teacher to state the principle in a merely didactic form, but strive, even though the work may be slow and long, to guide the pupil in such a manner, by a hint here, and a question there, that he will do the very thing for himself. Though you are the teacher, aim to have your pupil become a self-educated man, a self-educated woman. You will find that every new achievement thus made gives your pupil hope, courage, strength, discipline. He will learn to direct his efforts to an important end. He will acquire a mental habit of immense value.

This is a point of so much importance, and includes so large a part of my subject, that a few familiar illustrations will perhaps be permitted chiefly from my own experience.

By a little aid, a class of pupils in arithmetic may be taught to trace out a common principle, where they usually find many, as they think, independent and unrelated principles. For instance, in one place they find simple addition, in another compound, in another addition of federal money, in another addition of common fractions, in another, that of decimal fractions; each having some technical terms, and modes of expression, which seem to separate it from the others. After having examined these separately, give the class for an exercise the construction of a rule which will comprehend them all. The first time I tried this experiment with a class of a dozen it failed. I resorted to the black board, put down an example of units, tens and hundreds to be added, also of pounds, shillings and pence, of dollars, cents and mills, of tens, units, tenths and hundredths, of tens, units, and twenty-fifths, being careful all the time to use similar phraseology, saying denomination or column of units,

tens-denomination of hundredths, tenths-denomination of twenty-fifths, &c. We added one or two different examples. Almost simultaneously the whole class caught the principle, and gave the following rule, with no further aid from me except one restrictive clause, "In all cases of addition, collect into one sum all the parts of each denomination, beginning with the lowest, and change the value, if large enough, into the next higher denomination by dividing by as many as make one of that denomination, retain the remainder, and add the quotient to that higher denomination." By a slight modification, the principle may be extended to the other elementary processes of arithmetic, and what is spread over fifty or a hundred pages of the text book, at last compressed into a few words. This is never forgotten, and rewards all their previous labor. In arriving at this result, their minds have been conducted through a process not unlike that which led Newton to announce the great law of attraction.

In various applications of elementary arithmetic, it often happens that the pupil may be led to discover a common principle, where on first observation, no resemblance, but seeming dissimilarity appears. Take, for instance, the 24th Section of Colburn's Sequel. How many questions apparently unlike, in all of which the pupil should be led to perceive simply this, a certain part, or number of parts given to find the whole. Do not leave the section, till your pupil can readily perceive, whatever may be his method of operating, that the simple thing to be accomplished in each case is, from some given part or parts of a number or quantity, to deduce the whole. Do not be afraid of the time it will take.

It requires time. It is worth all the time it requires. Delay upon it day after day, if necessary, till the thing is done;-till the fundamental idea is grasped by your pupils.

One fundamental idea, distinctly perceived and clearly apprehended, is worth an infinity of hazy, half-formed notions. Such are worthless, either as foundation stone to build on, or as materials to be wrought into the super

structure.

The one fundamental idea, fully apprehended, is prolific, and becomes, as has been truly said, a starting point for a thousand others. Take time then. There is too much to do to be in a hurry. Turn over the leaves slowly. Be not content to produce the raw material, and strew it along without form and void, leaving darkness on the face of the deep. Distil your materials; collect the concentrated essence, and throw away the chaff.

Parents and pupils are apt to be impatient of such delay, and to measure proficiency, by the superficial contents, rather than the cubic, by the quantity rather than the quality. I claim it as the teacher's professional prerogative to decide how fast or how slowly his pupil shall advance. This prerogative let him assert fearlessly, and exercise it with sound discretion. It may usually be done in a manner to make the pupil feel that he is profitably employed.

Having paid some attention in detail to the nature and agencies of heat, might not the teacher propose to his class to bring in, the next day, a written report of whatever cases they can collect, in which man employs heat as a helper in works of art?

The result would be an interesting enumeration of many artificial processes, in which the agency of heat is employed. The following record may be taken as a specimen.

1. Man uses the expansive power of heat to force the particles of water apart, and applies the steam thus generated to propel the steam engine. In this manner, with almost creative power, he produces and directs a force, which performs the most exquisite works of art, or puts forth more than giant strength to overcome the most formidable obstacles on land and sea. It performs half the work of civilized man. It overcomes wind, and tide, and oceans, and mountains.

2. Heat is employed for purposes of distillation, separating liquids which are mixed, by reducing to vapour that which is evaporated at the lowest temperature.

3. It is employed to warm houses, and ventilate them. The methods of warming are various; sometimes by radiation, as from the open fire-place, or the heated surface of a stove; sometimes by heating air in an air chamber in the cellar, which by its increased levity will rise through apertures in the floor, and diffuse itself through the room. Sometimes heat is conveyed latent in steam through pipes to all parts of large buildings, and given out again by condensation. It is employed to carry smoke away from fire. A portion of air is heated by the fire, and in its ascent carries off smoke. Air flues carried up by the side of smoke flues form an effectual mode of ventilation. An open fireplace is a good ventilator.

4. It is used in baking and boiling food.

5. It is employed to hasten many chemical pro

cesses.

Others continue to communicate.

same.

Several have the

Now call upon one and another to recapitulate, in the order in which the facts were stated.

This will be a motive, if any is needed, to attention. If you think best, let all record the reports in a blank book; not when given you want attention only then-but afterwards.

Habits of

This exercise was exciting and pleasant. observation were strengthened, some of the various ways in which a great natural agent is employed by man, made familiar. If this part of the subject is left here by the teacher, after a few remarks, it will not be left by the class, but will be a subject of conversation and reflection. Within the next twenty-four hours, as many more instances will be collected and garnered up, and remembered.

For the next day, direct their attention to a new field of observation. Let them collect phenomena, in which heat exerts an essential agency without the interposition of any human power to direct or to control it. They report as follows,

A. The sun heats the air by shining on it.

B.

I have the same fact, but explain it differently. The sun does not heat the air by shining upon it. Air and other transparent media are thought to transmit heat without absorbing it. I have come to the conclusion that the earth first absorbs heat from the sun, and then warms the air in contact with it. After a few words of