The establishment of the Normal School accordingly indicates the commencement of a veritable revolution in the study of pure mathematics; with it demonstrations, methods, and important theories, buried in academical collections, appeared for the first time before the pupils, and encouraged them to recast upon new bases the works destined for instruction.
With some rare exceptions, the philosophers engaged in the cultivation of science constituted formerly in France a class totally distinct from that of the professors. By appointing the first geometers, the first philosophers, and the first naturalists of the world to be professors, the Convention threw new lustre upon the profession of teaching, the advantageous influence of which is felt in the present day. In the opinion of the public at large a title which a Lagrange, a Laplace, a Monge, a Berthollet, had borne, became a proper match to the finest titles. If under the empire, the Polytechnic School counted among its active professors councillors of state, ministers, and the president of the senate, you must look for the explanation of this fact in the impulse given by the Normal School.
You see in the ancient great colleges, professors concealed in some degree behind their portfolios, reading as from a pulpit, amid the indifference and inattention of their pupils, discourses prepared beforehand with great labour, and which reappear every year in the same form. Nothing of this kind existed at the Normal School; oral lessons alone were there permitted. The authorities even went so far as to require of the illustrious savans appointed to the task of instruction the formal promise never to recite any lectures which they might have learned by heart. From that time the chair has become a tribune where the professor, identified, so to speak, with his audience, sees in their looks, in their gestures, in their countenance, sometimes the necessity for proceeding at greater speed, sometimes, on the contrary, the necessity of retracing his steps, of awakening the attention by some incidental observations, of clothing in a new form the thought which, when first expressed, had left some doubts in the minds of his audience. And do not suppose that the beautiful impromptu lectures with which the amphitheatre of the Normal School resounded, remained unknown to the public. Short-hand writers paid by the State reported them. The sheets, after being revised by the professors, were sent to the fifteen hundred pupils, to the members of Convention, to the consuls and agents of the Republic in foreign countries, to all governors of districts. There was in this something certainly of profusion compared with the parsimonious and mean habits of our time. Nobody, however, would concur in this reproach, however slight it may appear, if I were permitted to point out in this very apartment an illustrious Academician, whose mathematical genius was awakened by the lectures of the Normal School in an obscure district town!
The necessity of demonstrating the important services, ignored in the present day, for which the dissemination of the sciences is indebted to the first Normal School, has induced me to dwell at greater length on the subject than I intended. I hope to be pardoned; the example in any case will not be contagious. Eulogiums of the past, you know, Gentlemen, are no longer fashionable. Every thing which is said, every thing which is printed, induces us to suppose that the world is the creation of yesterday. This opinion, which allows to each a part more or less brilliant in the cosmogonic drama, is under the safeguard of too many vanities to have any thing to fear from the efforts of logic.
I have already stated that the brilliant success of Fourier at the Normal School assigned to him a distinguished place among the persons whom nature has endowed in the highest degree with the talent of public tuition. Accordingly, he was not forgotten by the founders of the Polytechnic School. Attached to that celebrated establishment, first with the title of Superintendent of Lectures on Fortification, afterwards appointed to deliver a course of lectures on Analysis, Fourier has left there a venerated name, and the reputation of a professor distinguished by clearness, method, and erudition; I shall add even the reputation of a professor full of grace, for our colleague has proved that this kind of merit may not be foreign to the teaching of mathematics.
The lectures of Fourier have not been collected together. The Journal of the Polytechnic School contains only one paper by him, a memoir upon the "principle of virtual velocities." This memoir, which probably had served for the text of a lecture, shows that the secret of our celebrated professor's great success consisted in the combination of abstract truths, of interesting applications, and of historical details little known, and derived, a thing so rare in our days, from original sources.
We have now arrived at the epoch when the peace of Leoben brought back to the metropolis the principal ornaments of our armies. Then the professors and the pupils of the Polytechnic School had sometimes the distinguished honour of sitting in their amphitheatres beside Generals Desaix and Bonaparte. Every thing indicated to them then an active participation in the events which each foresaw, and which in fact were not long of occurring.
Notwithstanding the precarious condition of Europe, the Directory decided upon denuding the country of its best troops, and launching them upon an adventurous expedition. The five chiefs of the Republic were then desirous of removing from Paris the conqueror of Italy, of thereby putting an end to the popular demonstrations of which he everywhere formed the object, and which sooner or later would become a real danger.
On the other hand, the illustrious general did not dream merely of the momentary conquest of Egypt; he wished to restore to that country its ancient splendour; he wished to extend its cultivation, to improve its system of irrigation, to create new branches of industry, to open to commerce numerous outlets, to stretch out a helping hand to the unfortunate inhabitants, to rescue them from the galling yoke under which they had groaned for ages, in a word, to bestow upon them without delay all the benefits of European civilization. Designs of such magnitude could not have been accomplished with the mere personnel of an ordinary army. It was necessary to appeal to science, to literature, and to the fine arts; it was necessary to ask the coöperation of several men of judgment and of experience. Monge and Berthollet, both members of the Institute and Professors in the Polytechnic School, became, with a view to this object, the principal recruiting aids to the chief of the expedition. Were our colleagues really acquainted with the object of this expedition? I dare not reply in the affirmative; but I know at all events that they were not permitted to divulge it. We are going to a distant country; we shall embark at Toulon; we shall be constantly with you; General Bonaparte will command the army, such was in form and substance the limited amount of confidential information which had been imperiously traced out to them. Upon the faith of words so vague, with the chances of a naval battle, with the English hulks in perspective, go in the present day and endeavour to enroll a father of a family, a savant already known by useful labours and placed in some honourable position, an artist in possession of the esteem and confidence of the public, and I am much mistaken if you obtain any thing else than refusals; but in 1798, France had hardly emerged from a terrible crisis, during which her very existence was frequently at stake. Who, besides, had not encountered imminent personal danger? Who had not seen with his own eyes enterprises of a truly desperate nature brought to a fortunate issue? Is any thing more wanted to explain that adventurous character, that absence of all care for the morrow, which appears to have been one of the most distinguishing features of the epoch of the Directory. Fourier accepted then without hesitation the proposals which his colleagues brought to him in the name of the Commander-in-Chief; he quitted the agreeable duties of a professor of the Polytechnic School, to go—he knew not where, to do—he knew not what.
Chance placed Fourier during the voyage in the vessel in which Kléber sailed. The friendship which the philosopher and the warrior vowed to each other from that moment was not without some influence upon the events of which Egypt was the theatre after the departure of Napoleon.