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nature, about likes and dislikes, wishes, hopes, and fears; but it would be unsuitable and also unnecessary, for each must be conscious of a large field sadly uncultivated in this respect. I will simply express my strong belief, that that point of self-education which consists in teaching the mind to resist its desires and inclinations, until they are proved to be right, is the most important of all, not only in things of natural philosophy, but in every department of daily life.
One exercise of the mind which largely influences the power and character of the judgment, is the habit of forming clear and precise ideas. If, after considering a subject in our ordinary manner, we return upon it with the special purpose of noticing the condition of our thoughts, we shall be astonished to find how little precise they remain. On recalling the phenomena relating to a matter of fact, the circumstances modifying them, the kind and amount of action presented, the real or probable result, we shall find that the first impressions are scarcely fit for the foundation of a judgment, and that the second thoughts will be best. For the acquirement of a good condition of mind in this respect, the thoughts should be trained to a habit of clear and precise formation, so that vivid and distinct impressions of the matter in hand, its circumstances and consequences, may remain.
I am persuaded that natural things offer an admirable school for self-instructicn, a most varied field for the necessary mental practice, and that those who exercise themselves therein may easily apply the habits of thought thus formed to a social use. As a first step in such practice, clear ideas should be obtained of what is possible and what is impossible. Thus, it is impossible to create force. We may employ it; we may cvoke it in one form by its consumption in another; we may hide it for a period; but we can neither create nor destroy it. We may cast it away; but where we dismiss it, there it will do its work. If, therefore, we desire to consider a proposition respecting the employment or evolution of power, let us carry our judgment, educated on this point, with us. If the proposal include the double use of a force with only one excitement, it implies a creation of power, and that cannot be. If we could by the fingers draw a heavy piece of wood or stone upward without effort, and then, letting it sink, could produce by its gravity an effort equal to its weight, that would be a creation of power, and cannot be.
So again we cannot annihilate matter, nor can we create it. But if we are satisfied to rest upon that dogma, what are we to think of table-lifting? If we could make the table to cease from acting by the gravity upon the carth beneath it, or by reaction upon the hand supposed to draw it upwards, we should annihilate it, in respect of that very property which characterizes it as matter.
Considerations of this nature are very important aids to the judgment; and when a statement is made claiming our assent, we should endeavor to reduce it to some consequence which can be immediately compared with, and tried by, these or like compact and never failing truths. If incompatibility appears, then we have reason to suspend our conclusion, however attractive to the imagination the proposition may be, and pursue the inquiry further, until accordance is obtained; it must be a most uneducated and presumptuous mind that can at once consent to cast off the tried truth and accept in its place the mere loud assertion. We should endeavor to separate the points before us, and concentrate each, so as to evolve a clear type idea of the ruling fact and its consequences ; looking at the matter on every side, with the great purpose of distinguishing the constituent reality, and recognizing it under every variety of aspect.
In like manncr we should accustom ourselves to clear and definite language, especially in physical matters, giving to a word its true and full, but measured meaning, that we may be able to convey our ideas clearly to the minds of oth
Two persons cannot mutually impart their knowledge, or compare and rectify their conclusiɔns, unless both attend to the true intent and force of language. If by such words as attraction, electricity, polarity, or atom, they imply different things, they may discuss fucts, deny results, and doubt consequences for an indefinite time without any advantageous progress. I hold it as a great point in self-education that the student should be continually engaged in forming exact ideas, and in expressing them clearly by language. Such practice insensibly opposes any tendency to exaggeration or mistake, and increases the sense and love of truth in every part of life.
I should be sorry, however, if what I have said were understood as meaning that education for the improvement and strengthening of the judgment is to be al together repressive of the imagination, or confine the exercise of the mind to processes of a mathematical or mechanical character. I believe that, in the pursuit of physical science, the imagination should be taught to present the subject investigated in all possible, and even in impossible views; to search for analogies of likeness and (if I may say so) of opposition—inverse or contracted
I analogies; to present the fundamental idea in every form, proportion, and condition; to clothe it with suppositions and probabilities, that all cases may pass in review, and be touched, if needful, by the Ithuriel spear of experiment. But all this must be under government, and the result must not be given to society until the judgment, educated by the process itself, has been exercised upon it.
When the different data required are in our possession, and we have succeeded in forming a clear idea of each, the mind should be instructed to balance them one against another, and not suffered carelessly to hasten to a conclusion. This reserve is most essential; and it is especially needful that the reasons which are adverse to our expectations or our desires should be carefully attended to.
As a result of this wholesome mental condition, we should be able to form a proportionate judgment. The mind naturally desires to settle upon one thing or another; to rest upon an affirmative or a negative; and that with a degree of absolutism which is irrational and improper. In drawing a conclusion it is very difficult, but not the less necessary, to make it proportionate to the evidence : except where certainty exists (a case of rare occurrence), we should consider our decisions probablc only. The probability may appear very great, so that in affairs of the world we often accept such as certainty, and trust our welfare or our lives upon it. Still, only an uneducated mind will confound probability with certainty, especially when it encounters a contrary conclusion drawn by another from like data. Occasionally and frequently the exercise of the judg. ment ought to end in absolute reservation. It may be very distasteful, and, great fatigue, to suspend a conclusion, but as we are not infallible, so we ought to be cautious; we shall eventually find our advantage, for the man who rests in his position is not so far from right as he who, proceeding in a wrong direction, is ever increasing his distance.
The education which I advocate will require patience and labor of thought in every exercise tending to improve the judgment. It matters not on what subject a person's mind is occupied, be should engage in it with the conviction that it will require mental labor. A powerful mind will be able to draw a conclusion more readily and more correctly than one of moderate character, but both will surpass themselves if they make an earnest, careful investigation, instead of a careless or prejudiced one; and education for this purpose is the more necessary for the latter, because the man of less ability may, through it, raise his rank and amend his position.
This education has for its first and its last step kumility. It can commence only because of a conviction of deficiency; and if we are not disheartened under the growing revelations which it will make, that conviction will become stronger unto the end. But the humility will be founded, not on comparison of ourselves with the imperfect standards around us, but on the increase of that internal knowledge which alone can make us aware of our internal wants. The first step in correction is to learn our deficiencies, and having learned them, the next step is almost complete: for no man who has discovered that his judgment is hasty, or illogical, or imperfect, would go on with the same degree of haste, or irrationality, or presumption, as before. * *
I know that I fail frequently in that very exercise of judgment to which I call others, and have abundant reason to believe that much more frequently I stand manifest to those around me, as one who errs, without being corrected by knowing it.
In his evidence before the Public Schools Commission, Prof. Faraday expressed very decided opinions on several of the mooted questions of the school curriculum.
NEGLECT OF PHYSICAL SCIENCES AND NATURAL HISTORY.
That the natural knowledge which has been given to the world during the last fifty years should remain untouched, is to me a matter so strange that I find it difficult to understand it. This knowledge is required by men of ordinary intelligence in our lighthouse arrangements, and yet we do not find it here, although when we go over to France we find it in the class of men doing the same duty there—men who can give a reason, supply a correction, and act for themselves, if they see action is wanted. In just such service here we are obliged to displace man after man because they could not attend to the electric light intelligently. The French workman was not superior in natural intelligence, but the English keeper had not been in the way of having that instruction. My experience and observations among witnesses in courts of law, and among men of even good school education, have satisfied me of the too general want of judgment as well as of actual ignorance of natural things little or no power to give a reason why for what they say or do.
The sciences, of which I notice a great and general ignorance even among our best public school educated men—that of the air, the earth, the water-touch us at all points, every day, every hour, every where-they make up life. And it is difficult to make such adult minds comprehend simple explanations, which if adressed to young people in school or in the shop, will be both intelligible, interesting, and profitable. I never yet found a boy so young as not to be able to understand by simple explanation and to enjoy the point of an experiment. I find the grown up minds coming back to me with the same questions over and over again. They are not prepared to receive these notions. They need the A B C of the subjects.
I could teach a little boy of eleven years old, of ordinary intelligence, all those things in mechanics, hydrostatics, hydraulics, optics, which are usually taught at a much later period. These subjects, and chemistry and botany, should receive attention in apposite ways and times at school.
In matters of natural science, and all the uses and applications of the same, I should turn to a man untaught in other respects, but acquainted with these subjects, rather than to a classieal scholar, to find that mode or habit of mind to enable him to judge aptly in this department.
MATHEMATICS IN PUBLIC SCHOOL EDUCATION.
SIR J. F. W. HERSCHEL, who was knighted by Queen Victoria in 1838, as the best representative of the science of her kingdom at the time of her inauguration, thus speaks of Mathematies in the school curriculum :
Regarding as a “public school" any considerable permanent educational establishment in which a large number of youths go through a fixed and uniform course of school instruction, from the earliest age at which boys are usually sent to schools to that in which they either enter the universities or pass in some other mode into manly life, and in which it is understood that the education what is called a liberal one, with no special professional bias or other avowed objeet than to form a youth for general life and civilized society, I should consider any system radically faulty which should confine itself to the study of the classical languages, and to so much of Greek and Roman History as is necessary to un. derstand the classical authors, as its main and primary feature, and should admit, and that reluctantly, a mere minimum of extra classical teaching. Such a syatem must necessarily, I conceive, suffer to languish and become stunted and dwarfed for want of timely exereise, the reasoning faculty, in those years, between fourteen and twenty, when the mind has become capable of consecutive thought and of following out a train of logical argument to a legitimate conclusion. In those years it is quite as important that youths should have placed in their hands and be obliged to study books which may best initiate them in this domain of human thought as in that of classieal literature. To be able to express ourselves fluently in Latin or Greek prose or verse, to have attained an extensive familiarity with ancient literature, and a perfect knowledge of the niceties of its grammar, prosody, and idiom-all, in short, which is included in the idea of classical scholarship,—is no doubt very desirable, and I should be one of the last to depreciate it. But it is bought too dear if attained at the sacrifice of any reasonable prospect of improving the general intellectual char. acter by acquiring habits of concentrated thought, by familiarizing the mind with the contemplation of abstract truth, and by accustoming it to the attitude of investigation, induction, and generalization, while it is yet plastic and impressible.
It is these, and not mere utilitarian considerations as to the more favorable start which previous mathematical reading may afford a young man on entering a university, or the advantage in life which a certain amount of knowledgo acquired on a variety of other subjects may carry with it—or even as to the general expectation which society has begun to entertain that a young man calling himself educated shall not be wholly ignorant of at least the elements of mathematical and physical science (though these considerations are not without their weight), which incline me to advocate the accordance of a very decided place in public instruction in the upper forms to an elementary course of mathematics, carried in geometry as far as plane and spherical trigonometry, the most ordinary propositions in conie sections, and the doctrine of curves; in symbolic analysis as far as the general nature of equations and the development of functions in infinite series, and including, in the region of applied mathematics, at least the primary elements of statics and dynamics. Such a course might, I
think, commence with the average of boys about their 14th year, before which, however, I should expect the four rules of arithmetic, simple and compound, and decimal fractions to have been insisted on.
I know that it is a common idea that classical and mathematical proficiency are incompatible and simply fundamentally different constitutions of mind. This, however, (except as regards the higher degrees of proficiency which go to render a man distinguished, either as a scholar or a mathematician, and the proposition might then be extended to every other form of excellence) I disbelieve; if anything further be intended by such an assertion than that tastes differ, and that most men prefer to give their attention to subjects which fill the imagination and interest the feelings rather than to those which appeal to the unimpassioned reason, and call for a prolonged and steady exercise of the thinking powers. As to the common remark that a very large proportion of young men entering the universities with a high degree of classical training evince a repugnance to the mathematical studies there followed, and unfrequently rather ostentatiously declare, and proceed to illustrate in practice, their inaptitude for such studies, it proves nothing but that the one-sidedness of their previous education has produced its natural effect; and the consequence I believe to be that a great mass of good mental power, which might have become available to human progress if duly fostered and developed, has thus hitherto been lost to the community. All that I intend, however, in thus protesting against this prevalent notion, is to deprecate its being drawn into an argument for not insist. ing on attendance on the mathematical classes in the case of boys who really do make little progress, and throwing back into an unmitigated classical routine. In every school there are boys of all degrees of capacity and industry, and therefore of progress. But the absence of these qualities is never admitted as a reason for their being excused attendance at school hours, whatever be the lessons in hand, though it may, and must, retard their advance to higher classes. Besides mathematical and physical subjects there are to be considered the modern languages, history, geography, music, drawing, and a variety of other matters of a similar nature.
Dr. WHEWELL, Master of Trinity College, and Vice President of the University of Cambridge, in which he was also at different times, tutor, professor of mineralogy, moral philosophy, &c., in a treatise on Liberal Education, published first in 1835, and with additions in 1850, and commended to the Public School Commission in 1862, has the following remarks:
Any one who has thought at all on the subject of the education of the middle and higher classes in England, must be aware that the great classical schools cxercise a very powerful influence upon such educations. The flower of our Eng lish youth spend at these schools the years during which the greater part is acquired of all that youths do acquire in the way of learning. It is there that their mental habits in a great measure receive the form which they retain in after life. The tastes there generated, the estimates of different kinds of knowledge there communicated by the contagion of society, are not easily afterwards changed. Even if at the university they are introduced to new subjects of thought, new methods of study, new associates, new motives, still the influence of the school continues to be extremely powerful, and though it may be modified,