AUTHORITIES.

THE following account of the SYSTEM OF MILITARY EDUCATION IN FRANCE, except in the case of three or four schools, where credit is given to other authorities, is taken from an English Document entitled "Report of the Commissioners appointed (by the Secretary of War) to consider the best mode of reorganizing the system of Training Officers for the Scientific Corps: together with an Account of Foreign and other Military Education." Reference has been had, especially in the Programmes and Courses of Instruction to the original authorities referred to by the Commissioners.

I. GENERAL MILITARY ORGANIZATON OF FRANCE.

Vauchelle's Course d' Administration Militaire, 3 vols.

II. THE POLYTECHNIC.

1. Fourcy's Histoire de l'Ecole Polytechnique.

2. Décret portant l'Organisation, &c.

3. Règlement pour le Service Interieur.

4. Programme de l'Enseignement Interieur.

5. Programme des Connaissances Exigées pour Admission, &c.

6. Rapport de la Commission Mixte, 1850.

7. Répertoire de l'Ecole Polytechnique; by M. Marielle.

8. Calenders from 1833.

9. Pamphlets-by M. le Marquis de Chambray, 1836; by V. D.

Bugnot, 1837; by M. Arago, 1853.

III. SCHOOL OF APPLICATION AT METZ, AND St. CYR.

Décret Impérial, &c., 1854.

IV. SCHOOL FOR THE STAFF AT PARIS.

Manuel Réglementaire a l' Usage, &c.

V. ANNUAIRE DE L'INSTRUCTION PUBLIQUE, 1860.

MILITARY SYSTEM AND SCHOOLS OF FRANCE.

I. MILITARY SYSTEM.

THE French armies are composed of soldiers levied by yearly conscription for a service of seven years. Substitutes are allowed, but in accordance with a recent alteration, they are selected by the state. Private arrangements are no longer permitted; a fixed sum is paid over to the authorities, and the choice of the substitutes made by them.

The troops are officered partly from the military schools and partly by promotion from the ranks. The proportions are established by law. One-third of the commissions are reserved for the military schools, and one-third left for the promotion from the ranks. The disposal of the remaining third part is left to the Emperor. The promotion is partly by seniority and partly by selection. The following regulations exist as to the length of service in each rank before promotion can be given, during a period of peace:A second Lieutenant can not be promoted to Lieutenant under 2 years' service. A Lieutenant

A Captain

A Major

Captain
Major

2

A Lieutenant-Colonel

But in time of war these regulations are not in force. Up to the rank of captain, two-thirds of the promotion takes place according to seniority, and the other one-third by selection.

From the rank of captain to that of major (chef de bataillon ou d'escadron) half of the promotion is by seniority and the other half by selection, and from major upwards, it is entirely by selection.

The steps which lead to the selection are as follows:-The general officers appointed by the minister at war to make the annual inspections of the several divisions of the army of France, who are called inspectors-general, as soon as they have completed their tours of inspection, return to Paris and assemble together for the purpose of comparing their notes respecting the officers they have each seen, and thus prepare a list arranged in the order in which they recommend that the selection for promotion should be made.

We were informed that the present minister of war almost invariably promoted the officers from the head of this list, or, in other words, followed the recommendation of the inspector-general.

II. MILITARY SCHOOLS.

The principal Military Schools at present existing in France are the following:

1. The Polytechnic School at Paris (Ecole Impériale Polytechnique,) preparatory to

2. The Artillery and Engineers School of Application at Metz (Ecole Impériale d'Application de l'Artillerie et du Génie.)

3. The Military School at St. Cyr (Ecole Impériale Spéciale Militaire,) for the Infantry and Cavalry, into which the Officers' Department of the Cavalry School at Saumur has lately been absorbed.

4. The Staff School at Paris (Ecole Impériale d'Application d'Etat Major.)

5. The Military Orphan School (Prytanée Impériale Militaire) at La Flèche. 6. The Medical School (Ecole Impériale de Médicine et de Pharmacie Militaires) recently established in connection with the Hospital of Val-de-Grâce.

7. The School of Musketry (Ecole Normale de Tir) at Vincennes, founded ir 1842.

8. The Gymnastic School (Ecole Normale de Gymnastique) near Vincennes. 9. The Music School (Gymnase Musical.)

19. The Regimental Schools (Ecoles Régimentaires.)

The military schools are under the charge of the minister of war, with whom the authorities of the schools are in direct communication.

The expenses to the state of the military schools, including the pay of the military men who are employed in connection with them, for the year 1851, are as follows:

From this sum, 2,224,542fr., should be deducted 421,372fr. secured from paying pupils, leaving the total cost to the state to be 1,803,308fr., or about $360,000, for about 2,100 pupils. The cost to the state for training an officer of Artillery and Engineers is about $1,500, and that of an officer of the Staff is about $1,400.

SUBJECTS AND METHODS OF INSTRUCTION

IN MATHEMATICS AS PRESCRIBED FOR ADMISSION TO THE POLYTECHNIC SCHOOL OF FRANCE.

"L'ÉCOLE POLYTECHNIQUE" is too well known, by name at least, to need eulogy in this journal. Its course of instruction has long been famed for its completeness, precision, and adaptation to its intended objects. But this course had gradually lost somewhat of its symmetrical proportions by the introduction of some new subjects and the excessive development of others. The same defects had crept into the programme of the subjects of examination for admission to the school. Influenced by these considerations, the Legislative Assembly of France, by the law of June 5th, 1850, appointed a “ Commission" to revise the programmes of admission and of internal instruction. The President of the Commission was THENARD, its "Reporter" was LE VERRIER, and the other nine members were worthy to be their colleagues. They were charged to avoid the error of giving to young students, subjects and methods of instruction "too elevated, too abstract, and above their comprehension;" to see that the course prescribed should be "adapted, not merely to a few select spirits, but to average intelligences;" and to correct "the excessive development of the preparatory studies, which had gone far beyond the end desired.”

The Commission, by M. Le Verrier, prepared an elaborate report of 440 quarto pages, only two hundred copies of which were printed, and these merely for the use of the authorities. A copy belonging to a deceased member of the Commission (the lamented Professor Theodore Olivier), having come into the hands of the present writer, he has thought that some valuable hints for our use in this country might be drawn from it, presenting as it does a precise and thorough course of mathematical instruction, adapted to any latitude, and arranged in the most perfect order by such competent authorities. He has accordingly here presented, in a condensed form, the opinions of the Commission on the proper subjects for examination in mathematics, preparatory to admission to the Polytechnic School, and the best methods of teaching them.

The subjects which will be discussed are ARITHMETIC; GEOMETRY; ALGEBRA; TRIGONOMETRY; ANALYTICAL GEOMETRY; DESCRIPTIVE GEOMETRY.