ago I believed that electrolytes could conduct electricity by a conduction proper; that has also been denied by many through long time: though I believed myself right, yet circumstances have induced me to pay that respect to criticism as to reinvestigate the subject, and I have the pleasure of thinking that nature confirms my original conclusions.

Among those points of self-education which take up the form of mental d'scipline, there is one of great importance, and, moreover, difficult to deal with, because it involves an internal conflict, and equally touches our vanity and our ease. It consists in the tendency to deceive ourselves regarding all we wish for, and the necessity of resistance to these desires. It is impossible for any one who has not been constrained, by the course of his occupation and thoughts, to a habit of continual self-correction, to be aware of the amount of error in relation to judgment arising from this tendency. The force of the temptation which urges us to seek for such evidence and appearances as are in favor of our desires, and to disregard those which oppose them, is wonderfully great. In this respect we are all, more or less, active promoters of error. In place of practising wholesome self-abnegation, we ever make the wish the father to the thought: we receive as friendly that which agrees with, we resist with dislike that which opposes us; whereas the very reverse is required by every dictate of common sense. Let me illustrate my meaning by a case where the proof being easy, the rejection of it under the temptation is the more striking. In old times, a ring or a button would be tied by a boy to one end of a long piece of thread, which he would then hold at the other end, letting the button hang within a glass, or over a piece of slate-pencil, or sealing-wax, or a nail; he would wait and observe whether the button swung, and whether in swinging it tapped the glass as many times as the clock struck last, or moved along or across the slate-pencil, or in a circle or oval. In late times, parties in all ranks of life have renewed and repeated the boy's experiment. They have sought to ascertain a very simple factnamely, whether the effect was as reported; but how many were unable to do this? They were sure they could keep their hands immovable,—were sure they could do so whilst watching the result,‚—were sure that accordance of swing with an expected direction was not the result of their desires or involuntary motions. How easily all these points could be put to the proof by not looking at the objects, yet how difficult for the experimenter to deny himself that privilege. I have rarely found one who would freely permit the substance experimented with to be screened from his sight, and then its position changed.

The inclination we exhibit in respect of any report or opinion that harmonizes with our preconceived notions, can only be compared in degree with the incredulity we entertain towards everything that opposes them; and these opposite and apparently incompatible, or at least inconsistent, conditions are accepted simultaneously in the most extraordinary manner. At one moment a departure from the laws of nature is admitted without the pretence of a careful examination of the proof; and at the next, the whole force of these laws, acting undeviatingly through all time, is denied, because the testimony they give is disliked. It is my firm persuasion, that no man can examine himself in the most common things, having any reference to him personally, or to any person, thought, or matter related to him, without being soon made aware of the temptation and the difficulty of opposing it. I could give you many illustrations personal to myself, about atmospheric magnetism, lines of force, attraction, repulsion, unity of power, nature of matter, &c.; or in things more general to our common

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-instruction, 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 evoke 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 earth 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 manner 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 others. Two persons cannot mutually impart their knowledge, or compare and rectify their conclusions, 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 facts, 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 altogether 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 analogies; to present the fundamental idea in every form, proportion, and condi tion; 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 probable 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 judgment 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, he 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 humility. 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.

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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 classical 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 is what is called a liberal one, with no special professional bias or other avowed object 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 understand the classical authors, as its main and primary feature, and should admit, and that reluctantly, a mere minimum of extra classical teaching. Such a system must necessarily, I conceive, suffer to languish and become stunted and dwarfed for want of timely exercise, 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 classical 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 character 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 knowledge 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 conic 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