at the apex. He may now be shown how by describing a couple of circles, each of these triangles may be drawn with perfect correctness and without guessing; and after his failure he will duly value the information. Having thus helped him to the solution of his first problem, with the view of illustrating the nature of geometrical methods, he is in future to be left altogether to his own ingenuity in solving the questions put to him. To bisect a line, to erect a perpendicular, to describe a square, to bisect an angle, to draw a line parallel to a given line, to describe a hexagon, are problems which a little patience will enable him to find out. And from these he may be led on step by step to questions of a more complex kind; all of which, under judicious management, he will puzzle through unhelped. Doubtless, many of those brought up under the old regime, will look upon this assertion skeptically. We speak from facts, however, and those neither few nor special. We have seen a class of boys become so interested in making out solutions to these problems, as to look forward to their geometry-lesson as a chief event of the week. Within the last month, we have been told of one girls' school, in which some of the young ladies voluntarily occupy themselves with geometrical questions out of school-hours; and of another, in which they not only do this, but in which one of them is begging for problems to find out during the holidays-both which facts we state on the authority of the teacher. There could indeed be no stronger proofs than are thus afforded of the practicability and the immense advantage of selfdevelopment. A branch of knowledge which as commonly taught is dry and even repulsive, may, by following the method of nature, be made extremely interesting and profoundly beneficial. We say profoundly beneficial, because the effects are not confined to the gaining of geometrical facts, but often revolutionize the whole state of mind. It has repeatedly occurred, that those who have been stupefied by the ordinary school-drill-by its abstract formulas, by its wearisome tasks, by its cramming-have suddenly had their intellects roused, by thus ceasing to make them passive recipients, and inducing them to become active discoverers.

This empirical geometry which presents an endless series of problems, and should be continued along with other studies for years, may throughout be advantageously accompanied by those concrete applications of its principles which serve as its preliminary. After the cube, the octahedron, and the various forms of pyramid and prism have been mastered, may come the more complex regular bodies the dodecahedron, and the icosahedron-to construct which out of single pieces of cardboard requires considerable ingenuity. From these, the transition may naturally be made to such modified forms of the regular bodies as are met with in crystals-the truncated cube, the cube with its dihedral as well as its solid angles truncated, the octahedron and the various prisms as similarly modified; in imitating which numerous forms assumed by different metals and salts, an acquaintance with the leading facts of mineralogy will be incidentally gained. After long continuance in exercises of this kind, rational geometry, as may be supposed, presents no obstacles. Constantly habituated to contemplate relationships of form and quantity, and vaguely perceiving from time to time the necessity of certain results as reached by certain means, the pupil comes to regard the demonstrations of Euclid as the missing supplements to his familiar problems. His well-disciplined faculties enable him easily to master its successive propositions, and to appreciate their value; and he has the occasional gratification of finding some of his own methods proved to be true.

Thus he enjoys what is to the unprepared a dreary task. It only remains to add, that his mind will presently arrive at a fit condition for that most valuable of all exci for the reflective faculties-the making of original demon

strations.

THE ACQUISITION OF KNOWLEDGE SHOULD BE A PROCESS OF SELF-INSTRUCTION AND CONTINUOUS PLEASURE.

15. If progression from simple to complex, and from concrete to abstract, be considered the essential requirements as dictated by abstract psychology, then do these requirements that knowledge shall be self-mastered, and pleasurably mastered, become the tests by which we may judge whether the dictates of abstract psychology are being fulfilled. If the first embody the leading generalizations of the science of mental growth, the last are the chief canons of the art of fostering mental growth. For manifestly if the steps in our curriculum are so arranged that they can be successively ascended by the pupil himself with little or no help, they must correspond with the stages of evolution, in his faculties; and manifestly if the successive achievements of these steps are intrinsically gratifying to him, it follows that they require no more than a normal exercise of his powers.

But the making education a process of self-evolution has other advantages than this of keeping our lessons in the right order. In the first place, it guarantees a vividness and permanency of impression which the usual methods can never produce. Any piece of knowledge which the pupil has himself acquired, any problem which he has himself solved, becomes by virtue of the conquest much more thoroughly his than it could else be. The preliminary activity of mind which his success implies, the concentration of thought necessary to it, and the excitement consequent on his triumph, conspire to register all the facts in his memory in a way that no mere information heard from a teacher, or read in a school-book, can be registered. Even if he fails, the tension to which his faculties have been wound up insures his remembrance of the solution when given to him, better than half a dozen repetitions would. Observe again, that this discipline necessitates a continuous organization of the knowledge he acquires. It is in the very nature of facts and inferences, assimilated in this normal manner, that they successively become the premises of further conclusions. The solution of yesterday's problem helps the pupil in mastering today's. Thus the knowledge is turned into faculty as soon as it is taken in, and forthwith aids in the general function of thinking-does not lie merely written in the pages of an internal library, as when rote-learnt. Mark further, the importance of the moral culture which this constant self-help involves. Courage in attacking difficulties, patient concentration of the attention, perseverance through failures-these are characteristics which after-life specially requires; and these are characteristics which this system of making the mind work for its food specially produces. That it is thoroughly practicable to carry out instruction after this fashion we can ourselves testify; having been in youth thus led to successively solve the comparatively complex problems of Perspective. And that leading teachers have been gradually tending in this direction is indicated alike in the saying of Fellenberg, that "the individual, independent activity of the pupil is of much greater importance than the ordinary busy officiousness of many who assume the office of educators;" in the opinion of Horace Mann, that 'unfortunately education amongst us at present consists too much in telling, not

in training;" and in the remark of M. Marcel, that "what the learner discovers by mental exertion is better known than what is told to him."

À pleasurable state of feeling is far more favorable to intel cual action than one of indifference or disgust. Every one knows that things read, heard, or seen with interest, are better remembered than those read, heard, or seen with apathy. In the one case the faculties appealed to are actively occupied with the subject presented; in the other they are inactively occupied with it; and the attention is continually drawn away after more attractive thoughts. the impressions are respectively strong and weak.

Hence

No one can compare the faces and manners of two boys-the one made happy by mastering interesting subjects, and the other made miserable by disgust with his studies, by consequent failure, by cold looks, by threats, by punishment— without seeing that the disposition of the one is being benefited, and that of the other greatly injured. Whoever has marked the effect of intellectual success upon the mind, and the power of the mind over the body, will see that in the one case both temper and health are favorably affected; whilst in the other there is danger of permanent moroseness, of permanent timidity, and even of permanent constitutional depression. To all which considerations we must add the further one, that the relationship between teachers and their pupils is, other things equal, rendered friendly and influential, or antagonistic and powerless, according as the system of culture produces happiness or misery. Human beings are at the mercy of their associated ideas. A daily minister of pain can not fail to be regarded with a secret dislike, and if he causes no emotions but painful ones, will inevitably be hated. Conversely, he who constantly aids children to their ends, hourly provides them with the satisfactions of conquest, hourly encourages them through their difficulties and sympathizes in their successes, can not fail to be liked; nay, if his behavior is consistent throughout, must be loved. And when we remember how efficient and benign is the control of a master who is felt to be a friend, when compared with the control of one who is looked upon with aversion, or at best indifference, we may infer that the indirect advantages of conducting education on the happiness principle do not fall far short of the direct ones. To all who question the possibility of acting out the system here advocated, we reply as before, that not only does theory point to it, but experience commends it. To the many verdicts of distinguished teachers who since Pestalozzi's time have testified this, may be here added that of Professor Pillans, who asserts that "where young people are taught as they ought to be, they are quite as happy in school as at play, seldom less delighted, nay, often more, with the well-directed exercise of their mental energies, than with that of their muscular powers."

As suggesting a final reason for making education a process of self-instruction, and by consequence a process of pleasurable instruction, we may advert to the fact that, in proportion as it is made so, is there a probability that education will not cease when school-days end. As long as the acquisition of knowledge is rendered habitually repugnant, so long will there be a prevailing tendency to discontinue it when free from the coercion of parents and masters. And when the acquisition of knowledge has been rendered habitually gratifying, then will there be as prevailing a tendency to continue, without superintendence, that same self-culture previously carried on under superintendence. These results are inevitable. While the laws of mental association remain true-while men dislike the things and places that suggest painful recollections, and delight in

those which call to mind by-gone pleasures-painful lessons will make knowledge repulsive, and pleasurable lessons will make it attractive. The men to whom in boyhood information came in dreary tasks along with threats of punishment, and who were never led into habits of independent inquiry, are unlikely to be students in after years; while those to whom it came in the natural forms, at the proper times, and who remember its facts as not only interesting in themselves, but as the occasions of a long series of gratifying successes, are likely to continue through life that self-instruction commenced in youth.

IV. WHAT KNOWLEDGE IS MOST WORTH.

THE RELATIVE VALUES OF KNOWLEDGE.

1. Before there can be a rational curriculum, we must settle which things it most concerns us to know; or, to use a word of Bacon's, now unfortunately obsolete we must determine the relative values of knowledges.

Had we time to master all subjects we need not be particular. To quote the old song:

"But we that have but span-long lives" must ever bear in mind our limited time for acquisition. And remembering how narrowly this time is limited, not only by the shortness of life, but also still more by the business of life, we ought to be especially solicitous to employ what time we have to the greatest advantage. Before devoting years to some subject which fashion or fancy suggests, it is surely wise to weigh with great care the worth of the results, as compared with the worth of various alternative results which the same years might bring if otherwise applied.

How to live?-that is the essential question for us. Not how to live in the mere material sense only, but in the widest sense. The general problem which comprehends every special problem is-the right ruling of conduct in all directions under all circumstances. In what way to treat the body; in what way to treat the mind; in what way to manage our affairs; in what way to bring up a family; in what way to behave as a citizen; in what way to utilize all those sources of happiness which nature supplies-how to use all our faculties to the greatest advantage of ourselves and others-how to live completely? And this being the great thing needful for us to learn, is, by consequence, the great thing which education has to teach. To prepare us for complete living is the function which education has to discharge; and the only rational mode of judging of any educational course is, to judge in what degree it discharges such function.

Our first step must obviously be to classify, in the order of their importance, the leading kinds of activity which constitute human life. They may be naturally arranged into:-1. Those activities which directly minister to selfpreservation; 2. Those activities which, by securing the necessaries of life, indirectly minister to self-preservation; 3. Those activities which have for their

end the rearing and discipline of offspring; 4. Those activities which are involved in the maintenance of proper social and political relations; 5. Those miscellaneous activities which make up the leisure part of life, devoted to the gratification of the tastes and feelings.

KNOWLEDGE REQUISITE TO SELF-PRESERVATION.

2. Happily, that all-important part of education which goes to secure direct self-preservation, is in great part already provided for. Too momentous to be left to our blundering, Nature takes it into her own hands. While yet in its nurse's arms, the infant, by hiding its face and crying at the sight of a stranger, shows the dawning instinct to attain safety by flying from that which is unknown and may be dangerous; and when it can walk, the terror it manifests if an unfamiliar dog comes near, or the screams with which it runs to its mother after any startling sight or sound, shows this instinct further developed. Moreover, knowledge subserving direct self-preservation is that which it is chiefly busied in acquiring from hour to hour. How to balance its body; how to control its movements so as to avoid collisions; what objects are hard, and will hurt if struck; what objects are heavy, and injure if they fall on the limbs; which things will bear the weight of the body, and which not; the pains inflicted by fire, by missiles, by sharp instruments-these, and various other pieces of information needful for the avoidance of death or accident, it is ever learning. And when, a few years later, the energies go out in running, climbing, and jumping, in games of strength and games of skill, we see in all these actions by which the muscles are developed, the perceptions sharpened, and the judgment quickened, a preparation for the safe conduct of the body among surrounding objects and movements; and for meeting those greater dangers that occasionally occur in the lives of all Being thus, as we say, so well cared for by Nature, this fundamental education needs comparatively little care from us. What we are chiefly called upon to see, is, that there shall be free scope for gaining this experience, and receiving this discipline, that there shall be no such thwarting of Nature as that by which stupid schoolmistresses commonly prevent the girls in their charge from the spontaneous physical activities they would indulge in; and so render them comparatively incapable of taking care of themselves in circumstances of peril.

KNOWLEDGE REQUISITE TO INDUSTRIAL SUCCESS.

3. While every one is ready to indorse the abstract proposition that instruction fitting youths for the business of life is of high importance, or even to consider it of supreme importance; yet scarcely any inquire what instruction will so fit them. It is true that reading, writing, and arithmetic are taught with an intelligent appreciation of their uses; but when we have said this we have said nearly all. While the great bulk of what else is acquired has no bearing on the industrial activities, an immensity of information that has a direct bearing on the industrial activities is entirely passed over.

For, leaving out only some very small classes, what are all men employed in? They are employed in the production, preparation, and distribution of commodities. And on what does efficiency in the production, preparation, and distribution of commodities depend? It depends on the use of methods fitted to the respective natures of these commodities; it depends on an adequate knowledge of their physical, chemical, or vital properties, as the case may be: that is,