For their tasks the pupils should be given dumb maps, the names to be applied from memory, and maps to be copied. These copies should be true freehand sketches, without any scientific pretensions, and not manuscript editions of engraved maps, to produce which would be to lose much time in carrying out a false notion.

MATHEMATICS.

Arithmetic. Exposition, still elementary, but already in a certain degree based upon reasoning, of the four operations with whole and decimal numbers; study of fractions;-the metrical system; rule of three, rule of society, of interest, and of discount according to the method of reduction to unity; notions of relations and proportions. As tasks, numerous problems relating to common questions.

One part of the lesson should always be devoted to practice in mental calculation.

During this year also very difficult and delicate demonstrations should be avoided in these lessons, as also such synthetical and abstract definitions which ordinarily are merely retained by the memory.

So also in geometry, the teacher should admit as sufficient demonstrations by superposition, and should take evidence as his basis, whenever it is possible so to do. In a word, he should not forget that his pupils are of the age of four. teen or fifteen, and that they are destined for practical work.

Geometry. To trace from a given point as a centre, a circle which shall in tersect a straight line at a given point;-a circle which passes through three given points, &c. :—to divide an angle into two, four, &c., equal parts, &c.

The Inscribed Angle.-Measure of the inscribed angle;-every angle inscribed in a semicircle is a right angle;-to find a proportional mean of two given straight lines;-to raise a perpendicular on the extremity of a straight line which can not be prolonged, &c.

Tangents.-Every straight line perpendicular to the extremity of a diameter is tangent to the circumference ;-a tangent common to two circles;-bisector of the angle of two tangents:-application to the operations of the turner, &c. Circles being tangents to straight lines.-Concentric Circumferences.- Circles which intersect each other, or which touch each other.-Describe a circumference which passes through two given points, and is tangent to a drawn straight line, &c. The line of the centres of two circumferences which intersect each other is perpendicular to the common chord in its middle, &c. To draw cog-wheels which catch either into other cogged wheels, or into pinions, or into trundles, &c. Of the Triangle. The sum of the three angles of a triangle is equal to two right-angles, &c.

Of similar Triangles.-Two triangles are similar when the angles of one are equal to the angles of the other, &c.

Of Quadrilaterals.-The sum of the angles of a quadrilateral are equal to four right-angles, &c.;-of the symmetrical trapezium;-curved roofs, tenons, mortises, &c., are symmetrical trapeziums; of the lozenge and its properties; of the right-angle and the square; the facets of dice, the points of a backgammon board, &c.

Of Polygons.-Of regular polygons. To inscribe and circumscribe regular polygons on a circumference; to divide a given circumference into equal parts, &c.

Of Starred Polygons (polygones étoilés).—To deduct a regular, starred polygon from a regular ordinary polygon, &c.; equality of polygons; equality by symmetry; division of polygons.

Similarity of Polygons.-To draw a polygon similar to another. Making plans on the circumferentor (Lever des plans sur la planchette.) Application to the drawing of architectural roses, gothic crosses, &c.

Measurements.-Measurement of lines and surfaces. Surveying and leveling. The figures of which mention has been made in this course, all of which are much applied in arts and manufactures, should be drawn with rule and compass during the lessons in linear drawing.

It will be understood that, unless in exceptional cases, the professor of mathematics will not be able to take all his pupils into the country to carry out those practices in surveying which complete the course; but every Thursday, when the weather admits of it, some hours should be employed in practical operations in the grounds.

PHYSICS AND CHEMISTRY.

Preliminary Notions.—To awaken the curiosity of children, and to call forth in them the taste for observation, it will be sufficient that the professor should point out to them nature in full activity around them, and should fix their attention on the physical and chemical phenomena of which they are every day unconscious witnesses. He may also, without going beyond his subject, explain to them the use of the instruments and apparatus most commonly employed, and may fill his lessons with interesting experiments.

Physics. The first part of the year should be devoted to imparting to the pupils general notions of the most important properties of matter, such as weight, density, pressure, compressibility, and electricity; but he should take for his starting point phenomena known to the pupils, and should make them help to discover the explanations. Following up this rule, he should speak to them of dilatation, of fusion, of ebullition, and of conductibility; he should demonstrate by experiment the principle of Archimedes; he should explain the use of the barometer, of the pneumatic machine, and of the thermometer, and should conclude with the elementary phenomena of electrical statics. In conformity with the rules which are to guide these lessons, he should take care to derive the principle of Archimedes, of the barometer, &c., not from the properties of matter, looked at from an abstract point of view, but from the problems proposed to Archimedes by King Hieron, Galileo by the guardians of the fountains in Florence, &c.

Chemistry. Instead of commencing this preparatory course with the nomenclature, and an explanation of the diverse systems of crystallization, of definite and multiple proportions, &c., &c., the master should dwell on the number of chemical notions which the children have acquired from practical life, without being aware of it; he should endeavor to render these more precise, and teach the children to draw from them the most direct consequences, and he should point out to the pupils, by means of simple, inexpensive experiments, easy to reproduce, that there are bodies that are homogeneous, and others that are composite; that metals are indecomposable bodies, and that certain non-metallic bodies are in the same case; that chemists distinguish between acids, bases, alkalis, and salts; that heat liquefies and volatilizes; that there are fluids which

are liquid, and others that are viscous; that there are two kinds of dissolution -one that does not alter, and one that does alter bodies; that there are substances which are soluble, and others that are insoluble; finally, that to unite two bodies is to make a synthesis, and to separate two bodies is to make an analysis.

The instruction given this year should include neither measure nor number, but should be limited to simple ideas, which the master should endeavor to make comprehensible by means of lucid and well executed experiments.

NATURAL HISTORY.

The minds of the young people having been prepared by a more attentive observation of all that surrounds them, and their curiosity having been awakened by what they heard in the lessons of the preceding year, the professor should now commence a regular course of natural history, still keeping in mind that though his lessons are to be a little more scientific, he should not allow them to lose the character of interesting conversations. He should consequently endeavor to render science accessible, by concealing those of its features which might seem too abstract, while, at the same time, taking care that the details given should not suffer in accuracy; and he should fix the facts taught in the memory of the pupils by constantly referring to the phenomena observed in daily life, and which bear on the needs of domestic economy; finally, he should accustom the children to put order and method into their observations and their studies.

During the winter, the pupils should be occupied with zoülogy (vertebrata, principal mammals). After having imparted some general notions of the principal organs of an animal, such as the stomach, the intestines, the liver, the lungs, heart, &c., the master should fix the rules of classification: species, genera, families, orders, classes. Then a summary study should be made of the internal framework of the vertebrate animals. The principal differences should be pointed out which exist between animals having an internal skeleton: vertebrata covered with hair or fur, which are all mammals; vertebrata covered with feathers, which constitute birds; vertebrata with scaly skins, which are nearly all reptiles, amphibiæ, or fish. The groups of the most useful and the most interesting mammals should be dwelt upon, such as the quadrimana, carnivora, ruminants, and the principal aquatic mammals. A recapitulation of the natural classification of mammalia should then be gone through.

The demonstrations should be made as much as possible with the aid of stuffed animals, or of artificial parts of animals; or when this is not possible, with the aid of colored pictures of large dimensions.

The course should terminate with the history of man, and of the various human races.

In botany the professor should make known the external character and the principal organs of plants, the structure and the functions of the parts through which they derive their nutriment, and which cause their growth-root, stem, leaves. He should make a careful study of the parts that serve for reproduction-flower, fruit, seed. When examining the variations which each organ of the plant exhibits in accordance with its species, and with the diverse processes of culture, the professor should point out the uses to which those vegetable products are put which are employed in human industry. Roots, bulbs, and

edible onions; textile fibres derived from herbaceous stalks; woods, leaves serving for food and forage; flowers, fruits. The enumeration of all these affords an opportunity of instilling, by observation of common objects, all the most useful notions relative to the anatomy of plants, the composition of their tissues, and the laws which determine the relative disposition of their diverse organs, or of the parts of these,

In the course of geology, the particular tract of land in which the school is situated should be studied. The pupils should learn to distinguish the formations that surround them, to recognize the order of superposition and the differences of stratification in the different beds, the nature of the fossils found in them, and the deductions which may be drawn from these. Finally, during the excursions to which the study of this branch gives rise, the pupils should be practiced in collecting for themselves minerals of well defined character, in taking notes, and in making sketches of the arrangement of the rocks and the beds which they examine. Such personal observations enable them, in the following years, to understand by means of specimens, or of drawings, that which may be told them about countries and geological districts which they may not have an opportunity of examining directly.

COMMERCIAL ACCOUNTS.

Practical Exercises.-Explain that commerce is but a succession of exchanges: first merchandise for merchandise, in the beginning of societies, subsequently merchandise for money; peace and prosperity engender credit; sales to be paid in a given term; the accounts of each person then consists of what he owes, and of what is owing to him; meaning of the words debtor and creditor; active and passive; necessity of taking note of the sums to be received, and of the payments to be effected; what is understood by debiting and crediting; balance of accounts; balance to the debit, &c.

Synoptical table of the principal operations of commerce, buying and selling, forwarding merchandise, paying and receiving, to subscribe, to take, to nego tiate, &c.

An invoice, what it is, what is understood by the sum total, sale at so much per cent., remission of so much per cent., brutto weight, net weight, tare, show models of current accounts, of bills of exchange, and drafts to order; explain the meaning of the word drawer, drawee, indorsement, indorser, due date, mean date of payment.

The object of this elementary course is to teach the pupils to make some of the calculations which occur in commerce, and to write invoices, accounts of sales, bills of invoice, &c., in a word, to make them acquainted with all those details which constitute bookkeeping, properly so called. The professor should satisfy himself by numerous questionings, that all his explanations have been well understood; he should make the pupils practice a great deal by simulating simple operations, copying models of invoices, of drafts to order, of cheques, &c., he should also exact that the calculations and the writing should be executed very neatly and elegantly, and in consequence, that before any model is copied, all the results should be verified.

CALIGRAPHY AND DRAWING.

Continuation of the principles and practice, English handwriting, running

hand.

In the classes for linear drawing the notions of lines and surfaces, imparted in the course of the preceding year, should be recapitulated. Ordinary curves and conical curves should be drawn on the blackboard and explained. The exercises on paper should consist of mosaics, iron railings, balustrades, &c. Dull gray tints and black tints spread over the drawings should continue to be practiced, as the preparation for the coloring of solid bodies.

The imitative drawing should comprise architectural ornaments, and the human face. When the pupils are to copy an ornament or a face, a model in relief, of the same size as the drawing they have to execute, should be placed in the room, in order that they may constantly carry their eyes from the board to the model, and from the model to the board, so as clearly to understand what they are about. The models of graphic exercises on paper are inclosed in frames under glass, placed in front of each pupil so as to oblige the latter to draw them without taking any measurements on the model, and merely in accordance with the dimensions indicated in the text relating to each drawing.

This branch of instruction is one of those in which the greatest latitude is left to the teacher, as the lessons ought to be given with reference to the particular industry of the province. The programmes of the course of drawing, and the choice of models, are therefore left to the decision of the members of the Council of Improvement, who alone can have a sound judgment on the

matter.

GYMNASTICS.

Rhythmic movements, a little more sustained than the first series, and accompanied from time to time by a short and easy song, alternate movements with arms and legs accompanied by singing, jumping preceded by a run, jumping from a height not exceeding one metre thirty centimetres, exercises with dumb-bells on horizontal ladders or on oscillating lathes (perches oscillantes), &c.

SINGING.

Each lesson should open with exercises in solfaing. The master should sing out short musical phrases which the pupils should endeavor to reproduce. These phrases should never go beyond the extent of an octave. Towards the middle of the lesson the singing should be suspended for some minutes, during which the principles should be explained.

The musical tone, scale of tones, degrees, intervals, gamut, octave, means of representing tones by signs, notes, compass, the C clef, intonation, duration, time, simple time, f. 3, 4, breve, semibreve, minim, equivalent rests.

The lesson should conclude with a song sung in unison, and two-part choruses.

EXAMINATION PRELIMINARY TO ADVANCEMENT.

At the end of the first school year the pupils are subjected to an examination in all the subjects included in the courses which they have just finished, in order to prove that they are competent to take part in and profit by, those which are about to commence. The judgment of the examining professors, together with the reasons on which it is founded, is entered in minutes signed by them, and transmitted to the rector. The pupils are placed according to merit, In making out this list the work of the whole year is taken into account; the list of the places held by each pupil during each week are consequently taken into consideration, and a triple value is even attributed to the number