the lead as the great and indispensable foundation of all learning. It is not only impossible to dispense with them, but impossible to place them anywhere else than at the beginning of all intellectual education. No man can possibly attain to the knowledge of anything in the world without first attaining some mathematical knowledge or power. That mathematical knowledge may have been gained unconsciously, and may not have arranged itself in a distinct scientific form in his mind; but it must be there, for there cannot possibly be any intellectual life whatever upon our planet which does not begin with a perception of mathematical truth. A natural method of education requires us therefore, to pay our earliest attention to the development of the child's power to grasp the truths of space and time.

Mathesis would naturally divide itself into three great branches, treating of space, of time, and of number. Geometry unfolds the laws of space; algebra those of time; and arithmetic those of number. Other branches of Mathematics are generated by the combination of these three fundamental branches. Now, geometry, arithmetic, and algebra, should be taught in a natural order. There is a difficulty in deciding, simply from the logical sequence, what that order is, because the fundamental ideas of the three studies are so nearly independent of each other. Pure algebra, as the science of time, cannot, however, be evolved without reference to number and space; it will, to say the least, in the very process of its evolution, generate arithmetic. But geometry can be evolved without the slightest reference to time, although not, to any extent, without reference to number. The idea of number is one of the earliest abstractions from our contemplation of the material world.

The relative order in which these studies should be pursued will, however, be made more manifest on reference to the order of development of the child's powers. Number, though an early abstraction from phenomena in space, is a much higher and more difficult conception than conceptions of form. The child recognizes the shape of individual things long before he can count them, and geometry should therefore precede arithmetic in his education. But time is much more difficult of comprehension than space, it requires a riper effort of the mind to conceive of pure time without events, than of pure space without bodies. The latter remains, so to speak, visible to the mental eye; the former does not even in imagination address any of the senses. Geometry is, therefore, the first study in an intellectual course of education; generating and leading to arithmetic, and through that to algebra; preparing the way also for Physics, and thus for History, Metaphysics, and Theology. We must begin intellectual education

with geometry, leading the child through other studies as rapidly and in such order as the amount of his geometrical knowledge justifies and demands. Some knowledge of geometry is gained by an infant within a week of its birth; and when it first comes to school it has usually gained at first hand from nature a sufficient knowledge of the laws of space to serve as a basis for a good deal of other information picked up here and there.

If, now, we consider the order of subdivision in physical study, we shall find here, also, three principal departments of science; mechanical, chemical, and vital. The laws of color, sound, odor, and flavor, may appear at first sight irreducible to either of these three divisions; but a closer examination of the question will show us that this arises simply from an intermingling of psychological relations with the physical phenomena. The three divisions of Physics naturally follow each other as we have named them. Some knowledge of mechanics, that is, of the laws of force and motion, is necessary to any knowledge of chemistry, and some knowledge of chemistry and of mechanics is necessary for any thorough understanding of plants and animals. But it is evident that all knowledge of Natural History must begin with observation; and that one of the uses of the previous knowledge of Mathematics is to teach the child to observe with accuracy. The senses through which we observe material phenomena are, of all the human powers, the earliest to be developed, and should, therefore, be the first to receive a deliberate cultivation. Now, the mechanical relations of bodies, including color and sound, are those most obvious to sense; the chemical are more difficult of discovery, and the effect of vital powers can scarce be perceived without an interpretation from our own consciousness. Thus it is manifest that the order of arrangement in these three departments of Physics is conformed to the order of development of the human powers; and we may add that, in every subdivision of these smaller departments of science, the same principles of classification will give us both a theoretical and practical guide to the natural and most effective mode of teaching them; give first that which is most dependent upon direct perception, and, afterward, that which is more dependent upon an analysis of consciousness; give first that which is most nearly a simple function of space, and, afterward, that which demands the conception of time or of force.

we must

In attempting to subdivide the great department of History, we shall find difficulties arising from the complexity of the objects of human thought and action, and from the multiplicity of modes in which men have expressed their thoughts and emotions. But we are

inclined to make our primary division fourfold. In the first division we should place Agriculture, Trade, and Manufactures; in the second the Fine Arts; in the third Language and the history of thought; in the fourth Education, Politics, and Political Economy. That is, the first division should embrace the history of men's operations on material things to produce a tangible product; the second should treat of men's use of forms, colors, and tones, in the expression of thought; the third, of the expression of thought through words; the fourth, of men's action on each other.

In Psychology we might, perhaps, divide man into intellect, heart, and will, giving rise to intellectual, aesthetic, or moral and religious philosophy.

In Theology we should be obliged to feel cautiously our way by the light of Scripture. A natural division might be to consider the Divine Being as being first the Creator of the world, secondly the Father of all spiritual beings. The first would lead us to what is called, generally, Natural Religion, the second to themes more peculiar to Revealed Religion; the first would treat of the relation of the physical world to its Maker, the second of our own relation to Him.

Thus, out of the five great branches of learning, Mathesis, Physics, History, Metaphysics, and Theology, we have made, as a first essay toward a subdivision, fifteen classes, to wit: Geometry, Arithmetic, Algebra; Mechanics, Chemistry, Biology; Trade, Art, Language, Law; Intellectual Philosophy, Esthetics, Ethics; Natural Theology, Religion. We believe that all sound education gives, with or without the consciousness of the pupil and the teacher, instruction in all of these fifteen studies; and that there is no period of a child's life in which he ought not to be receiving direct instruction in at least some of the classes of study belonging to each of the five great branches. This instruction should be adapted to the child's age, consisting, at first, principally of those studies which come first upon our list, and of those which are named first under each branch; and giving only prophetic hints and foretastes of the higher parts of the course.

A true system of intellectual education would take the child at the age of five years and give it daily instruction in the simplest facts of geometry and arithmetic. Geometry should be taught at first without reasoning, simply as a matter of perception, either by diagrams, or, still better, by tangrams, bricks, geometrical solids, and simple models. for generating curves and curved surfaces. The latter would belong to a period five or seven years later in the child's life, when the imagination is to be exercised as well as perception. Arithmetic should

also be first taught by actual concrete numbers; nothing being better than a handful of beans. With these the properties of prime and composite numbers, the commutative principle of the factors in multiplication, and similar arithmetical truths, may be shown to very young scholars; and the laws of derivation or differentiation illustrated to older pupils. If there is any soundness in the views which we have given of the hierarchy of science, and of the development of the human powers, such works as Warren Colburn's inimitable First Lessons must not be the first lessons, but must be reserved to the age of twelve or thirteen years.

In the department of Physics, the child of five years should be trained in habits of observation. Every school for young children should have a cabinet of all the minerals common to the neighborhood of the school-house, and of all the most common plants, insects, and other animals, or, at least, good, well-colored drawings of them, — and the teacher should take frequent walks with the children, requiring them to look for natural objects, and name them according to the lists accompanying the cabinet, until the child can name, at sight, several hundred of the plants and insects of his native town. The attention of the pupil should be directed not only to the form, but to the color, odor, sounds, tastes, roughness, or smoothness, of the various objects. The simple mechanical powers should be illustrated by simple apparatus. Attention should also be directed to the most obvious chemical phenomena, such as the oxidation of metals, the burning of coal, &c. By the age of seven or eight years, geography must be taught; at first wholly from the globe, afterwards from maps and books. It is also important to give the child early ideas of the true nature of the sun, moon, planets, and stars; their size, motions, and relative distances. These Natural Sciences, which are usually reserved for the high school, are, in fact, especially adapted, in their rudiments, for the primary school; and if the main facts were set clearly before the child's mind, at the age of from eight to twelve years, they would enlarge and develop his powers, both of observation and of conception or imagination, and he would be much better fitted to study them logically at the age of sixteen or eighteen.

In the department of History there will be no call for special instruction until the age of seven or eight years. The scholar may then be taught to observe, in the fields and shops of the neighborhood, the modes of cultivation, the machinery and manufactures, the articles of commerce, and the modes of packing and transporting them. He must be encouraged also to draw, and to sing; the drawing being at first the simplest copying of the outlines of leaves, flowers, &c., and

the singing being at first simply by rote. Language he will have learned orally from his earliest years, but at the age of five or six he must be taught to analyze words into their phonetic elements, and a few weeks or months afterward be taught letters as the representatives of these phonetic elements. Spelling, in the ordinary sense, must be strictly avoided for some years, as it has a mischievous effect on the child's whole nature, slight and usually unnoticed, but real and mischievous, as far as it goes. In order to insure good habits of reading let a phonetic alphabet (books in the Cincinnati alphabet are most accessible) be used for at least two years, and let there be a daily drill in phonetic analysis and synthesis of words for four or five years. As for Law, its rudiments will be incidentally taught, sufficiently for so early an age, by the discipline of the school-house, by accidental references to political questions, and by the rules of honor in the games and sports of the playground.

In the fourth great branch of study, the teaching will, at this early age, be also incidental. The child will learn something of its intellectual powers, its tastes, and its obligations, from its attempts at study, at drawing and singing, and at keeping the rules of school. And in the fifth great branch of Theology the child of tender age must have his reverence for the Divine Being deepened, and his conceptions of His attributes enlightened, by being taught to look upon crystals, plants, and animals, as the workmanship of His Wisdom, - the pleasures of home and of the school-room as the gifts of His love, the actions of even children as pleasing or displeasing to Him in His holy oversight of men.

It would be tedious if we went on to greater length in defining the studies for each succeeding age, as we have defined them for pupils from five to seven years of age. We will, therefore, endeavor to show, in a tabular form, the order of study in each of the particular subdivisions of our five great branches. The left-hand column contains the age of the pupil, beginning with his entrance into the primary school at five, and ending with his graduation from college at twenty-two; the succeeding columns contain the studies. By the term incidental instruction, we signify that oral instruction which circumstances from time to time furnish the teacher an opportunity of giving, or that written teaching which the child will find in all the well chosen books that it reads at home or at school. This tabular view is not proposed as a Procrustean bed, but as a typical plan of studies, which should be somewhat modified by the circumstances and abilities of each student.