which the representations of the objects are to be drawn; E s is a small pin of wood, having a hole at the top to which the eye is applied, fixed at the distance of about 6 inches from the glass pane; the surface of the pane is covered with a thin coating of gum, for the purpose of retaining the chalk lines traced upon it. When any drawing is to be rubbed off, it is only necessary to warm the surface of the gum before the fire, so as to make it perfectly free from moisture, then lightly rub off the chalk marks with a silk handkerchief. Let the advanced pupils occasionally practise drawing from simple objects, with this simple apparatus, and they will insensibly acquire a knowledge of the principles and practice of perspective representations.

Model lessons on Drawing.

(1.) On the drawing of a Circle. I am going to show you how to draw a circle with the hand. Draw the

straight line B D equal to the length of the diameter of the circle which you wish to make. Find the middle or centre c of this line. Do you think that I have got the middle exactly? James Carter says that I have taken the point too much to the left. I think that he is right, therefore I shall place it a little further to the right. I must now look at your slates to see that you are all going along with me.

Through the centre c draw the straight line E C F, perpendicular to B D. Now, to which side does E F lean? Please, sir (we may suppose the pupil to answer), it leans

neither to the one side nor the other; that is to say, E F is at right angles to B D.

Teacher. How many right angles have we got here? Pupil. Four right angles.

Teacher. Now I am going to cut these right angles through their middles by two straight lines: thus we have GH and I J. Mark off C G, C E, C I. C H, and с J, each

equal to C D or C B. What will these distances be called? Trace the circle lightly through these points. Having done this, I must mend some portions before I attempt to draw the full line. I now proceed to finish off the circum ference. We may now rub out the lines of construction, just as a builder takes away his scaffolding after he has completed the house.

The teacher may now put a few questions relative to the various lines connected with the circle.

(2.) On the drawing of a Spiral. I am going to show you how to draw a spiral. Draw the dotted lines OD and o E at right angles to each other. With o as the centre, draw the concentric quadrants E F and A B of any convenient size; (what do you mean by concentric?)— mark off F K, K I, and I D, each equal to B F; then draw the semicircles B C D, F G I, D V K, and K I; which will be the spiral required to be drawn.

Teacher. Of what parts is the exterior spiral A B C D V K I composed?

Pupil. It is composed of one quadrant and three semicircles.

Teacher. What is the size of the semicircle B C D as compared with the semicircle D V K?

Pupil. The diameter B D of the first is double the diameter K D of the second.

WRITING.

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This branch of education may be thoroughly taught, in a common school, on the collective system. In conducting such lessons as writing, it is desirable that the master should exercise his classes, in all their movements, in habits of military precision and promptitude. In order to follow out the collective system in relation to this subject, the writing to be copied should be written by the master on the black-board, or large sheets containing copies should be suspended in front of the class. After the copy books and pens have been distributed, the master gives the order,—" open copy books;" then all the pupils in the class must obey the order at the same moment: the master may next say, "take up pens;" then all the pupils must, in like manner, promptly and exactly obey the order: he may next say, prepare to write;" every boy, in this case, must place his copy book and his own body in the proper position for writing, this position having been previously explained by the master; he may now say, "begin writing ;" and all the class commence their work at the same moment. Similar orders may be given when the pupils have finished the first line. The master must then rapidly inspect the copy books, giving a hint to each pupil as he passes him, and afterwards he will make some more enlarged remarks upon the writing, addressed to the whole class, as it generally happens that the faults of one boy are common to the whole class. We do not mean to say that an intelligent teacher will slavishly follow this plan, or indeed any other plan that might be proposed at the same time it should be observed, that the plan here given must contain the leading elements of every efficient plan which might be devised.

Every teacher will, of course, adapt the details of a plan to suit his peculiar tastes and habits of thought.

Mulhauser's method of writing seems to be well adapted for giving the first elementary lessons in writing; but the method should not be carried beyond its legitimate limits. In order to give a finish to writing, no method can supersede that of carefully prepared copy heads, such as those given by Butterworth, Foster, Story, and others.

PRACTICAL GEOMETRY AND MENSURATION.

The pupils should be taught these subjects after the collective system of teaching, followed up by individual exercises. Each pupil in the class should be provided with a pair of compasses, a ruler, and if possible a scale, having a diagonal scale of equal parts on one side, and a protractor on the other, and a little triangular square (see the author's Geometry and Mensuration). The master should be provided with a large pair of wooden compasses, having a chalk holder at the extremity of one of its legs; a long ruler; a large wooden protractor, which need not be very exactly made, and a large T square. He should construct his figures without the aid of any other instru

ments.

The master should draw the geometrical problem on the black-board on a large scale, taking care to excite the attention of the pupils in the class, time after time, by putting various suggestive questions to them, such as we have given in connection with the teaching of drawing, &c.

Familiar and common-sense expositions (without aspiring to strictness of demonstration) should be given relative to the methods of construction. In the same manner, the leading problems of mensuration should be taught.

A lesson on Geometry. Subject- A perpendicular, a right angle. Illustrative method. From the concrete to the abstract.

When a man stands upright, he stands perpendicular