Perhaps the most fantastic proposition that Maupertuis,[114] the renowned president of the Berlin Academy, ever put forward for the approval of his contemporaries was that of founding a city in which, to instruct and discipline young students, only Latin should be spoken. Maupertuis's Latin city remained an idle wish. But for centuries Latin and Greek institutions exist in which our children spend a goodly portion of their days, and whose atmosphere constantly surrounds them, even when without their walls.

For centuries instruction in the ancient languages has been zealously cultivated. For centuries its necessity has been alternately championed and contested. More strongly than ever are authoritative voices now raised against the preponderance of instruction in the classics and in favor of an education more suited to the needs of the time, especially for a more generous treatment of mathematics and the natural sciences.

In accepting your invitation to speak here on the relative educational value of the classical and the mathematico-physical sciences in colleges and high schools, I find my justification in the duty and the necessity laid upon every teacher of forming from his own experiences an opinion upon this important question, as partly also in the special circumstance that in my youth I was personally under the influence of school-life for only a short time, just previous to my entering the university, and had, therefore, ample opportunity to observe the effects of widely different methods upon my own person.

Passing now, to a review of the arguments which the advocates of instruction in the classics advance, and of what the adherents of instruction in the physical sciences in their turn adduce, we find ourselves in rather a perplexing position with respect to the arguments of the first named. For these have been different at different times, and they are even now of a very multifarious character, as must be where men advance, in favor of an institution that exists and which they are determined to retain at any cost, everything they can possibly think of. We shall find here much that has evidently been brought forward only to impress the minds of the ignorant; much, too, that was advanced in good faith and which is not wholly without foundation. We shall get a fair idea of the reasoning employed by considering, first, the arguments that have grown out of the historical circumstances connected with the original introduction of the classics, and, lastly, those which were subsequently adduced as accidental afterthoughts.

Instruction in Latin, as Paulsen[115] has minutely shown, was introduced by the Roman Church along with Christianity. With the Latin language were also transmitted the scant and meagre remnants of ancient science. Whoever wished to acquire this ancient education, then the only one worthy of the name, for him the Latin language was the only and indispensable means; such a person had to learn Latin to rank among educated people.

The wide-spread influence of the Roman Church wrought many and various results. Among those for which all are glad, we may safely count the establishment of a sort of uniformity among the nations and of a regular international intercourse by means of the Latin language, which did much to unite the nations in the common work of civilisation, carried on from the fifteenth to the eighteenth century. The Latin language was thus long the language of scholars, and instruction in Latin the road to a liberal education—a shibboleth still employed, though long inappropriate.

For scholars as a class, it is to be regretted, perhaps, that Latin has ceased to be the medium of international communication. But the attributing of the loss of this function by the Latin language to its incapacity to accommodate itself to the numerous new ideas and conceptions which have arisen in the course of the development of science is, in my opinion, wholly erroneous. It would be difficult to find a modern scientist who had enriched science with as many new ideas as Newton has, yet Newton knew how to express those ideas very correctly and precisely in the Latin language. If this view were correct, it would also hold true of every living language. Originally every language has to adapt itself to new ideas.

It is far more likely that Latin was displaced as the literary vehicle of science by the influence of the nobility. By their desire to enjoy the fruits of literature and science, through a less irksome medium than Latin, the nobility performed for the people at large an undeniable service. For the days were now past when acquaintance with the language and literature of science was restricted to a caste, and in this step, perhaps, was made the most important advance of modern times. To-day, when international intercourse is firmly established in spite of the many languages employed, no one would think of reintroducing Latin.[116]

The facility with which the ancient languages lend themselves to the expression of new ideas is evidenced by the fact that the great majority of our scientific ideas, as survivals of this period of Latin intercourse, bear Latin and Greek designations, while in great measure scientific ideas are even now invested with names from these sources. But to deduce from the existence and use of such terms the necessity of still learning Latin and Greek on the part of all who employ them is carrying the conclusion too far. All terms, appropriate and inappropriate,—and there are a large number of inappropriate and monstrous combinations in science,—rest on convention. The essential thing is, that people should associate with the sign the precise idea that is designated by it. It matters little whether a person can correctly derive the words telegraph, tangent, ellipse, evolute, etc., if the correct idea is present in his mind when he uses them. On the other hand, no matter how well he may know their etymology, his knowledge will be of little use to him if the correct idea is absent. Ask the average and fairly educated classical scholar to translate a few lines for you from Newton's Principia, or from Huygens's Horologium, and you will discover at once what an extremely subordinate rÔle the mere knowledge of language plays in such things. Without its associated thought a word remains a mere sound. The fashion of employing Greek and Latin designations—for it can be termed nothing else—has a natural root in history; it is impossible for the practice to disappear suddenly, but it has fallen of late considerably into disuse. The terms gas, ohm, AmpÈre, volt, etc., are in international use, but they are not Latin nor Greek. Only the person who rates the unessential and accidental husk higher than its contents, can speak of the necessity of learning Latin or Greek for such reasons, to say nothing of spending eight or ten years on the task. Will not a dictionary supply in a few seconds all the information we wish on such subjects?[117]

It is indisputable that our modern civilisation took up the threads of the ancient civilisation, that at many points it begins where the latter left off, and that centuries ago the remains of the ancient culture were the only culture existing in Europe. Then, of course, a classical education really was the liberal education, the higher education, the ideal education, for it was the sole education. But when the same claim is now raised in behalf of a classical education, it must be uncompromisingly contested as bereft of all foundation. For our civilisation has gradually attained its independence; it has lifted itself far above the ancient civilisation, and has entered generally new directions of progress. Its note, its characteristic feature, is the enlightenment that has come from the great mathematical and physical researches of the last centuries, and which has permeated not only the practical arts and industries but is also gradually finding its way into all fields of thought, including philosophy and history, sociology and linguistics. Those traces of ancient views that are still discoverable in philosophy, law, art, and science, operate more as hindrances than helps, and will not long stand before the development of independent and more natural views.

It ill becomes classical scholars, therefore, to regard themselves, at this day, as the educated class par excellence, to condemn as uneducated all persons who do not understand Latin and Greek, to complain that with such people profitable conversations are not to be carried on, etc. The most delectable stories have got into circulation, illustrative of the defective education of scientists and engineers. A renowned inquirer, for example, is said to have once announced his intention of holding a free course of university lectures, with the word "frustra"; an engineer who spent his leisure hours in collecting insects is said to have declared that he was studying "etymology." It is true, incidents of this character make us shudder or smile, according to our mood or temperament. But we must admit, the next moment, that in giving way to such feelings we have merely succumbed to a childish prejudice. A lack of tact but certainly no lack of education is displayed in the use of such half-understood expressions. Every candid person will confess that there are many branches of knowledge about which he had better be silent. We shall not be so uncharitable as to turn the tables and discuss the impression that classical scholars might make on a scientist or engineer, in speaking of science. Possibly many ludicrous stories might be told of them, and of far more serious import, which should fully compensate for the blunders of the other party.

The mutual severity of judgment which we have here come upon, may also forcibly bring home to us how really scarce a true liberal culture is. We may detect in this mutual attitude, too, something of that narrow, mediÆval arrogance of caste, where a man began, according to the special point of view of the speaker, with the scholar, the soldier, or the nobleman. Little sense or appreciation is to be found in it for the common task of humanity, little feeling for the need of mutual assistance in the great work of civilisation, little breadth of mind, little truly liberal culture.

A knowledge of Latin, and partly, also, a knowledge of Greek, is still a necessity for the members of a few professions by nature more or less directly concerned with the civilisations of antiquity, as for lawyers, theologians, philologists, historians, and generally for a small number of persons, among whom from time to time I count myself, who are compelled to seek for information in the Latin literature of the centuries just past.[118] But that all young persons in search of a higher education should pursue for this reason Latin and Greek to such excess; that persons intending to become physicians and scientists should come to the universities defectively educated, or even miseducated; and that they should be compelled to come only from schools that do not supply them with the proper preparatory knowledge is going a little bit too far.

After the conditions which had given to the study of Latin and Greek their high import had ceased to exist, the traditional curriculum, naturally, was retained. Then, the different effects of this method of education, good and bad, which no one had thought of at its introduction, were realised and noted. As natural, too, was it that those who had strong interests in the preservation of these studies, from knowing no others or from living by them, or for still other reasons, should emphasise the good results of such instruction. They pointed to the good effects as if they had been consciously aimed at by the method and could be attained only through its agency.

One real benefit that students might derive from a rightly conducted course in the classics would be the opening up of the rich literary treasures of antiquity, and intimacy with the conceptions and views of the world held by two advanced nations. A person who has read and understood the Greek and Roman authors has felt and experienced more than one who is restricted to the impressions of the present. He sees how men placed in different circumstances judge quite differently of the same things from what we do to-day. His own judgments will be rendered thus more independent. Again, the Greek and Latin authors are indisputably a rich fountain of recreation, of enlightenment, and of intellectual pleasure after the day's toil, and the individual, not less than civilised humanity generally, will remain grateful to them for all time. Who does not recall with pleasure the wanderings of Ulysses, who does not listen joyfully to the simple narratives of Herodotus, who would ever repent of having made the acquaintance of Plato's Dialogues, or of having tasted Lucian's divine humor? Who would give up the glances he has obtained into the private life of antiquity from Cicero's letters, from Plautus or Terence? To whom are not the portraits of Suetonius undying reminiscences? Who, in fact, would throw away any knowledge he had once gained?

Yet people who draw from these sources only, who know only this culture, have surely no right to dogmatise about the value of some other culture. As objects of research for individuals, this literature is extremely valuable, but it is a different question whether it is equally valuable as the almost exclusive means of education of our youth.

Do not other nations and other literatures exist from which we ought to learn? Is not nature herself our first school-mistress? Are our highest models always to be the Greeks, with their narrow provinciality of mind, that divided the world into "Greeks and barbarians," with their superstitions, with their eternal questioning of oracles? Aristotle with his incapacity to learn from facts, with his word-science; Plato with his heavy, interminable dialogues, with his barren, at times childish, dialectics—are they unsurpassable?[119] The Romans with their apathy, their pompous externality, set off by fulsome and bombastic phrases, with their narrow-minded, philistine philosophy, with their frenzied sensuality, with their cruel and bestial indulgence in animal and man baiting, with their outrageous maltreatment and plundering of their subjects—are they patterns worthy of imitation? Or shall, perhaps, our science edify itself with the works of Pliny who cites midwives as authorities and himself stands on their point of view?

Besides, if an acquaintance with the ancient world really were attained, we might come to some settlement with the advocates of classical education. But it is words and forms, and forms and words only, that are supplied to our youth; and even collateral subjects are forced into the strait-jacket of the same rigid method and made a science of words, sheer feats of mechanical memory. Really, we feel ourselves set back a thousand years into the dull cloister-cells of the Middle Ages.

This must be changed. It is possible to get acquainted with the views of the Greeks and Romans by a shorter road than the intellect deadening process of eight or ten years of declining, conjugating, analysing, and extemporisation. There are to-day plenty of educated persons who have acquired through good translations vivider, clearer, and more just views of classical antiquity than the graduates of our gymnasiums and colleges.[120]

For us moderns, the Greeks and the Romans are simply two objects of archÆological and historical research like all others. If we put them before our youth in fresh and living pictures, and not merely in words and syllables, the effect will be assured. We derive a totally different enjoyment from the Greeks when we approach them after a study of the results of modern research in the history of civilisation. We read many a chapter of Herodotus differently when we attack his works equipped with a knowledge of natural science, and with information about the stone age and the lake-dwellers. What our classical institutions pretend to give can and actually will be given to our youth with much more fruitful results by competent historical instruction, which must supply, not names and numbers alone, nor the mere history of dynasties and wars, but be in every sense of the word a true history of civilisation.

The view still widely prevails that although all "higher, ideal culture," all extension of our view of the world, is acquired by philological and in a lesser degree by historical studies, still the mathematics and natural sciences should not be neglected on account of their usefulness. This is an opinion to which I must refuse my assent. It were strange if man could learn more, could draw more intellectual nourishment, from the shards of a few old broken jugs, from inscribed stones, or yellow parchments, than from all the rest of nature. True, man is man's first concern, but he is not his sole concern.

In ceasing to regard man as the centre of the world; in discovering that the earth is a top whirled about the sun, which speeds off with it into infinite space; in finding that in the fixed stars the same elements exist as on earth; in meeting everywhere the same processes of which the life of man is merely a vanishingly small part—in such things, too, is a widening of our view of the world, and edification, and poetry. There are here perhaps grander and more significant facts than the bellowing of the wounded Ares, or the charming island of Calypso, or the ocean-stream engirdling the earth. He only should speak of the relative value of these two domains of thought, of their poetry, who knows both.

The "utility" of physical science is, in a measure, only a collateral product of that flight of the intellect which produced science. No one, however, should underrate the utility of science who has shared in the realisation by modern industrial art of the Oriental world of fables, much less one upon whom those treasures have been poured, as it were, from the fourth dimension, without his aid or understanding.

Nor may we believe that science is useful only to the practical man. Its influence permeates all our affairs, our whole life; everywhere its ideas are decisive. How differently does the jurist, the legislator, or the political economist think, who knows, for example, that a square mile of the most fertile soil can support with the solar heat annually consumed only a definite number of human beings, which no art or science can increase. Many economical theories, which open new air-paths of progress, air-paths in the literal sense of the word, would be made impossible by such knowledge.

The eulogists of classical education love to emphasise the cultivation of taste which comes from employment with the ancient models. I candidly confess that there is something absolutely revolting in this to me. To form the taste, then, our youths must sacrifice ten years of their life! Luxury takes precedence over necessity. Have the future generations, in the face of the difficult problems, the great social questions, which they must meet, and that with strengthened mind and heart, no more important duties to fulfil than these?

But let us assume that this end were desirable. Can taste be formed by rules and precepts? Do not ideals of beauty change? Is it not a stupendous absurdity to force one's self artificially to admire things which, with all their historical interest, with all their beauty in individual points, are for the most part foreign to the rest of our thoughts and feelings, provided we have such of our own. A nation that is truly such, has its own taste and will not go to others for it. And every individual perfect man has his own taste.[121]

And what, after all, does this cultivation of taste consist in? In the acquisition of the personal literary style of a few select authors! What should we think of a people that would force its youth a thousand years from now, by years of practice, to master the tortuous or bombastic style of some successful lawyer or politician of to-day? Should we not justly accuse them of a woful lack of taste?

The evil effects of this imagined cultivation of the taste find expression often enough. The young savant who regards the composition of a scientific essay as a rhetorical exercise instead of a simple and unadorned presentation of the facts and the truth, still sits unconsciously on the school-bench, and still unwittingly represents the point of view of the Romans, by whom the elaboration of speeches was regarded as a serious scientific (!) employment.

Far be it from me to underrate the value of the development of the instinct of speech and of the increased comprehension of our own language which comes from philological studies. By the study of a foreign language, especially of one which differs widely from ours, the signs and forms of words are first clearly distinguished from the thoughts which they express. Words of the closest possible correspondence in different languages never coincide absolutely with the ideas they stand for, but place in relief slightly different aspects of the same thing, and by the study of language the attention is directed to these shades of difference. But it would be far from admissible to contend that the study of Latin and Greek is the most fruitful and natural, let alone the only, means of attaining this end. Any one who will give himself the pleasure of a few hours' companionship with a Chinese grammar; who will seek to make clear to himself the mode of speech and thought of a people who never advanced as far as the analysis of articulate sounds, but stopped at the analysis of syllables, to whom our alphabetical characters, therefore, are an inexplicable puzzle, and who express all their rich and profound thoughts by means of a few syllables with variable emphasis and position,—such a person, perhaps, will acquire new, and extremely elucidative ideas upon the relation of language and thought. But should our children, therefore, study Chinese? Certainly not. No more, then, should they be burdened with Latin, at least in the measure they are.

It is a beautiful achievement to reproduce a Latin thought in a modern language with the maximum fidelity of meaning and expression—for the translator. Moreover, we shall be very grateful to the translator for his performance. But to demand this feat of every educated man, without consideration of the sacrifice of time and labor which it entails, is unreasonable. And for this very reason, as classical teachers admit, that ideal is never perfectly attained, except in rare cases with scholars possessed of special talents and great industry. Without slurring, therefore, the high importance of the study of the ancient languages as a profession, we may yet feel sure that the instinct for speech which is part of every liberal education can, and must, be acquired in a different way. Should we, indeed, be forever lost if the Greeks had not lived before us?

The fact is, we must carry our demands further than the representatives of classical philology. We must ask of every educated man a fair scientific conception of the nature and value of language, of the formation of language, of the alteration of the meaning of roots, of the degeneration of fixed forms of speech to grammatical forms, in brief, of all the main results of modern comparative philology. We should judge that this were attainable by a careful study of our mother tongue and of the languages next allied to it, and subsequently of the more ancient tongues from which the former are derived. If any one object that this is too difficult and entails too much labor, I should advise such a person to place side by side an English, a Dutch, a Danish, a Swedish, and a German Bible, and to compare a few lines of them; he will be amazed at the multitude of suggestions that offer themselves.[122] In fact, I believe that a really progressive, fruitful, rational, and instructive study of languages can be conducted only on this plan. Many of my audience will remember, perhaps, the bright and encouraging effect, like that of a ray of sunlight on a gloomy day, which the meagre and furtive remarks on comparative philology in Curtius's Greek grammar wrought in that barren and lifeless desert of verbal quibbles.

The principal result obtained by the present method of studying the ancient languages is that which comes from the student's employment with their complicated grammars. It consists in the sharpening of the attention and in the exercise of the judgment by the practice of subsuming special cases under general rules, and of distinguishing between different cases. Obviously, the same result can be reached by many other methods; for example, by difficult games of cards. Every science, the mathematics and the physical sciences included, accomplish as much, if not more, in this disciplining of the judgment. In addition, the matter treated by those sciences has a much higher intrinsic interest for young people, and so engages spontaneously their attention; while on the other hand they are elucidative and useful in other directions in which grammar can accomplish nothing.

Who cares, so far as the matter of it is concerned, whether we say hominum or hominorum in the genitive plural, interesting as the fact may be for the philologist? And who would dispute that the intellectual need of causal insight is awakened not by grammar but by the natural sciences?

It is not our intention, therefore, to gainsay in the least the good influence which the study of Latin and Greek grammar also exercises on the sharpening of the judgment. In so far as the study of words as such must greatly promote lucidity and accuracy of expression, in so far as Latin and Greek are not yet wholly indispensable to many branches of knowledge, we willingly concede to them a place in our schools, but would demand that the disproportionate amount of time allotted to them, wrongly withdrawn from other useful studies, should be considerably curtailed. That in the end Latin and Greek will not be employed as the universal means of education, we are fully convinced. They will be relegated to the closet of the scholar or professional philologist, and gradually make way for the modern languages and the modern science of language.

Long ago Locke reduced to their proper limits the exaggerated notions which obtained of the close connexion of thought and speech, of logic and grammar, and recent investigators have established on still surer foundations his views. How little a complicated grammar is necessary for expressing delicate shades of thought is demonstrated by the Italians and French, who, although they have almost totally discarded the grammatical redundancies of the Romans, are yet not surpassed by the latter in accuracy of thought, and whose poetical, but especially whose scientific literature, as no one will dispute, can bear favorable comparison with the Roman.

Reviewing again the arguments advanced in favor of the study of the ancient languages, we are obliged to say that in the main and as applied to the present, they are wholly devoid of force. In so far as the aims which this study theoretically pursues are still worthy of attainment, they appear to us as altogether too narrow, and are surpassed in this only by the means employed. As almost the sole, indisputable result of this study we must count the increase of the student's skill and precision in expression. One inclined to be uncharitable might say that our gymnasiums and classical academies turn out men who can speak and write, but, unfortunately, have little to write or speak about. Of that broad, liberal view, of that famed universal culture, which the classical curriculum is supposed to yield, serious words need not be lost. This culture might, perhaps, more properly be termed the contracted or lopsided culture.

While considering the study of languages we threw a few side glances at mathematics and the natural sciences. Let us now inquire whether these, as branches of study, cannot accomplish much that is to be attained in no other way. I shall meet with no contradiction when I say that without at least an elementary mathematical and scientific education a man remains a total stranger in the world in which he lives, a stranger in the civilisation of the time that bears him. Whatever he meets in nature, or in the industrial world, either does not appeal to him at all, from his having neither eye nor ear for it, or it speaks to him in a totally unintelligible language.

A real understanding of the world and its civilisation, however, is not the only result of the study of mathematics and the physical sciences. Much more essential for the preparatory school is the formal cultivation which comes from these studies, the strengthening of the reason and the judgment, the exercise of the imagination. Mathematics, physics, chemistry, and the so-called descriptive sciences are so much alike in this respect, that, apart from a few points, we need not separate them in our discussion.

Logical sequence and continuity of ideas, so necessary for fruitful thought, are par excellence the results of mathematics; the ability to follow facts with thoughts, that is, to observe or collect experiences, is chiefly developed by the natural sciences. Whether we notice that the sides and the angles of a triangle are connected in a definite way, that an equilateral triangle possesses certain definite properties of symmetry, or whether we notice the deflexion of a magnetic needle by an electric current, the dissolution of zinc in diluted sulphuric acid, whether we remark that the wings of a butterfly are slightly colored on the under, and the fore-wings of the moth on the upper, surface: indiscriminately here we proceed from observations, from individual acts of immediate intuitive knowledge. The field of observation is more restricted and lies closer at hand in mathematics; it is more varied and broader but more difficult to compass in the natural sciences. The essential thing, however, is for the student to learn to make observations in all these fields. The philosophical question whether our acts of knowledge in mathematics are of a special kind is here of no importance for us. It is true, of course, that the observation can be practised by languages also. But no one, surely, will deny, that the concrete, living pictures presented in the fields just mentioned possess different and more powerful attractions for the mind of the youth than the abstract and hazy figures which language offers, and on which the attention is certainly not so spontaneously bestowed, nor with such good results.[123]

Observation having revealed the different properties of a given geometrical or physical object, it is discovered that in many cases these properties depend in some way upon one another. This interdependence of properties (say that of equal sides and equal angles at the base of a triangle, the relation of pressure to motion,) is nowhere so distinctly marked, nowhere is the necessity and permanency of the interdependence so plainly noticeable, as in the fields mentioned. Hence the continuity and logical consequence of the ideas which we acquire in those fields. The relative simplicity and perspicuity of geometrical and physical relations supply here the conditions of natural and easy progress. Relations of equal simplicity are not met with in the fields which the study of language opens up. Many of you, doubtless, have often wondered at the little respect for the notions of cause and effect and their connexion that is sometimes found among professed representatives of the classical studies. The explanation is probably to be sought in the fact that the analogous relation of motive and action familiar to them from their studies, presents nothing like the clear simplicity and determinateness that the relation of cause and effect does.

That perfect mental grasp of all possible cases, that economical order and organic union of the thoughts which comes from it, which has grown for every one who has ever tasted it a permanent need which he seeks to satisfy in every new province, can be developed only by employment with the relative simplicity of mathematical and scientific investigations.

When a set of facts comes into apparent conflict with another set of facts, and a problem is presented, its solution consists ordinarily in a more refined distinction or in a more extended view of the facts, as may be aptly illustrated by Newton's solution of the problem of dispersion. When a new mathematical or scientific fact is demonstrated, or explained, such demonstration also rests simply upon showing the connexion of the new fact with the facts already known; for example, that the radius of a circle can be laid off as chord exactly six times in the circle is explained or proved by dividing the regular hexagon inscribed in the circle into equilateral triangles. That the quantity of heat developed in a second in a wire conveying an electric current is quadrupled on the doubling of the strength of the current, we explain from the doubling of the fall of the potential due to the doubling of the current's intensity, as also from the doubling of the quantity flowing through, in a word, from the quadrupling of the work done. In point of principle, explanation and direct proof do not differ much.

He who solves scientifically a geometrical, physical, or technical problem, easily remarks that his procedure is a methodical mental quest, rendered possible by the economical order of the province—a simplified purposeful quest as contrasted with unmethodical, unscientific guess-work. The geometer, for example, who has to construct a circle touching two given straight lines, casts his eye over the relations of symmetry of the desired construction, and seeks the centre of his circle solely in the line of symmetry of the two straight lines. The person who wants a triangle of which two angles and the sum of the sides are given, grasps in his mind the determinateness of the form of this triangle and restricts his search for it to a certain group of triangles of the same form. Under very different circumstances, therefore, the simplicity, the intellectual perviousness, of the subject-matter of mathematics and natural science is felt, and promotes both the discipline and the self-confidence of the reason.

Unquestionably, much more will be attained by instruction in the mathematics and the natural sciences than now is, when more natural methods are adopted. One point of importance here is that young students should not be spoiled by premature abstraction, but should be made acquainted with their material from living pictures of it before they are made to work with it by purely ratiocinative methods. A good stock of geometrical experience could be obtained, for example, from geometrical drawing and from the practical construction of models. In the place of the unfruitful method of Euclid, which is only fit for special, restricted uses, a broader and more conscious method must be adopted, as Hankel has pointed out.[124] Then, if, on reviewing geometry, and after it presents no substantial difficulties, the more general points of view, the principles of scientific method are placed in relief and brought to consciousness, as Von Nagel,[125] J. K. Becker,[126] Mann,[127] and others have well done, fruitful results will be surely attained. In the same way, the subject-matter of the natural sciences should be made familiar by pictures and experiment before a profounder and reasoned grasp of these subjects is attempted. Here the emphasis of the more general points of view is to be postponed.

Before my present audience it would be superfluous for me to contend further that mathematics and natural science are justified constituents of a sound education,—a claim that even philologists, after some resistance, have conceded. Here I may count upon assent when I say that mathematics and the natural sciences pursued alone as means of instruction yield a richer education in matter and form, a more general education, an education better adapted to the needs and spirit of the time,—than the philological branches pursued alone would yield.

But how shall this idea be realised in the curricula of our intermediate educational institutions? It is unquestionable in my mind that the German Realschulen and Realgymnasien, where the exclusive classical course is for the most part replaced by mathematics, science, and modern languages, give the average man a more timely education than the gymnasium proper, although they are not yet regarded as fit preparatory schools for future theologians and professional philologists. The German gymnasiums are too one-sided. With these the first changes are to be made; of these alone we shall speak here. Possibly a single preparatory school, suitably planned, might serve all purposes.

Shall we, then, in our gymnasiums fill out the hours of study which stand at our disposal, or are still to be wrested from the classicists, with as great and as varied a quantity of mathematical and scientific matter as possible? Expect no such proposition from me. No one will suggest such a course who has himself been actively engaged in scientific thought. Thoughts can be awakened and fructified as a field is fructified by sunshine and rain. But thoughts cannot be juggled out and worried out by heaping up materials and the hours of instruction, nor by any sort of precepts: they must grow naturally of their own free accord. Furthermore, thoughts cannot be accumulated beyond a certain limit in a single head, any more than the produce of a field can be increased beyond certain limits.

I believe that the amount of matter necessary for a useful education, such as should be offered to all the pupils of a preparatory school, is very small. If I had the requisite influence, I should, in all composure, and fully convinced that I was doing what was best, first greatly curtail in the lower classes the amount of matter in both the classical and the scientific courses; I should cut down considerably the number of the school hours and the work done outside the school. I am not with many teachers of opinion that ten hours work a day for a child is not too much. I am convinced that the mature men who offer this advice so lightly are themselves unable to give their attention successfully for as long a time to any subject that is new to them, (for example, to elementary mathematics or physics,) and I would ask every one who thinks the contrary to make the experiment upon himself. Learning and teaching are not routine office-work that can be kept up mechanically for long periods. But even such work tires in the end. If our young men are not to enter the universities with blunted and impoverished minds, if they are not to leave in the preparatory schools their vital energy, which they should there gather, great changes must be made. Waiving the injurious effects of overwork upon the body, the consequences of it for the mind seem to me positively dreadful.

I know of nothing more terrible than the poor creatures who have learned too much. Instead of that sound powerful judgment which would probably have grown up if they had learned nothing, their thoughts creep timidly and hypnotically after words, principles, and formulÆ, constantly by the same paths. What they have acquired is a spider's web of thoughts too weak to furnish sure supports, but complicated enough to produce confusion.

But how shall better methods of mathematical and scientific education be combined with the decrease of the subject-matter of instruction? I think, by abandoning systematic instruction altogether, at least in so far as that is required of all young pupils. I see no necessity whatever that the graduates of our high schools and preparatory schools should be little philologists, and at the same time little mathematicians, physicists, and botanists; in fact, I do not see the possibility of such a result. I see in the endeavor to attain this result, in which every instructor seeks for his own branch a place apart from the others, the main mistake of our whole system. I should be satisfied if every young student could come into living contact with and pursue to their ultimate logical consequences merely a few mathematical or scientific discoveries. Such instruction would be mainly and naturally associated with selections from the great scientific classics. A few powerful and lucid ideas could thus be made to take root in the mind and receive thorough elaboration. This accomplished, our youth would make a different showing from what they do to-day.[128]

What need is there, for example, of burdening the head of a young student with all the details of botany? The student who has botanised under the guidance of a teacher finds on all hands, not indifferent things, but known or unknown things, by which he is stimulated, and his gain made permanent. I express here, not my own, but the opinion of a friend, a practical teacher. Again, it is not at all necessary that all the matter that is offered in the schools should be learned. The best that we have learned, that which has remained with us for life, outlived the test of examination. How can the mind thrive when matter is heaped on matter, and new materials piled constantly on old, undigested materials? The question here is not so much that of the accumulation of positive knowledge as of intellectual discipline. It seems also unnecessary that all branches should be treated at school, and that exactly the same studies should be pursued in all schools. A single philological, a single historical, a single mathematical, a single scientific branch, pursued as common subjects of instruction for all pupils, are sufficient to accomplish all that is necessary for the intellectual development. On the other hand, a wholesome mutual stimulus would be produced by this greater variety in the positive culture of men. Uniforms are excellent for soldiers, but they will not fit heads. Charles V. learned this, and it should never be forgotten. On the contrary, teachers and pupils both need considerable latitude, if they are to yield good results.

With John Karl Becker I am of the opinion that the utility and amount for individuals of every study should be precisely determined. All that exceeds this amount should be unconditionally banished from the lower classes. With respect to mathematics, Becker,[129] in my judgment, has admirably solved this question.

With respect to the upper classes the demand assumes a different form. Here also the amount of matter obligatory on all pupils ought not to exceed a certain limit. But in the great mass of knowledge that a young man must acquire to-day for his profession it is no longer just that ten years of his youth should be wasted with mere preludes. The upper classes should supply a truly useful preparation for the professions, and should not be modelled upon the wants merely of future lawyers, ministers, and philologists. Again, it would be both foolish and impossible to attempt to prepare the same person properly for all the different professions. In such case the function of the schools would be, as Lichtenberg feared, simply to select the persons best fitted for being drilled, whilst precisely the finest special talents, which do not submit to indiscriminate discipline, would be excluded from the contest. Hence, a certain amount of liberty in the choice of studies must be introduced in the upper classes, by means of which it will be free for every one who is clear about the choice of his profession to devote his chief attention either to the study of the philologico-historical or to that of the mathematico-scientific branches. Then the matter now treated could be retained, and in some branches, perhaps, judiciously extended,[130] without burdening the scholar with many branches or increasing the number of the hours of study. With more homogeneous work the student's capacity for work increases, one part of his labor supporting the other instead of obstructing it. If, however, a young man should subsequently choose a different profession, then it is his business to make up what he has lost. No harm certainly will come to society from this change, nor could it be regarded as a misfortune if philologists and lawyers with mathematical educations or physical scientists with classical educations should now and then appear.

The view is now wide-spread that a Latin and Greek education no longer meets the general wants of the times, that a more opportune, a more "liberal" education exists. The phrase, "a liberal education," has been greatly misused. A truly liberal education is unquestionably very rare. The schools can hardly offer such; at best they can only bring home to the student the necessity of it. It is, then, his business to acquire, as best he can, a more or less liberal education. It would be very difficult, too, at any one time to give a definition of a "liberal" education which would satisfy every one, still more difficult to give one which would hold good for a hundred years. The educational ideal, in fact, varies much. To one, a knowledge of classical antiquity appears not too dearly bought "with early death." We have no objection to this person, or to those who think like him, pursuing their ideal after their own fashion. But we may certainly protest strongly against the realisation of such ideals on our own children. Another,—Plato, for example,—puts men ignorant of geometry on a level with animals.[131] If such narrow views had the magical powers of the sorceress Circe, many a man who perhaps justly thought himself well educated would become conscious of a not very flattering transformation of himself. Let us seek, therefore, in our educational system to meet the wants of the present, and not establish prejudices for the future.

But how does it come, we must ask, that institutions so antiquated as the German gymnasiums could subsist so long in opposition to public opinion? The answer is simple. The schools were first organised by the Church; since the Reformation they have been in the hands of the State. On so large a scale, the plan presents many advantages. Means can be placed at the disposal of education such as no private source, at least in Europe, could furnish. Work can be conducted upon the same plan in many schools, and so experiments made of extensive scope which would be otherwise impossible. A single man with influence and ideas can under such circumstances do great things for the promotion of education.

But the matter has also its reverse aspect. The party in power works for its own interests, uses the schools for its special purposes. Educational competition is excluded, for all successful attempts at improvement are impossible unless undertaken or permitted by the State. By the uniformity of the people's education, a prejudice once in vogue is permanently established. The highest intelligences, the strongest wills cannot overthrow it suddenly. In fact, as everything is adapted to the view in question, a sudden change would be physically impossible. The two classes which virtually hold the reins of power in the State, the jurists and theologians, know only the one-sided, predominantly classical culture which they have acquired in the State schools, and would have this culture alone valued. Others accept this opinion from credulity; others, underestimating their true worth for society, bow before the power of the prevalent opinion; others, again, affect the opinion of the ruling classes even against their better judgment, so as to abide on the same plane of respect with the latter. I will make no charges, but I must confess that the deportment of medical men with respect to the question of the qualification of graduates of your Realschulen has frequently made that impression upon me. Let us remember, finally, that an influential statesman, even within the boundaries which the law and public opinion set him, can do serious harm to the cause of education by considering his own one-sided views infallible, and in enforcing them recklessly and inconsiderately—which not only can happen, but has, repeatedly, happened.[132] The monopoly of education by the State[133] thus assumes in our eyes a somewhat different aspect. And to revert to the question above asked, there is not the slightest doubt that the German gymnasiums in their present form would have ceased to exist long ago if the State had not supported them.

All this must be changed. But the change will not be made of itself, nor without our energetic interference, and it will be made slowly. But the path is marked out for us, the will of the people must acquire and exert upon our school legislation a greater and more powerful influence. Furthermore, the questions at issue must be publicly and candidly discussed that the views of the people may be clarified. All who feel the insufficiency of the existing rÉgime must combine into a powerful organisation that their views may acquire impressiveness and the opinions of the individual not die away unheard.

I recently read, gentlemen, in an excellent book of travels, that the Chinese speak with unwillingness of politics. Conversations of this sort are usually cut short with the remark that they may bother about such things whose business it is and who are paid for it. Now it seems to me that it is not only the business of the State, but a very serious concern of all of us, how our children shall be educated in the public schools at our cost.