VIII.-MATHEMATICS.

1. Review of arithmetic and algebra; higher equations and equations with several unknown quantities; fundamental principles of the differential calculus, and its application to the development of functions in series, and the evaluation of indeterminate forms; maxima and minima of functions; interpolation, and the analysis of equations.

2. Geometry and stereometry; analytic geometry of two and three dimensions; theory of co-ordinates; equations of surfaces; conic sections; higher plane curves; rectification, quadrature, and cubature; solids of revolution; Simpson's rules.

3. Trigonometry-The application of spherical trigonometry and the use of tables, with special reference to the problems of navigation.

4. Pure mechanics.-Determination of centers of gravity; principles of dynamics; law of falling bodies; path of projectiles; the pendulum; moments of turning, moments of inertia.

IX. PHYSICS AND CHEMISTRY.

Higher knowledge of the principles of chemistry, and the important substances and processes in use in naval arts, or in fabrication of ordnance or machinery; gravitation and phenomena connected therewith; molecular energy, hardness, elasticity, capillarity, crystallization; statics and dynamics of solids and fluids; undulatory theory; reflection and refraction of light, interference, polarization, and chemical action of light; use of the spectroscope; photography; telescope. Theory of heat; measurement and effect of heat; expansion, liquefaction, evaporation, conduction of heat, capacity for heat, heat-unit, and equivalent of work; electricity, magnetism; correlation of forces; measurement and application of forces. Theory of the compass, disturbing influences, &c. Physical geography and meteorology, with practice in the use of meteorological instruments; methods of graphic representation of meteorological phenomena, law of storms, terrestrial magnetism.

The programme of the officers' professional examination (See-OffizierBerufsprüfung) and the grouping of studies are as follows:

FIRST CLASS: COEFFICIENT, 3.

I. NAVIGATION.

Nine papers are given, of one hour each, of which six are practical and three descripOf the last, one is on instruments, one on deviation, and one on coast sur

tive. veying.

II. GUNNERY.

Six papers, of an hour each, of which one is on powder, three on the structure, fabrication, and inspection of guns and ammunition, and two on the use and working of guns.

III. STEAM-ENGINEERING.

Four papers, of which two are descriptive, and two involving the theory of the steamengine, and calculations. Three hours are allowed for this subject.

SECOND CLASS: COEFFICIENT, 2.

IV.-SHIP-BUILDING AND NAVAL ARCHITECTURE.

The same number of papers and hours as in the preceding subject, divided equally between a mathematical and a descriptive treatment of the subject.

V.-LAND TACTICS.

One hour and a half.

VI.-PHYSICS.

Four hours are allowed, and six papers are given, on the following subjects, respectively: Chemistry, mechanics, light and heat, electricty, physical geography, and meteorology.

THIRD CLASS: COEFFICIENT, 1.

VII.-FORTIFICATION.

Two papers of an hour each, one on field and permanent fortification, and one on coast defense.

VIII.-DRAWING.

The examination in drawing consists of the inspection of drawings made during the course of instruction, which must include at least the following: One hydrographical survey, one topographical survey (using the plane table); three drawings of objects pertaining to ordnance, one of which is an isometric projection; one calculated trajectory; one working drawing for ship-building; and three on detail parts of engines.

IX.-MATHEMATICS.

Four hours allowed. Six papers are given, of which two are in pure mathematics, two in geometry and stereometry, one in mechanics, and one in the application of mathematics to navigation.

Upon the close of the examination, the board transmits to the faculty of the Naval School its proceedings, and a summary of the results of the examination. The faculty thereupon makes up its general report or petition (Gesuchsliste) for the award of certificates of proficiency as officers, to those sub-lieutenants who have passed, which it transmits to the Admiralty, together with the proceedings of the board, and a list arranged according to conduct. In the transactions of the board must appear recommendations in regard to officers who failed at their examinations, stating whether they should be granted a second trial. A report to the Emperor is drawn up by the Admiralty on the basis of these reports from the board and from the Naval School, with the previons certificates and reports from the captain of the midshipmen's training ship; and the Minister requests the award of certificates in accordance therewith, which is forthwith granted. Sub-lieutenants who show extraordinary proficiency, receive the commendation of the Emperor. The seniority of the officers having been determined by the report, commissions as sub-lieutenants, and later, as lieutenants, are granted by the Emperor as vacancies occur; but in any case the passing of the examination and a total of five years' sea-service are indispensable qualifications for a commission.

CHAPTER XXVIII.

THE NAVAL ACADEMY.

The students of the Naval Academy are of two classes, viz, officers ordered to the Academy for study in the regular course, and officers entered as transient students (Hospitanten). For admission to the latter class, that is, for the purpose of attending a partial course or certain special lectures, it is only necessary for an officer to have permission. from the superior officer under whose orders he is for the time being. The conditions of entrance as a, regular student are, however, much more exacting. In the first place, only those officers are ordered who show by their general character and conduct, by their professional zeal, and by their mental attainments that they will make the most of the privilege of attendance at the Academy to advance the interests of the service. They must then pass an examination of a peculiar character. Certain subjects are drawn up and published in November of each year by the Admiralty in the departments of military history, seamanship and naval tactics, navigation, gunnery, marine engineering, and ship-building. The candidate selects any three of these subjects, and is required to work up a paper in each subject. The papers that he prepares must be sent in to the Direction of the Naval Academy and School by the 1st of June in the following year, with a statement of the works of reference and other means of assistance employed. Applications for orders to the Academy on behalf of any individual are sent, before July, by his commanding officer to the Admiralty through the Commander-in-Chief of the station; and they must contain a report upon the qualifications of the candidate, and an explicit statement of the points referred to above, including character, ability, &c. At the same time the director of the Academy presents to the committee on studies a report of the opinion of the committee of the faculty appointed to examine the papers of candidates; and the papers themselves are also turned over to the committee on studies. The report of the examining committee states in terms whether the candidates, in the papers they have presented, have shown sufficient experience, proficiency, talent for observation, sound judgment, and practical skill to appear qualified to receive with advantage a further education. The reports, accompanied by the opinion of the committee on studies, are then sent to the Admiralty, with which rests the final decision upon the application.

The course at the Academy covers three years or classes, the session lasting from October to May, in each year. The general arrangement

of the studies is such that the first or lowest class (Cœtus) takes up the auxiliary sciences forming a groundwork and preparation for scientific study in general, and for professional study in particular; the second class continues this fundamental training and takes up professional studies; and the third completes the professional course, and has a full course in those branches of natural and social science which concern most nearly the duties of a naval officer.

The subjects in the course of instruction of each class are as follows:

FIRST CLASS.

1. Logic, ethics, and the elements of psychology.

2. A short review of elementary mathematics, and the fundamental principles of analytical geometry and higher calculus.

3. Organic and inorganic chemistry.

4. The whole range of pure physics, treated both experimentally and mathematically. 5. Naval organization and naval tactics.

6. Tactics of land forces, considered strategically, and with special reference to landing parties.

7. Permanent fortification, especially in coast-defense.

8. Military administrative law and international law.

SECOND CLASS.

1. Thorough course in higher mathematics, especially in its application to geometry, mechanics, and the calculation of probabilities.

2. History of naval wars.

3. Ordnance and gunnery.

4. Steam-engineering. 5. Naval architecture.

6. Nautical astronomy.

7. Coast survey.

* Electricity, particularly in its application to torpedoes.

9. Laws of war; maritime law.

10. Sanitary administration, especially in relation to the conditions of life on shipboard.

11. General survey of the history of civilization.

1. History of naval wars.

2. Ordnance and torpedoes.

3. Steam-engineering.

4. Naval architecture.

THIRD CLASS.

3. Nautical astronomy, the construction of charts, and the principles of geodesy.

6. Observation with instruments, including the preparation and use of all the instruments employed in navigation, and in geodetic surveys.

7. Physical geography.

* History of civilization.

9. Construction of harbors.

19. Natural history of the sea.

11. Political economy.

* All the above studies are obligatory with the exception of the last, which the student may take or not, as he pleases.

*These three subjects are electives, but the student is required to take one of them. Of these four elective subjects each student is required to take two. All the other subjects are obligatory.

In addition to the course described, opportunity is given to the students to extend and perfect their knowledge of foreign languages. Instruction in this branch includes English, French, and Danish, and, when practicable, Russian and Spanish also. All this is independent of the regular course, but each student is required during all the years of attendance to take instruction in at least one foreign language.

During the summer months, from May till the end of September, the students of the Academy return to active service, being ordered either to a cruising-ship, or to the gunnery-ship, or attached for the time to the coast survey, or to the torpedo division. During the session practical instruction is confined to certain excursions made in connection with the course of study. These include, in the first class, topographical surveys by students who have had no such practice before; and, in the second class, hydrographic surveys in a small vessel attached to the station. There is also a special course of instruction in observing with fixed instruments at the observatory, and practice in the use of nautical, astronomical, and geodetic instruments, the latter in connection with triangulations and geodetic surveys.

Instruction is given in the usual academic manner, by lectures and questioning, supplemented by laboratory work, and by the use of draw.. ings, models, and apparatus, of which there is a full collection at the Academy. The method of instruction here, as in all German institutions, aims directly at the thorough understanding of the fundamental principles of the subjects studied. To clear up obscurities, and to keep alive an active interest on the part of the students, the closest attention is directed to special cases and circumstances as they arise in the service, and to the demands of actual practice. The freest interchange of opinions between teachers and students is encouraged, and every method is adopted to stimulate thoughtful and intelligent effort, by informal expositions and discussions, by the preparation of written papers, and by frequent interrogations of and by the students.

Besides the questions, problems, &c., given out from time to time during the session, short examinations are held quarterly in each subject. Papers are set by the professors, and each examination lasts an hour, the students working under the supervision of the instructor. The results of the examination are tabulated, and sent, together with the report of the director, to the committee on studies. At the final examination for the year, another merit roll is made out, giving the general results for the year; and a report of the Direction on the work done by students is sent in to the committee on studies. Upon the result of these examinations depends the return of the student for the next year's course. At the close of the three years, a diploma or certificate is given by the committee on studies, to each graduate, and the form of the certificate depends upon the character of the student's work, as shown from time to time in the quarterly and annual examinations.

Officers ordered as students to the Academy are entirely detached