The American Journal of Education

been created; every day new things are being cultivated, and manufacturers are opening new outlets for themselves, which give rise to combinations unknown to ancient commerce, and which more than ever insure success to those who are best informed, and have the most general instruction; hence the necessity for a course of commercial geography for the pupils of the special schools, who are one day to be merchants, or manufacturers, or agriculturists. The school can not take the place of the usual apprenticeship, which can alone form practical workers; but it is useful to know beforehand the commercial geography of distant countries; to be acquainted with the products furnished by the mining, the manufacturing, and the agricultural industry of the principal regions; the places of origin, and the importance of the raw materials which are most largely consumed; the products consumed and manufactured by the principal cities and countries; the means of communication, the weights, measures, and coinage in use; the mode of sale; in a word, the information required by every merchant who wishes to be instructed as to the transactions and the wants in the principal quarters of the commercial world.

The study of the physical geography of France should be taken up again, because every man ought first of all to be acquainted with the territorial riches of his own country, and more particularly of his own department, on which the teacher ought to dwell; because also of their offering familiar examples, easy to understand; the following year the relations of France with other countries should be studied. The professor should describe the principal agricultural regions, and point out their climatic conditions; he should speak of the different kinds of cultivation, of natural and artificial meadows, of vineyards, forests, the rearing of domestic animals, &c.; he should describe mining industry, point out the localities in which the raw materials, such as coal, iron ore, &c., are found, and where great mechanical and chemical industries have been developed, &c.; finally, he should indicate the navigable routes, the railways and roads, and conclude with a table of exports and imports, to which he should add a statement of the population, lastly, he should enumerate the countries with which France entertains the most active commercial intercourse, and devote a few lessons to our colonies, showing their relations with the mother country.

MATHEMATICS.

Commercial Arithmetic.-Recapitulation of the rules of calculation of fractions, and the properties of proportions; practical rule for the extraction of the square; rule of three; of society and of simple interest, already learnt by the method of reduction; explication of the rules of discount, of composition, of allegation, of compound interest and of annuities; numerical exercises relative to public rentes and loans; details concerning the sinking fund (aissé d'amortissement), and the Bank of France; show that by means of letters and cor.ventional signs calculations may be abridged, and operations generalized; give a foreshadowing of algebra by writing down in letters the results obtained.

The task should be numerous exercises in answering common questions.

Solid Geometry.-The professor should take care that the course retain its character of practical usefulness; he should therefore not proceed in strictly scientific order, nor demonstrate theorums independently of their application; he should, on the contrary, conduct the whole course of the instruction, so as to

elucidate constantly by application. When arrived at solid geometry, he should make use of small plates of cork, of 25 to 30 centimetres in length and breadth, to represent the planes, and of wooden sticks with points to represent the lines; with these plates and these sticks he should construct the figures, the properties of which he is going to explain, then, having presented it to the pupils from different points of view, he should draw it on the board, and during the course of his demonstration he should successively pass from the figure to the diagram, and from the diagram to the figure.

Each pupil being furnished with a similar apparatus, but on a smaller scale, should himself reproduce the proposed figure. In this way the course of this year prepares the pupils for the lessons of descriptive geometry.

Of the Plane. From the perpendicular to the plane. No more than one perpendicular can be drawn through a given point on to a plane; to draw a perpendicular line from a given point to a plane without the aid of the T square, &c.; two lines perpendicular to the same plane are parallel; horizontal plane; planes mutually parallel, &c.; of the angle of two planes; trace a line of the greatest inclination on an inclined plane, &c.

Cylindrical Surfaces.-Production of cylindrical surfaces; straight, complete, truncated cylinder; to trace a straight and complete cylindrical surface, the length and the radius of which are given; production of a cylindrical surface; to draw a straight and truncated cylindrical surface, of which the radius is known.

Conic Surfaces. Straight conic surfaces may be produced (engendrée) by the revolution of triangles, rectangular bodies, &c.; to draw a straight and complete conic surface; application to the arts. Developable surfaces: left hand surfaces; examples, wings of a mill, the moldboard of a plough, winding stairs, &c. Spherical surfaces: production of the spherical surface; to draw a spherical surface, the radius of which is given.

The Prism-Straight, oblique, complete, truncated prisms; to draw a straight and complete prism, an oblique prism; principal propositions as to prisms; the cube; the pyramid; regular polyhedrons; the sphere.

Measurements. To measure the lateral surface of a prism, a cylinder, a pyramid, of the trunk of a straight cone (tronc de cône droit), of a truncated pyramid, &c. To measure the surface of a spherical concave (calotte), of a zone, of a sphere, &c. To measure the volume of a prism, of a cylinder, of a parallelepidon, of a cube, &c., of the sphere, &c., &c.

The professor should have at command a collection of solids, in wood or pasteboard, or made of glass-plates, pasted together at the edges, and which allow the angles to be seen, and he should constantly make use of these to render comprehensible his propositions as to volumes, truncation, and conic sections. In the same way as he realized the solid figures of geometry, and exhibited them to the pupils before drawing them on the board and explaining their various properties; he should exhibit the volumes in wood, and allow them to pass through the hands of all the pupils, before drawing on the board the body of which he is going to treat.

PHYSICS.

General properties of liquid bodies, heat, dynamic electricity.-During this year's course the teaching should still remain simple, because it is addressed to

children; algebraic formulas should be left aside, as they can almost always be advantageously replaced by numerical examples; the principles will therefore be not so much demonstrated by theoretical considerations, as they will be made comprehensible by experience.

Apparatus for measurement. Vernier. Dividing machine. Compressibility and elasticity of bodies. Saturation (trempe). Balance. Methods of double weights. Exercise the pupils in exact weighing. Properties of liquids. The principle of Archimedes. Pascal's hydraulic press. Areometers. The barometer. The pneumatic machine. Mariotte's law. Syphons. Aerostats. &c.

The second part of the course should comprise heat and its applications. Refrigerating mixtures. Latent heat, heating of baths and of rooms. Hygrometry. Mists. Clouds. Rain. Snow. Winds. Dew.

The course should conclude with dynamic electricity, the electric pile, magnets, and electric telegraphis.

CHEMISTRY.

The Metalloids and the Alkaline Metals.-The lessons of this year should bear upon the principles of chemistry, and the professor should base all his reasonings on experiments. He should make the pupils acquainted with the composition of bodies as regards the nature of their elements, by means of distinct reactions; he should give the centesimal composition of essential bodies in round numbers, without insisting on quantitative analysis, except as regards air, water, carbonic acid, marine salts, chalk, plaster of Paris, and some other equally common composites, which should be taken as examples. This course should commence with the study of metalloids and their most important applications in manufactures, &c. Next, metals in general and the most common alloys should be examined; lastly, the salts in general, and the carbonates, the sulphates, and the azotates in particular, should be the objects of attention. The course should terminate with the study of the alkaline metals, to which should be added some details relating to the calcareous substances, limestones, mortars, plasters, and ammoniacal salts.

NATURAL HISTORY.

The professor should continue to give an elementary and practical character to the lessons.

In zoology, after having recapitulated the general characteristics of the ver tebrate animals, he should pass on to the study of birds; their conformation is in accordance with their mode of life; the instincts of family and of race are manifested in the construction of their nests, in the bringing up of their young, and in their migrations in search of milder climates. The history of reptiles will furnish the professor with opportunities for useful hints as to the distinctive characteristics of the venomous and the non-venomous serpents. With the history of fishes and their mode of organization, should be combined the study of the resources which they offer as means of alimentation. The history of insects should serve as a basis for interesting lessons on the instinct of bees, or the metamorphoses and the products of silk-worms. Then, after having imparted some notions as to molluscs, the snail and the oyster; as to zoophytes; sponges, etc.; and as to infusoria; the eels of paste and of vinegar; as to monads, &c., the professor should recapitulate the principal characteristics of the most important branches, classes and families.

Botany.-Vegetable physiology, or the life of plants, should be the subject of the lessons of this year. Germination, the part played by the root, by the leaves, by the stem; the influence of light on the green and on the other colored parts; the composition of the sap, and the part which it plays; the formation of the cells, the fibres, and the vessels, of the tissues composed of the elementary organs, of starch, sugar, oils, and resinous juices; further, the relations which exist between the plants and the air, the soil and the waters of the earth, should also be dwelt upon, and will afford numerous opportunities for direct applications, full of interest.

The lessons in geology should be devoted to the study of the complete series of strata, passing rapidly over those formations which are of no importance from an industrial point of view, or which are not found in any considerable extent in France; but the slate and coal formations should be dwelt upon, so also the brown freestone of the Vosges, the saliferous rocks, the chalk formations of the Jura; tlre tertiary basins, and, above all, the formations immediately surrounding the locality in which the school is situated.

ACCOUNTS.

Course Preparatory to Bookkeeping.—The pupils are acquainted with the vo cabulary, and know how to make out the various accounts which serve to verify the first operations, the master may therefore now turn his attention to the books usually kept in connection with commercial dealings, prove the necessity of them, and explain the plan on which they are generally kept.

He should first mention the three obligatory books, quoting the article of the code which prescribes the use of them, then the most usual auxiliary books; he should explain the note of discount and of back exchange, and the account of redraft; he should accustom the pupils to make out such accounts themselves by setting them numerous exercises. He should next occupy himself with current accounts, bearing interest, and with the three methods, viz., the direct, the indirect, and the Hamburgh method. Lastly, he should teach the pupils how to keep the day-book, the object and utility of which he should explain, giving a detailed account of the arrangement and of the specification of the articles.

The pupils can not be too much practiced in entering into the day-book the items of sales, purchases, discount, &c, for these exercises will make them understand the operations, and will directly prepare them for keeping the journal with which they will have to occupy themselves the following year.

This course completes the preliminary knowledge which the pupils require in order to be able to understand bookkeeping, properly so called, which will be taught to them during the course of the ensuing year.

CALIGRAPHY AND DRAWING.

End of the lessons: round hand, Italian hand, models of capitals, &c., applications of divers kinds of handwriting.

Continuation of ornamental and linear drawing, according to the method adopted the previous year.

Ornamental Drawing.-Copying figures and ornaments. Commencement of hatching to represent relief. The model from which the drawings are to be made should always be placed in the class-room.

Linear Drawing: principles of the methods of projection for the representation of lines, surfaces, and solids.. Representation of the relief of bodies by means of simple lines and washing in colors. Details of the practice of washing. Elementary notions of architecture, and distinctive characteristics of the principal orders.

Before commencing each architectural drawing, the pupil should make a sketch of the plan to be executed, in a separate copybook, and should carefully note down the dimension (les cotes). These sketches should be done in pencil, or in ink, without the help of rule or compass, and should serve for constructing the plan.

Some suitable plan should be selected to exercise the pupils in using the ruler, and the use of conventional tints should be explained to them.

GYMNASTICS.

Marching and running, regulated by singing; exercises on the rope ladder, on the oscillating plank, on the smooth rope, on the pole, under the horizontal ladder, on the parallel bars, &c.; jumping from height of not more than one metre thirty centimetres, exercises on the horse, on the inclined ladder, on the horizontal pole, on the arm-swing, and on the horizontal bar.

SINGING.

Continuation of the explanation of the principles.

Study of the chromatic scale; modified tones; accidents.

Second study of the diatonic scale.

On the intervals of tones; study of the tetrachords; major and minor keys; typical scale of do and of la.

Construction of scales similar to this typical one, on the first sound of the superior tetrachord, or on the fourth tone of the inferior tetrachord; position of the sharps.

Position of the flats.

Study of the key fa.

Binary and ternary groups.

With the lessons in theory should always be combined practice, intonation, dictation, and singing in unison should terminate each lesson.

THIRD YEAR.

SUBJECTS OF INSTRUCTION.

Ethics.

Course of literary composition..

1 hour weekly.
2

History of French literature.