alteration in its shape? P. You have stretched it out,— it is longer than it was at first. T. Now I release it,now the stretching force ceases to act,-what do you now observe? P. It has returned to its original shape. T. This property is called elasticity, and the india-rubber is said to be elastic. Now tell me, in your own language, what you mean by the property of elasticity? P. That if the body be stretched out, and then let go (released) from the force, it will return to its original shape. T. True; but we may express the same thing thus: elasticity is that property whereby a body returns to its original shape after the force which has altered its shape is withdrawn.

DEFINITIONS OF FORM should be given in connection with the actual construction of the figures which we wish to define. As our geometrical definitions and postulates are based upon experience and observation, one of the first steps in mathematical instruction is to show how geometrical figures may be described in accordance with their definitions, and, at the same time, to aid the mind of the pupil in forming general or abstract conceptions of these figures. The best way of showing the possibility of drawing a perfect figure, is actually to draw it with a greater or less degree of accuracy, according to the conditions of its abstract definition. Thus, if we wish to give the definition of a circle, we should take a string and describe a circle with it, before the pupil, saying to him at the same time:- the figure bounded by this chalk line is called a circle; the fixed point about which the string revolves is called the centre of the circle; the length of the string, which constantly remains the same, is the radius; the chalk line itself, which forms the boundary of the figure, is called the circumference; and the line drawn through the centre, meeting the circumference on opposite sides, is called the diameter. Now what have you to say about the distance of the circumference of a circle from its centre? P. It is always the same. T. In other words, you would say, that the radii of a circle are all equal to one another. Now although this circle is not so perfect as it is possible to draw one,

yet you can tell me what a perfect circle is. P. A circle is a figure bounded by a line which is everywhere at the same distance from a point within it called the

centre.

In like manner the pupil should be led to give in his own language the definitions of the terms radius, diameter, circumference, &c. Without materially altering the language employed by the pupil, the teacher may find it desirable to improve or correct it.

Above all things, children should be accustomed to write their own ideas in their own language. The writing of the contents of a book is better than the study of a whole commentary upon it; and the writing of the subject-matter of a single page, often stimulates the appetite for learning more powerfully than the reading of a whole folio. On this subject Richter observes: "Since writing signifies but the sign of things, and brings us through it to the things themselves, it is a stricter isolator and clearer collector of the ideas than even speech itself. Sound teaches quickly and generally; writing, uninterruptedly and with more accuracy. It is certain that our representation is much more a mental seeing than hearing, and that our metaphors play far more on an instrument of colour than of sound, and therefore writing which lingers under the eyes must assist the formation of ideas to a much greater extent than the rapid flight of sound. The scholar indeed carries it so far, that, when he reflects, he really seems to read a printed page; and when he speaks, to give a little declamation out of a quickly and well written pamphlet. Let the boys write out their own thoughts sooner than copy yours, so that they may learn to exchange the heavy-ringing coin of sound into more convenient paper money. And let them be spared the writing-texts of schoolmasters, containing the praises of industry, of writing, of their master, or of some old prince; in short, subjects about which the teacher can produce nothing better than his pupils. Every representation without some actual object or motive is poison. I cannot understand schoolmasters! Must the man even

in childhood preach from the appointed Sunday text, and never choose one for himself from nature's bible? Something similar may be said about the writing of open letters (an unsealed one is almost inevitably half untrue) which the teachers of girls' schools require, in order, say they, to exercise their pupils in epistolary style. A nothing writes to a nothing: the whole affair, undertaken by the desire of the teacher, not of the heart, is a certificate of the death of thoughts, an announcement of the burning of the materials. Happy is it if the commanded volubility of the child, arising from coldness and addressed to emptiness, do not accustom her to insincerity. If letters must be forthcoming, let them be written to some fixed person, about some definite thing. But what need of 'so much ado about nothing,' since - not even excepting political or literary newspapers - nothing can be written so easily as letters on any subject when there is a motive for them, and the mind is fully informed of the matter."

CHAP. III.

CULTIVATION OF THE INTELLECTUAL FACULTIES, CONTINUED. -CULTIVATION OF THE FACULTY OF ATTENTION.

In all our exercises of the senses, the faculty of ATTENTION should be assiduously cultivated, by all the artifices which we may have within our power. The habit of directing the faculties promptly and intensely to whatever subject comes before them, lays the foundation of the intellectual character. This habit requires careful cultivation: all the pupils should be expected to concentrate the whole of their powers of observation on the subject brought before them; imperfect perception should be carefully guarded against, and erroneous conceptions promptly corrected; no subject should be dismissed until all its

legitimate points of interest have been fairly exhausted; and carelessness, lassitude, or indifference should never be permitted for one moment to exist. Besides the im

mediate benefits arising from such a course of education, it exerts a most momentous influence on the future characters of the pupils, -it decides, in a great measure, as Fellenberg observes, "whether they shall be superficial and desultory throughout life, or whether they shall maintain the contrary habits of application and accuracy with honourable perseverance." So much depends upon the faculty of attention, that its culture should form a leading subject of practical education.

To cultivate the faculty of attention, the effort on the part of the child must be voluntary. By constraint, you may get a child to learn the task you have assigned him; but by this exercise you do not cultivate his power of attention, - you have only stimulated the child to exertion by the fear of punishment, or it may be by the hope of reward. By displaying the wonders of nature or art to a child, you render his attention voluntary, and out of a passive servile creature you make an active selfdependent agent. The best means of cultivating the habit of attention, therefore, is to associate pleasure with the exertions of the pupil, especially the pleasure which flows from success.

We

To cultivate the faculty of attention our teaching should be suggestive; that is to say, we should always leave something for our pupils to work out themselves; we should never do anything for them which they can do for themselves; and whenever we assist them, it should be done in such a way as to lead them as speedily as possible to go on without assistance. should not seek to remove the fair difficulties which lie in a pupil's way, but rather teach him how to surmount them. Never do anything, says Abbott, for a scholar, but teach him to do it for himself. How many cases occur, in the schools of this country, where the boy brings his slate to the teacher, saying, he cannot do a certain sum! The teacher takes the slate and pencil,— performs the work in silence, brings out the result,

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returns the slate to the hands of his pupil, who walks off to his seat, and goes to work on the next example, perfectly satisfied with the manner in which he is getting on. Such a practice, obviously, cannot conduce to the cultivation of the faculty of attention.

We weaken the habit of attention, by requiring our pupils to study too many things at once, or matters which are above their capacity; by directing their minds too long to any one subject; by urging them up to, or beyond, the point of fatigue; or by repeating too frequently the same exercises without variation. Whenever an exercise becomes too easy or too monotonous for our pupils, it then ceases to engage their attention, and acts injuriously upon their minds by engendering habits of listlessness and indifference. When a child, for example, writes the whole page of a copy head, we generally find that the last line is the worst written.

A skilful teacher will sometimes turn to account the incidental circumstances, which are calculated to draw off the attention of his pupils from his lesson: a butterfly enters the schoolroom, in a moment all eyes are upon it; instead of scolding them for this apparent violation of order, he cheerfully enters into their thoughts and feelings, catches the butterfly, and forthwith gives them a conversational lecture upon their beautiful winged visitor. Faraday never lectures so brilliantly as when he happens to fail in making an experiment.

When children become wearied out with long or intense attention, their enthusiasm may often be revived by bringing in some fresh motive for exertion. Darwin thus happily illustrates this principle:-"A little boy, who was tired of walking, begged of his papa to carry him. Here,' says the reverend doctor, ride upon my gold-headed cane;' and the pleased child, putting it between his legs, galloped away with delight."

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On the cultivation of the habit of attention Miss Edgeworth observes: "Whatever is connected with pain or pleasure commands our attention: but to make this general observation useful in education, we must examine what degrees of stimulus are necessary for different