suffer, nay, even advise their children to chose the identical ignis fatuus which has lured them on "o'er moss and fell," through tangled brake and oozy swamp all their lives.

C-But what more can be done for Clarence than has been done? You can not make a sober, sedate, model boy of him,— such a one as we read of in the Sunday School books. Take his fun and jokes away, and he would be the stupidest fellow in town. Science has not yet discovered how to make an owl out of a parrot.

M.-Who proposes to do that? I certainly do not. Instead of endeavoring to repress his fancy and imagination, I would prune them of their wild luxuriance, and train them for use, not show. They are the only faculties of his mind yet developed. The true course is to make him submit to parental authority: force him, if necessary, to forsake his disreputable haunts and evil associations: place him where all the faculties of his mind would be disciplined by proper incentives, judicious restraint, and hard study. His habits are formed, but not confirmed. He may try for a time to free himself from the strong hand which holds him firmly in its grasp; but each day his struggles will become weaker; his active mind will learn to seek enjoyment in the new objects with which he is surrounded; his chastened fancy will spread its wings in a purer atmosphere, and his imagination learn to rear structures replete with symmetry and beauty. This can not be done in our shop. The school is the place for him. The groveling utilitarianism which begrudges the time and expense of training and disciplining his untamed nature, is the result of either the most stupid ignorance or the most miserly parsimony.

Parenthood is a holy thing. Jones ignores his plainest demands-thoughtlessly, ignorantly, I trust. How can he look his boy in the face without a sinking of the heart, from contrition, amazes me. Should you and I ever hear the patter of little feet in our own homes, may God's grace give us wisdom to teach them how to walk in right paths.

AN institution for training men to train the young would be a fountain of living waters sending forth streams to refresh present and future ages.-Dr. Channing.

HOW TO TEACH NOTATION.

BY PROF. A. SCHUYLER.

In presenting this subject to a class, it is important first to give the pupils a clear idea of a unit. This idea is best conveyed to the mind by presenting some single object to the eye. A variety of objects should be presented, one at a time, till the idea is clearly apprehended that unity is not the exclusive characteristic of any one object in particular, but that it is a property of every single object. In a similar manner, the idea of two, three, etc., should be made clear to the mind.

We have found by experience that dots on the blackboard are the best objects for illustration, since they are in full view of the class, and an unlimited number can be made. Thus, the single dot (.) will be the primary unit, which we will call a unit of the first order and denote by the figure 1. Then two dots (..) will be two units of the first order, which we will denote by the figure 2. Let this number be analyzed thus, pointing to the dots: 2 1 and 1. In like manner, three dots (...) will be three units of the first order, which we will denote by the figure 3. Analyze thus: 32 and 1 or 1 and 2, or 1, 1 and 1. In a similar way, the numbers up to nine should be represented and analyzed.

=

The definition of number may now be given, thus: A number is a unit or a collection of units. The absence of number is denoted by the figure 0, called a cipher, naught, or zero.

Let now the blackboard be cleared, and the question asked: How many dots are on the board? Not any, will be the ready response. How can this fact (the absence of dots) be denoted? By the zero, thus: 0.

The preceding will be sufficient for one lesson.

Let the following be written on the board, and analyzed in the review:

0

2

If we should go on in the same way for the succeeding numbers, arranging the dots in rows and denoting the number in each row by a single figure, we should find that an indefinite number of figures would be required. This method is evidently impracticable.

The difficulty is obviated by the following artifice: Let us call a row of ten dots a full or complete row, thus:

How many rows have we here? One.

The one dot we called a unit of the first order, and the one row we shall call a unit of the second order.

We shall write units of the first order in the first or right hand place, and units of the second order in the second place, just at the left of the first place. IIow then is the one row of dots to be denoted? Since it is a unit, we shall denote it by the figure 1; but this notation alone would not distinguish it from the dot, we therefore write the 1 in the second place, and since we have but the one row and no more dots, we fill the first place with the 0, thus 10, which denotes one unit of the second order.

Eleven dots are arranged and denoted thus:

and one of the first.

11, which is one unit of the second order

Twelve, thus:

12.

Twenty dots would form two units of the second order, or two rows, thus:

20.

Let now the pupils be required to express, in dots, the numbers denoted by the following expressions: 1, 2, 3, etc.; 10, 11, 12, 13, etc.; 20, 21, 22, etc.; 30, 31, 32, etc.; 40, 41, 42, etc., etc., etc. Let the dots also first be made, and then required to be denoted by the proper figures.

If the question, Why were just ten dots taken to form a complete row? is not asked by the scholars, it should be by the teacher. There is no necessity in taking this number, for any other number might have been taken. This forms an excellent opportunity for the teacher to point out the distinction between a necessary principle and that which is merely conventional. But

there is undoubtedly a reason why ten units of the first order, rather than any other number, were taken to form one unit of the second order. It probably originated in the practice of counting by means of the fingers and thumbs.

The above will be sufficient for the second lesson.

Suppose now we have dots just sufficient to form ten rows, we' would arrange them into a square, thus:

How many squares have we here? One. This one square is then a unit, but it is neither a unit of the first order (a dot), nor a unit of the second order (a row of ten dots), but ten such rows, forming one square. We therefore call it a unit of the third order, and denote it thus, 100. The naughts in the second and first places denote the absence of rows and dots in addition to those in the square. This gives a clear idea of one hundred.

Let now the scholars be required to express in dots the numbers denoted by the following expressions: 100, 101, 102, etc.; 110, 111, 112, etc.; 120, 121, 122, etc., etc.

Let the dots also be first written, and required to be denoted by the proper figures. This will be the proper limit for the third lesson.

If we have ten units of the third order, or ten squares of dots, we place the squares, side by side, thus forming a rectangle of dots, and this will be a unit of the fourth order, denoted thus, 1000. It will not be necessary actually to make this rectangle of dots on the board, for the imagination, which ought to be cultivated, will readily form the correct picture of it in the mind, and when this is done, the mind will have a true conception of one thousand.

Ten of these rectangles would form a larger square, or a unit

of the fifth order, denoted thus, 10,000, and of this, the imagination is to form the picture, which will be the true conception of one ten thousand.

Ten of these squares will form a larger rectangle, or a unit of the sixth order, denoted thus, 100,000, and of which the picture. formed by the imagination will be the true conception of one hundred thousand.

Ten of these larger rectangles form a still larger square, or a unit of the seventh order, thus denoted, 1,000,000, of which the picture formed by the imagination will be the true conception of a million.

This process might be continued to any extent, and it will be found that every unit of an odd order is a square, and every unit of an even order a rectangle. The names of these orders of units should now be given, thus: Units, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, billions, etc.

It will be observed that ten units of the first order equal one of the second, ten of the second, one of the third, etc., and in general, ten units of any order equal one unit of the next higher order, and conversely, one unit of any order equals ten units of the next lower order.

Time will be required thus to teach, but the practice of hurrying classes over subjects so rapidly that it is impossible to understand them, can not be too severely reprehended.

COMPARATIVE GEOGRAPHY.

BY T. E. SULIOT.

'Geography can just as little be contented with being a mere description of the earth and a catalogue of its divisions, as a detailed account of the objects in nature can take the place of a thorough and real natural history."—Ritter's Comparative Geography.

Within the present generation, great improvements have been made in the teaching of geography in our schools. Many years ago, in his report of his educational tour through Europe, Horace