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struction and working of railways, of docks, of transatlantic mail-steamers, &c., would still be mere projects.

The principle articles of the laws relative to banking operations, to commercial assets, protests, bill of exchange, bills to order, and cheques, should also be cited.

The professor should impart some summary notions as to failures and fraudulent bankruptcies; he should explain, more or less in detail, according to the character of the locality, the general laws of our maritime commerce; he should mention the system of customs, of entrepôts, of patents, of apprenticeship, and the authority conferred on the conseils de prud'hommes.

Finally, the professor should explain the rules of competency of the mercantile tribunals, and the forms with the aid of which the trader may, in case of contention, obtain the recognition of his rights.

RURAL, INDUSTRIAL, AND COMMERCIAL ECONOMY.

After having explained the object of political economy, the professor should give an idea of the general laws by means of which man makes nature contribute to his wants. He should treat of production in general, of the distribution of wealth, the necessary consequence of the division of labor, of consumption, of revenue, of public contributions. After the statement of general principles, should follow the question of agricultural enterprise, ablocations, and outlets; of industrial enterprises and industrial property, of associatious, of capital, and the part it plays; machinery, and the causes of variations in the rate of interest; tariffs, and routes of communication; currency and savings, credit, banking, insurance, &c.

With the knowledge of the natural and necessary laws on which commerce is founded, the pupil receives the germs of that feeling of confidence, of those rational convictions which contribute to keep up the courage of the well-informed members of the industrial classes during moments of political or commercial crisis, and which serve to guide and to regulate their conduct.

This course constitutes in a manner the philosophy of the industrial professions, and for this reason it has been placed at the end of the special instruction.

MATHEMATICS.

Conclusion of Algebra.-Repetition of equations of the first and second degree with one unknown quantity; problems of the second degree; maxima and minima; progressions; logarithms; use of tables; application to questions of compound interest, to savings' banks, to deferred annuities, &c.; calculation of the savings which a father must capitalize in order to redeem a debt, to accumulate a dowry, or to leave a certain sum to his children at his death, &c.; numerous exercises on analogous questions.

Notions of Rectilinear Trigonometry.—Establishment of the fundamental formula; use of tables; rules for calculation; resolution of triangles in the most simple cases; exercises.

Eight or ten lessons only should be devoted to these first elements of trigonometry, a knowledge of which is useful for the execution of many practical works.

Common Curves.-Construction of an eclipse by points, and by a continuous

movement; tracing of a tangent and a normal; properties of elliptic mirrors; industrial applications of the ellipse and the ellipsoid; identical propositions on the hyperbole and the parabola; reflectors; movement of projectiles; suspen sion bridges; leveling (raccordement) of roads and canals. &c.; elliptical paraboloid; light-houses; ear-trumpets, &c.; oval; spiral; screw; helix, &c.

Descriptive Geometry. —Continuation and Conclusion. - All the diagrams (épures) should, as during the course of the preceding year, be drawn on a fixed scale; each theoretic question should be presented with numerical data, and should thus be transformed into an application, properly so called.

Surfaces in general; generation of surfaces by a line which changes situation and form according to certain laws; conic surfaces; cylindrical surfaces; surfaces of revolution; construction of tangential planes; to determine the shadows of a cylinder of revolution, of a cone (tronc de cone); intersection of two surfaces; application to the intersection of two cylinders of revolution of the same radius, and the axes of which meet; intersection of a cylinder and of a cone; ruled surfaces. Notions as to numbered plans; relation between this method and that of projections. Drawing plans; determination of horizontal sections. Outlines of perspective; to construct the perspective of different objects, such as a cross, a door with a flight of steps leading to it, &c., &c.

Many practical exercises, connected with all the parts of the course, should be gone through. The diagrams of descriptive geometry and the plans of buildings should be revised, valued, and signed by the professor.

MECHANICS.

Continuation and Conclusion.-The lessons should begin with a succinct recapitulation of the laws of the various kinds of motion, the action of the forces, and the transmission of motion in machines. Next, the motive powers commonly used in industry should be examined, viz., animals, water, steam, and wind. Lastly, after a short description of some special motors, the pupils should end with the study of the principal machines in use in the locality.

The professor should take care always to prepare the minds of the pupils by some experimental demonstrations, and by the explanation of the mechanical facts which they may have had opportunities of observing.

He should also place before them small models of machines, for the colored engravings do not suffice to show the play and the functions of the various organs which they represent.

These models should, besides, be used in the drawing-lessons of this year's course. Free-hand sketches (numbered) of them should first be made, thereafter an exact representation with aid of rule and compass, the effects of light and shade being washed in.

The programme of this course, like that of technical chemistry, should vary according to the special industry of each locality; thus the pupils should study, as the case may be, machines employed in metallurgy, or those used for the manufacture of textile fabrics, or for navigation, or in agriculture, &c., &c.

The professor should, therefore, consult the principal manufacturers, &c., of the place before drawing up his programme, and should afterwards present it to the Conseil de Perfectionnement for examination and approval. It should subsequently be published by the rector in the journals of thé department.

PHYSICS.

Recapitulation and Complement.—Some parts of this science present considerable difficulties; it is good, therefore, to go over the same ground several times. The professor should repeat, and at the same time complete and develop certain theories, such as those of heat, of light, and of optical instruments, besides certain points which may not have been thoroughly understood. But the lessons should retain their elementary and purely experimental character. At the end of the course applications should be made, if desirable, to the requirements of the local industry, by taking determinate examples, and submitting to numerical calculation the elements of some industrial undertaking of the kind most common in the locality.

Lastly, recent discoveries of utility or interest should be descanted upon.

CHEMISTRY.

Technical Chemistry applied to the industry of the locality.-The instruction given during this year should be practical, industrial, and appropriate to the requirements of the locality. At Caen and Chartres, for instance, agriculture and manures should be the subjects of study; at Creil, Sarrequemines, Toulouse, Limoges, &c, porcelain and pottery; at Cahors, Dijohn, Bordeaux, Cognac, Montpellier, &c., the making of wine, and the distillation of spirits; at Rouen, Mulhouse, Lyons, Saint-Etienne, Vienne, Lodève, &c., the processes of dyeing; at Amiens, Valenciennes, and Lille, the fabrication of sugar; at Alais, Creusot, Langres, and Nancy, metallurgy.

The programme of the course in each of the special schools should be prepared by the professor, submitted to the Conseil de Perfectionnement, and published by the rector, as mentioned with respect to the course of mechanics.

Part of the Thursday morning and Sunday afternoons are devoted to manipulations, and to visits to the principal industrial establishments in the environs.

NATURAL HISTORY, Applied to AGRICULTURE, INDUSTRY AND HYGIENICS. Zoology. The professor should treat of animals as the producers of alimentary substances; consequently of the breeding and fattening of cattle, sheep, &c.; next he should consider the animals as producers of motive power, &c. The structure and growth of the hair will furnish him with opportunities for speaking of furs and wools, and of the trade of the nations of the far north, of the influence of climate and seasons on the fur of animals; he should descant upon the horny substances, the mode of their formation, and the uses to which they are put; hoofs, horns, tortoise-shell, whalebone. He should terminate with the history of insects, useful or hurtful to agriculture; on the one hand the ichneumons, and the other parasites; cantharides, cochineal, silkworms, bees, &c.; on the other hand wasps, grasshoppers, weevils, caterpillars, and the insects which attack the vines and the olive trees.

The course of botany should continue this year with respect to the monocotyledons and the rest of the vegetable kingdom, that which was done with respect to the dicotyledons during the course of the preceding year. Cereals, the vegetation of the prairies, the sugar-cane, palm-trees, and their various and important products, should be studied during the first lessons. The acotyledons furnish an opportunity of narrating to the pupils many interesting details

regarding lichens and their alimentary and coloring properties, respecting seaweeds and their uses in agriculture, concerning edible and poisonous mushrooms, truffles, rush, and other diseases of vegetables caused by parasitical fungi. The professor should continue to encourage the pupils to collect as great a number of plants as possible, and should assist them in analyzing the principal organs, and determining the families, the genera and the species to which the plants belong. Some of the regular walks should be exchanged for herborizations, which should not be directed so much towards gathering a great number of different species, or exploring a great extent of country, as towards studying minutely a limited portion of the country, and determining with care the plants which compose the local flora, or which are cultivated there.

The course of geology should be completed by some notions of meteorology, which ought to have a place in the system of special instruction. The sea and the composition of its waters, the atmosphere and its perturbations; the study of the winds, and of the clouds, of climates, and their influence on the geographical distribution of the various plants: orange trees, olive trees, vines, cereals, fruit trees, forest trees, &c., &c.

The science of hygienics is a complex one, which demands a knowledge of several other sciences, viz., of chemistry, physics, and physiology. The pupils of the special schools should not therefore go through a complete course of hygienics, but should merely be taught the principal results to which the study of this science has led. The part played by alimentation; the influence of age, of rest, of labor on the organism; the exigencies of a wholesome alimentary regimen; the dangers of the use of alcoholic drinks; suspended animation; assistance to be given to persons suffering from asphyxia; the ventilation of dwelling-houses and of stables; the dangers of unhealthy dwellings; statistics showing the gradual increase in the average duration of life in France, which has taken place in proportion to the increase in the general well being.

COMMERCIAL ACCOUNTS.

The course of the first three years is calculated to form bookkeepers; the object of the fourth course is the study of accounting (comptabilité) properly so called. The instruction herein should enable the young men to establish systems of account for all kinds of commercial and industrial undertakings; it teaches them to open books, to draw up inventories, and to understand later how the operations of merchants, commission agents, bankers, &c, are combined; summary explanation of the knowledge necessary for a banker; calcu lations of commission; examples of fictitious operations, for the purpose of showing how the accounts between a merchant and his agent are established and regulated; making up of merchants' and bankers' balances; organization of the documents, and of the auxiliary books of bankers, shipowners, &c., &c. Lastly, establishment of a general system of accounts, comprising the opera tions of bankers, of shipowners belonging to various countries, who fit out vessels, send them on voyages, engage in commercial transactions with each other, and draw up their inventories. Finally, some notions of our financial system, and of the institution of the Cour des Comptes (Court of Accounts).

DRAWING.

Free-hand drawing of trees, ornaments, flowers, animals, and plants from

nature; many exercises from memory, some original compositions, and a certain number of drawings from casts: some of these drawings may be done in outline with the pen, and shaded with a brush.

During the lessons in geometrical drawing, the pupils who have already learnt to make plans of separate pieces of machinery should draw from sketches previously made by themselves, entire machines on a given scale.

They should also copy drawings suited to the industry of the locality, such as designs for silk textures at St. Etienne, for laces at Puy, &c., &c.

Pupils who show a decided talent for sculpture, may also do a little modeling in clay from bassi-relievi in plaster.

All the models should be selected by the Conseil de Perfectionnement.

GYMNASTICS.

Running and marching, with accompaniment of singing, and other exercises, as in the preceding courses.

SINGING.

Continuation of the sol-fa exercises, of musical dictations, singing in unison, and in two, three, and four parts.

Elementary notions of harmony; principal consonant and dissonant accords; their fundamental position; their reversal; their connection; shorthand annotation of harmonies, numbered bass.

Cadences: perfect, imperfect, broken, &c.; suspension; use of pedals.
Accompaniment to singing.

Studies of sacred music; differences between the modes of music and the modes of church music; notions of plain song; musical plain song; execution of some pieces of Palestrina, Handel, &c.

Abridged history of music; æsthetical ideas resulting from the analysis of a few works of modern dimensions selected from the Italian, French, and German schools.

DURATION OF THE LESSONS AND EXERCISES.

The pupils who enter the preparatory course, are, on an average, twelve years of age; it is, therefore, necessary that the school day should be divided among short and varied exercises, that the young minds may not be fatigued, and that their attention be kept ever alive. Each lesson in class, as also the subsequent preparation for lessons (études) ought not to last longer than one hour; the tasks given should not be longer than that they may be completed in this time.

In all the schools of central Europe it is admitted that the attention of children can not be kept up for two consecutive hours, and that if professors have to speak during such a period of time, they can not do so without considerable fatigue. Even in France in some large private establishments and in the lycée of the Prince Imperial, the practice of shorter lessons in class has been introduced; experience has, therefore, already been gained.

But whatever may be the duration of a lesson, the pupil will derive but little benefit from it if it be not immediately followed by a time of study during which he may repeat to himself and reflect upon the subject treated by the professor, make the manipulations indicated in the class, write an appropriate theme, or prepare the exercises, or interrogatories which have reference to the lesson.

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