multiplication or division, they are left in a hazy mist of doubt and conjecture as to the right or wrong of the teacher's work. Now, I charge no blame upon the scholars, but upon their parents and teachers. Our common schools are the architects of the foundations upon which our academies and colleges are to raise superstructures, and if they are not upon the rock of correct fundamental beginnings, how can it be expected that the building will be easily reared, or finally established? Parents often dictate the position or study which they wish their children to take, where the teacher is the only proper one to dictate, for parents are always ambitious, and in their inordinate desire to see Johnny and Jimmy ciphering, or Sophia and Maria conjugating the verb "to love," they overlook the true attainments of their unintentionally abused children, while the teacher could look at the matter rationally, and without prejudices. Scholars have the idea that the sooner they are initiated into the mysteries of the slate and pencil the better, and their parents are ever ready to foster the propensity whenever they see it germinate.

Now, this is all wrong, for it is an incontrovertible fact that a thorough course in mental arithmetic is the best preparation a scholar can have for beginning any other branch of mathematical knowledge. By a thorough course of mental arithmetic, I do not mean the mechanical, hum-drum operations usually gone through in our common schools, but something more varied and extensive; something in which not only the tyros could be interested and instructed, but also the most advanced in school.

In our common schools it has become a mark of inferiority to be studying mental arithmetic; and how often do we see a fortunate or rather, unfortunate-little fellow just graduated from the mental arithmetic class, exulting over and taunting a knight of the homespun coat and jacket, who is a whole head taller than himself, just because he cannot cipher and domineer over a slate and pencil? There is no common school in this State in which a mental arithmetic class, embracing the whole school, would not be of immense benefit, and, saving the feelings of those who are dabbling in the higher mathematics and learned languages, it seems to me that not a little good might be done by a similar class, even in our academies. Some might be indignant, and feel imposed upon, inasmuch as they did not “ go away to school" to study mental arithmetic; but I will venture to say that after a week's trial they could be easily persuaded that the study, proper, was not any more for little boys and girls than for grown up ones. However much they may affect to despise the idea, facts warrant the assertion, that nine out of every ten need mental more than practical arithmetic. S. S. R.

MILTON, Nov. 5, 1859.

THE TRUE ORDER OF STUDIES.

BY PRES. HILL, ANTIOCH, OHIC.

(Continued from the November Number.)

To the second great division in the hierarchy of science we have given the name of Natural History. The word Physics might also have been used, but, in either case, the meaning of the term is to be so far extended as to include all the studies of the material world in its natural state. Inasmuch as matter is formed and governed in subjection to the laws of space and time, this study of the material world logically demands a previous knowledge of mathematics; and no natural phenomenon is understood until the geometrical or algebraical law, suggested and exemplified by it, has been, at least partially, comprehended. In proportion as the scholar's knowledge of mathematics is enlarged, his power of comprehending the physical universe is increased. And, inasmuch as a knowledge of geometry is the earliest mathematical acquirement, those parts of natural history which depend upon the perception of forms may be earlier acquired than those which depend on mechanical, chemical, or physiological considerations.

Thus, although the fundamental principle of our classification places. mechanics before chemistry, and chemistry before biology, our fundamental principles of education allow, and require, some instruction, in botany and zoology before any is given in chemistry or mechanics.

A perfect knowledge of animals requires a knowledge of the vegetable world, which is their food; a perfect knowledge of plants requires a knowledge of their chemical constituents, and of their chemical relation to the soil and to the air; a perfect knowledge of chemistry requires a knowledge of mechanical forces. Thus, in the hierarchy, mechanics is the first department of Natural History. But we must, of course, be understood as now giving to the word mechanies a much wider signification than usual. We are including the consideration of all those phenomena of nature that arise from mechanical laws, that is, from forces whose prime effects have been shown to depend on motion. A discussion of the boundary between mechanics and chemistry, showing, for example, why we place color under mechanics, and taste under chemistry, although interesting in a metaphysical view, and necessary for a clear understanding of the philosophy of our subject, will not be required in a purely practical consideration of the course of studies, such as we are now engaged upon.

There have lately been published several treatises on the philosophy of common things, some of which, although crowded with errors and puer

ilities, have a very extensive circulation. Others, free from these faults, are defective from their not containing the most fruitful facts and principles of mechanics. It is not surprising that text-books on these subjects should be grossly deficient, when we recollect that in geometry and arithmetic, the oldest and simplest sciences, it has been very difficult to find perfectly unexceptionable treatises, and still more difficult to find teachers · who will use the best books in the best manner. We trust that, through

the increasing attention now given to education, and especially through the influence of normal schools, recognizing teaching as a distinct and high profession, we may hereafter have better text-books upon all subjects and also teachers capable of teaching in the best way, even if the manuals for instruction should be imperfect. In all departments of Natural History the best text-books are the objects themselves, of which you would ¡teach

The earliest instruction of a child in the direct principles of mechanics should begin, we think, at the age of seven or eight years, and at first be incidental, that is, founded on the occurrences of the moment. In his use of little bricks for building, for example, he will have practical lessons, from which the teacher may deduce and render clear to the pupil some of the principal properties of the center of gravity, and of the state of stable and unstable equilibrium. In playing with marbles and balls, Opportunities occur for showing distinctly to a child the law of the composition of forces, the accelerating effect of a constantly acting force, the increase of momentum by the increase of velocity, and the like. The laws of elasticity, also, and of the reflection of motion, may be exemplified in the rebounding of balls, the return of echoes, and the use of mirrors. Of course, it will be worse than useless to give to the child simply stereotyped phrases, or vague and indistinct ideas, such as are too often found in popular text-books; but, if the teacher has himself clear ideas on these subjects, he will find the child eight or ten years old ready to receive them. Even the principal laws of optics, of acoustics and thermotics, may be incidentally taught. The optical toys, which are in almost every household, musical instruments, burning-glasses, and the phenomena of dew, rain, frost, and snow, will give the needed opportunities. Only let the caution be continually borne in mind, that it is much better to confess to a child your ignorance of a subject, than to attempt to give an answer to his question while your own views are ill-defined and unsatisfactory.

One of the earliest studies, commencing, perhaps, at the age of seven years, should be geography. Let it be taught, at first, by the aid of a globe, without reference to maps. The immense magnitude of the earth will be apprehended by the child only when, in later years, he has traveled distances that have an appreciable ratio to the earth's circumference. At first he must be content with understanding accurately its form and motions. In describing these, the teacher should be careful to use the globe

only as an illustration, not as though it were the thing of which he is speaking, else the child will never transfer his conceptions from the globe to the earth. In the course of thirteen years' service upon a school committee we have never found a teacher who gave to the scholars a clear conception of the physical boundaries between the five zones, and but few who even attempted it. The differences of climate and the number of degrees of extent are taught, but the child does not know what appearances of the heavenly bodies decide the position of the tropics and polar circles. Nor do we find that scholars in general gain any clear conception of the actual direction of places. Their views, being derived from maps, are necessarily errroneous. From one of the Holbrook Co.'s globes a child can readily be made to see that a straight line from one point on the globe to another, would always go through a portion of the earth, so that to point directly towards any distant place he must always point more or less downward.

The following extract from the instructions of the school committe in Waltham to the teachers of the sub-primary schools will serve as an example of the mode of teaching geography: "Begin with the globe; set it where the sun may shine upon it; bring Waltham to the top, and make the north pole point to the north. Lay a marble on the top of the globe, and show them that the light and shadow on the marble and on the globe are similarly situated. Explain the roundness of the earth; that it is only a bigger globe, under the little globe, as that is under the marble; and that the light and shade fall on it as they do on the globe and marble, making night in the shadow, day in the sunshine. Give them vivid conceptions of the size of the earth, by showing them how small upon the globe would be the landscape visible from Prospect Hill; how near to the point which represents Waltham would be the point representing the distant Monadnoc. Show them in what countries the sun is then rising, and in what setting, and where it is vertical, by simple reference to the light and shadow on the globe; and, after an hour's attention to other studies or amusements, return to the globe, and show them how the light has traveled round. Show them, according to the season of the year, whether the north or south pole remains in light or shadow all the day. Repeat this lesson at all seasons of the year, but especially do not forget it at the equinoxes and solstices. Explain how reflection from the globe diminishes the intensity of the shadow on the marble, and the reflection from the window-seat partially enlightens the under side of the globe, while there is no window seat under the earth to reflect light upon China and New Holland. Make the amount of reflection from the windowseat more apparent to them by covering it alternately with a black veil and a white handkerchief. In like manner, although the globe will, after sunset, be in the shadow of the earth, there is no larger body below the earth to cast a shadow on our antipodes.

"Take your children occasionally to walk; go on the hills; show them

how the presence of a brook or river can be foretold from the extent of the valley, the nature of the soil, and the kind of vegetations, whether forests or grass; show them the roundness of the earth from the increasing dip of the horizon, as you ascend; make them perceive how beautiful the illusion by which we always exaggerate vertical heights, and under-estimate horizontal distances; call their attention to the differences in soils, and in the rocks, and point out the effects of soil and of location upon vegetation."

The earliest lessons in astronomy may be given at a very tender age. As by the globe in the sunshine the best illustration of day and night can be given, so the idea of the moon and her motions is best communicated by procuring a ball a little over one quarter the diameter of the globe, and holding it about one hundred and ten times its own diameter from the globe. If now the moon is visible when the sun is shining, let the pupil lay the side of his head upon the globe, while the teacher holds the ball at the proper distance, in such a position that, to the child, it shall appear to be just over the moon. The sunshine upon the ball will appear to him to be of the same size and shape as the visible part of the moon. The endeavor in astronomy, as in geography, should be to lead the child's mind away from the illustration to the thing illustrated. for this reason it will be with difficulty that the school-teacher can go in astronomy to any advantage beyond the relations of the sun, earth, and moon. In order to give clear conceptions concerning the planets, stars, and nebulæ, the teacher must meet the pupils in the evening, when those bodies are visible. But it is of so much importance that the child should have early a distinct conception of the relations of the solar systems that few teachers would be unwilling to perform this extra labor. Astronomy and geography are to be used as the most powerful of all studies to develop the imagination; that is, the ability to conceive clearly and distinctly unseen phenom

ena.

Chemical relations are more abstruse than mechanical. It requires some maturity of mind in order to distinguish chemical compounds from mechanical mixtures; and yet, at the age of nine or ten years, the simplest phenomena of chemical change begin to excite the child's curiosity; and it will be greatly to his advantage if that curiosity is gratified with correct explanations and sound 'principles, instead of being lulled by a plausible pretence of explanation. Oxidation, especially in the forms of combustion and rust, is the most prominent instance of chemical metamorphosis, and will afford to the skillful teacher the opportunity of giving, in what we have called an incidental way, many of the fundamental principles of chemical affinity, atomic proportion, atomic combinations, the stability or instability of chemical equilibrium, and so on. We acknowledge that this implies a large amount of intellectual life in the teacher; but one who is intrusted with the direction of these earliest movements of the expanding mind should be a person not only of some acquirements,