with a dry analysis of elements, which, in the | join these dots by lines; on doing which he teaching of language, has been exploded, is perceives that the lines he makes hide, or coto be re-instituted in the teaching of drawing. incide with, the outlines of the object. And The abstract is to be preliminary to the con- then on being asked to put a sheet of paper crete. Scientific conceptions are to precede on the other side of the glass, he discovers empirical experiences. That this is an inver- that the lines he has thus drawn represent sion of the normal order, we need scarcely the object as he saw it. They not only look repeat. It has been well said concerning the like it, but he perceives that they must be custom of prefacing the art of speaking any like it, because he made them agree with its tongue by a drilling in the parts of speech outlines; and by removing the paper he can and their functions, that it is about as reason- repeatedly convince himself that they do able as prefacing the art of walking by a agree with its outlines. The fact is new and course of lessons on the bones, muscles, and striking; and serves him as an experimental nerves of the legs; and much the same thing demonstration, that lines of certain lengths, may be said of the proposal to preface the art placed in certain directions on a plane, can of representing objects by a nomenclature represent lines of other lengths, and having and definitions of the lines which they yield other directions in space. Subsequently, by on analysis. These technicalities are alike gradually changing the position of the object repulsive and needless. They render the study distasteful at the very outset; and all with the view of teaching that, which, in the course of practice, will be learnt unconsciously. Just as the child incidentally gathers the meanings of ordinary words from the conversations going on around it, without the help of dictionaries; so, from the remarks on objects, pictures, and its own drawings, will it presently acquire, not only without effort but even pleasurably, those same scientific terms which, if presented at first, are a mystery and a weariness.

he may be led to observe how some lines shorten and disappear, whilst others come into sight and lengthen. The convergence of parallel lines, and, indeed, all the leading facts of perspective may, from time to time, be similarly illustrated to him. If he has been duly accustomed to self-help, he will gladly, when it is suggested, make the attempt to draw one of these outlines upon paper, by the eye only; and it may soon be made an exciting aim to produce, unassisted, a representation, as like as he can, to one subsequently sketched on the glass. Thus, without the unintelligent If any dependence is to be placed upon the mechanical practice of copying other drawgeneral principles of education that have ings, but by a method at once simple and atbeen laid down, the process of learning to tractive-rational, yet not abstract, a famildraw should be throughout continuous with iarity with the linear appearances of things, those efforts of early childhood described and a faculty of rendering them, may be, above, as so worthy of encouragement. By step by step, acquired. To which advantages the time that the voluntary practice thus ini- ald these:-that even thus early the pupil tiated has given some steadiness of hand, and learns, almost unconsciously, the true theory some tolerable ideas of proportion, there will of a picture-namely, that it is a delineation have arisen a vague notion of body as pre- of objects as they appear when projected on a senting its three dimensions in perspective. plane placed between them and the eye; and And when, after sundry abortive, Chinese- that when he reaches a fit age for commenclike attempts to render this appearance on ing scientific perspective he is already thorpaper there has grown up a pretty clear per- oughly acquainted with the facts which ception of the thing to be achieved, and a de-form its logical basis.

"A child has been in the habit of using cubes for arithmetic; let him use them also for the elements of geometry. I

It

sire to achieve it, a first lesson in empirical As exhibiting a rational mode of communiperspective may be given by means of the cating primary conceptions in geometry, we apparatus occasionally used in explaining cannot do better than quote the following perspective as a science. This sounds formid-passage from Mr. Wyse:able; but the experiment is both comprehensive and interesting to any boy or girl of ordinary intelligence. A plate of glass so framed as to stand vertically on the table, being placed before the pupil, and a book, or like simple object, laid on the other side of it, he is requested, whilst keeping the eye in one position, to make ink dots upon the glass, so that they may coincide with, or hide the corners of this object. He is then told to

stractions.

would begin with solids, the reverse of the usual plan.
saves all the difficulty of absurd definitions, and bad explana-
tions on points, lines, and surfaces, which are nothing but ab-
elements of geometry; it at once exhibits points, straight lines,
parallel lines, angles, parallelograms, etc., etc. These cubes
are divisible into various parts. The pupil has already been
familiarized with such divisions in numeration, and he now
proceeds to a comparison of their several parts, and of the
relation of these parts to each other.
From thence he

A cube presents many of the principal

...

advances to globes, which furnish him with elementary no- | propensity to cut out things in paper, to make, tions of the circle, of curves generally, etc., etc.

Being tolerably familiar with solids, he may now substi- to build a propensity which, if duly encour tute planes. The transition may be made very easy. Let the aged and directed, will not only prepare the cube, for instance, be cut into thin divisions, and placed on way for scientific conceptions, but will develdivisions: so with all the others. Globes may be treated in op those powers of manipulation in which the same manner; he will thus see how surfaces really are most people are so deficient. generated, and be enabled to abstract them with facility in every solid.

paper: he will then see as many plane rectangles as he has

"He has thus acquired the alphabet and reading of geometry. He now proceeds to write it.

The simplest operation, and therefore the first. is merely to place these planes on a piece of paper, and pass the pencil

round them. When this has been frequently done, the plane

may be put at a little distance, and the child required to copy

it, and so on."

When the observing and inventive faculties have attained the requisite power, the pupil may be introduced to empirical geometry; that is-geometry dealing with methodical solutions, but not with the demonstrations of them. Like all other transitions in education, this should be made not formally but incidentA stock of geometrical conceptions having ally; and the relationship to constructive art been obtained, in some such manner as this should still be maintained. To make a tetrarecommended by Mr. Wyse, a further step hedron in cardboard, like one given to him, is may, in course of time, be taken, by introduc- a problem which will alike interest the pupil, ing the practice of testing the correctness of and serve as a convenient starting-point. In all figures drawn by the eye; thus alike excit- attempting this, he finds it needful to draw ing an ambition to make them exact, and con- four equilateral triangles arranged in special tinually illustrating the difficulty of fulfilling positions. Being unable in the absence of an that ambition. There can be little doubt that exact method to do this accurately he discovgeometry had its origin (as, indeed, the word ers on putting the triangles into their respecimplies) in the methods discovered by artisans tive positions, that he cannot make their and others, of making accurate measurement sides fit, and that their angles do not properly for the foundations of buildings, areas of in- meet at the apex. He may now be shown how closures, and the like; and that its truths came by describing a couple of circles, each of these to be treasured up, merely with a view to their triangles may be drawn with perfect correctimmediate utility. They should be introduced ness and without guessing; and after his failto the pupil under analogous relationships. ure he will duly value the information. HavIn the cutting out of pieces for his card-houses, in the drawing of ornamental diagrams for coloring, and in those various instructive occupations which an inventive teacher will lead him into, he may be for a length of time advantageously left, like the primitive builder, to tentative processes; and will so gain an abundant experience of the difficulty of achieving his aims by the unaided senses. When, having meanwhile undergone a valuable discipline of the perceptions, he has reached a fit age for using a pair of compasses, he will, whilst duly appreciating these as enabling him to verify his ocular guesses, be still hindered by the difficulties of the approximative method. In this stage he may be left for a further period: partly as being yet too young for anything higher; partly because it is desirable that he should be made to feel still more strongly the want of systematic contri

ing 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 sceptically. 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 advan- | finding some of his own methods proved to be tage of self-development. A branch of knowl- true. Thus he enjoys what is to the unpreedge which as commonly taught is dry and pared a dreary task. It only remains to add, even repulsive, may, by following the method that his mind will presently arrive at a fit of nature, be made extremely interesting and condition for that most valuable of all exerprofoundly beneficial. We say profoundly cises for the reflective faculties-the making beneficial, because the effects are not confined of original demonstrations. Such theorems to the gaining of geometrical facts, but often as those appended to the successive books of revolutionize the whole state of mind. It has the Messrs. Chambers' Euclid, will soon berepeatedly occurred, that those who have been come practicable to him; and in proving them stupefied by the ordinary school-drill-by its the process of self-development will be not abstract formulas, by its wearisome tasks, by intellectual only, but moral. its cramming-have suddenly had their intel- To continue much further these suggestions lects roused, by thus ceasing to make them would be to write a detailed treatise on educapassive recipients, and inducing them to be- tion, which we do not purpose. The foregocome active discoverers. The discouragement | ing outlines of plans for exercising the percepbrought about by bad teaching having been tions in early childhood for conducting objectdiminished by a little sympathy, and sufficient lessons for teaching drawing and geometry, perseverance induced to achieve a first success, must be considered as roughly-sketched illusthere arises a revulsion of feeling affecting the trations of the method dictated by the genwhole nature. They no longer find them-eral principles previously specified. We beselves incompetent; they too can do some-lieve that on examination they will be found thing. And gradually as success follows suc- not only to progress from the simple to the cess, the incubus of despair disappears, and complex, from the concrete to the abstract, they attack the difficulties of their other from the empirical to the rational; but to satstudies with a courage that insures conquest.isfy the further requirements that education This empirical geometry which presents an- shall be a repetition of civilization in little, endless series of problems, and should be con- that it shall be as much as possible a process tinued along with other studies for years, may of self-evolution, and that it shall be pleasurathroughout be advantageously accompanied ble. That there should be one type of method by those concrete applications of its principles capable of satisfying all these conditions, tends which serve as its preliminary. After the alike to verify the conditions, and to prove cube, the octahedron, and the various forms that type of method the right one. And when of pyramid and prism have been mastered, we add that this method is the logical outmay come the more complex regular bodies-come of the tendency, characterizing all modthe dodecahedron, and the icosahedron-to ern systems of instruction-that it is but an construct which out of single pieces of card-adoption in full of the method of nature which board requires considerable ingenuity. From they adopt partially-that it displays this these, the transition may naturally be made complete adoption of the method of nature, to such modified forms of the regular bodies not only by conforming to the above princias are met with in crystals-the truncated ples, but by following the suggestions which cube, the cube with its dihedral as well as its the unfolding mind itself gives, facilitating its solid angles truncated, the octahedron and the spontaneous activities, and so aiding the devarious prisms as similarly modified; in imi-velopments which nature is busy with-when tating which numerous forms assumed by we add this, there seems abundant reason to different metals and salts, an acquaintance conclude, that the mode of procedure above with the leading facts of mineralogy will be exemplified, closely approximates to the true incidentally gained. After long continuance one. in exercises of this kind, rational geometry, as may be supposed, presents no obstacles. A few paragraphs must be appended in furConstantly 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

ther inculcation of the two general principles, alike the most important and the least attended to: we mean the principle that throughout youth, as in early childhood and in maturity, the process shall be one of self-instruction; and the obverse principle, that the mental action induced by this process shall be throughout intrinsically grateful. If progression from simple to complex, and from concrete to abstract, be considered the essential

requirements as dictated by abstract psychol- | duces. That it is thoroughly practicable to ogy, then do these requirements that knowl-carry out instruction after this fashion we edge shall be self-mastered, and pleasurably can ourselves testify; having been in youth mastered, become the tests by which we may thus led to successively solve the comparajudge whether the dictates of abstract psy- tively complex problems of Perspective. And chology are being fulfilled. If the first em- that leading teachers have been gradually Body the leading generalizations of the science tending in this direction is indicated alike in of mental growth, the last are the chief can- the saying of Fellenberg, that "the individons of the art of fostering mental growth. ual, independent activity of the pupil is of For manifestly if the steps in our curriculum | much greater importance than the ordinary are so arranged that they can be successively busy officiousness of many who assume the 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.

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."

But the making education a process of self- Similarly with the correlative requirement, evolution has other advantages than this of that the method of culture pursued shall be keeping our lessons in the right order. In the one productive of an intrinsically happy acfirst place, it guarantees a vividness and per- tivity,-an activity not happy in virtue of exmanency of impression which the usual meth-trinsic rewards to be obtained, but in virtue ods can never produce. Any piece of knowl- of its own healthfulness. Conformity to this edge which the pupil has himself acquired, requirement not only guards us against any problem which he has himself solved, be- thwarting the normal process of evolution, but comes by virtue of the conquest much more incidentally secures positive benefits of imthoroughly his than it could else be. The portance. Unless we are to return to an aspreliminary activity of mind which his suc- cetic morality, the maintenance of youthful cess implies, the concentration of thought nec- happiness must be considered as in itself a essary to it, and the excitement consequent worthy aim. Not to dwell upon this, how. on his triumph, conspire to register all the ever, we go on to remark that a pleasurable facts in his memory in a way that no mere state of feeling is far more favorable to intel information heard from a teacher, or read in lectual action than one of indifference or dis a school-book, can be registered. Even if he gust. Every one knows that things read, fails, the tension to which his faculties have heard, or seen with interest, are better remem been wound up insures his remembrance of bered than those read, heard, or seen with the solution when given to him, better than apathy. In the one case the faculties ap half a dozen repetitions would. Observe again, pealed to are actively occupied with the sub that this discipline necessitates a continuous ject presented; in the other they are inac organization of the knowledge he acquires. tively occupied with it; and the attention i It is in the very nature of facts and infer- continually drawn away after more attractive ences, assimilated in this normal manner, thoughts. Hence the impressions are respec that they successively become the premises tively strong and weak. Moreover, the intel <of further conclusions,—the means of solving lectual listlessness which a pupil's lack of in still further questions. The solution of yes-terest in any study involves, is further com terday's problem helps the pupil in mastering plicated by his anxiety, by his fear of conse to-day's. Thus the knowledge is turned into quences, which distract his attention, and in faculty as soon as it is taken in, and forth-crease the difficulty he finds in bringing hi with aids in the general function of thinking faculties to bear upon these facts that are re -does not lie merely written in the pages of pugnant to them. Clearly, therefore, the ef an internal library, as when rote-learnt. ficiency of any intellectual action will, othe Mark further, the importance of the moral things equal, be proportionate to the gratifi culture which this constant self-help involves.cation with which it is performed. Courage in attacking difficulties, patient con- It should be considered also, that importan centration of the attention, perseverance moral consequences depend upon the habitua through failures-these are characteristics pleasure or pain which daily lessons produce which after-life specially requires; and these No one can compare the faces and manners o are characteristics which this system of mak-two boys-the one made happy by mastering ing the mind work for its food specially pro- | interesting subjects, and the other made mis

erable by disgust with his studies, by conse- tion of knowledge has been rendered habituquent failure, by cold looks, by threats, by ally gratifying, then will there be as prevailpunishment without seeing that the disposi-ing a tendency to continue, without superintion of the one is being benefited, and that of tendence, that same self-culture previously the other greatly injured. Whoever has carried on under superintendence. These remarked 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 cannot 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, cannot 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."

sults 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 bygone 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.

CHAPTER III.

MORAL EDUCATION.

STRANGELY enough, the most glaring defect in our programmes of education is entirely overlooked. While much is being done in the detailed improvement of our systems in respect both of matter and manner, the most pressing desideratum has not yet been even recognized as a desideratum. To prepare the young for the duties of life is tacitly admitted by all to be the end which parents and schoolmasters should have in view; and happily the value of the things taught, and the goodness of the method followed in teaching them, are now ostensibly jugded by their fitness to this end. The propriety of substituting for an exclusively classical training a training in which the modern languages shall have a share, is argued on this ground. The necessity of increasing the amount of science is urged for like reasons. But though some care is taken to fit youth of both sexes for so

As suggesting a final reason for making ed-ciety and citizenship, no care whatever is ucation 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 schooldays 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 acquisi

taken to fit them for the still more important position they will ultimately have to fill--the position of parents. While it is seen that for the purpose of gaining a livelihood, an elaborate preparation is needed, it appears to be thought that for the bringing up of children, no preparation whatever is needed. While many years are spent by a boy in gaining knowledge, of which the chief value is that it constitutes "the education of a gentleman;