The general methods of Descriptive Geometry,—their uses in Stone-cutting and Carpentry, in Linear Perspective, and in the determination of the Shadows of bodies,—constitute one of the most fruitful branches of the applications of mathematics. The course has always been given at the Polytechnic School with particular care, according to the plans traced by the illustriousMonge, but no part of the subject has heretofore been required for admission. The time given to it in the school, being however complained of on all sides as insufficient for its great extent and important applications, the general methods of Descriptive Geometry will henceforth be retrenched from the internal course, and be required of all candidates for admission.
As to the programme itself, it is needless to say any thing, for it was established byMonge, and the extent which he gave to it, as well as the methods which he had created, have thus far been maintained. We merely suppress the construction of the shortest distance between two right-lines, which presents a disagreeable and useless complication.
Candidates will have to present to the examiner a collection of their graphical constructions (épures) of all the questions of the programme, signed by their teacher. They are farther required to make free-hand sketches of five of theirépures.
PROGRAMME OF DESCRIPTIVE GEOMETRY.Problems relating to the point, to the straight line, and to the plane.7Through a point given in space, to pass a right line parallel to a given right line, and to find the length of a part of that right line.Through a given point, to pass a plane parallel to a given plane.To construct the plane which passes through three points given in space.Two planes being given, to find the projections of their inter.A right line and a plane being given, to find the projections of the point in which the right line meets the plane.Through a given point, to pass a perpendicular to a given plane, and to construct the projections of the point of meeting of the right line and of the plane.Through a given point, to pass a right line perpendicular to a given right line, and to construct the projections of the point of meeting of the two right lines.A plane being given, to find the angles which it forms with the planes of projection.Two planes being given, to construct the angle which they form between them.Two right lines which cut each other being given, to construct the angle which they form between them.To construct the angle formed by a right line and by a plane given in position in space.Problems relating to tangent planes.To draw a plane tangent to a cylindrical surface or to a conical surface, 1othrough a point taken on the surface; 2othrough a point taken out of the surface; 3oparallel to a given right line.Through a point taken on a surface of revolution, whose meridian is known, to pass a plane tangent to that surface.
PROGRAMME OF DESCRIPTIVE GEOMETRY.
Problems relating to the point, to the straight line, and to the plane.7
Through a point given in space, to pass a right line parallel to a given right line, and to find the length of a part of that right line.
Through a given point, to pass a plane parallel to a given plane.
To construct the plane which passes through three points given in space.
Two planes being given, to find the projections of their inter.
A right line and a plane being given, to find the projections of the point in which the right line meets the plane.
Through a given point, to pass a perpendicular to a given plane, and to construct the projections of the point of meeting of the right line and of the plane.
Through a given point, to pass a right line perpendicular to a given right line, and to construct the projections of the point of meeting of the two right lines.
A plane being given, to find the angles which it forms with the planes of projection.
Two planes being given, to construct the angle which they form between them.
Two right lines which cut each other being given, to construct the angle which they form between them.
To construct the angle formed by a right line and by a plane given in position in space.
Problems relating to tangent planes.
To draw a plane tangent to a cylindrical surface or to a conical surface, 1othrough a point taken on the surface; 2othrough a point taken out of the surface; 3oparallel to a given right line.
Through a point taken on a surface of revolution, whose meridian is known, to pass a plane tangent to that surface.
Problems relating to the inter of surfaces.To construct the made, on the surface of a right and vertical cylinder, by a plane perpendicular to one of the planes of projection.—To draw the tangent to the curve of inter.—To make the development of the cylindrical surface, and to refer to it the curve of inter, and also the tangent.To construct the inter of a right cone by a plane perpendicular to one of the planes of projection. Development and tangent.To construct the right of an oblique cylinder.—To draw the tangent to the curve of inter. To make the development of the cylindrical surface, and to refer to it the curve which served as its base, and also its tangents.To construct the inter of a surface of revolution by a plane, and the tangents to the curve of inter.—To resolve this question, when the generating line is a right line which does not meet the axis.To construct the inter of two cylindrical surfaces, and the tangents to that curve.To construct the inter of two oblique cones, and the tangents to that curve.To construct the inter of two surfaces of revolution whose axes meet.
Problems relating to the inter of surfaces.
To construct the made, on the surface of a right and vertical cylinder, by a plane perpendicular to one of the planes of projection.—To draw the tangent to the curve of inter.—To make the development of the cylindrical surface, and to refer to it the curve of inter, and also the tangent.
To construct the inter of a right cone by a plane perpendicular to one of the planes of projection. Development and tangent.
To construct the right of an oblique cylinder.—To draw the tangent to the curve of inter. To make the development of the cylindrical surface, and to refer to it the curve which served as its base, and also its tangents.
To construct the inter of a surface of revolution by a plane, and the tangents to the curve of inter.—To resolve this question, when the generating line is a right line which does not meet the axis.
To construct the inter of two cylindrical surfaces, and the tangents to that curve.
To construct the inter of two oblique cones, and the tangents to that curve.
To construct the inter of two surfaces of revolution whose axes meet.
The preceding six heads complete the outline of the elementary course of mathematical instruction which it was the object of this article to present; but a few more lines may well be given to a mere enumeration of the other requirements for admission to the school.
Mechanicscomes next. The programme is arranged under these heads: Simple motion and compound motion; Inertia; Forces applied to a free material point; Work of forces applied to a movable point; Forces applied to a solid body; Machines.
Physicscomprises these topics: General properties of bodies; Hydrostatics and hydraulics; Densities of solids and liquids; Properties of gases; Heat; Steam; Electricity; Magnetism; Acoustics; Light.
Chemistrytreats of Oxygen; Hydrogen; Combinations of hydrogen with oxygen; Azote or nitrogen; Combinations of azote with oxygen; Combination of azote with hydrogen, or ammonia; Sulphur; Chlorine; Phosphorus; Carbon.
Cosmographydescribes the Stars; the Earth; the Sun; the Moon; the Planets; Comets; the Tides.
HistoryandGeographytreat of Europe from the Roman Empire to the accession of Louis XVI.
Germanmust be known sufficiently for it to be translated, spoken a little, and written in its own characters.
Drawing, besides theépuresof descriptive geometry, must have been acquired sufficiently for copying an academic study, and shading in pencil and in India ink.
Will not our readers agree with M. Coriolis, that “There are very few learned mathematicians who could answer perfectly well at an examination for admission to the Polytechnic School”?
Thereare strictly speaking no Junior Military Schools preparatory to the Polytechnic School, or to the Special Military School at St. Cyr. These schools are recruited in general from theLycéesand other schools for secondary instruction, upon which they exert a most powerful influence. Until 1852 there was no special provision made in the courses of instruction in theLycéesfor the mathematical preparation required for admission into the Polytechnic, and the Bachelor’s degree in science could not be obtained without being able to meet the requirements in Latin, rhetoric, and logic for graduation in the arts, which was necessary to the profession of law, medicine, and theology. In consequence, young men who prepared to be candidates for the preliminary examinations at the Polytechnic and the St. Cyr, left theLycéesbefore graduation in order to acquire more geometry and less literature in the private schools, or under private tuition.
A new arrangement, popularly called theBifurcation, was introduced by the Decrees of the 10th of April, 1852; and has now come into operation. The conditions demanded for the degree in science were adapted to the requirements of the Military Schools; and in return for this concession it is henceforth to be exacted from candidates for the Military Schools. The diploma of arts is no longer required before the diploma of science can be given. The instruction, which in the upper classes of theLycéeshad hitherto been mainly preparatory for the former, takes henceforth at a certain point (called that ofBifurcation) two different routes, conducting separately, the one to the baccalaureate of arts, the other to that of science. The whole system of teaching has accordingly been altered. Boys wanting to study algebra are no longer carried through a long course of Latin; mathematics are raised to an equality with literature; and thus military pupils—pupils desirous of admission at the Polytechnic and St. Cyr, may henceforth, it is hoped, obtain in theLycéesall the preparation which they had latterly sought elsewhere.
Under this new system the usual course for a boy seems to be the following:—
He enters theLycée, in the Elementary Classes; or, a little later, in the Grammar Classes, where he learns Latin and begins Greek. At the age of about fourteen, he is called upon to pass an examination for admission into the Upper Division, and here, in accordance with the new regulations, he makes his choice for mathematics or for literature, the studies henceforth being divided, one course leading to the bachelorship of science, the other to that of arts.
In either case he has before him three yearly courses, three classes—the Third, the Second, and what is called the Rhetoric. At the close of this, or after passing, if he pleases, another year in what is called the Logic, he may go up for his bachelor’s degree. The boy who wants to go to St. Cyr or the Polytechnic chooses, of course, the mathematical division leading to the diploma he will want, that of a bachelor ofscience. He accordingly begins algebra, goes on to trigonometry, to conic s, and to mechanics, and through corresponding stages in natural philosophy, and the like. If he chooses to spend a fourth year in the Logic, he will be chiefly employed in going over his subjects again. He may take his bachelor’s degree at any time after finishing his third year; and he may, if he pleases, having taken that, remain during a fifth or even a sixth year, in the class of Special Mathematics.
If he be intended for St. Cyr, he may very well leave at the end of his year in Rhetoric, taking of course his degree. One year in the course of Special Mathematics will be required before he can have a chance for the Polytechnic. Usually the number of students admitted at the latter, who have not passed more than one year in themathematiques spécialesis very small. Very probably the young aspirant would try at the end of his first year in this class, and would learn by practice to do better at the end of the second.
The following are the studies of the mathematical of the upper division as laid down by the ordinance of 30th August, 1854.
The Third Class(Troisième,) at fourteen years old.Arithmetic and first notions of Algebra. Plane Geometry and its applications. First notions of Chemistry and Physics. General notions of Natural History; Principles of classification. Linear and imitative Drawing.The Second Class(Seconde,) at fifteen years old.Algebra; Geometry, figures in space, recapitulation; Applications of Geometry, notions of the geometrical representations of bodies by projections; Rectilineal Trigonometry; Chemistry; Physics; and Drawing.The Rhetoric, at sixteen years old.Exercises in Arithmetic and Algebra; Geometry; notions on some common curves; and general recapitulation; Applications of Geometry; notions of leveling and its processes; recapitulation of Trigonometry; Cosmography; Mechanics; Chemistry concluded and reviewed; Zoölogy and Animal Physiology; Botany and Vegetable Physiology; Geology; Drawing. (The pupil may now be ready for the Degree and for St. Cyr.)The Logic, at seventeen years old.Six lessons a week are employed in preparation for the bachelorship of science, and in a methodical recapitulation of the courses of the three preceding years according to the state of the pupil’s knowledge.Two lessons a week are allowed for reviewing the literary instruction; evening lessons in Latin, French, English, and German, and in History and Geography, having been given through the whole previous time.The Special Mathematics, at eighteen and nineteen years old.Five lessons a week are devoted to these studies; in the other lessons the pupils join those of the Logic class for reviewing all their previous subjects, whether for the bachelorship in science or for competition for admission at theEcole Normaleor the Polytechnic.
The Third Class(Troisième,) at fourteen years old.
Arithmetic and first notions of Algebra. Plane Geometry and its applications. First notions of Chemistry and Physics. General notions of Natural History; Principles of classification. Linear and imitative Drawing.
The Second Class(Seconde,) at fifteen years old.
Algebra; Geometry, figures in space, recapitulation; Applications of Geometry, notions of the geometrical representations of bodies by projections; Rectilineal Trigonometry; Chemistry; Physics; and Drawing.
The Rhetoric, at sixteen years old.
Exercises in Arithmetic and Algebra; Geometry; notions on some common curves; and general recapitulation; Applications of Geometry; notions of leveling and its processes; recapitulation of Trigonometry; Cosmography; Mechanics; Chemistry concluded and reviewed; Zoölogy and Animal Physiology; Botany and Vegetable Physiology; Geology; Drawing. (The pupil may now be ready for the Degree and for St. Cyr.)
The Logic, at seventeen years old.
Six lessons a week are employed in preparation for the bachelorship of science, and in a methodical recapitulation of the courses of the three preceding years according to the state of the pupil’s knowledge.
Two lessons a week are allowed for reviewing the literary instruction; evening lessons in Latin, French, English, and German, and in History and Geography, having been given through the whole previous time.
The Special Mathematics, at eighteen and nineteen years old.
Five lessons a week are devoted to these studies; in the other lessons the pupils join those of the Logic class for reviewing all their previous subjects, whether for the bachelorship in science or for competition for admission at theEcole Normaleor the Polytechnic.
It will only be necessary to add a few sentences in explanation of the methods pursued in the upper classes of theLycées. The classes are large—from 80 to above 100; the lessons strictly professorial lectures, with occasional questions, as at the Polytechnic itself. In large establishments the class is divided, and two professors are employed, giving two parallel courses on the same subject. To correct and fortify this general teaching, we find, corresponding to the interrogations of the Polytechnic, what are here called conferences. The members of the large class are examined first of all in small detachments of five or six by their own professors once a week; and, secondly, a matter of yet greater importance, by the professor who is conducting the parallel course, and by professors who are engaged for this purpose from otherLycéesand preparatory schools, and from among therépétiteursof the Polytechnic and the Ecole Normale themselves. It appeared by the table of the examinations of this latter kind which had been passed by the pupils of the class of Special Mathematics at theLycéeSt. Louis, that the first pupil on the list had in the interval between the opening of the school and the date of our visit (February 16th) gone through as many as twenty-four.
The assistants, who bear the name ofrépétiteursat theLycées, do not correspond in any sense to those whom we shall hereafter notice at the Ecole Polytechnique. They are in theLycéesmere superintendents in thesalles d’étude, who attend to order and discipline, who give some slight occasional help to the pupils, and may beemployed in certain cases, where the parents wish for it, in giving private tuition to the less proficient. The system ofsalles d’étudeappears to prevail universally; the number of the pupils placed in each probably varying greatly. At the Polytechnic we found eight or ten pupils in each; at St. Cyr as many as 200. The number considered most desirable at theLycéeof St. Louis was stated to be thirty.
It thus appears that in France not only do private establishments succeed in giving preparation for the military schools, but that even in the first-class public schools, which educate for the learned professions, it has been considered possible to conduct a series of military or science classes by the side of the usual literary or arts classes. The common upper schools are not, as they used to be, and as with us they are,Grammarschools, they are alsoScienceschools. In everyLycéethere is, so to say, a sort of elementary polytechnic department, giving a kind of instruction which will be useful to the future soldier, and at the same time to others, to those who may have to do with mines, manufactures, or any description of civil engineering. There is thus no occasion for Junior Military Schools in France, for all the schools of this class are more or less of a military character in their studies.
The conditions of admission to the examination for the degree of Bachelor of Science are simply, sixteen years of age, and the payment of fees amounting to about 200 fr. (10l.) Examinations are held three times a year by the Faculties at Paris, Besançon, Bordeaux, Caen, Clermont, Dijon, Grenoble, Lille, Lyons, Marseilles, Montpellier, Nancy, Poitiers, Rennes, Strasburg, and Toulouse, and once a year at Ajaccio, Algiers, and nineteen other towns. There is a written examination of six hours, and a viva voce examination of an hour and a quarter. It is, of course, only apassexamination, and is said to be much less difficult than the competitive examination for admission to St. Cyr.—Report of English Commissioners, 1856.
Theorigin of theEcole Polytechniquedates from a period of disorder and distress in the history of France which might seem alien to all intellectual pursuits, if we did not remember that the general stimulus of a revolutionary period often acts powerfully upon thought and education. It is, perhaps, even more than the Institute, the chiefscientificcreation of the first French Revolution. It was during the government of the committee of public safety, when Carnot, as war minister, was gradually driving back the invading armies, and reorganizing victory out of defeat and confusion, that the first steps were taken for its establishment. A law, dating the 1st Ventose, year II., the 12th of March 1794, created a “Commission des Travaux Publics,” charged with the duty of establishing a regular system for carrying on public works; and this commission ultimately founded a central school for public works, and drew up a plan for the competitive examination of candidates for admission to the service. It was intended at first to give a complete education for some of the public services, but it was soon changed into a preparatory school, to be succeeded by special schools of application. This was the Ecole Polytechnique.
The school and its planwere both owing to an immediate and pressing want. It was to be partly military and partly civil. Military, as well as civil education had been destroyed by the revolutionists. The committee of public safety had, indeed, formed a provisional school for engineers at Metz, to supply the immediate wants of the army on the frontier, and at this school young men were hastily taught the elements of fortification, and were sent direct to the troops, to learn as they best could, the practice of their art. “But such a method,” says the report accompanying the law which founded the school, “does not form engineersin any true sense of the term, and can only be justified by the emergency of thetime. The young men should be recalled to the new school to complete their studies.” Indeed no one knew better than Carnot, to use the language of the report, “that patriotism and courage can notalwayssupply the want of knowledge;” and in the critical campaigns of 1793–4, he must often have felt the need of the institution which he was then contributing to set on foot. Such was the immediate motive for the creation of this school. At first, it only included the engineers amongst its pupils. But the artillery were added within a year.
We must not, however, omit to notice its civil character, the combination of which with its military object forms its peculiar feature, and has greatly contributed to its reputation. Amongst its founders were men, who though ardent revolutionists, were thirsting for the restoration of schools and learning, which for a time had been totally extinguished. The chief of these, besides Carnot, were Monge and Fourcroy, Berthollet and Lagrange. Of Carnot and Lagrange, one amongst the first of war ministers, the other one of the greatest of mathematicians, we need not say more. Berthollet, a man of science and practical skill, first suggested the school; Monge, the founder of Descriptive Geometry, a favoritesavantof Napoleon though a zealous republican, united to real genius that passion for teaching and for his pupils, which makes thebeau idéalof the founder of a school; and Fourcroy was a man of equal practical tact and science, who at the time had great influence with the convention, and was afterwards intrusted by Napoleon with much of the reorganization of education in France.
When the school first started there was scarcely another of any description in the country. For nearly three years the revolution had destroyed every kind of teaching. The attack upon the old schools, in France, as elsewhere, chiefly in the hands of the clergy, had been begun by a famous report of Talleyrand’s, presented to the legislative assembly in 1791, which recommended to suppress all the existing academies within Paris and the provinces, and to replace them by an entirely new system of national education through the country. In this plan a considerable number of military schools were proposed, where boys were to be educated from a very early age. When the violent revolutionists were in power, they adopted the destructive part of Talleyrand’s suggestions without the other. All schools, from the university downwards, were destroyed; the large exhibitions orBourses, numbering nearly 40,000, were confiscated or plundered by individuals, and even the military schools and those for the public works (which were absolutelynecessary for the very roads and the defense of the country) were suppressed or disorganized. The school of engineers at Mézières (an excellent one, where Monge had been a professor,) and that of the artillery at La Fère, were both broken up, whilst the murder of Lavoisier, and the well known saying in respect to it, that “the Republic had no need of chemists,” gave currency to a belief, which Fourcroy expressed in proposing the Polytechnic, “that the late conspirators had formed a deliberate plan to destroy the arts and sciences, and to establish their tyranny on the ruins of human reason.”
Thus it was on the ruin of all the old teaching, that the new institution was erected; a trulyrevolutionaryschool, as its founders delighted to call it, using the term as it was then commonly used, as a synonym for all that was excellent. And then for the first time avowing the principle of public competition, its founders, Monge and Fourcroy, began their work with an energy and enthusiasm which they seem to have left as a traditional inheritance to their school. It is curious to see the difficulties which the bankruptcy of the country threw in their way, and the vigor with which, assisted by the summary powers of the republican government, they overcame them. They begged the old Palais Bourbon for their building; were supplied with pictures from the Louvre; the fortunate capture of an English ship gave them some uncut diamonds for their first experiments; presents of military instruments were sent from the arsenals of Havre; and even the hospitals contributed some chemical substances. In fine, having set their school in motion, the government and its professors worked at it with such zeal and effect, that within five months after their project was announced, they had held their first entrance examination, open to the competition of all France, and started with three hundred and seventy-nine pupils.
The account of one of these first pupils, who is among the most distinguished still surviving ornaments of the Polytechnic, will convey a far better idea of the spirit of the young institution than could be given by a more lengthy description. M. Biot described to us vividly the zeal of the earliest teachers, and the thirst for knowledge which, repressed for awhile by the horrors of the period, burst forth with fresh ardor amongst the French youth of the time. Many of them, he said, like himself, had been carried away by the enthusiasm of the revolution, and had entered the army. “My father had sent me,” he added, “to a mercantile house, and indeed I never felt any great vocation to be a soldier, butQue voulez vous?les Prussiens etaient en Champagne.” He joined the army, served two years under Dumouriez, and returned to Paris in the reign of terror,“tosee from his lodgings in the Rue St. Honore the very generals who had led us to victory, Custine and Biron, carried by in the carts to the guillotine. “Imagine what it was when we heard that Robespierre was dead, and that we might return safely to study after all this misery, and then to have for our teachers La Place, Lagrange, and Monge. We felt like men brought to life again after suffocation. Lagrange said, modestly, “Let me teach them arithmetic.” Monge was more like our father than our teacher; he would come to us in the evening, and assist us in our work till midnight, and when he explained a difficulty to one of ourchefs de brigade, it ran like an electric spark through the party.” The pupils were not then, he told us, as they have since been, shut up in barracks, they were left free, but there was no idleness or dissipation amongst them. They were united in zealous work and in goodcamaraderie, and any one known as a bad character was avoided. This account may be a little tinged by enthusiastic recollections, but it agreed almost entirely with that of M. de Barante, who bore similar testimony to the early devotion of the pupils, and the unique excellence of the teaching of Monge.
We are not, however, writing a history of this school, and must confine ourselves to such points as directly illustrate its system of teaching and its organization. These may be roughly enumerated in the following order:
1. Its early history is completed by the law of its organization, given it by La Place in his short ministry of the interior. This occurred in the last month of 1799, a memorable era in French history, for it was immediately after the revolution of the 18th of Brumaire, when Napoleon overthrew the Directory and made himself First Consul. One of his earliest acts was to sign the charter of his great civil and military school. This charter or decree deserves some attention, because it is always referred to as the law of the foundation of the school. It determined the composition of the two councils of instruction and improvement, the bodies to which the direction of the school was to be, and still is, intrusted; some of its marked peculiarities in the mode and subject of teaching. It is important to notice each of the two points.
The direction of the schoolwas at first almost entirely in the hands of its professors, who formed what is still called its Council of Instruction. Each of them presided over the school alternately for one month, a plan copied from the revolutionary government ofthe Convention. In the course of a few years, however, another body was added, which has now the real management of the school. This is called the “Council of Improvement” (Conseil de perfectionnement,) and a part of its business is to see that the studies form a good preparation for those of the more special schools (écoles d’application) for the civil and military service. It consists of eminent men belonging to the various public departments supplied by the school, and some of the professors. It has had, as far as we could judge, an useful influence;first, as a body not liable to be prejudiced in its proposals by the feelings of the school, and yet interested in its welfare and understanding it;secondly, as having shown much skill in the difficult task of making the theoretical teaching of the Polytechnic a good introduction to the practical studies of the public service;thirdly, as being sufficiently influential, from the character of its members, to shield the school from occasional ill-judged interference. It should be added that hardly any year has passed without the Council making a full report on the studies of the school, with particular reference to their bearing on the Special Schools of Application.
The method of scientific teachinghas been peculiar from the beginning. It is the most energetic form of what may be called therepetitorialsystem, a method of teaching almost peculiar to France, and which may be described as a very able combination of professional and tutorial teaching. The object of therépétiteur, or private tutor, is to second every lecture of the professor, to explain and fix it by ocular demonstration, explanations, or examination. This was a peculiarity in the scheme of Monge and Foureroy. The latter said, in the first programme, “Our pupils must not only learn, they must at once carry out their theory. We must distribute them into small rooms, where they shall practice the plans of descriptive geometry, which the professors have just shown them in their public lectures. And in the same manner they must go over in practice (répéteront) in separate laboratories the principal operations of chemistry.” To carry out this system the twenty best pupils, of whom M. Biot was one, were selected asrépétiteurssoon after the school had started. Since then the vacancies have always been filled by young but competent men, aspiring themselves to become in turn professors. They form a class of teachers more like the highest style of private tutors in our universities, or what are called in GermanyPrivat-docenten, than any other body—with this difference, that they do not give their own lectures, but breaking up the professor’s large class into small classes of five and six pupils, examinethese inhislecture. The success of this attempt we shall describe hereafter.
2. A change may be noticed which was effected very early by the Council of Improvement—the union of pupils for artillery and engineers in a single school of application. The first report in December 1800, speaks of the identity in extent and character of the studies required for these two services; and in conformity with its recommendation, the law of the 3rd of October 1802, (12th Vendémiaire, XI.) dissolved the separate artillery school at Châlons, and established the united school for both arms in the form which it still retains at Metz.
3.In 1805 a curious change was made, and one very characteristic of the school. The pupils have always been somewhat turbulent, and generally on the side of opposition. In the earliest times they were constantly charged withincivisme, and the aristocracy was said to have “taken refuge within its walls.” In fact, one of its earliest and of its few greatliterarypupils, M. de Barante, confirmed this statement, adding, as a reason, that the school gave for a while the only good instruction in France. It was in consequence of some of these changes that the pupils who had hitherto lived in their own private houses or lodgings in Paris, were collected in the school building. This “casernement” said to be immediately owing to a burst of anger of Napoleon, naturally tended to give the school a more military character; but it was regarded as an unfortunate change by its chief scientific friends. “Ah! ma pauvre école!” M. Biot told us he had exclaimed, when he saw their knapsacks on their beds. He felt, he said, that the enthusiasm of free study was gone, and that now they would chiefly work by routine and compulsion.
4.The year 1809 may be called the epoch at which the school attained its final character. By this time the functions, both of boards and teachers, were accurately fixed, some alterations in the studies had taken place, and the plan of a final examination had been drawn up, according to which the pupils were to obtain their choice of the branch of the public service they preferred. In fact, the school may be said to have preserved ever since the form it then assumed, under a variety of governments and through various revolutions, in most of which, indeed, its pupils have borne some share; and one of which, the restoration of 1816, was attended with its temporary dissolution.
Thus, during the first years after its foundation the Polytechnic grew and flourished in the general dearth of public teaching, beingindeed not merely the only great school, but, until the Institute was founded, the only scientific body in France. Working on its first idea of high professorial lectures, practically applied and explained byrépétiteurs, its success in its own purely scientific line was, and has continued to be, astonishing. Out of its sixteen earliest professors, ten still retain an European name. Lagrange, Monge, Fourcroy, La Place, Guyton de Morveau were connected with it. Malus, Hauy, Biot, Poisson, and De Barante, were among its earliest pupils. Arago, Cauchy, Cavaignac, Lamoricière, with many more modern names, came later. All the great engineers and artillerymen of the empire belonged to it, and the long pages in its calendar of distinguished men are the measure of its influence on the civil and military services of France. In fact its pupils, at a time of enormous demands, supplied all the scientific offices of the army, and directed all the chief public works, fortresses, arsenals, the improvement of cities, the great lines of roads, shipbuilding, mining—carried out, in a word, most of the great improvements of Napoleon. He knew the value of his school, “the hen” as he called it, “that laid him golden eggs”—and perhaps its young pupils were not improved by the excessive official patronage bestowed by him upon “the envy of Europe,” “the first school in the world.” It can not, however, be matter of surprise, that its vigor and success should have caused Frenchmen, even those who criticise its influence severely, to regard it with pride as an institution unrivaled for scientific purposes.
It is not necessary to give any detailed account of the later history of the school, but we must remark that disputes have frequently arisen with regard to the best mode of harmonizing its teaching with that of the special schools of application to which it conducts. These disputes have been no doubt increased by the union of a civil and military object in the same school. The scientific teaching desirable for some of the higher civil professions has appeared of doubtful advantage to those destined for the more practical work of war. There has been always a desire on the one side to qualify pure mathematics by application, a strong feeling on the other that mathematical study sharpens the mind most keenly for some of the practical pursuits of after life. We should add, perhaps, that there has been some protest in France (though little heard among the scientific men who have been the chief directors of the school) against theesprit faux, the exclusive pursuit of mathematics to the utter neglect of literature, and the indifference to moral and historical studies. Some one or other of these complaintsany one who studies theliterature, the pamphlets, and history of the school will find often reproduced in the letters of war ministers, of artillery and engineer officers commanding the school of application at Metz, or of committees from the similar schools for the mines and the roads and bridges. The last of these occasions illustrates the present position of the school.
On the 5th of June 1850, the legislative assembly appointed a mixed commission of military men and civilians, who were charged to revise all the programs of instruction, and to recommend all needful changes in the studies of the pupils, both those preparatory to entrance9and those actually pursued in the school. The commission was composed as follows:—