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. Specimens of the questions given at the written and oral examination are given in the Appendix.* FRENCH. 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 Ro mains. LATIN. Third class and grammar classes. Latin grammar: Explanation and recitation upon Latin authors. Authors designated: Cæsar, Gallic war; Virgil, Eneid, 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 establishments 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. Charlemagne; his wars and his government. Re-establishment of the empire. Louis le Débonnaire. Treaty of Verdun. Charles the Bald. The Normans. Dismemberment of the empire into kingdoms and of France into great fiefs. 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. The Crusades. The Kingdom of Jerusalem and the Latin Empire of Constantinople, Progress of royal power in France. Enfranchisement of the communes. Louis VI. Philip Angustus. War of the Albigenses. Reign of Saint Louis. Arts, letters, and schools in the twelfth and thirteenth centuries; commerce and industry. Tabular summary of the different States of Europe in 1270. NOTE.-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). Configuration of Europe. Extreme longitude and latitude. Oceans that bound Europe; 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. Isothermal lines, maritime and inland climates, winds and rains. Races, languages, religion. British Isles: Rapid review of the physical geography. Territorial formation; surface, configuration, and limits; great divisions. Principal cities. Agriculture (cereals, industrial 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; surface, 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 administration. Gerany.-Review of physical geography. Territorial formation; surface, configuration, and boundaries. 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. Population. Austria-Hungary.-Review of its physical geography. Territorial formation; surface, configuration, and boundaries; provinces and countries included in it. Principal cities. 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, configuration, 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; configuration, and boundaries. Ancient division into provinces. Principal cities. Agrialture. Industry. Commerce. Government and administration. Population. Colonies. Spain.-Review of physical geography. Territorial formation; surface, configuration, 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 formation; surface, configuration, and boundaries. Mainland, Archipelago and Ionian Isles. Principal cities. Agriculture. 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. Government and administration. Russia.-Review of physical geography. Territorial formation, surface, configuration, and boundaries of the Russian Empire in Europe and in Asia. Great divisions of Russia in Europe. Principal cites. Agriculture. Fisheries. Mines. Industry. Railways. Sea-coast and interior navigation. Commerce. Government and administration. 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. Commerce, government and administration. Population. Denmark. Review of physical geography. Territorial formation; surface, configuration, and boundaries. Principal cities. Agriculture. Railways. Navigation. Commerce. 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.) GEOGRAPHY OF FRANCE. 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 tributaries; canals; lakes, ponds, marshes. Climate and principal productions. Political geography. Ancient provinces, with their capitals. Departments by provinces, and departments by basins; their principal cities; other important cities. Principal railways. Population. 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. 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 having a common 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 пpon 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 and 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. Equations of second degree with one unknown quantity. Double solution. Imaginary values. Properties of trinomials of the second degree. Questions of maxima and minima which may be resolved by equations of the second degree. Principal 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 logarithmic calenlations 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 define the logarithms of numbers less than 1, it is sufficient to extend to these unmbers the fundamental property of logarithms. Let a be a number less than 1, and let Pa× 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 Thus it is proper to call the logarithm of P, diminished by n, the logarithm of a. In reducing this to a single characteristic, it is evident that it will contain a number of 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 position of points equidistant from two intersecting right lines. Parallel lines. Sum of the angles of a triangle, of a polygon. Properties of parallel ograins. The circumference of the circle. their distances from the center. Mutual relations of arcs and chords, of chords and 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 tangent 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 curve whatever. Theorem of the square described on the hypotenuse of a right-angled triangle. Numerous numerical applications. Elements of surveying. Use of the chain and the surveyor's square. Proportional lines. Second class. 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 mean 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 finished 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 difference; applications to the construction of roots of equations of the second degree with one unknown quantity. |
