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of the required branches, the school system is sufficiently flexible to admit a slight modification in his favor.

The programmes of the lycées that define the requirements for admission to the Naval School are given below in the form in which they appear in the circular published for the information of candidates. Speci. mens of the questions given at the written and oral examination are given in the Appendix.*

FRENCII.

Programme of third class and of the grammar classes (4th, 5th, and 6th).

French grammar: Study of the French language and literature; explanation and

recitation of French authors. Desiguated works: La Fontaine, Fables; Fénelon, Télémaque; Voltaire, Charles XII; Montesquieu, Grandeur et Décadence des Romains.

LATIN.

Third class and grammar classes.

Latin grammar: Explanation and recitation upon Latin authors. Authors designated:

Cæsar, Gallic war; Virgil, Æneid, I, II, and III books.

GREEK.

Third class and grammar classes.

Greek grammar: Explanation and recitation upon Greek authors. Authors designated:

Xenophon, Anabasis, or Expedition of Cyrus.

ENGLISH.

Third class.

Grammar: Revision of syntax; idioms; proverbs; general rules of prosody. Exercises: Explanation and recitation ; exercises of conversation; money, weights,

and measures of England taught in English. Authors designated : W. Irving, Christopher Columbus (abridged by the author);

Macaulay, Lays of Ancient Rome.

HISTORY

Third class.

History of Europe from the fifth to the end of the thirteenth century (395–1270).
Gaul under the Roman Empire: Invasion of the Barbarians; the Germans, their es-

tablishments in Italy, the States they founded. The Kingdom of the Franks: Clovis, Brunehaut, Dagobert; conquests in Germany;

government and institutions; the Salic law. Justinian; his wars and legislative work. Mahomet: Conquests of the Arabs; high character of the Arabic civilization. Pepin d’Heristal; Charles Martel; Pepin the Short. Charlemagne; his wars and his goverument. Re-establishment of the empire. Louis

le Débonnaire. Treaty of Verdun. Charles the Bald. The Normans. Disinem

berment of the empire into kingdoms and of France into great tiefs. The feudal system. State of the church in the tenth century. The Empire. Otto the Great. The quarrel of investitures. Gregory VII. Innocent

III and Innocent IV. Frederick Barbarossa and Frederick II.

*Note H

Norman conquest of England. Henry II. Magna Charta.
Thie Crusades. The Kingdom of Jerusalem and the Latin Empire of Constantinople,
Progress of royal power in France. Enfranchisement of the communes. Louis VI.

Philip Augustus. War of the Albigenses. Reign of Saint Louis.
Arts, letters, and schools in the twelfth and thirteenth centuries; commerce and in-

dustry.
Tabular summary of the ditferent States of Europe in 1270.

NUTE.-Ancient history is studied in the lower classes of the Lycées; modern history (after 1270) in the higher classes. The historical course at the Naval School corresponds to the latter course.

GEOGRAPHY.

Third class.

Physical, political, and statistical geography of Europe (omitting France). Contiguration of Europe. Extreme longitude and latitude. Oceans that bound

Enrope; gulfs and straits; islands; peninsulas and capes; description of the coasts, Geological formation; mountain system; chains and peaks; principal summits, plateaux and plains. General direction of water-courses. Basins, rivers, streams, lakes. Isotherinal lines, maritime and inland climates, winds and rains. Races,

languages, religion. British Isles : Rapid review of the physical geography. Territorial formation; surface,

configuratiou, and limits; great divisions. Principal cities. Agriculture (cereals, iodustrial products, pasturage, cattle raising). Fisheries. Mines (coal and iron). Metallurgical (iron and steel) and textile industries. Canals and railways. Navigation. Commerce. Government and administration. Army and navy. Budget

and debt. Population. Possessions in Europe. Colonies.
Netherlands.-Rapid review of the physical geography. Territorial formation ; sur-
face, configuration, and boundaries; provinces. Principal cities. Agriculture
(dikes and polders). Fisheries. Canals and railways. Navigation. Commerce.

Government and administration. Population. Colonies.
Grand-duchy of Luxembourg.-Mines and commerce. Government and administra-

tion. Ger i any.-Review of physical geography. Territorial formation ; surface, configura

tion, and bonndaries. Kingdom of Prussia and its old and new provinces. Secondary states. Principal cities. Agriculture. Fisheries. Mines. Metallurgical and textile industries. Canals and railways. Navigation. Commerce. Government and administration, Germanic Confederation of 1815. Zollverein. North German Confederation of 1866. German Empire of 1871. Army, navy, and finances.

Popnlation.
Austria-Hungary.—Review of its physical geography. Territorial formation; surface,

configuration, and boundaries; provinces and countries included in it. Principal eities. Agriculture. Mines. Industries. Railways. Coast and river navigation. Commerce. Government and administration Army and finances. "Population.

Races and languages.
Switzerland.-Review of its physical geography. Territorial formation; surface, con-

tiguration, and boundaries. German, French, and Italian cantons. Principal cities. Agriculture. Commerce. Means of transit. Government and administration.

Population.
Portugal.- Review of physical geography. Territorial formation; surface; configura-

tion, and boundaries. Ancient division into provinces. Principal cities. Agriculture. Industry. Commerce. Government and administration. Population.

Colonies.
Bpain. - Review of physical geography. Territorial formation; surface, contiguration,

and boundaries. Ancient division into kingdoms and provinces. Principal cities. Agriculture. Industry. Commerce. Mines. Means of transit. Government and

administration. Population. Colonies. Republic of Andorra. Italy:-Review of physical geography. Territorial formation. Ancient division into

States. Surface, configuration, and boundaries. Countries and provinces. Principal cities. Agriculture. Mines. Industries. Railways. Navigation. Commerce. Government and administration. Army and finances. Population. Republic of

San Marino. Greece.-Review of physical geography. Territorial foripation; surface, configuration,

and boundaries. Mainland, Archipelago and Ionian Isles. Principal cities. Agri

culture. Navigation. Commerce. Government and administration. Population. Turkey in Europe. Review of physical geography. Territorial formation, surface,

and boundaries of the Ottoman Empire in Europe, in Asia, and in Africa. Great divisions of Turkey in Europe; Archipelago, and Candia. Principal cities. Agriculture. Navigation. Commerce. Government and administration. Population.

Races and religions. Principalities of Roumania, Servia, and Montenegro.—Review of physical geography.

Principal cities. Agriculture. Navigation of the Lower Danube. Commerce. Gov.

ernment and administration. Russia.—Review of physical geography. Territorial formation, surface, configuration,

and boundaries of the Russian Empire in Enrope and in Asia. Great divisions of Russia in Europe. Principal cites. Agriculture. Fisheries. Mines. Industry. Railways. Sea-coast and interior navigation. Commerce. Government and ad

ministration. Army, navy, and finances. Population. Norway and Sweden.-Review of physical geography. Territorial formation; surface,

configuration, and boundaries. Principal cities. Great divisions. Agriculture. Fisheries. Mines. Canals and railways. Navigation. C'ommerce, government

and administration. Population. Denmark.-Review of physical geography. Territorial formation ; surface, configuration, and boundaries. Principal cities. Agriculture. Railways. Navigation. Com

Government and administration. Population. Iceland, Faroe Islands, and colonies. General review.—Comparison of the extent aud resources of different States. Weights,

measures, and money. Density of population. Military forces. (Demonstration and exercises at the black-board and wall-map. Map drawing.)

merce.

GEOGRAPHY OF FRANCE.

Fourth class. Configuration and dimensions of France; surface; extreme latitude and longitude. Seas and coasts; gulfs, islands, peninsulas, capes, dunes, rocks and shoals, salt

marshes, lagoons, principal ports, sea and inland frontiers, territorial losses of

France in 1871. Contour. Mountain chains, peaks and plateaux; altitude; perpetual snows, glaciers,

torrents, passes, roads, tunnels, waters, waterfalls, and basins; rivers and their trib

utaries; canals; lakes, ponds, marshes. Climate and principal productions. Political geography. Ancient provinces, with their capitals. Departments by prov

inces, and departments by basins; their principal cities; other important cities. Principal railways. Populatiov. Colonies. (Demonstration and exercises at the black-board and wall-map Map drawing.

Study of the military map of France.)

ARITHMETIC.

Third class.
Decimal numeration.
The four processes with whole numbers.
Decimals. Processes and examples.

Characteristics of divisibility by 2,3,5, 9, and 11.
Definition of prime numbers and of numbers prime to each other. Resolution of a

number into its prime factors (no theoretical developments). Greatest common divisor and least common multiple. Common fractions. Reduction of fractions to lowest terms; reduction to fractions baring a cominon denominator. Processes with fractions. Conversion of common

fractions into decimals. Square and square root of whole numbers and decimals. Metric system. Ratio and proportion. Ratio of two magnitudes. Proportional magnitudes. Problems upon proportional magnitudes. Questions of interest and discount; formulas for working them out. The class of elementary mathematics reviews the third-class programme, completing it by a few lessons on the properties of prime numbers, repeating decimals, and the errors arising in the extraction of roots.

ALGEBRA.

Class of elementary mathematics, Review au completion of the second-class programme (see below). Discussion of the formulas that resolve a system of equations of the first degree with

two unknown quantities. Examples. Eupations of serond degree with one unknown quantity. Donble solution. Imagi

dary values. Properties of trinomials of the second degree. Questions of maxima and minima which may be resolved by equations of the second

devree. Prioripal properties of arithmetical and geometrical progressions. Theory of logarithms deduced from progressions. Logarithms to the base 10. Tables.

Characteristics. Introduction of negative characteristics to extend logarithnic calcalations to numbers less than 1.* Use of tables. Compound interest and annuities. Application of logarithms to these question.

Second class.

Algebraic operations (not including the division of polynomials).
Equations of the first degree. Examples. Equations of the second degree with one

unknown quantity. Applications to some of the problems of arithmetic and geometry.

GEOMETRY.

Third class.

Right line and plane. Broken line. Curved line. Angle. Generation of angles by the rotation of a right line about one of its points. Right angle.

* To detine the logarithms of numbers less than 1, it is sufficient to extend to these onmbers the fundamental property of logarithms. Let a be a number less than 1, and let P=1 X 10", supposed to be greater than or at least equal to 1. P will have a logarithm, and if it is desired to extend to this product the fundamental property, we shall have,

P log a or log

ion

log P-n. Thus it is proper to call the logarithm of P, diminished by n, the logarithm of a. In redncing this to a single characteristic, it is evident that it will contain a number os negative units, equal to the position that the first significant figure of a occupies to the right of the decimal point.

Triangles. Simple cases of equality. Properties of the isosceles triangle. Cases of

equality of right-angled triangles. Geometrical position of points equidistant from two given points. Geometrical posi

tion of points equidistant from two intersecting right lines. Parallel lines. Sun of the angles of a triangle, of a polygon. Properties of parallel

ograms. The circunference of the circle. Mutual relations of arcs and chords, of chords and

their distances from the center. Tangents. Intersection and contact of two cir

cles. Measurement of angles. Inscribed angles. Use of the rule and compasses in construction, on paper. Tracing of perpendiculars

and parallels ; use of the triangle. Determination of angles in degrees, minutes, and

seconds. Protractor. Elementary problems upon the construction of angles and triangles. To draw a tan

gent to a circle through a given point without. To draw a tangent parallel to a given line. To draw a line tangent to two circles. To describe on a given line a

segment which shall contain a given angle. Measurement of areas. Area of the rectangle, parallelogram, triangle, trapezoid; of

any polygon. Approximate area of a figure bounded by any carve whatever. Theorem of the square described on the hypotenuse of a right-angled triangle. Numer

ous nunerical applications. Elements of surveying. Use of the chain and the surveyor's square.

Second class. Proportional lines. Similar polygons. Conditions of similarity of triangles. Ratio of the perimeters of

similar polygons. Relations between the perpendicular let fall from the right angle of a right-angled triangle upon the hypotenuse, the segments of the hypotenuse, the hypotenuse itself, and the legs. Theorem relating to the square of the side of a triangle, opposite to a right angle, an acute angle, or an obtuse angle. Theorem

relating to the secants of a circle passing through the same point. Problems: to divide a line into equal parts, into parts proportional to given lengths;

to find a fourth proportional to three given lines, a mea! proportional between two

given lines ; to construct on any line a polygon similar to a given polygon. Regular polygons; inscription of regular polygons in a circle; square, hexagon.

Method of determining the ratio of the circumference to the diameter; applications. Area of a regular polygon; of a circle, of a circular sector. Ratio of the areas of

two similar figures. The plane and the right line in space. Perpendiculars and oblique lines drawn to a

plane. Parallelism of right lines and planes. Dihedral angles. Perpendicular

planes. Elementary notions of trihedral and polyhedral angles. Construction of plans; use of the metric scale, the semicircle, square, and plane table. Topographical surveying; sea-level, sight; method of describing the height of a

point; lines of level ; interpretation of topographical charts.

Class of elementary mathematics.

The course begins with a rapid review of the course of the third and second classes, amplifying certain points, especially in regard to the inscribing of regular polygons (case of the decagon) and the determination of the ratio of the circumference to the diameter by the isoperimetrical method. The review is tinished by exercises and problems upon the comparison of areas; the construction of a square equivalent to a given polygon; the construction of a square whose ratio to a given square is equal to the ratio of two given lines; the construction of a rectangle equivalent to a given square, the sum or difference of whose adjacent sides is equal to a given sum or diference; applications to the construction of roots of equations of the second degree with one unknown quantity.

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