Part 51

JOSEPH FOURIER.

BIOGRAPHY READ AT A PUBLIC ASSEMBLY 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 principal ornaments of your learned collections.

In the present day, biographies are less confined in their object. The convulsions which France has experienced in emancipating herself from the swaddling-clothes of routine, of superstition 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 Assembly. 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 passionate 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 arsenals 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 Koenigstein, 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 Assembly, 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 illustrious 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 Assembly 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 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 pass 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 associated 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:

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 illustrious geometer Lambert, was a tailor. This circumstance 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 circumstance as a fact of no importance: nobody, in effect, thinks in the present day, nobody 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 illustrious colleague Legendre, was rejected with a severity of expression of which you may judge yourselves: "Fourier," replied the minister, "not being noble, 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 title of nobility; 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 illustration 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, assumed the habit of a Benedictine, and repaired to the Abbey of St. Benoit-sur-Loire, where he intended to pass 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 circumstance did not prevent his former masters from appointing him to the principal chair of mathematics in the Military School of Auxerre, and bestowing upon him numerous tokens of a lively and sincere affection. I venture to assert 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 titular 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 Institute of Egypt; at Grenoble, 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 space in the life of a man of science of the first rank without being important and difficult. The subject of algebraic analysis 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 analysis 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 illustrious 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 substituting 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 principal 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 quantities. 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 principal Academies of Europe have solemnly sanctioned, and from which the historian of the sciences dares not deviate without falling into arbitrary assumptions and confusion, M. Budan ought to be considered as the inventor. I will assert with equal assurance 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 nobody 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 competitor?--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 quantities.

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 analytical 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 Assembly. Fourier abandoned himself also to this movement of the human mind. He embraced with enthusiasm the principles of the Revolution, and he ardently associated himself with every thing grand, just, and generous which the popular impulse offered. His patriotism made him accept the most difficult missions. We may assert, that never, even when his life was at stake, did he truckle to the base, covetous, and sanguinary passions which displayed themselves on all sides.