Part 1 — THE POLYTECHNIC SCHOOL OF FRANCE.

THE POLYTECHNIC SCHOOL OF FRANCE.

CONTENTS.

Page.

Polytechnic School at Paris, 11

Subjects of Instruction as Prescribed for Admission in 1850, 13

Preparatory Course in the Lycees, 49

History, Management, Conditions of Admission, Course of Study, Examinational System, and Results, 55

I. Foundation and History, 55

Out growth of the Necessities of the Public Service in 1794, 56

High Scientific Ability of its first Teachers, 58

Peculiar Method of Scientific Teaching, 59

Characteristic features of the Répétitorial System, 59

The Casernement, or Barrack Residence of the Pupils, 60

Permanent Organization in 1809, 60

Commission of 1850, 62

II. Outline of the Plan, Objects, and Management, 63

Public Services provided for in its General Scientific Course, 63

Admission by Competition in an Open Examination, 63

Annual Charge for Board and Instruction, 64

Exhibitions, (or bourses, demi-bourses,) and Outfits (trousseaux,) 64

Length of Course of Study, 64

Number of Professors and Teachers, besides its Military Staff, 64

Military Establishment, 65

Civil Establishment, 65

General Control and Supervision, 65

1. Board of Administration, 65

2. Board of Discipline, 65

3. Board of Instruction, 65

4. Board of Improvement, 66

III. Conditions and Examinations for Admission, 66

Who may be Candidates for Admission, 66

Subjects of Entrance Examination, 66

Preliminary Examination, 67

Written Examination, 67

Oral Examination, 68

Scale of Merit, and Latitude in Amount of Credit given, 68

Reports of Examiners to Minister of War, 69

Co-efficients of Influence, varying with the Study and Mode of Examination, 69

Decision of Jury on all the Documents of each Candidate, 70

Final Action of the Minister of War, 70

IV. School Buildings, Course and Method of Study, 70

Situation, Number, and Purposes of Buildings, 70

Daily Routine of Exercises, 72

Method of Teaching and Study, 73

Professorial and Répétitorial, 74

Interrogations, Général, 74

Interrogations, Particulieres by the Répétiteurs, 74

One Répétiteur to every eight Pupils, 74

System of Credits for every Lecture, every Interrogation, and Exercise, 75

Final Admission to Public Service, depends on daily and hourly fidelity, 76

Division of First Year’s Work into three portions, 76

First portion—Analysis and Descriptive Geometry, 76

Second portion—Mechanics, Geodesy, Physics, &c., 76

Third portion—General Private Study, 76

Number and Subjects of Lectures in Second Course, 78

V. Examinational System, 78

Ordinary Examinations, 78

1. By Professors on their own Lectures, both Written and Oral, 78

2. By Examiners on the Manipulations of the Pupils, 78

3. By Répétiteurs every ten or fourteen days, 78

4. By Professors and Répétiteurs at the close of each Course, 79

First Annual Examination, 79

Table—Co-efficient of Influence in Second Division of First Year’s Course, 79

Specimen of Credits gained by one Student in First Year’s Course, 80

Persons excluded from the Second Year’s Course, 81

Second Annual or Great Final Examination, 81

Conducted by the same Examiners as the First, 81

Oral, and extends over the whole Two Years’ Course, 81

Results based on each Day’s Study’s, Year’s, and Examination’s results, 82

Tables—Co-efficients of Influence in Final Classification, &c., 82

Order in which the Public Services are Selected, 83

VI. General Remarks on Character and Results of the Polytechnic School, 84

Appendix, 88

Public Services Beside the Army Supplied by This School, 88

1. Gunpowder and Saltpetre, 88

2. Navy, 88

3. Marine Artillery and Foundries, 88

4. Naval Architects. School of Application at L’Orient, 88

5. Hydrographers, 88

6. Roads and Bridges. School of Application at Paris, 89

7. Mining Engineers. School of Mines at Paris and St. Etienne, 89

8. Tobacco Department 90

9. Telegraphs, 90

Programmes of Internal Instruction During the Two Years of Study, 91

1. Analysis, 91

First Year—Calculus, Differential, 91

First Year—Calculus, Integral, 93

Second Year—Calculus, Integral, (continuation,) 94

2. Descriptive Geometry and Stereotomy, 97

First Year—Descriptive Geometry, Geometrical Drawing, 97

Second Year—Stereotomy: Wood-work, 103

Second Year—Masonry, 103

3. Mechanics and Machines, 104

First Year—Kinematics, 105

First Year—Equilibrium of Forces, 105

Second Year—Dynamics, 112

Second Year—Hydrostatics, 115

Second Year—Hydraulics, 115

Second Year—Machines in Motion, 116

4. Physics, 116

First Year—General Properties of Bodies, Hydrostatics, Hydrodynamics, 117

First Year—Heat, 119

First Year—Statical Electricity, 123

Second Year—Dynamical Electricity, 124

Second Year—Acoustics, 125

Second Year—Optics, 126

5. Manipulations in Physics, 129

First and Second Year, 130

Distribution of Time, 131

THE POLYTECHNIC SCHOOL AT PARIS8

I. FOUNDATION AND HISTORY.

The origin of the Ecole Polytechnique dates 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 chief scientific creation 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 plan were 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 engineers in any true sense of the term, and can only be justified by the emergency of the time. 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 not always supply 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 favorite savant of Napoleon though a zealous republican, united to real genius that passion for teaching and for his pupils, which makes the beau idéal of 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 or Bourses, numbering nearly 40,000, were confiscated or plundered by individuals, and even the military schools and those for the public works (which were absolutely necessary 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 truly revolutionary school, 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, but Que 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, “to see 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 our chefs 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 good camaraderie, 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 school was 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 of the 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 teaching has been peculiar from the beginning. It is the most energetic form of what may be called the repetitorial system, 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 the répétiteur, 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 as répétiteurs soon 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 Germany Privat-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, examine these in his lecture. 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 with incivisme, and the aristocracy was said to have “taken refuge within its walls.” In fact, one of its earliest and of its few great literary pupils, 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, being indeed 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 by répétiteurs, 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 the esprit 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 complaints any one who studies the literature, 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 entrance9 and those actually pursued in the school. The commission was composed as follows:—

M. Thenard, Member of the Academy of Sciences, and of the Board of Improvement of the Polytechnic School, President.

Le Verrier, Member of the Academy of Sciences and of the Legislative Assembly, Reporter.

Noizet, General of Brigade of Engineers.

Poncelet, General of Brigade of Engineers, Commandant of the Polytechnic School, Member of the Academy of Sciences.

Piobert, General of Brigade of Artillery, Member of the Academy of Sciences.

Mathieu, Rear Admiral.

Duhamel, Member of the Academy of Sciences, Director of Studies at the Polytechnic School.

Mary, Divisional Inspector of Roads and Bridges.

Morin, Colonel of Artillery, Member of the Academy of Sciences.

Regnault, Engineer of Mines, Member of the Academy of Sciences.

Olivier, Professor at the Conservatoire des Arts et Metiers.

Debacq, Secretary for Military Schools at the Ministry of War, Secretary.

A chronic dispute which has gone on from the very first year of the school’s existence, between the exclusive study of abstract mathematics on the one hand, and their early practical application on the other, was brought to a head (though it has scarcely been set at rest) by this commission. All the alterations effected have been in the direction of eliminating a portion of the pure mathematics, and of reducing abstract study to the limits within which it was believed to be most directly applicable to practice. The results, however, are still a subject of vehement dispute, in which most of the old scientific pupils of the Polytechnic, and many of what may be styled its most practical members, the officers of the artillery and engineers, are ranged on the side of “early and deep scientific study versus early practical applications.” It is, indeed, a question which touches the military pupils nearly, since it is in their case particularly that the proposed abstract studies of the Polytechnic might be thought of the most doubtful advantage. We do not try to solve the problem here, though the facts elsewhere stated will afford some materials for judgment. We incline to the opinion of those who think that the ancient genius loci, the traditional teaching of the school, will be too strong for legislative interference, and that, in spite of recent enactments, abstract science and analysis will reign in the lecture-rooms and halls of study of the Polytechnic, now as in the days of Monge.

II. AN OUTLINE OF THE MANAGEMENT AND OF THE ESTABLISHMENT OF THE SCHOOL, ETC.

The Polytechnic, as we have said, is a preparatory and general scientific school; its studies are not exclusively adapted for any one of the departments to which at the close of its course the scholars will find themselves assigned; and on quitting it they have, before entering on the actual discharge of their duties of whatever kind, to pass through a further term of teaching in some one of the schools of application specially devoted to particular professions.

The public services for which it thus gives a general preparation are the following:

Military: Under the Minister at War.

Artillery (Artillerie de terre.)

Engineers (Génie.)

The Staff Corps (Corps d’Etat Major.)

The Department of Powder and Saltpetre (Poudres et Salpétres.)

Under the Minister of Marine.

Navy, (Marine.)

Marine Artillery (Artillerie de mer.)

Naval Architects (Génie maritime.)

The Hydrographical Department (Corps des Ingénieurs Hydrographes.)

Civil: Under the Minister of Public Works.

The Department of Roads and Bridges (Ponts-et-chaussées.)

The Department of Mines (Mines.)

Under the Minister of the Interior.

The Telegraph Department (Lignes Télégraphiques.)

Under the minister of Finance.

The Tobacco Department (Administration des Tabacs.)

To these may be added at any time, by a decree on the part of the government, any other departments, the duties of which appear to require an extensive knowledge of mathematics, physics, or chemistry.

Admission to the school is, and has been since its first commencement in 1794, obtained by competition in a general examination, held yearly, and open to all. Every French youth, between the age of sixteen and twenty, (or if in the army up to the age of twenty-five,) may offer himself as a candidate.

A board of examiners passes through France once every year, and examines all who present themselves, that have complied with the conditions, which are fully detailed in the decree given in the appendix. It commences at Paris.

A list of such of the candidates as are found eligible for admittance to the Polytechnic is drawn up from the proceedings of the board, and submitted to the minister at war; the number of places likely to be vacant has already been determined, and the minister fixes the number of admissions accordingly. The candidates admitted are invariably taken in the order of merit.

The annual charge for board and instruction is 40l. (1,000 fr.,) payable in advance in four installments. In addition there is the cost of outfit, varying from 20l. to 24l. Exhibitions, however, for the discharge of the whole or of one-half of the expense (bourses and demi-bourses,) are awarded by the state in favor of all the successful candidates, whose parents can prove themselves to be too poor to maintain their children in the school. Outfits and half outfits (trousseaux) and demi-trousseaux) are also granted in these cases, on the entrance of the student into the school; and the number of these boursiers and demi-boursiers amounts at the present time to one-third of the whole.

The course of study is completed in two years. On its successful termination which is preceded by a final examination, the students are distributed into the different services, the choice being offered them in the order of their merit, and laid down in the classified list drawn up after the examination. If it so happen that the number of places or the services which can be offered is not sufficient for the number of qualified students, those at the bottom of the list are offered service in the infantry or cavalry, and those who do not enter the public service, are supplied with certificates of having passed successfully through the school. Students who have been admitted into the school from the army, are obliged to re-enter the army.

All others, as has been said, have the right of choosing, according to their position on the list, the service which they prefer, so far, that is, as the number of vacancies in that service will allow; or they may if they please decline to enter the public service at all.

Such is a general outline of the plan and object of the school. We may add that, besides its military staff, it employs no less than thirty-nine professors and teachers; that it has four boards of management, and that ten scientific men unconnected with the school, and amongst the most distinguished in France, conduct its examinations. The magnitude of this establishment for teaching may be estimated by the fact, that the number of pupils rarely exceeds three hundred and fifty, and is often much less.

A fuller enumeration of these bodies will complete our present sketch.

I. The military establishment consists of:—

The Commandant, a General Officer, usually of the Artillery or the Engineers, at present a General of Artillery.

A Second in Command, a Colonel or Lieutenant-Colonel, chosen from former pupils of the school; at present a Colonel of Engineers.

Three Captains of Artillery and Three Captains of Engineers, as Inspectors of Studies, chosen also from former pupils of the school.

Six Adjutants (adjoints,) non-commissioned officers, usually such as have been recommended for promotion.

II. The civil establishment consists of:—

1. A Director of Studies, who has generally been a civilian, but is at present a Lieutenant-Colonel of Engineers.

2. Fifteen Professors, viz.:—Two of Mathematical Analysis. Two of Mechanics and Machinery. One of Descriptive Geometry. Two of Physics. Two of Chemistry. One of Military Art and Fortification. One of Geodesy. One of Architecture. One of French Composition. One of German. One of Drawing. Of these one is an officer of the Staff, another of the Artillery, and a third of the Navy; two are Engineers in Chief of the Roads and Bridges; nine are civilians, of whom two are Members of the Academy of Sciences.

3. Three Drawing Masters for Landscape and Figure Drawing; one for Machine Drawing, and one for Topographical Drawing.

4. Nineteen Assistant and Extra Assistant Teachers, (répétiteurs and répétiteurs adjoints) whose name and functions are both peculiar.

5. Five Examiners for Admission, consisting at present of one Colonel of Artillery, as President, and four civilians.

6. Five Examiners of Students (civilians,) four of them belonging to the Academy of Sciences.

7. There is also a separate Department for the ordinary Management of Administration of the affairs of the school, the charge of the fabric and of the library and museums; and a Medical Staff.

III. The general control or supervision of the school is vested, under the war department, in four great boards of councils, viz.:—

1. A board of administration, composed of the commandant, the second in command, the director of studies, two professors, two captains, and two members of the administrative staff. This board has the superintendence of all the financial business and all the minutiae of the internal administration of the school.

2. A board of discipline, consisting of the second in command, the director, two professors, three captains (of the school,) and two captains of the army, chosen from former pupils. The duty of this board is to decide upon cases of misconduct.

3. A board of instruction, whose members are, the commandant, the second in command, the director, the examiners of students, and the professors; and whose chief duty is to make recommendations relating to ameliorations in the studies, the programmes of admission and of instruction in the school, to—

4. A board of improvement, charged with the general control of the studies, formed of—

The Commandant, as President.

The Second in Command.

The Director of Studies.

Two Delegates from the Department of Public Works.

One Delegate from the Naval Department.

One Delegate from the Home Department.

Three Delegates from the War Department.

Two Delegates from the Academy of Sciences.

Two Examiners of Students.

Three Professors of the School.

III. CONDITIONS AND EXAMINATIONS FOR ADMISSION.

The entrance examination is held yearly in August; the most important conditions for admission to it are always inserted in the Moniteur early in the year, and are—

1st. All candidates must be bachelors of science.

2nd. All candidates (unless they have served in the army) must have been as much as sixteen and not more than twenty years old on the 1st of January preceding.

3rd. Privates and non-commissioned officers of the army must be above twenty and under twenty-five years of age; must have served two years, and have certificates of good conduct.

4th. Candidates who propose to claim pecuniary assistance (a bourse or demi-bourse) must present formal proofs of their need of it.

The subjects of the entrance examination are the following:—

Arithmetic, including Vulgar and Decimal Fractions, Weights and Measures, Involution and Evolution; Simple Interest.

Geometry of Planes and Solids; application of Geometry to Surveying; Properties of Spherical Triangles.

Algebra, including Quadratic Equations with one unknown quantity, Series and Progressions in general; Binomial Theorem and its applications; Logarithms and their use; on Derived Functions; on the Theory of Equations; on Differences; application of the Theory of Differences to the Numerical Solution of Equations.

Plane and Spherical Trigonometry; Solution of Triangles; application of Trigonometry to Surveying.

Analytical Geometry, including Geometry of two dimensions; Co-ordinates; Equations of the first and second degree, with two variables; Tangents and Asymptotes; on the Ellipse, Hyperbola, and Parabola; Polar Co-ordinates; Curved Lines in general.

Geometry of three dimensions, including the Theory of Projections; Co-ordinates; the Right Line and Plane; Surfaces of the second degree; Conical and Cylindrical Surfaces.

Descriptive Geometry; Problems relative to a Point, Right Line and Plane; Tangent Planes; Inter of Surfaces.

Mechanics; on the Movement of a Point considered geometrically; on the Effect of Forces applied to points and bodies at rest and moving; on the Mechanical Powers.

Natural Philosophy, including the Equilibrium of Liquids and Gasses; Heat; Electricity; Magnetism; Galvanism; Electro-magnetism and Light; Cosmography.

Chemistry, the Elements; French; German; Drawing, and (optionally) Latin.

This examination is partly written and partly oral. It is not public, but conducted in the following manner:—

Five examiners are appointed by the minister of war to examine the candidates at Paris, and at the several towns named for the purpose throughout France.

Two of these examiners conduct what may be called a preliminary examination (du premier degré,) and the other three a second examination (du second degré.) The preliminary examiners precede by a few days in their journey through France those who conduct the second examination. The written compositions come before either.

The preliminary examination (du premier degré) is made solely for the purpose of ascertaining whether the candidates possess sufficient knowledge to warrant their being admitted to the second examination; and the second examination serves, in conjunction with the written compositions, for their classification in the order of merit.

Prior to the examination, each candidate is called upon to give in certain written sheets containing calculations, sketches, plans and drawings, executed by him at school during the year, certified and dated by the professor under whom he has studied. Care is taken to ascertain whether these are the pupils’ own work, and any deception in this matter, if discovered, excludes at once from the competition of the school.

This done, the candidates are required to reply in writing to written or printed questions, and to write out French and German exercises; great care being taken to prevent copying. This written examination occupies about twenty-four hours during three and a half separate days, as shown in the following table. It usually takes place in the presence of certain official authorities, the examiners not being present.

First Sitting.

Hours.

Arithmetic, 1

Geometry, 1

Latin, 1

3

Second Sitting.

Algebra, 1

History, geography, and French, 3

4

Third Sitting.

Descriptive geometry, and diagram, or sketch, 4

Fourth Sitting.

Mechanics, 1

Physics, chemistry, and cosmography, 2

3

Fifth Sitting.

Applied analysis, 1½

German exercise, 1½

3

Sixth Sitting.

Solution of a triangle by logarithms 3

Seventh Sitting.

Drawing 4

Total 24

Next each candidate is examined orally for three-quarters of an hour, on two successive days, by each of the two examiners separately, and each examiner makes a note of the admissibility or non-admissibility of the candidate.

At the close of this oral examination, the notes relating to the various candidates are compared, and if the examiners differ as to the admissibility of any candidate, he is recalled, further orally examined, and his written exercises carefully referred to, both examiners being present. A final decision is then made.

The preliminary examiners then supply the others with a list of the candidates who are entitled to be admitted to the second oral examination. On this occasion each candidate is separately examined for one hour and a half by each examiner, but care is taken that in all the principal subjects of study the candidate is examined by at least two out of the three examiners.

Each examiner records his opinion of the merits of every candidate in replying, orally and in writing, by awarding him a credit varying between O and 20, the highest number indicating a very superior result.

This scale of merit is employed to express the value of the oral replies, written answers, or drawings. It has the following signification, and appears to be generally in use in the French military schools:—

20 denotes perfect.

19 18 denotes very good.

17 16 15 denotes good.

14 13 12 denotes passable.

11 10 9 denotes middling.

8 7 6 denotes bad.

5 4 3 denotes very bad.

2 1 denotes almost nothing.

0 denotes nothing

Considerable latitude is granted to the examiner engaged in deciding upon the amount of credit to be allowed to the student, for the manner in which he replies to the various questions. He is expected to bear in mind the temperament of the candidate, his confidence or timidity, as well as the difficulty of the questions, when judging of the quality of the reply, more value being given for an imperfect answer to a difficult question than for a more perfect reply to an easy one.

The reports of the examiners, together with the various documents belonging to each candidate, are sent from each town to the minister at war, who transmits them to the commandant of the Polytechnic School to make out a classified list.

Very different value of course is attached to the importance of some of the subjects, when compared with others; and the measure of the importance is represented in French examinations by what are termed co-efficients of influence, varying for the several subjects of study and kind of examination. The particular co-efficients of influence for each subject in these written and oral examinations, are as follows:—

Co-efficients of Influence.

Oral examination— analytical mathematics, 20

Oral examination— geometrical ditto, 14 52

Oral examination— physics and mechanics, 16

Oral examination— German language, 2

Written compositions on mathematical subjects, 5

Written compositions on descriptive geometry, drawing, and description, 5 34

Written compositions on logarithmic calculations of a triangle, 2

Written compositions on mechanics, 2

Written compositions on physics or chemistry, 4

German exercise, 1

French composition, 5

Latin translation, 5

Copy of a drawing, 5

Total, 86

In order to make out the above mentioned classified list, the respective credits awarded by the examiners to each candidate are multiplied by the co-efficients representing the weight or importance attached to each subject; and the sum of their products furnishes a numerical result, representing the degree of merit of each candidate.

A comparison of these numerical results is then made, and a general list of all the candidates is arranged in order of merit.

This list, and the whole of the documents from which it has been drawn up, are then submitted to a jury composed of the

Commandant of the School.

The Second in Command.

The Director of Studies.

Two Members of the Board of Improvement.

The Five Examiners.

It is the special business of this jury carefully to scrutinize the whole of the candidates’ documents, drawings, &c., and they further take care that a failure in any one branch of study is duly noted, as such failure is a sufficient reason for the exclusion of the candidate from the general list.

As soon as this general list has been thoroughly verified, it is submitted to the minister of war, who is empowered to add one-tenth to the number actually required for the public services; and thus it may happen that one-tenth of the pupils may annually be disappointed.

IV. THE SCHOOL BUILDINGS AND THE COURSE AND METHOD OF STUDY.

A brief description of the buildings may be a suitable introduction to an account of the studies that are pursued, and the life that is led in them.

The Polytechnic School stands near the Pantheon, and consists of two main buildings, one for the official rooms and the residence of the commandant and director of studies, the other, and larger one, for the pupils. Detached buildings contain the chemical lecture room and laboratory, the laboratory of natural philosophy, the library, fencing and billiard rooms.

The basement floor of the larger building contains the kitchen and refectories. On the first floor, are the two amphitheaters or great lecture rooms, assigned respectively to the pupils of the two years or divisions, in which the ordinary lectures are given. The rooms are large and well arranged; the seats fixed, the students’ names attached to them. The students are admitted by doors behind the upper tier of seats; at the foot of all is a platform for the professor, with a blackboard facing his audience, and with sufficient room for a pupil to stand and work questions beside him. Room also is provided for one of the captains, inspectors of studies, whose duty it is to be present, for the director of studies, whose occasional presence is expected, and for the assistant teachers or répétiteurs, who in the first year of their appointment are called upon to attend the course upon which they will have to give their subsequent questions and explanations. On this floor are also the museums, or repositories of models, instruments, machines, &c., needed for use in the amphitheaters, or elsewhere. The museum provided for the lecturer on Physics (or Natural Philosophy) appeared in particular to be well supplied.

The whole of the second floor is taken up with what are called the salles d’interrogation, a long series of small cabinets or studies, plainly furnished with six or eight stools and a table, devoted to the interrogations particulières, which will presently be described.

The third floor contains the halls of study, salles d’étude, or studying rooms, in which the greater part of the student’s time during the day is passed—where he studies, draws, keeps his papers and instruments, writes his exercises, and prepares his lectures. These are small chambers, containing eight or, exceptionally, eleven occupants. A double desk runs down the middle from the window to the door, with a little shelf and drawers for each student. There is a blackboard for the common use, and various objects are furnished through the senior student, the sergeant, a selected pupil, more advanced than the rest, who is placed in charge of the room, and is responsible for whatever is handed in for the use of the students. He collects the exercises, and generally gives a great deal of assistance to the less proficient. “When I was sergeant,” said an old pupil, “I was always at the board.” The spirit of camaraderie, said to exist so strongly among the Polytechnic students, displays itself in this particular form very beneficially. Young men of all classes work heartily and zealously together in the salles d’étude, and no feeling of rivalry prevents them from assisting one another. The sergeant does not, however, appear to exercise any authority in the way of keeping discipline.

These chambers for study are arranged on each side of a long corridor which runs through the whole length of the building, those of the juniors being separated from those of the seniors by a central chamber or compartment, the cabinet de service, where the officers charged with the discipline are posted, and from hence pass up and down the corridor, looking in through the glass doors and seeing that no interruption to order takes place.

The fourth story is that of the dormitories, airy rooms, with twelve beds in each. These rooms are arranged as below, along the two sides of a corridor, and divided in the same manner into the senior and junior side. A non-commissioned officer is lodged at each end of the corridor to see that order is kept.

Such is the building into which at the beginning of November the successful candidates from the Lycées and the Ecoles préparatoires are introduced, in age resembling the pupils whom the highest classes of English public schools send annually to the universities, and in number equal perhaps to the new under-graduates at one of the largest colleges at Cambridge. There is not, however, in other points much that is common, least of all in the methods and habits of study we are about to describe. This will be best understood by a summary of a day’s work.

The students are summoned to rise at half-past five, have to answer the roll-call at six, from six to eight are to occupy themselves in study, and at eight they go to breakfast. On any morning except Wednesday, at half-past eight, we should find the whole of the new admission assembled in an amphitheater, permanent seats in which are assigned to them by lot, and thus placed they receive a lecture from a professor, rough notes of which they are expected to take while it goes on. The first half hour of the hour and a half assigned to each lecture is occupied with questions put by the professor relating to the previous lecture. A name is drawn by lot, the student on whom the lot falls is called up to the blackboard at which the professor stands, and is required to work a problem and answer questions. The lecture concluded, the pupils are conducted to the salles d’étude, which have just been described, where they are to study. Here for one hour they devote themselves to completing and writing out in full the notes of the lecture they have just heard. The professor and his assistants, the répétiteurs, are expected to follow and make a circuit through the corridors, to give an opportunity to ask for information on any difficult points in the lecture. A lithographed summary of the substance of the lecture, extending perhaps to two octavo pages, is also furnished to each studying room for the use of its pupils.

The lecture, as we have said, commences at half-past eight o’clock; it lasts an hour and a half; the hour of writing up the notes brings us to eleven. The young men are now relieved by a change of occupation, and employ themselves (still in their places in the rooms of study) at drawing. A certain number, detached from the rest, are sent to the physical and chemical laboratories. The rotation is such as to admit each student once a month to two or three hours’ work at a furnace for chemistry, and once in two months to make experiments in electricity, or other similar subjects. In this way, either at their drawing or in the laboratories, they spend three hours, and at two o’clock go to their dinner in the refectories below, and after dinner are free to amuse themselves in the court-yard, the library, the fencing and the billiard rooms, till five. At five they return to the studying rooms, and for two hours, on Mondays and Fridays, they may employ themselves on any work they please (étude libre;) on Tuesday there is a lecture in French literature, and on Thursday in German; at seven o’clock they commence a lesson, which lasts till nine, in landscape and figure drawing, or they do exercises in French writing or in German; at nine they go down to supper; at half-past nine they have to answer to a roll-call in their bedrooms, and at ten all the lights are put out.

Wednesday is a half-holiday, and the pupils are allowed to leave the school after two o’clock, and be absent till ten at night. The morning is occupied either in study, at the pleasure of the students, or in set exercises till eleven, when there is a lecture of one hour and a half, followed, as usual, by an hour of special study on the subject of the lecture. On Sunday they are allowed to be absent almost the whole day till ten P.M. There is no chapel, and apparently no common religious observance of any kind in the school.

Such is a general sketch of the ordinary employment of the day; a couple of hours of preparatory study before breakfast, a lecture on the differential calculus, on descriptive geometry, on chemistry, or natural philosophy, followed by an hour’s work at notes; scientific drawing till dinner; recreation; and general study, or some lighter lecture in the evening. Were we merely to count the hours, we should find a result of eleven or eleven and a half hours of work for every day but Wednesday, and of seven and a half hours for that day. It is to be presumed, however, that though absolute idleness, sleeping, or reading any book not authorized for purposes of study, is strictly prohibited, and when detected, punished, nevertheless the strain on the attention during the hours of drawing and the lectures of the evening is by no means extreme. Landscape and figure drawing, the lecture in French literature, and probably that in German, may fairly be regarded as something like recreation. Such, at least, was the account given us of the lectures on literary subjects, and it agrees with the indifference to literature which marks the school. Of wholesome out-of-door recreation, there certainly seems to be a considerable want. There is nothing either of the English love of games, or of the skillful athletic gymnastics of the German schools.

The method of teaching is peculiar. The plan by which a vast number of students are collected as auditors of professorial lectures is one pursued in many academical institutions, at the Scotch universities, and in Germany. Large classes attend the lectures in Greek, in Latin, and in mathematics at Glasgow; they listen to the professor’s explanations, take notes, are occasionally questioned, and do all the harder work in their private lodgings. Such a system of course deserves in the fullest sense the epithet of voluntary; a diligent student may make much of it; but there is nothing to compel an idle one to give any attention.

It seems to have been one especial object pursued in the Polytechnic to give to this plan of instruction, so lax in itself, the utmost possible stringency, and to accumulate upon it every attainable subsidiary appliance, every available safeguard against idleness. Questions are expressly put vivâ voce by the professor before his lecture; there is a subsequent hour of study devoted to the subject; there is the opportunity for explanation to individual students; the exaction of notes written out in full form; the professor also gives exercises to the students to write during their hours of general study, which he examines, and marks; general vivâ voce examinations (interrogations générales,) conducted by the professors and répétiteurs, follow the termination of each course of lectures; and lastly, one of the most important and peculiar parts of the method, we have what are called the interrogations particulières. After every five or six lectures in each subject, each student is called up for special questioning by one of the répétiteurs. The rooms in which these continual examinations are held have been described. They occupy one entire story of the building; each holds about six or eight pupils, with the répétiteurs. Every evening, except Wednesday, they are filled with these little classes, and busy with these close and personal questionings. A brief notice, at the utmost of twenty-four hours, is served upon the students who are thus to be called up. Generally, after they have had a certain number of lectures, they may expect that their time is at hand, but the precise hour of the summons can not be counted upon. The scheme is continually varied, and it defies, we are told, the efforts of the ablest young analysts to detect the law which it follows.

It will be seen at once that such a system, where, though nominally professorial, so little is left to the student’s own voluntary action, where the ordinary study and reading, as it is called in our English universities (here such an expression is unknown) is subjected to such unceasing superintendence and surveillance, and to so much careful assistance, requires an immense staff of teachers. At the Polytechnic, for a maximum of 350 pupils, a body of fifteen professors and twenty-four répétiteurs, are employed, all solely in actual instruction, and in no way burdened with any part of the charge of the discipline or the finance, or even with the great yearly examinations for the passage from the first to the second division, and for the entrance to the public services.

With a provision of one instructor to every eight students, it is probable that in England we should avoid any system of large classes, from the fear of the inferior pupils being unable to keep pace with the more advanced. We should have numerous small classes, and should endeavor, above all things, to obtain the advantage of equality of attainment in the pupils composing them.

The French, on the other hand, make it their first object to secure one able principal teacher in each subject, a professor whom they burden with very few lectures. And to meet the educational difficulty thus created, to keep the whole large class of listeners up to the prescribed point, they call in this numerous and busily employed corps of assistants to repeat, to go over the professor’s work afresh, to whip in, as it were, the stragglers and hurry up the loiterers. Certainly, one would think, a difficult task with a class of 170 freshmen in such work as the integral and differential calculus. It is one, however, in which they are aided by a stimulus which evidently acts most powerfully on the students of the Polytechnic School. During the two years of their stay, the prospect of their final admission to the public services can rarely be absent from the thoughts even of the least energetic and forethinking of the young men. Upon their place in the last class list will depend their fortune for life. A high position will secure them not only reputation, but the certainty of lucrative employment; will put it in their power to select which service they please, and in whichever they choose will secure them favorable notice. Let it be remembered that fifty-three of these one hundred and seventy are free scholars, born of parents too poor to pay 40l. a year for their instruction; to whom industry must be at all times a necessity, and industry during their two years at the Polytechnic the best conceivable expenditure, the most certainly remunerative investment of their pains and labor. The place on the final class list is obviously the prize for which this race of two years’ length has to be run. What is it determines that place? Not by any means a final struggle before the winning-post, but steady effort and diligence from first to last throughout the course. For the order of the class list is not solely determined by success in the examination after which it is drawn up, but by the result of previous trials and previous work during the whole stay at the school.

For, during the whole time, every written exercise set by the professor, every drawing, the result of every interrogation particulière by the répétiteurs, and of each general interrogation by the professors and répétiteurs, is carefully marked, and a credit placed according to the name of the student and reserved for his benefit, in the last general account. The marks obtained in the examination which closes the first year of study form a large element in this last calculation. It had been found that the work of the first year was often neglected: the evil was quickly remedied by this expedient. The student, it would seem, must feel that he is gaining or losing in his banking account, so to call it, by every day’s work; every portion of his studies will tell directly for or against him in the final competition, upon which so much depends.

Such is the powerful mechanism by which the French nation forces out of the mass of boys attending their ordinary schools the talent and the science which they need for their civil and military services. The efforts made for admission to this great scientific school of the public services, the struggle for the first places at the exit from it, must be more than enough, it is thought, to establish the habits of hard work, to accumulate the information and attainment, and almost to create the ability which the nation requires for the general good.

We may now follow the student through his course of two years’ study. The first year’s work may be mainly divided into three portions of unequal length; two of them of about four months each (with an additional fortnight of private study and examination,) are mainly given to hard lecturing, whilst the third portion of two months is devoted to private study and to the examinations.

In accordance with this arrangement of the year, the four hardest subjects are thus distributed. Analysis and descriptive geometry, the staple work of the school—its Latin, as M. de Barante called it—come in the first four months; there is then a pause for private study and a general examination in these two subjects (interrogations générales as distinct from the interrogations particulières of the répétiteurs.) This brings us to the middle of March. Analysis and geometry are then laid aside for the rest of the year, and for the next portion of four months the pupils work at mechanics and geodesy, private study and a general examination completing this course also. Important lectures on physics and chemistry run on during both these periods, and are similarly closed by private study and a general examination. The less telling evening classes of French literature and German end at the beginning of June, and landscape and figure drawing only last half the year. It may be observed also, that, as a general rule, there is on each day one, and only one, really difficult lecture. This is immediately preceded and followed by private study, but then comes something lighter, as a relief, such as drawing or work in the laboratories.

The chief feature in the third portion of the year is the complete break in the lectures for general private study (étude libre,) a month or six weeks before the closing examination at the end of the year. The immediate prospect of this prevents any undue relaxing of the work; and it is curious to observe here how private efforts and enforced system are combined together, for even the private efforts are thus systematized and directed. The closing examination of the first year begins on the 1st and ends on the 25th of September.

The total number of lectures in each branch of study, with the dates when they respectively commence and finish, and the period when the general examinations (interrogations générales) take place, are exhibited in the following tables, and we should add that the interval between the close of each course and the commencement of the chief yearly examination is devoted to free study.

TABLE FOR THE SECOND OR LOWER DIVISION, FOLLOWING THE FIRST YEAR’S COURSE OF STUDY.

NL No. of Lectures

E Annual Examination

Subject of Study. NL Course of Lectures General Examinations Interrogations Générales. E

Commenced. Finished. Commenced. Finished.

Analysis 48 3rd Nov. 25 Feb. 13th March 18th March *

Mechanics & Machines 40 21st March 29th June 24th July 2nd August

Descriptive Geometry 38 3rd Nov. 3rd March 13th March 18th March

Physics 34 2nd “ 28th June 10th July 19th July

Chemistry 38 5th “ 17th “ 10th “ 19th “

Geodesy 35 20th March 30th “ 24th “ 2nd August

French Literature 30 8th Nov. 6th “

German 30 2nd “ 15th “

Figure and Landscape Drawing 50 4th “ 28th April

Total 343

* Begins on the 1st Sept., and ends on the 25th Sept.

The work of the second year is almost identical in its general plan with that of the first. A continuation of analysis with mechanics in place of descriptive geometry is the work of the first four months, then comes the private study and the interrogations générales, and then again, from the middle of March to the middle of July, work of a more professional character, stereotomy, the art of war and topography, forms the natural completion of the pupil’s studies. Chemistry and physics follow the same course as during the first year, and terminate with the private study and the general examination at the beginning of August. The evening lectures in French literature and German end about the middle of June, and those in figure and landscape drawing at the beginning of May. The last portion is again given to private study and the great Final Examination.

TABLE FOR THE FIRST OR UPPER DIVISION, FOLLOWING THE SECOND YEAR’S COURSE OF STUDY.

NL No. of Lectures

E Annual Examination

Subject of Study. NL Course of Lectures General Examinations Interrogations Générales. E

Commenced. Finished. Commenced. Finished.

Analysis 32 11th Nov. 3rd March 13th March 18th March *

Mechanics and Machines 42 10th “ 2nd “ 13th “ 18th “

Stereotomy 32 20th Mar. 26th June 10th July. 19th July.

Physics 36 12 Nov. 29th “ 24th “ 2nd Aug.

Chemistry 38 14th “ 28th “ 24th “ 2nd “

Architecture and Construction 40 10th “ 8th “

Military Art and Fortification 20 21st Mar. 21st “ 10th “ 19th July.

Topography 10 3rd Jan. 21st “

French literature 30 11th Nov. 9th “

German 30 14th “ 19th “

Figure and Landscape Drawing 48 12th “ 2nd May.

Total 358

* Begins on the 10th Sept. and ends on the 10th Oct.

V. THE EXAMINATIONS, PARTICULARLY THAT OF THE FIRST YEAR AND THE FINAL ONE.

We have now brought the pupil nearly to the end of his career, but must previously say a few words about his examinations, the chief epochs which mark his progress, and the last of which fixes his position almost for life. For this purpose it is necessary to recapitulate briefly what has been said in different places of the whole examinatorial system of the Polytechnic School.

1. All the professors require the students in their studying rooms, to answer questions in writing on the courses as they go through them: a different question is given to each student, and every third question is of such a nature as to involve a numerical example in the reply.

These questions are given in the proportion of one to about every four lectures, and the replies after being examined by the professor or répétiteur, are indorsed with a credit, varying from 0 to 20, and the paper is then given back to the student, to be produced at the close of the year.

2. Credits are assigned to the students for their ordinary manipulations in chemistry and physics, during the first year; and at the close of each year, for their manipulations, in chemistry alone, before the examiners.

3. The répétiteurs examine, (in the interrogations particulières,) every ten or fourteen days, from six to eight students during a sitting of two hours, on the subject of study lectured on since the previous examination of the same kind. All these students must continue present, and at the close the répétiteur assigns to each a previous examination of the same kind. All these students must continue present, and at the close the répétiteur assigns to each a credit entirely dependent on the manner in which each has replied. The professors and captains inspectors are occasionally present at these examinations, which are discontinued at certain periods according to the instructions of the director of studies.

4. At different intervals of time, from a fortnight to a month, as may happen, after the close of the course in each branch of study, general examinations (interrogations générales) are made by the professors and répétiteurs. From four to six students are examined together for at least two hours, and at the conclusion the professor makes known to the director of studies the credit he has granted to each student for the manner in which he has passed his examination.

Such may be called the minor or ordinary examinations. But there is an annual closing examination at the end of each year, which we will now describe. The first year’s annual examination commences on the 1st and ends on the 25th September. It is carried on by special examiners, (a different set from those who conduct the entrance examinations,) and not by the professors. These give to every student a credit between 0 and 20 in each branch of study, according to the manner in which he replies.

The following table shows the co-efficients of influence allowed to the different studies of the first year, subdivided also among the particular classes of examination to which the student has been subjected. The component parts of the co-efficients as well as the co-efficients themselves, slightly vary from year to year, dependent on the number of examinations:—

TABLE I.—FIRST YEAR’S COURSE OF STUDIES: SECOND DIVISION.

TC Total Co-efficients. (repeated)

WA Written Answers to Professors’ Questions.

ER Examinations by Répétiteurs. (Int. Part.)

GE General Examinations. (Int. Gen.)

Man. Manipulations.

O Ordinary.

Ex At Examination.

SN Sheets of notes on descriptive Geometry.

GD Graphical Representations and Drawing.

1st First Annual Examination.

Nature of Study. TC Co-efficient of Influence awarded to TC

WA ER GE Man. SN GD 1st

O Ex

Analysis, 56 9 10 9 . . . . . . . . 28 56

Mechanics, 60 7 9 8 . . . . . . 14 22 60

Descriptive Geometry, 48 . . 7 7 . . . . 4 12 18 48

Geodesy, 39 6 5 7 . . . . . . 3 18 39

Physics, 45 6 9 7 2 . . . . . . 21 45

Chemistry, 45 5 9 7 4 2 . . . . 18 45

French Literature, 12 12 . . . . . . . . . . . . . . 12

German Language, 10 2 3 . . . . . . . . . . 5 10

Drawing, 10 . . . . . . . . . . . . 10 . . 10

Shading & Tinting Plans, . . . . . . . . . . . . . . . . . . 3

At the conclusion of this examination the director of studies prepares a statement for each student, exhibiting the credits he has obtained at each of the preceding examinations in each subject, multiplied by the co-efficient of influence, and the sum of the products represents the numerical account of the student’s credit in each branch of study.

As the process is somewhat intricate, we append the following example, to show the nature of the calculation performed, in order to ascertain the amount of credits due to each student:—

REPORT OF THE CREDITS GAINED IN THE FIRST YEAR’S COURSE OF STUDY BY M. N., STUDENT AT THE POLYTECHNIC SCHOOL.

CI Co-efficient of Influence (twice)

Cr Credit obtained by the Student.

SP Sum of Products.

MC Mean Credit in each Subject of the Course.

Subject of Examination CI Nature of Examination or Proof. Cr CI Product SP MC

Analysis, 56 Written answers to Professors’ questions 17.16 9 154.44

Examinations by répétiteurs (interrogations particulières) 15.47 10 154.70 845.81 15.00

General Examination (interrogations générales) 13.71 9 123.39

Annual Examination 14.75 28 413.28

Mechanics 60 Written answers to Professors’ questions 13.45 7 94.15

Examinations by répétiteurs 12.72 9 114.48 664.13 11.07

General Examination 11.37 8 90.96

Graphical representations and drawing 5.61 14 78.54

Annual Examination 13.00 22 286.00

Descriptive Geometry 48 Examinations by répétiteurs 17.15 7 120.05

General Examination 11.72 7 82.04 633.15 13.19

Sheets of notes 12.45 4 49.80

Graphical representation and drawing 11.88 12 142.76

Annual Examination 13.25 18 238.50

Geodesy 39 Written answers to Professors’ questions 9.16 6 54.96

Examinations by répétiteurs 7.85 5 39.25 229.01 5.87

General Examination 5.74 7 40.18

Graphical representation and drawing 4.36 3 13.08

Annual Examination 4.53 1 81.54

Physics 45 Written answers to Professors’ questions 2.76 6 13.56

Examinations by répétiteurs 3.54 9 31.86 112.21 2.49

General Examination 5.74 7 40.18

Ordinary manipulation 1.55 2 3.10

Annual Examination 1.84 21 38.84

Chemistry 45 Written answers to Professors’ questions 2.46 5 12.30

Examinations by répétiteurs 3.25 9 29.95 131.16 2.91

General Examination 2.47 7 17.29

Ordinary manipulation 2.26 4 9.04

Manipulation at Exam 1.58 2 3.16

Annual Examination 3.34 18 60.12

French Literature 12 Written answers to Professors’ questions 5.46 12 67.68 67.68 5.64

German Language 10 Written answers to Professors’ questions 6.57 2 13.14

Examinations by répétiteurs 4.86 3 14.58 55.92 5.59

Annual Examination 5.64 5 28.20

Drawing 10 Graphical representation and drawing 4.36 10 43.60 43.60 4.36

Shading and Tinting Plans 3 Graphical representation and drawing 3.86 3 11.58 11.58 3.86

Sum 10)70.07

General Mean Credit, = (7.00)

It is important to remark that any student whose mean credit, given in the eighth column of the preceding table, in any branch of study does not exceed three, or whose general mean credit for the whole of the studies being the arithmetical mean of all the values recorded in the eighth column, and given at the bottom in the example, does not exceed six, is considered to possess an insufficient amount of instruction to warrant his being permitted to pass into the first division for the second year’s course. He is accordingly excluded from the school, unless he has been prevented from pursuing his studies by illness, in which case, when the facts are thoroughly established, he will be allowed a second year’s study in the second division, comprising the first year’s course of study.

We now pass to the second annual or great final examination for admission to the public services, remarking only that in the interrogations générales of the second year the principal subjects of both years are included.

The final examinations for admission into the public service commence about the 10th September, and last about one month. They are conducted by the same examiners who examined at the close of the first year. These are five in number, and appointed by the minister of war. One of these takes analysis; a second, mechanics; a third, descriptive geometry and geodesy; the fourth, physics; and the fifth, chemistry.

The examination in military art and topography is conducted by a captain of engineers specially appointed for the purpose; and in the same manner the examination in German is carried on by a professor, usually a civilian, specially but not permanently appointed.

The questions are oral, and extend over the whole course of study pursued during the two years. Each student is taken separately for one hour and a quarter on different days by each of the five examiners; each examiner examines about eight students daily.

A table, very similar to that already given, is prepared under the superintendence of the Director of studies for every student, to ascertain the numerical amount of his credits in each branch of study, the co-efficients of influences for the particular subject of study and nature of examination being extracted from a table similar to that in page 80, and when these tables have all been completed, a general list of all the students is made out, arranged in the order of their merits.

Formerly, conduct was permitted to exercise some slight influence on their position, but that is no longer the case.

The same regulations exist, as regards the minimum amount of credit that will entitle the students to enter into the public service, as have already been stated above in reference to the passage from the first to the second year’s course of study.

TABLE II. SECOND YEAR’S COURSE OF STUDY: FIRST DIVISION.

RP Result of previous Year’s Examination.

WA Written Answers to Professors’ Questions.

ER Examinations by Répétiteurs. (Int. Part.)

GE General Examinations. (Int. Gen.)

Man. Manipulations.

O Ordinary.

Ex At Examination.

SN Sketches and Notes in Architecture

GD Graphical Representations and Drawing

EA Examination in Architecture

2d 2d Annual or Final Examination.

TC Total Co-Efficients.

TC Co-efficient of Influence awarded to TC

RP WA ER GE Man. SN GD 2d

O Ex

Analysis, 28 8 10 9 . . . . . . . . . . 26 81

Mechanics, 25 8 12 9 . . . . . . 10 . . 28 92

Descriptive Geometry, 36 . . . . . . . . . . . . . . . . . . 36

Geodesy, . . 6 5 7 . . . . . . 1 . . 18 37

Physics, 23 5 10 8 . . . . . . . . . . 22 68

Chemistry, 20 5 10 8 4 2 . . . . . . 19 68

Architecture, . . . . . . . . . . . . 12 14 10 . . 36

Military Art and Tophography, . . . . 3 5 . . . . . . 9 . . 8 25

French Literature, 6 12 . . . . . . . . . . . . . . . . 18

German, 5 2 3 . . . . . . . . . . . . . . 15

Drawing, 5 . . . . . . . . . . . . 10 . . . . 15

Shading and Tinting, 2 . . . . . . . . . . . . 3 . . . . 5

From the preceding tables and explanations, it will be apparent that, as the whole of the students for each year are compelled to follow precisely the same course of study, the system of professorial instruction, combined with the constant tutelage and supervision exercised by the répétiteurs, and the examinations (interrogations particulières) of the répétiteurs, at short intervals of time, have for their principal object the keeping alive in the minds of the students the information which has been communicated to them. As a stimulus to continuous and unceasing exertion, it will be seen by an inspection of the tables of the co-efficients of influence, that the manner in which the students acquit themselves from day to day, and from week to week, is made an element, and a very important one, in determining their final position in the list arranged according to merit, exceeding as it does in most instances the influence exerted on their classification by their final examination at the close of each year. This principle thus recognizes not only their knowledge at the end of each year, but also the manner in which they have proved it to the professors and répétiteurs in the course of the year; and with reference to the second year’s study, the final result of the first year’s classification exercises an influence amounting to about one-third of the whole, in the final classification at the end of the second year.

It follows also, that as the examinations at the end of each year are made by examiners, otherwise unconnected with the school, and not by the professors belonging to it, the positions of the students in the classified list is partly dependent on the judgment of the professors with whom they are constantly in communication, and partly on the public examiners, whom they meet only in the examination rooms.10

The examiners of the students are not frequently changed, and practically the same may be said of the examiners for admission.

PR By Professors and Répétiteurs.

Ex By Examiners.

Y1 By the results of the first Year’s Examination.

CL In the Classified List at the end of 2nd year.

Subjects of Study. Per-centage of influence exercised on the position of the Students.

During the 1st Year. During the 2nd Year. CL

PR Ex Y1 PR Ex PR Ex

Analysis, 50.0 50.0 34.5 32.5 33.0 49.75 50.25

Mechanics, 63.2 36.7 27.2 42.4 30.4 59.6 40.40

Descriptive Geometry, 62.5 37.5 100.0 0.0 0.0 62.5 37.5

Geodesy, 53.8 46.2 0.0 51.4 48.6 * 51.4 48.6

Physics, 53.3 46.7 33.8 33.8 32.4 51.8 48.2

Chemistry, 60.0 40.0 29.4 43.2 27.4 60.8 39.2

Architecture, . . . . 0.0 100.0 0.0 100.0 100.0

Military Art and Topography, . . . . 0.0 68.0 32.0 68.0 32.0

French Literature, 100.0 0.0 33.3 66.7 0.0 100.0 0.0

German Language, 100.0 0.0 33.3 33.3 33.4 66.7 33.3

Drawing 100.0 0.0 33.3 66.7 0.0 100.0 0.0

Shading and Tinting Plans, 100.0 0.0 40.0 60.0 0.0 100.0 0.0

*

* When taught in the 2nd year

The students at the head of the list have generally since the wars of the first Empire entered into the civil rather than into the military services, the former being much better remunerated.

The services are usually selected by preference, nearly in the following order:—

The Roads and Bridges (Ponts et chaussées) and Mines (Mines,) very nearly on an equality.

Powder and Saltpetre (Poudres et Salpêtres.)

Naval Architects (Génie maritime.)

Engineers (Génie militaire.)

The Artillery (Artillerie de terre.) and the Staff Corps (Etat Major,) very nearly on an equality.

The Hydographical Corps (Ingénieurs Hydrographes.)

Tobacco Department (Administration des Tabacs.)

Telegraph Department (Lignes Télégraphiques.)

Navy (Marine.)

Marine Artillery (Artillerie de mer.)

Such, at least, is the result of a comparison of the selections made by the students during eight different years.

This preference of the civil to the military services has been the subject of frequent complaints on the part of the military authorities to the minister of war.

No steps have, however, been taken by the French government to prevent the free choice of a profession being granted to the most successful students.

We have now followed the student at the Polytechnic to the end of his school career. He is then to pass to his particular School of Application, in which (as the name implies) he is taught to apply his science to practice. It is difficult to state precisely the amount of such science which the highest pupils may be thought to possess on leaving; the best idea of it will be gained by reference to the programmes of the most important of the lectures. It is also needless to dwell again on the main features of the school—the emulation called forth, the minute method, the great prizes offered for sustained labor. We must, however, make some remarks on these points before concluding our account, so far as they bear on the subject of military education.

VI. GENERAL REMARKS.

1. Keeping out of sight for the moment some defects both in the principles and details of the education of this school, the method of teaching adopted seems to us excellent, and worthy of careful study. In this remark we allude principally to the skillful combination of two methods which have been generally thought incompatible; for it unites the well-prepared lecture of a German professor, with the close personal questioning of a first-rate English school or college lecture. But besides this, its whole system is admirably adapted for the class of pupils it educates.

These pupils are generally not of the wealthy classes; they are able, and struggling for a position in life. On all these grounds their own assistance in the work may be calculated upon. Yet they are not left to themselves to make the most of their professors’ lectures. The aid of répétiteurs, even more valuable in its constant “prudent interrogations,” than in the explanations afforded, is joined to the stimulus given by marking every step of proficiency, and by making all tell on the last general account. But though the routine and method of the school are so elaborate, play is given to the individual freedom of the pupils in their private work, and this is managed so skillfully that the private work is made immediately to precede the final examination, on which mainly depends the pupil’s place for life. Thus from first to last they are carried on by their system without being cramped by it; every circumstance favorable to study is made the most of; rigorous habit, mental readiness, the power of working with others, and the power of working for themselves, the ambition for immediate and permanent success, all the objects and all the methods which students ever have in view, support and stimulate those of the Polytechnic in their two years’ career.

2. The mainspring, however, of the school’s energy is the competition amongst the pupils themselves, and this could hardly exist without the great prizes offered to the successful. This advantage, added to the general impulse of the early days of the Empire, has no doubt powerfully contributed to the great position of the school. It has made it a kind of university of the élite mathematicians, and as in England young men look to the prizes of the universities, and the professions to which they lead, as their best opening in life, so in France, ever since the first revolution, the corresponding class has inclined to the active and chiefly military career which is offered by the great competitive school of the country.

3. A preparatory school of this remarkable character can not but exercise a very powerful influence over those three-fourths of its pupils who leave it to enter the army. The obvious question is whether the attempt is not made to teach more than is either necessary or desirable for military purposes, and to this suspicion may be added the fact that the civil prizes being more in request than the military, many of those who enter the army do so in the first instance reluctantly, and that the pupils at the bottom of the list appear to be often such marked failures as to imply either great superficiality or premature exhaustion.

4. In studying the Polytechnic School we have had these points constantly brought before us, and feeling the difficulty of discussing them fully, we beg to invite attention to the evidence sent us in reply to some questions which we addressed on the subject to some distinguished scientific officers and civilians connected with the school. We will give briefly the result of our own inquiries.

5. The complaint of General Paixhans has been quoted. He urges that a considerable proportion of the army pupils are mere queues de promotion, and quite insufficient to form le corps et surtout la tête of troops d’élite.

Other not inconsistent complaints we heard ourselves, of the mental exhaustion and the excessively abstract tendencies of many of the military pupils of the school.

6. Such are the complaints. There is certainly reason to think that, with regard to the twenty or thirty lowest pupils on the list, those of General Paixhans are well founded. These are the breaks down, and we are at first surprised that, entering as they must do,11 with high attainments, they should fall so low as the marks in the tables (with which we are most liberally supplied) prove to be the case.

At the same time, we believe that no teaching ever has provided or will provide against many failures out of one hundred and seventy pupils, even among those who promised well at first: and if the standard of the majority of pupils is high at the Polytechnique, and the point reached by the first few very high, it is no reproach that the descent amongst the last few should be very rapid.

With regard to the assertion, that the teaching is excessive and leads too much to abstract pursuits for soldiers, it may be partially true. Perhaps the general passion for science has led to an overstrained teaching for the army, even for its scientific corps; and yet would it be allowed by officers of the highest scientific ability, either in the French or the English army, that less science is required for the greatest emergencies of military than for those of civil engineering, or for the theory of projectiles than for working the department of saltpetre?

It may, however, be true that an attempt is made at the Polytechnic to exact from all attainments which can only be reached by a few.

7. With this deduction, we must express our opinion strongly in favor of the influence of the Polytechnic on the French army. We admit that in some instances pupils who have failed in their attempt at civil prizes enter the army unwillingly, but they are generally soon penetrated with its esprit de corps, and they carry into it talent which it would not otherwise have obtained. Cases of overwork no doubt occur, as in the early training for every profession, but (following the evidence we have received) we have no reason to think them so numerous as to balance the advantage of vigorous, thoughtful study directed early towards a profession which, however practical, is eminently benefited by it. “It can not be said,” was the verdict of one well fitted to express an opinion, “that there is too much science in the French army.”

8. Assuming, however, the value of the scientific results produced in the French army by the Polytechnic, it by no means follows that a similar institution would be desirable in another country. Without much discussion it may be safely said that the whole history and nature of the institution—the offspring of a national passion for system and of revolutionary excitement—make it thoroughly peculiar to France.

9. Some obvious defects must be noticed. The curious rule of forbidding the use of all books whatever is a very exaggerated attempt to make the pupil to rely entirely on the professors and répétiteurs. The exclusive practice of oral examination also seems to us a defect. Certainly every examination should give a pupil an opportunity of showing such valuable qualities as readiness and power of expression; but an examination solely oral appears to us an uncertain test of depth or accuracy of knowledge; and however impartial or practiced an examiner may be, it is impossible that questions put orally can present exactly the same amount of difficulty, and so be equally fair, to the several competitors.

At the same time, although in all great competing examinations the chief part of the work (in our opinion) should be written, the constant oral cross-questioning of the minor examinations at the Polytechnic, appeared to be one of the most stimulating and effective parts of their system,

10. A more serious objection than any we have named lies against the exclusive use of mathematical and scientific training, to the neglect of all other, as almost the only instrument of education. The spirit of the school, as shown especially by its entrance examinations, is opposed to any literary study. This is a peculiar evil in forming characters for a liberal profession like the army. Such a plan may indeed produce striking results, if the sole object is to create distinguished mathematicians, though even then the acuteness in one direction is often accompanied by an unbalanced and extravagant judgment in another. But a great school should form the whole and not merely a part of the man; and as doing this, as strengthening the whole mind, instead of forcing on one or two of its faculties—as giving, in a word, what is justly called a liberal education—we are persuaded that the system of cultivating the taste for historical and other similar studies, as well as for mere science, is based on a sounder principle than that which has produced the brilliant results of the Polytechnic.

11. It may be added, in connection with the above remark, that as the entrance examination at the Polytechnic influences extensively the teaching of the great French schools, and is itself almost solely mathematical, it tends to diffuse a narrow and exclusive pursuit of science, which is very alien from the spirit of English teaching.

12. We may sum up our remarks on the Polytechnic School thus:—

Regarded simply as a great Mathematical and Scientific School, its results in producing eminent men of science have been extraordinary. It has been the great (and a truly great) Mathematical University of France.

Regarded again as a Preparatory School for the public works, it has given a very high scientific education to civil engineers, whose scientific education in other countries (and amongst ourselves) is believed to be much slighter and more accidental.

Regarded as a school for the scientific corps of the army, its peculiar mode of uniting in one course of competition candidates for civil and military services, has probably raised scientific thought to a higher point in the French than in any other army.

Regarded as a system of teaching, the method it pursues in developing the talents of its pupils appears to us the best we have ever studied.

It is in its studies and some of its main principles that the example of the Polytechnic School may be of most value. In forming or improving any military school, we can not shut our eyes to the successful working at the Polytechnic of the principle, which it was the first of all schools to initiate, the making great public prizes the reward and stimulus of the pupil’s exertions. We may observe how the state has here encouraged talent by bestowing so largely assistance upon all successful, but poor pupils, during their school career. We may derive some lessons from its method of teaching, though the attempt to imitate it might be unwise. Meanwhile, without emulating the long established scientific prestige of the Polytechnic, we have probably amongst ourselves abundant materials for a military scientific education, at least as sound as that given at this great School.

NOTE.

In addition to the Schools of Application for Artillery and Engineers at Metz, and of Infantry and Cavalry at St. Cyr, of which a pretty full account will be given, the following Public Services are supplied by the Polytechnic School.

Gunpowder and Saltpetre.—(Poudres et Salpêtres.)

In France the manufacture of gunpowder is solely in the hands of the Government. The pupils of the Polytechnic who enter the gunpowder and saltpetre service, are sent in succession to different powder-mills and saltpetre refineries, so as to gain a thorough acquaintance with all the details of the manufacture.

On first entering the service they are named élèves des poudres. They afterwards rise successively to the rank of assistant-commissary, commissary of the third, of the second, and of the first class.

Navy.—(Marine.)

A small number of the pupils of the Polytechnic enter the Navy. They receive the rank of élève de première classe, from the date of their admission.

They are sent to the ports to serve afloat. After two years’ service they may be promoted to the rank of enseigne de vaisseau, on passing the necessary examinations, on the same terms precisely as the élèves de premiere classe of the Naval School.

Marine Artillery.—(Artillerie de la Marine.)

The French marine artillery differs from the English corps of the same name, in not serving afloat. Its duties are confined to the ports and to the colonies. It is governed by the same rules and ordinances as the artillery of the army.

The foundries of La Villeneuve, Rochefort, Ruelle, Névers, and Saint Gervais are under its direction.

The officers of the marine artillery are liable to be sent on board ship to study naval gunnery, so as to be in a position to report upon alterations or improvements in this science.

Naval Architects.—(Génie Maritime.)

The naval architects are charged with the construction and repair of vessels of war, and with the manufacture of all the machinery required in the ports and dockyards. The factories of Indret and La Chaussade are under their direction.

The pupils of the Polytechnic enter the corps of naval architects with the rank of élève du Génie Maritime. They are sent to the School of Application of Naval Architects at L’Orient. After two years’ instruction they undergo an examination, and, if successful, they are promoted to the rank of sub-architect of the third class, so far as vacancies admit. They may be advanced to the second class after a service of two years.

Hydrographers.—(Ingénieurs Hydrographes.)

The hydrographers are stationed at Paris. They are sent to the coast to make surveys, and the time so spent reckons as a campaign in determining their pension. On their return to Paris they are employed in the construction of maps and charts.

The hydrographers have the same rank and advantage as the naval architects.

On leaving the Polytechnic, the pupils enter the corps of hydrographers with the rank of élève hydrographe. After two years’ service, and one season employed on the coast, they become sub-hydrographers without further examination.

Roads and Bridges.—Government Civil Engineers.—(Fonts et Chaussées.)

The Polytechnic furnishes exclusively the pupils for the Government Civil Engineer Corps. On leaving the Polytechnic, the pupils enter the School of Application in Paris. The course of instruction here extends over a period of three years. It commences each year on the first of November, and lasts till the 1st of April. After the final examination, the pupils are arranged according to the results of the examination and the amount of work performed.

The pupils enter the college with the rank of élève de troisième classe. They rise successively to the second and to the first class, on making the requisite progress in their studies.

From the 1st of May to the 1st of November the élèves of the second and the third class are sent on duty into the provinces. The élèves of the first class who have completed their three years’ course of instruction, are employed in the duties of ordinary engineers, or are detached on special missions. In about three years after quitting the college, they may be appointed ordinary engineers of the second class.