s.trious geometer Lambert, was a tailor. This circ.u.mstance would formerly have occupied a large place in the _eloge_ of our learned colleague; thanks to the progress of enlightened ideas, I may mention the circ.u.mstance as a fact of no importance: n.o.body, in effect, thinks in the present day, n.o.body even pretends to think, that genius is the privilege of rank or fortune.

Fourier became an orphan at the age of eight years. A lady who had remarked the amiability of his manners and his precocious natural abilities, recommended him to the Bishop of Auxerre. Through the influence of this prelate, Fourier was admitted into the military school which was conducted at that time by the Benedictines of the Convent of St. Mark. There he prosecuted his literary studies with surprising rapidity and success. Many sermons very much applauded at Paris in the mouth of high dignitaries of the Church were emanations from the pen of the schoolboy of twelve years of age. It would be impossible in the present day to trace those first compositions of the youth Fourier, since, while divulging the plagiarism, he had the discretion never to name those who profited by it.

At thirteen years Fourier had the petulance, the noisy vivacity of most young people of the same age; but his character changed all at once, and as if by enchantment, as soon as he was initiated in the first principles of mathematics, that is to say, as soon as he became sensible of his real vocation. The hours prescribed for study no longer sufficed to gratify his insatiable curiosity. Ends of candles carefully collected in the kitchen, the corridors and the refectory of the college, and placed on a hearth concealed by a screen, served during the night to illuminate the solitary studies by which Fourier prepared himself for those labours which were destined, a few years afterwards, to adorn his name and his country.

In a military school directed by monks, the minds of the pupils necessarily waver only between two careers in life--the church and the sword. Like Descartes, Fourier wished to be a soldier; like that philosopher, he would doubtless have found the life of a garrison very wearisome. But he was not permitted to make the experiment. His demand to undergo the examination for the artillery, although strongly supported by our ill.u.s.trious colleague Legendre, was rejected with a severity of expression of which you may judge yourselves: "Fourier,"

replied the minister, "not being n.o.ble, could not enter the artillery, although he were a second Newton."

Gentlemen, there is in the strict enforcement of regulations, even when they are most absurd, something respectable which I have a pleasure in recognizing; in the present instance nothing could soften the odious character of the minister's words. It is not true in reality that no one could formerly enter into the artillery who did not possess a t.i.tle of n.o.bility; a certain fortune frequently supplied the want of parchments.

Thus it was not a something undefinable, which, by the way, our ancestors the Franks had not yet invented, that was wanting to young Fourier, but rather an income of a few hundred livres, which the men who were then placed at the head of the country would have refused to acknowledge the genius of Newton as a just equivalent for! Treasure up these facts, Gentlemen; they form an admirable ill.u.s.tration of the immense advances which France has made during the last forty years.

Posterity, moreover, will see in this, not the excuse, but the explanation of some of those sanguinary dissensions which stained our first revolution.

Fourier not having been enabled to gird on the sword, a.s.sumed the habit of a Benedictine, and repaired to the Abbey of St. Benoit-sur-Loire, where he intended to pa.s.s the period of his noviciate. He had not yet taken any vows when, in 1789, every mind was captivated with beautifully seductive ideas relative to the social regeneration of France. Fourier now renounced the profession of the Church; but this circ.u.mstance did not prevent his former masters from appointing him to the princ.i.p.al chair of mathematics in the Military School of Auxerre, and bestowing upon him numerous tokens of a lively and sincere affection. I venture to a.s.sert that no event in the life of our colleague affords a more striking proof of the goodness of his natural disposition and the amiability of his manners. It would be necessary not to know the human heart to suppose that the monks of St. Benoit did not feel some chagrin upon finding themselves so abruptly abandoned, to imagine especially that they should give up without lively regret the glory which the order might have expected from the ingenious colleague who had just escaped from them.

Fourier responded worthily to the confidence of which he had just become the object. When his colleagues were indisposed, the t.i.tular professor of mathematics occupied in turns the chairs of rhetoric, of history, and of philosophy; and whatever might be the subject of his lectures, he diffused among an audience which listened to him with delight, the treasures of a varied and profound erudition, adorned with all the brilliancy which the most elegant diction could impart to them.

MEMOIR ON THE RESOLUTION OF NUMERICAL EQUATIONS.

About the close of the year 1789 Fourier repaired to Paris and read before the Academy of Sciences a memoir on the resolution of numerical equations of all degrees. This work of his early youth our colleague, so to speak, never lost sight of. He explained it at Paris to the pupils of the Polytechnic School; he developed it upon the banks of the Nile in presence of the Inst.i.tute of Egypt; at Gren.o.ble, from the year 1802, it was his favourite subject of conversation with the Professors of the Central School and of the Faculty of Sciences; this finally, contained the elements of the work which Fourier was engaged in seeing through the press when death put an end to his career.

A scientific subject does not occupy so much s.p.a.ce in the life of a man of science of the first rank without being important and difficult. The subject of algebraic a.n.a.lysis above mentioned, which Fourier had studied with a perseverance so remarkable, is not an exception to this rule. It offers itself in a great number of applications of calculation to the movements of the heavenly bodies, or to the physics of terrestrial bodies, and in general in the problems which lead to equations of a high degree. As soon as he wishes to quit the domain of abstract relations, the calculator has occasion to employ the roots of these equations; thus the art of discovering them by the aid of an uniform method, either exactly or by approximation, did not fail at an early period to excite the attention of geometers.

An observant eye perceives already some traces of their efforts in the writings of the mathematicians of the Alexandrian School. These traces, it must be _acknowledged_, are so slight and so imperfect, that we should truly be justified in referring the origin of this branch of a.n.a.lysis only to the excellent labours of our countryman Vieta.

Descartes, to whom we render very imperfect justice when we content ourselves with saying that he taught us much when he taught us to doubt, occupied his attention also for a short time with this problem, and left upon it the indelible impress of his powerful mind. Hudde gave for a particular but very important case rules to which nothing has since been added; Rolle, of the Academy of Sciences, devoted to this one subject his entire life. Among our neighbours on the other side of the channel, Harriot, Newton, Maclaurin, Stirling, Waring, I may say all the ill.u.s.trious geometers which England produced in the last century, made it also the subject of their researches. Some years afterwards the names of Daniel Barnoulli, of Euler, and of Fontaine came to be added to so many great names. Finally, Lagrange in his turn embarked in the same career, and at the very commencement of his researches he succeeded in subst.i.tuting for the imperfect, although very ingenious, essays of his predecessors, a complete method which was free from every objection.

From that instant the dignity of science was satisfied; but in such a case it would not be permitted to say with the poet:

"Le temps ne fait rien a l'affaire."

Now although the processes invented by Lagrange, simple in principle and applicable to every case, have theoretically the merit of leading to the result with certainty, still, on the other hand, they demand calculations of a most repulsive length. It remained then to perfect the practical part of the question; it was necessary to devise the means of shortening the route without depriving it in any degree of its certainty. Such was the princ.i.p.al object of the researches of Fourier, and this he has attained to a great extent.

Descartes had already found, in the order according to which the signs of the different terms of any numerical equation whatever succeed each other, the means of deciding, for example, how many real positive roots this equation may have. Fourier advanced a step further; he discovered a method for determining what number of the equally positive roots of every equation may be found included between two given quant.i.ties. Here certain calculations become necessary, but they are very simple, and whatever be the precision desired, they lead without any trouble to the solutions sought for.

I doubt whether it were possible to cite a single scientific discovery of any importance which has not excited discussions of priority. The new method of Fourier for solving numerical equations is in this respect amply comprised within the common law. We ought, however, to acknowledge that the theorem which serves as the basis of this method, was first published by M. Budan; that according to a rule which the princ.i.p.al Academies of Europe have solemnly sanctioned, and from which the historian of the sciences dares not deviate without falling into arbitrary a.s.sumptions and confusion, M. Budan ought to be considered as the inventor. I will a.s.sert with equal a.s.surance that it would be impossible to refuse to Fourier the merit of having attained the same object by his own efforts. I even regret that, in order to establish rights which n.o.body has contested, he deemed it necessary to have recourse to the certificates of early pupils of the Polytechnic School, or Professors of the University. Since our colleague had the modesty to suppose that his simple declaration would not be sufficient, why (and the argument would have had much weight) did he not remark in what respect his demonstration differed from that of his compet.i.tor?--an admirable demonstration, in effect, and one so impregnated with the elements of the question, that a young geometer, M. Sturm, has just employed it to establish the truth of the beautiful theorem by the aid of which he determines not the simple limits, but the exact number of roots of any equation whatever which are comprised between two given quant.i.ties.

PART PLAYED BY FOURIER IN OUR REVOLUTION.--HIS ENTRANCE INTO THE CORPS OF PROFESSORS OF THE NORMAL SCHOOL AND THE POLYTECHNIC SCHOOL.--EXPEDITION TO EGYPT.

We had just left Fourier at Paris, submitting to the Academy of Sciences the a.n.a.lytical memoir of which I have just given a general view. Upon his return to Auxerre, the young geometer found the town, the surrounding country, and even the school to which he belonged, occupied intensely with the great questions relative to the dignity of human nature, philosophy, and politics, which were then discussed by the orators of the different parties of the National a.s.sembly. Fourier abandoned himself also to this movement of the human mind. He embraced with enthusiasm the principles of the Revolution, and he ardently a.s.sociated himself with every thing grand, just, and generous which the popular impulse offered. His patriotism made him accept the most difficult missions. We may a.s.sert, that never, even when his life was at stake, did he truckle to the base, covetous, and sanguinary pa.s.sions which displayed themselves on all sides.

A member of the popular society of Auxerre, Fourier exercised there an almost irresistible ascendency. One day--all Burgundy has preserved the remembrance of it--on the occasion of a levy of three hundred thousand men, he made the words honour, country, glory, ring so eloquently, he induced so many voluntary enrolments, that the ballot was not deemed necessary. At the command of the orator the contingent a.s.signed to the chief town of the Yonne formed in order, a.s.sembled together within the very enclosure of the a.s.sembly, and marched forthwith to the frontier.

Unfortunately these struggles of the forum, in which so many n.o.ble lives then exercised themselves, were far from having always a real importance. Ridiculous, absurd, and burlesque motions injured incessantly the inspirations of a pure, sincere, and enlightened patriotism. The popular society of Auxerre would furnish us, in case of necessity, with more than one example of those lamentable contrasts.

Thus I might say that in the very same apartment wherein Fourier knew how to excite the honourable sentiments which I have with pleasure recalled to mind, he had on another occasion to contend with a certain orator, perhaps of good intentions, but a.s.suredly a bad astronomer, who, wishing to escape, said he, from _the good pleasure_ of munic.i.p.al rulers, proposed that the names of the north, east, south, and west quarters should be a.s.signed by lot to the different parts of the town of Auxerre.

Literature, the fine arts, and the sciences appeared for a moment to flourish under the auspicious influence of the French Revolution.

Observe, for example, with what grandeur of conception the reformation of weights and measures was planned; what geometers, what astronomers, what eminent philosophers presided over every department of this n.o.ble undertaking! Alas! frightful revolutions in the interior of the country soon saddened this magnificent spectacle. The sciences could not prosper in the midst of the desperate contest of factions. They would have blushed to owe any obligations to the men of blood, whose blind pa.s.sions immolated a Saron, a Bailly, and a Lavoisiere.

A few months after the 9th Thermidor, the Convention being desirous of diffusing throughout the country ideas of order, civilization, and internal prosperity, resolved upon organizing a system of public instruction, but a difficulty arose in finding professors. The members of the corps of instruction had become officers of artillery, of engineering, or of the staff, and were combating the enemies of France at the frontiers. Fortunately at this epoch of intellectual exaltation, nothing seemed impossible. Professors were wanting; it was resolved without delay to create some, and the Normal School sprung into existence. Fifteen hundred citizens of all ages, despatched from the princ.i.p.al district towns, a.s.sembled together, not to study in all their ramifications the different branches of human knowledge, but in order to learn the art of teaching under the greatest masters.

Fourier was one of these fifteen hundred pupils. It will, no doubt, excite some surprise that he was elected at St. Florentine, and that Auxerre appeared insensible to the honour of being represented at Paris by the most ill.u.s.trious of her children. But this indifference will be readily understood. The elaborate scaffolding of calumny which it has served to support will fall to the ground as soon as I recall to mind, that after the 9th Thermidor the capital, and especially the provinces, became a prey to a blind and disorderly reaction, as all political reactions invariably are; that crime (the crime of having changed opinions--it was nothing less hideous) usurped the place of justice; that excellent citizens, that pure, moderate, and conscientious patriots were daily ma.s.sacred by hired bands of a.s.sa.s.sins in presence of whom the inhabitants remained mute with fear. Such are, Gentlemen, the formidable influences which for a moment deprived Fourier of the suffrages of his countrymen; and caricatured, as a partisan of Robespierre, the individual whom St. Just, making allusion to his sweet and persuasive eloquence, styled a _patriot in music_; who was so often thrown into prison by the decemvirs; who, at the very height of the Reign of Terror, offered before the Revolutionary Tribunal the a.s.sistance of his admirable talents to the mother of Marshal Davoust, accused of the crime of having at that unrelenting epoch sent some money to the emigrants; who had the incredible boldness to shut up at the inn of Tonnerre an agent of the Committee of Public Safety, into the secret of whose mission he penetrated, and thus obtained time to warn an honourable citizen that he was about to be arrested; who, finally, attaching himself personally to the sanguinary proconsul before whom every one trembled in Yonne, made him pa.s.s for a madman, and obtained his recall!

You see, Gentlemen, some of the acts of patriotism, of devotion, and of humanity which signalized the early years of Fourier. They were, you have seen, repaid with ingrat.i.tude. But ought we in reality to be astonished at it? To expect grat.i.tude from the man who cannot make an avowal of his feelings without danger, would be to shut one's eyes to the frailty of human nature, and to expose one's self to frequent disappointments.

In the Normal School of the Convention, discussion from time to time succeeded ordinary lectures. On those days an interchange of characters was effected; the pupils interrogated the professors. Some words p.r.o.nounced by Fourier at one of those curious and useful meetings sufficed to attract attention towards him. Accordingly, as soon as a necessity was felt to create Masters of Conference, all eyes were turned towards the pupil of St. Florentine. The precision, the clearness, and the elegance of his lectures soon procured for him the unanimous applause of the fastidious and numerous audience which was confided to him.

When he attained the height of his scientific and literary glory, Fourier used to look back with pleasure upon the year 1794, and upon the sublime efforts which the French nation then made for the purpose of organizing a Corps of Public Instruction. If he had ventured, the t.i.tle of Pupil of the original Normal School would have been beyond doubt that which he would have a.s.sumed by way of preference. Gentlemen, that school perished of cold, of wretchedness, and of hunger, and not, whatever people may say, from certain defects of organization which time and reflection would have easily rectified. Notwithstanding its short existence, it imparted to scientific studies quite a new direction which has been productive of the most important results. In supporting this opinion at some length, I shall acquit myself of a task which Fourier would certainly have imposed upon me, if he could have suspected, that with just and eloquent eulogiums of his character and his labours there should mingle within the walls of this apartment, and even emanate from the mouth of one of his successors, sharp critiques of his beloved Normal School.