It is said that amongst the superior classes of the Hindoos, it is customary to have in their dwellings a particular apartment, which is called "Knodhagara," or "the chamber of anger," and into which any member of the household who feels himself to be out of temper immediately retires, remaining there until solitude has calmed and tranquillized him. It would be very useful if every teacher could have his or her Knodhagara, for their temper is often severely tried; but as this cannot be, let them not commit the grievous error of converting the schoolroom into such an apartment.

Patience and good temper will achieve much, even with the leastpromising children, while hurry and irritation daunt the timid, harden the ill-disposed, and prevent our winning the affections of our pupils ; without which we may drive, but shall not be able to lead: and in such a position, when we cannot get to their hearts, it is of very little use to work at their heads.

Another point which is of great importance to a teacher's success, is, that she should maintain a spirit of cheerfulness. The schoolroom need not, and ought not, to be a sad place. A cheerful instructress will make her lessons interesting, and thereby gain the willing attention of her pupils; and, besides, she will insensibly infuse into them some of her own spirit. The mind of a young girl is easily impressible, and will generally take the tone of those she is with in early youth. We all know how depressing it is to the spirits to associate intimately with those who take a gloomy and discontented view of life; it seems to draw the sunshine out of our hearts. A teacher who is always discontented with her pupils' efforts, whose brow is gloomy, and on whose lips the smile of sympathy and encouragement is never seen to play, must produce a similar effect upon her scholars. A single word of encouragement, judiciously applied, will do more to stimulate a child to renewed exertion, than a long lecture. Thus, if we have to return a faulty exercise, and can say truthfully, "This is not right; but I can see you have taken pains; try again, and you will succeed at last," the disappointment in the child's mind is softened at once. She feels that her efforts, though unsuccessful, have been appreciated; and she will repeat them with renewed energy, determined not to lose the good opinion that has been formed of her.

It is most essential to maintain obedience in the education of the young. In little children this obedience must be of a passive character; but we should not allow it to continue so. As the reasoning faculties begin to expand, we should make them see the reasons for such and such modes of conduct, and seek rather to guide and assist them in judging for themselves than to wish that they should be blindly guided by us. Parents and teachers are sometimes apt to forget this, and the consequence is, that when death or other circumstances separate the connection between them, their pupils are cast upon the world like a vessel that has lost its helm, without any power of judging or directing their course aright in the new position in which they are placed.

It is very important also to inculcate early habits of careful and accurate observation. We should teach children to reason upon what they see, to inquire into the causes that produce certain results. The science of botany, so frequently a favourite study with girls, affords us

peculiar facilities for teaching this habit, as it requires great care and nicety of observation. This remark applies, however, in a greater or less degree to all studies. Nothing will be well accomplished that is done carelessly and inaccurately; and it would be well if all would apply to their conduct the old adage," Whatever is worth doing at all is worth doing well."

One other motto may also usefully be inculcated," Bear and forbear," as it will prove through life an invaluable assistant in the discharge of domestic and social duties; but to teach this properly, it must be exemplified by the teacher's own conduct in her intercourse with her pupils. Above all, she must plant in their minds a loving, trusting principle of religion as the mainspring from which they should act, and by which they should guide their thoughts and words, as well as deeds. C.

THE MATHEMATICIANS.

66
FROM THE MINING JOURNAL."

SIR,-Thanks to the perseverance of Mr. Jelinger Symons, we have at length a palpable instance, prominently brought forward to every sound capacity, of the ill effects wrought on the understanding by a too exclusive study of the sophistries of the calculus. It is now two centuries since this form of mathematics substituted in our universities the logic of Aristotle. It assumed a similar position as an exercise for the juvenile faculties, to prepare them for the business of life; and had it rested there, it would have been well; but, precisely like its prototype, it has been pursued further, and its professors have fallen into the very same error that Bacon exposed, and given a false resting-place to their minds, in the vain belief that any set of phrases or symbols wielded, selon les règles, in the seclusion of four walls, could open the secrets of nature and supply the place of reasoning, built upon the firm basis of physical facts, which can be obtained only by patient experimental toil, and by years-nay, centuries-of jealous observation and interrogation-not of fictions, but of realities. Nothing is more to be regretted than when powerful and acute minds, which under proper direction might do science service, are seen to be emasculated under the frivolities of a barren system. That the calculus has led to a neglect of geometry is an old complaint; yet few persons could have been prepared for the utter deficiency of correct geometrical conception exhibited in the authoritative denunciations by the Times correspondent and others of Mr. Symons's heresy. The simplest attention to the elementary definitions of points and lines would have prevented all this exposure. An act of rotation necessitates the consideration of only one mathematical point-the centre of the rotating system; an act of revolution necessitates the consideration of a second mathematical point, at an appreciable distance from the first, so that between the two points a line may be drawn. The second or revolving point may be a second centre of rotation, as in the case of the earth, or it may not, as in the case of the moon: the first evincing two motions, requiring two separate

forces; the second one motion, caused by one force. The whole controversy is as simple as the dispute whether there be any difference between the arithmetical numbers one and two. How, then, is it that intellects of the first calibre can have been led into the attempt to confound and identify such elementary differences as negative and positive, one and two, and make themselves appear, as Dr. Lardner has it, “ridiculously wrong?" Merely by the prejudice of system-a memorable instance that the wise are not always certainly wise. The simple mechanical facts, as they are, cannot be suffered to stand alone; they must be reconciled with "astronomy," as a certain collegiate theory is termed, which exists by and for the calculus. It having been assumed, about two centuries since, that the heavenly bodies, which by their distance, sublimity, and the magnitude of space, compared to our own littleness, stimulate the marvellous and the mysterious, and attract a peculiar attention, continue to move by an impulse, "impressed on them at some unknown period of time, it becomes necessary for the philosophers of this school to endeavour to subject all their movements, as well as they can, to the known conditions of projected bodies. It is this attempt which has induced that class who call themselves " professed astronomers" to strain themselves to the conclusion, that the path of the earth in its orbit with a double motion is not essentially different to the path of the moon in her orbit with a single motion. Both bodies must be furnished with the orthodox projectile twirl. Mr. Jelinger Symons has at length got in the thin end of the wedge before the face of a scientific association, and long before the end of this century we shall see that gigantic delusion, the theory of the perpetual motion of the planets, under the influence of a forceless force, shattered to pieces, and swept away into the well-stored limbo of past philosophical errors, though perhaps distinguished above them all by the magnitude of its absurdity, and perversion of physical fact.

After

We have no right, under any sound philosophy, to attribute to the great and distant bodies of the universe, merely because they are great and distant, qualities or properties quite at variance with our own physical experience. It more resembles politics than science to speculate at large upon remote grandeur which we cannot approach. wasting their intellects in framing these loose systems, and affecting to comprehend them, their authors turn round to the unenlightened and heretical public of common sense, and superciliously exclaim, "You are not initiated; you cannot understand the unknown tongue." What answer should be made to a gardener who told us that the poke he gave to a bean in planting it made the roots grow downwards, and that the pulling out his planting-stick made the stalk follow upwards? All these things are the secrets of trade. Why should not the gardener, as well as the mathematician, have his profitable mystery?

The late controversy has supplied striking instances of those " vermicular" questions, which Lord Bacon warns us are so apt to be engendered in minds addicted to the stagnation of leisurely abstractions. Our opponents seem to attach the greatest importance to their capacity for realizing the conception of an abstract axis, or axis passing through any or every part of a revolving body, through the Peak of Teneriffe, through St. Paul's, through their heads, or through the moon. From the habitual conviction that all their ideas are great, they think this a

great idea, and deplore the doomed inability of the mere practical man to comprehend such sublimity. Were they to ascend from this bathos of the trivial, and study the most commonplace of mechanical facts, the daily conversion of circular to reciprocating motion, they might amuse themselves not only with abstract axes, but with concrete axles stuck into any revolving body as thick as "quills upon the fretful porcupine;" we might have less of such very vain and pretentious theories, and they themselves might have a better appreciation of the solemnities they put forth with the assertion, that “ only astronomers and mathematicians can comprehend them." They are mere pedantic puerilities, magnified by their ignorance of what is truly important into a "vast profound," which they believe none but themselves can fathom. It is time that a science so valuable as mathematics, when properly pursued, should be confined to its due limits, and the small professors of it set at their right level. DAVID MUSHET.

INDUSTRY.-Industry must be taught a child as one amongst the most important duties of life; habits of industry must then be implanted in him; and in no way will he gain these better than by living in an atmosphere of which this forms one of the principal and chief ingredients. He must read of it in his lessons; he must see it in the work of the school; he must catch it in the conduct and character of his master. Every effort must be made to overcome any spirit of idleness; and in the work and order of the school every means should be used to illustrate the benefits arising from industry, and the baneful effects of sloth and idleness. As practice is better than precept, through the untiring energy of the master not a child should be allowed to be without occupation even for a moment. I know how difficult it is to carry this out; but it does not belong to the subject under consideration to enter upon these difficulties or their remedies.-Rev. John Freeman.

LITTLE KINDNESSES.-Little acts of kindness, gentle words, loving smiles-they strew the path of life with flowers: the sun seems to shine brighter for them, and the green earth to look greener; and He who bade us "love one another looks with favour upon the gentle and kind-hearted, and He pronounced the meek blessed.-Canadian Journal of Education.

EDUCATION OF YOUNG LADIES.-It seems sometimes odd enough to me, that while young ladies are so sedulously taught all the accomplishments that a husband disregards, they are never taught the great one he would prize. They are taught to be exhibitors, he wants a companion.-Godolphin.

APTNESS TO TEACH.-The great secret seems to be this :-to be able easily to descend from an elevation far above a pupil to a level with his capacity. There must be a freedom and fulness of language, a power of choosing with rapidity words which are at once correct and easy of application; there must be a clearness of ideas,-order, method, and arrangement; there must be no jumping from one part of the subject to another every step of the lesson must be progressive. This requires a faculty of remembering what has been already demonstrated, and also a faculty of looking forward to the various parts which will be required, each in its turn, to complete the scheme.-Rev. J. Freeman.

THE PRESENT SYSTEM OF OVER-SCHOOLING.

NORMOUS injury is being done by the absurdly protracted hours

it is usual to begin work at eight or half-past eight (but often at seven), and, with something like two hours for meals and recreation, prolong schooling even for young children till tea-time. Incredible as it may appear, the mental labour of the day is not even then complete; for in most schools, if not in all schools, the lessons for the next morning have then to be learned in addition to the foregone work; and when, all the intellectual energy being wearied and exhausted, such a tax on the brain is more than usually oppressive and noxious.

The injury thus done to health is great. Many a young constitution receives the seeds of future premature decay, and countless ailments are thus engendered for the sake of acquirements which, even were they thus attained, would indeed be dearly purchased. But how infinite is the folly of the system when, in addition to its sanatory evil, its utter inutility is taken into account! We cannot cram minds as we cram bales, by hydraulic pressure.

Lord Stanley, at a recent opening of an Oldham "Lyceum" (as it was sillily called), most sensibly remarked as follows:-" It was not true that a large amount of leisure was requisite in order to obtain a considerable proportion of learning. The brain, like the body, could only bear a certain amount of active exertion: nay, of all organizations it was the most delicate,-the most easily put out of repair, and the most difficult to set right when once disorganized. It was liable to suffer in many ways; from too little work in those whose labour was mechanical only, or who do not work at all; or from too much work in those whose labour employed chiefly or exclusively the intellectual faculties. It was idle to suppose that the majority of men, though free from any pressure of business, though independent of a profession or trade, could, whatever the amount of their leisure, or however much they might desire it, occupy anything like the whole, or even the greater part, in study.

"If no external circumstances interposed to limit their exertions, nature would, and did. The mind only retained its freshness for a limited time, and if that time were exceeded, exhaustion ensued; little was learned, and the seeds of future mischief were sown in the constitution. What he contended for, then, was this,-that no man willing to study need despond, because he could only command a portion, it might be, of his evenings, whilst others were masters of the whole day. It was bad arithmetic in these matters to compute that four times as much could be learned in four hours as in one. It would be just as reasonable to argue, that because a good dinner daily gave a man health and strength, therefore four such dinners every day would make a man four times as strong and healthy. It would be just as reasonable to argue (what all who have looked even into the elements of finance know to be untrue), that if they doubled the rate of a tax, they would double also the amount it would produce."

Now what is true as addressed to working men, is just as true when applied to our own children. We firmly believe that a vast injury is being done to the soundness of future learning, by the inordinate over