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l the four faculties to form one University a mere relic of the Middle Ages t Many valid arguments have been adduced for separating them. Why not dismiss the medical faculty to the iiospitals of our great towns, the scientific men to the Poly- technic Schools, and form special seminaries for the theologians and jurists? Long may the German universities be preserved from such a fate ! Then, indeed, would the connection between the different sciences bo finally broken. How essential that connection is, not only from an university point of view, as tending to keep alive the intellectual energy of the country, but also on material grounds, to secure the successful application of that energy, will be evident from a few considerations. First, then, I would say that union of the different faculties is necessary to maintain a healthy equilibrium among the in- tellectual energies of students. Each study tries certain of our intellectual faculties more than the rest, and strengthens them accordingly by constant exercise. But any sort of one-sided development is attended with danger ; it disqualifies us for using those faculties that are less exercised, and so renders us less capable of a general view ; above aU it leads us to overvalue ourselves. Any one who has found himself much more suc- cessful than others in some one department of intellectual labour, is apt to forget that there are many other things which they can do better than he can : a mistake — I would have every student remember — which is the worst enemy of all intellectual activity. How many men of ability have forgotten to practise that criticism of themselves which is so essential to the student, and 60 hard to exercise, or have been completely crippled in their progress, because they have thought dry, laborious drudgery beneath them, and have devoted all their energies to the quest of brilliant theories and wonder-working discoveries ! How many such men have become bitter misanthropes, and put an end to a melancholy existence, because they have failed to obtain among their fellows that recognition which must be vron by 10 ON THE RELATION OF labour and results, but which is ever withheld from mere self-con- scious genius ! And the more isolated a man is, the more liable is he to this danger ; while, on the other hand, nothing is more inspiriting than to feel yourself forced to strain every nerve to win the admiration of men whom you, in your turn, must admire. In comparing the intellectual processes involved in the pursuit of the several branches of science, ■v.e are struck by certain generic diflerences, dividing one group of sciences from another. At the same time it must not be forgotten that every man of conspicuous ability has his own. special mental constitution which fits him for one line of thought rather than another. Compare the work of two contemporary investigators even in closely allied branches of science, and you will generally be able to convince yourself that the more distinguished the men are the more clearly does their individuality come out, and the less qualified would either of them be to carry on the other's researches. To-day I cau, of course, do nothing more than characterise Bome of the most general of these diflerences. I have already noticed the enormous mass of the materials accumulated by science. It is obvious that the organisation and arrangement of them must be proportionately perfect, if we are not to be hopelessly lost in the maze of erudition. One of the reasons why we can so far surpass our predecessors in each individual study is that they have shown us how to organise our knowledge. This organisation consists, in the first place, of a mechanical aiTangement of materials, such as is to be found in our cata- logues, lexicons, registers, indexes, digests, scientific and literary annuals, systems of natural histoiy, and the like. By these appliancas thus much at least is gained, that such know- ledge as cannot be cairied about in the memory is immedi- ately accessible to anyone who wants it. With a good lexicon i, school-boy of the present day can achieve results in the inter- pretation of the classics which an Erasmus, with the erudition of a lifetime, could hardly attain. Works of this kind form, so to speak, our intellectual principal with the interest of which we ti-ade : it is, so to speak, like capital invested in land. The NATURAL SCIENCE TO GENERAL SCIENCE. ll learning buried in catalogues, lexicons, and indexes looks as bai-e and uninviting as the soil of a farm ; the uninitiated cannot Bee or appreciate the labour and capital already invested there j to them the work of the ploughman seems infinitely dull, weary, and monotonous. But though the compiler of a lexicon or of a system of natural history must be prepared to encounter labour as weary and as obstinate as the ploughman's, yet it need not be supposed that his work is of a low type, or that it is by any means as dry and mechanical as it looks when we have it before us in black and white. In thLs, as in any other sort of scientific work, it is necessary to discover every fact hj careful observation, then to verify and collate them, and to separate what is important from what is not. All this requires a. man with a thorough grasp both of the object of the compilation and of the matter and methods of the science; and for such a man every detail has its bearing on the whole, and its special interest. Otherwise dictionary-making would be the vilest drudgery imaginable.' That the influence of the progressive development of scientific ideas extends to these works is obvious from the constant demand for new lexicons, new natural histories, new digests, new catalogues of stars, all denoting advancement in the art of methodising and organising science. But our knowledge is not to lie dormant in the shape of catalogues. The very fact that we must carry it about in black and white shows that our intellectual mastery of it is incomplete. It is not enough to be acquainted with the facts; scientific knowledge begins only when their laws and their causes are un- veiled. Our materials must be worked up by a logical process; and the first step is to connect like with like, and to elaborate a general conception embracing them all. Such a conception, as the name implies, takes a number of single facts together, and stands as their representative in our mind. We call it a general conception, or the conception of a genus, when it embraces a number of existing objects; we call it a law when it embraces a series of incidents or occurrences. When, for example, I havo * Condcndaque lexica mandat damaatis. — Tb. 12 ON THE RELATION OF made out that all mammals — that is, all warm-blooded, vivi- parous animals — breathe through lungs, have two chambei-s in the heart, and at least three tympanal bones, I need no longer remember these anatomical peculiarities in the individual cases of the monkey, the dog, the horse, and the whale; the general rule includes a vast number of single instances, and represents them in my memory. When I enunciate the law of refraction, not only does this law embrace all cases of rays falling at all possible angles on a plane surface of water, and inform me of the result, but it includes all cases of rays of any colour incident on transparent surfaces of any form and any constitution what- soever. This law, therefore, includes an infinite number of cases, which it would have been absolutely impossible to carry in one's memory. Moreover, it should be noticed that not only does this law include the cases which we ourselves or other men have already observed, but that we shall not hesitate to apply it to new cases, not yet observed, with absolute confidence in the reliability of our results. In the same way, if we were to find a new species of mammal, not yet dissected, we are entitled to assume, with a confidence bordering on a certainty, that it has lungs, two chambers in the heart, and three or more tympanal bones. Thus, when we combine the results of experience by a pro- cess of thought, and form conceptions, whether general concep- tions or laws, we not only bring our knowledge into a form in which it can be easily used and easily retained, but we actually enlarge it, inasmuch as we feel ourselves entitled to extend the rules and the laws we have discovered to all similar cases that may be hereafter presented to us. The above-mentioned examples are of a class in which the mental process of combining a number of single ca.ses so as to form conceptions is unattended by farther difficulties, and can be distinctly followed in all its stages. But in complicated cases it is not so easy completely to separate like facts from unlike, and to combine them into a clear well-defined conception. Assume that we know a man to be ambitious ; we shall perhaps be able to predict with tolerable certainty that if he has to act under NATURAL SCIENCE TO GENERAL SCIENCE. 13 r'?rtam conditions, he will follow the dictates of his ambition, and decide on a certain line of action. But, in the first place, we cannot define with absolute precision what constitutes an ambitious man, or by what standard the intensity of his ambition is to be measured; nor, again, can we say precisely what degree of ambition must operate in order to impress the given direction on the actions of the man under those particular circumstances. Accordingly, we institute comparisons between the actions of the man in question, as far as we have hitherto observed them, and those of other men who in similar cases have acted as he has done, and we draw our inference respecting his future actions without being able to express either the major or the minor pre- miss in a clear, sharply defined form — perhaps even without hav- ing convinced ourselves that our anticipation rests on such an analogy as I have described. In such cases our decision proceeds only from a certain psychological instinct, not from conscious reasoning, though in reality we have gone through an intellectual process identical with that which leads us to assume that a newly discovered mammal has lungs. This latter kind of induction, which can never be perfectly assimilated to forms of logical reasoning, nor pressed so fir as to establish universal laws, plays a most important part in human life. The whole of the process by which we translate our sen- sations into perceptions depends upon it, as appears especially from the investigation of what are called illusions. For in- stance, when the retina of the eye is irritated by a blow, we imagine we see a light in our field of vision, because we have, throughout onx lives, felt irritation in the optic nerves only when there was light in the field of vision, and have become accustomed to identify the sensations of those nerves with the presence of light in the field of vision. Moreover, such is the complexity of the influences affecting the formation both of character in general and of the mental condition at any given moment, that this same kind of induction necessarily plays a leading part in the investigation of psychological processes. In fact, in ascribing to ourselves free-will, that is, full power to act aa we please without being subject to a stern inevitable law of 14 ON THE RELATION OF csiusality, we deny iw toto the possiblity of referring at Ipast one of the ways in which our mental activity expresses itself to a rigorous law. We might possibly, in opposition to logical induction which reduces a question to clearly defined universal propositions, call this kind of reasoning (esthetic induction, because it is most con- spicuous in the higher class of works of art. It is an essential part of an artist's talent to reproduce by words, by form, by colour, or by music, the external indications of a character or a state of mind, and by a kind of instinctive intuition, uncon- trolled by any definable rule, to seize the necessary steps by which we pass from one mood to another. If we do find that the artist has consciously worked after general rules and abstrac- tions, we think his work poor and commonplace, and cease to admire. On the contrary, the works of great artists bring be- fore us characters and moods with such a lifelikeness, with such a wealth of individual traits and such an overwhelming con- viction of truth, that they almost seem to be more real than the reality itself, because all disturbing influences are eliminated. Now if, after these reflections, we proceed to review the difTerent sciences, and to classify them according to the method by which they must arrive at their results, we are brought face to face with a generic diSerence between the natural and the moral sciences. The natural sciences are for the most part in a position to reduce their inductions to sharply defined general rules and principles; the rooral sciences, on the other hand, have, in by far the most numerous cases, to do with conclusions arrived at by psychological instinct. Philology, in so far as it is concerned with the interpretation and emendation of the texts handed down to us, must seek to feel out, as it were, the meaning which the author intended to express, and the accessory notions which he wished hia words to suggest: and for that pur- pose it is necessary to start with a correct insight, both into the personality of the author, and into the genius cf the language in which he wrote. All this affords sco]ie for aesthetic, but not for strictly logical, induction. It is only possible to pass judgment, if you have ready in your memory a great number of NATLfRAL SCIENCE TO GENERAL SCIENCE. 15 Biniilar facts, to be instantaneously confronted with the question yoa are trying to solve. Accordingly, one of the first requisites for studies of this class ia an accuiute and ready memory. Many celebrated historians and philologists have, in fact, astounded their contemporaries by their extraordinary strength of memory. Of course memory alone ia insufficient without a knack of everywhere discovering real resenablanoe, and without a delicately and fully trained insight into the springs of human action ; while this again is unattainable without a certain warmth of sympathy and an interest in observing the working of other men's minds. Intercourse with our fellow-men in daily life must lay the foundation of this insight, but the study of history and art serves to make it richer and completer, for there we aee men acting under comparatively unusual conditions, and thus come to appreciate the full scope of the energies which lie hidden in our breasts. None of this group of sciences, except grammar, lead us, as a rule, to frame and enunciate general laws, valid under all circum- stances. The laws of grammar are a product of the human will, though they can hardly be said to have been framed de- liberately, but rather to have grown up gradually, as they were wanted. Accordingly, they present themselves to a learner rather in the form of commands, that is, of laws imposed by external authority. With these sciences theology and jurisprudence are naturally connected. In fact, certaia branches of history and philology serve both as stepping-stones and as handmaids to them. The general laws of theology and jurisprudence are likewise com- mands, laws imposed by external authority to regulate, from a moral or juridical point of view, the actions of mankind ; not laws which, like those of nature, contain generalisations from a vast multitude of facts. At the same time the application of a grammatical, legal, moral, or theological rule is couched, like the application of a law of nature to a particular case, in the forms of logical inference. The rule forms the major premiss of the syllogism, while the minor must settle whether the case in ques- tion satisfies the conditions to which the rule is intended to 16 ON THE RELATION OF apply. The solution of this latter problem, whether in gram- matical analysis, where the meaning of a sentence is to be evolved, or in the legal criticism of the credibility of the facts alleged, of the intentions of the parties, or of the meaning of the documents they have put into court, virill, in most cases, be again a matter of psychological insight. On the other hand, it should not be forgotten that both the syntax of fully developed languages and a system of jurisprudence gradually elaborated, aa ours has been, by the practice of more than 2,000 years,' have reached a high pitch of logical completeness and consistency; so that, speaking generally, the cases which do not obviously fall under some one or other of the laws actually laid down are quite exceptional. Such exceptions there will always be, for the legis- lation of man can never have the absolute consistency and perfection of the laws of nature. In such cases there is no course open but to try and guess the intention of the legislator; or, if needs be, to supplement it after the analogy of his decisions in similar cases. Grammar and jurisprudence have a certain advantage aa means of training the intellect, inasmuch as they tax pretty equally all the intellectual powers. On this account secondary education among modern European nations is based mainly upon the grammatical study of foreign languages. The mother- tongue and modern foreign languages, when acquired solely by pi-actice, do not call for any conscious logical exercise of thought, though we may cultivate by means of them an appreciation for artistic beauty of expression. The two classical languages, Latin and Greek, have, besides their exquisite logical subtlety and aesthetic beauty, an additional advantage, which they seem to possess in common with most ancient and original languages — they indicate accurately the relations of words and sentences to each other by numerous and distinct inflexions. Languages are, as it were, abraded by long use; grammatical distinctions are cut down to a minimum for the sake of brevity and rapidity ' It should be remembered that the Roman law, which has only partially and indirectly influenced English practice, is the recognised basis of German jurisprudence. — Tb. NATURAL SCIENCE TO GENERAL SCIENCE. 17 of expression, and are thus made less and less definite, as ia obvious from the comparison of any modern European language with Latin; in English the process has gone further than in any other. This seems to me to be really the reason why the modern languages are far less fitted than the ancient for instru- ments of education.' As grammar is the staple of school education, legal studies are used, and rightly, as a means of training persons of maturer age, even when not specially required for professional purposes. We now come to those sciences which, in respect of the kind of intellectual labour they require, stand at the opposite end of the series to philology and history ; namely, the natural and physical sciences. I do not mean to say that in many branches even of these sciences an instinctive appreciation of analogies and a certain artistic sense have no part to play. On the contrary, in natural history the decision which characteristics are to be looked upon as important for classification, and which as unimportant, what divisions of the animal and vegetable kingdoms are more natural than others, is really left to an instinct of this kind, acting without any strictly definable rule. And it is a very suggestive fact that it was an artist, Goethe, who gave the first impulse to the researches of comparative anatomy into the analogy of corresponding organs in different animals, and to the parallel theory of the metamorphosis of leaves in the vegetable kingdom; and thus, in fact, really pointed out the direction which the science has followed ever since. But even in those departments of science where we have to do with the least understood vital processes, it is, speaking genei'ally, far easier to make out general and compre- hensive ideas and principles, and to express them in definite language, than in cases where we must base our judgment on the analysis of the human mind. It ia only when we come to the experimental sciences to which mathematics are applied, and especially when we come to pure mathematics, that wa * Those to whom Germaa 13 not a foreign tongue may, perhaps, be per- mitted to hold different views on the efficacy of modern languages in educa- tion.— Te. I. 18 ON THE RELATION OF see the peculiar characteristics of the natural and physical Bcienoes fully brought out. The essential differentia of these sciences seems to me to consist in the comparative ease with -which the individual results of observation and experiment are combined under genei-al laws of unexceptionable validity and of an extra- ordinarily comprehensive character. In the moral sciences, on the other hand, this is just the point where insuperable diffi- culties are encountered. In mathematics the general propo- sitions which, under the name of axioms, stand at the head of the reasoning, are so few in number, so comprehensive, and so immediately obvious, that no proof whatever is needed for them. Let me remind you that the whole of algebra and arithmetic is developed out of the three axioms : — ' Things which are equal to the same things are equal to one another.' ' If equals be added to equals, the wholes are equal.' ' If unequals be added to equals, the wholes are unequal.' And the axioms of geometry and mechanics are not more numerous. The sciences we have named are developed out ot these few axioms by a continual process of deduction from them in more and more complicated cases. Algebra, however, does not confine itself to findiDg the sum of the most hetero- geneous combinations of a finite number of magnitudes, but in the higher analysis it teaches us to sum even infinite series, be terms of which increase or diminish according to the most various laws ; to solve, in fact, problems which could never be completed by direct addition. An instance of this kind shows us the conscious logical activity of the mind in its purest and most perfect form. On the one hand we see the laborious nature of the process, the extreme caution with which it is necessary to advance, the accuracy required to determine exactly the scope of such universal principles as have been attained, the difficulty of forming and understanding abstract conceptions. On the other hand, we gain confidence in the certainty, the range, and the fertility of this kind of intellectual work. The fertility of the method comes out more strikingly in NATURAL SCIENCE TO GENERAL SCIENCE. VJ applied mathematics, especially in mathematical physics, in- cluding, of course, physical astronomy. From the time when Newton discovered, by analysing the motions of the planets on mechanical principles, that every particle of ponderable matter in the universe atti-acts every other particle with a force vary- ing inversely as the square of the distance, astronomers have been able, in virtue of that one law of gravitation, to calculate with the greatest accuracy the movements of the planets to the remotest past and the most distant future, given only the posi- tion, velocity, and mass of each body of our system at any one time. More than that, we recognise the operation of this law in the movements of double stars, whose distances from us are so great that their light takes years to reach us ; in some cases, indeed, so groat that all attempts to measure thera have failed. This discovery of the law of gravitation and its consequences is the most imposing achievement that the logical power of the human mind has hitherto performed. I do not mean to say that there have not been men who in power of abstraction have equalled or even surpassed Newton and the other astronomers, who either paved the way for his discovery, or have carried it out to its legitimate consequences; but there has never been presented to the human mind such an admirable subject as those involved and complex movements of the planets, which hitherto had served merely as food for the astrological super- stitions of ignorant star-gazers, and were now reduced to a single law, capable of rendering the most exact account of the minutest detail of their motions. The principles of this magnificent discovery have been suc- cessfully applied to several other physical sciences, among which physical optics and the theory of electricity and magnetism are especially worthy of notice. The experimental sciences have one great advantage over the natural sciences in the investiga- tion of general laws of nature : they can change at pleasure the conditions under which a given result takes place, and can thus confine themselves to a small number of characteristic instances, in order to discover the law. Of course its validity must then 02 20 ON THE RELATION OP stand the test of application to more complex cases. Accord- ingly the physical sciences, when once the right methods have been discovered, have made proportionately rapid progress. Not only have they allowed us to look back into primaeval chaos, where nebulous masses were forming themselves into suns and planets, and becoming heated by the energy of their contraction ; not only have they permitted us to investigate the chemical constituents of the solar atmosphere and of the remotest fixed stars, but they have enabled us to turn the forces of surrounding nature to our own uses and to make them the ministers of our will. Enough has been said to show how widely the intellectual processes involved in this group of sciences differ, for the most part, from those required by the moral sciences. The mathe- matician need have no memory whatever for detached facts, the physicist hardly any. Hypotheses based on the recollection of similar cases may, indeed, be useful to guide one into the right track, but they have no real value till they have led to a precise and strictly defined law. Nature does not allow us for a moment to doubt that we have to do with a rigid chain of cause and effect, admitting of no exceptions. Therefore to us, as her students, goes forth the mandate to labour on till we have dis- covered unvarying laws ; till then we dare not rest satisfied, for then only can our knowledge grapple victoriously with time and space and the forces of the universe. The iron labour of conscious logical reasoning demands great persevei-ance and great caution ; it moves on but slowly, and is rarely illuminated by brilliant flashes of genius. It knows little of that facility with which the most varied instances come thronging into the memory of the philologist or the historian. Rather is it an essential condition of the methodical progress of mathematical reasoning that the mind should remain concen- trated on a single point, undisturbed alike by collateral ideas on the one hand, and by wishes and hopes on the other, and moving on steadily in the direction it has deliberately chosen. A cele- brated logician, Mr. John Stuart Mill, expresses his conviction that the inductive sciences have of late done more for the advance NATURAL SCIENCE TO GENERAL SCIENCE. 21 of logical methods than the labours of philosophers properly so cilled. One essential ground for such an assertion must un- doubtedly be that in no department of knowledge can a fault in the chain of reasoning be so easily detected by the incorrect- ness of the results as in those sciences in which the results of reasoning can be most directly compared with the facts of nature. Though I have maintained that it is in the physical sciences, and especially in such branches of them as are treated mathe- matically, that the solution of scientific problems has been most successfully achieved, you will not, I trust, imagine that I wish to depreciate other studies in comparison with them. If the natural and physical sciences have the advantage of great per- fection in form, it is the privilege of the moral sciences to deal with a richer material, with questions that touch more nearly the interests and the feelings of men, with the human mind itself, in fact, in its motives and the difierent branches of its activity. They have, indeed, the loftier and the more difficult task, but yet they cannot afford to lose sight of the example of their rivals, which, in form at least, have, owing to the more ductile nature of their materials, made greater progress. Not only have they something to learn from them in point of method, but they may also draw encouragement from the greatness of their results. And I do think that our age has learnt many lessons from the physical sciences. The absolute, unconditional reverence for facts, and the fidelity with which they are col- lected, a certain distrustfulness of appearances, the effort to detect in all cases relations of cause and effect, and the tendency to assume their existence, which distinguish our century from preceding ones, seem to me to point to such an influence. I do not intend to go deeply into the question how f j,r mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school educa- tion. But it is, in reality, one of the questions of the day. Id proportion as the range of science extends, its system and or- ganisation must be improved, and it must inevitably come about that individual students will find themselves compelled to go 22 ON THE RELATION OF through a stricter course of training than grammar is in a [josition to supply. What strikes me in my own experience oi students who pass from our classical schools to scientific and medical studies, is, first, a certain laxity in the application of fetrictly universal laws. The grammatical rules in which they have heen exercised are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premisses at i glance, and inasmuch as the de- cision of disputed questions often depends on an sesthetic feeling for beauty of expression, and for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to a certain indolence and vagueness of thought, the sad efiects of which are not confined to sub- sequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognised but that of one's own inteUigence. So much for the several branches of science considered aa exercises for the intellect, and as supplementing each other in that respect. But knowledge is not the sole object of man upon earth. Though the sciences arouse and educate the subtlest powers of the mind, yet a man who should study simply for the sake of knowing, would assuredly not fulfil the purpose of his existence. We often see men of considerable endowments, to whom their good or bad fortune has secured a comfortable livelihood or good social position, without giving them, at the same time, ambition or energy enough to make them work, dragging out a weary, unsatisfied existence, while all the time they fancy they are following the noblest aim of life by constantly devoting themselves to the increase of their knowledge, and the cultivation of their minds. Action alone gives a man a life NATURAL SCIENCE TO GENERAL SCIENCE. 23 worth living ; and therefore he must aim either at the practical application of his knowledge, or at the extension of the limits of science itself. For to extend the limits of science is really to work for the progress of humanity. Thus we pass to the second link, uniting the different sciences, the connection, namely, between the subjects of which they treat. Knowledge is power. Our age, mwe than any other, is in a position to demonstrate the truth of this maxim. We have taught the forces of inanimate nature to minister to the wants of human life and the designs of the human intellect. The application of steam has multiplied our physical strength a milhon-fold ; weaving and spinning machines have relieved us of labours the only merit of which consisted in a deadening monotony. The intercourse between men, with its far-reaching influence on material and intellectual progress, has increased io an extent of which no one could have even dreamed within the lifetime of the older among us. But it is not merely on the machines by which our powers are multiplied ; not merely on rifled cannon and armoui'-plated ships ; not merely on accumu- lated stores of money and the necessaries of life, that the power of a nation rests : thoagh these things have exercised so unmistak- able an influence that even the proudest and most obstinate des- potisms of our times have been forced to think of removing restric- tions on industry, and of conceding to the industrious middle classes a due voice in their councils. But political organisation, the administration of justice, and the moral discipline of individual citizens are no less important conditions of the prejjonderance of civilised nations; and so surely a-s a nation remains in- accessible to the influences of civilisation in these respects, so surely is it on the high road to destruction. The several con- ditions of national prosperity act and react on each other; where the administi-ation of justice is uncertain, where the interests of the majority cannot be asserted by legitimate means, the development of the national resources, and of the power depending upon them, is impossible ; nor, again, is it possible to make good soldiers except out of men who have learnt under just laws to educate the sense of honour that characterises an 24 ON THE RELATION OF independent man, certainly not out of those who have lived the submissive slaves of a capricious tyrant. Accordingly every nation is interested in the progress of know ledge on the simple ground of self-preservation, even were there no higher wants of an ideal character to be satisfied; and not merely in the development of the physical sciences, and their technical application, but also in the progress of legal, political, and moral sciences, and of the accessory historical and philological studies. No nation which would be independent and influential can afford to be left behind in the race. Nor has this escaped the notice of the cultivated peoples of Europe. Never before was so large a part of the public resources devoted to universities, schools, and scientific institutions. We in Heidelberg have this year occasion to congratulate ourselves on another rich endowment granted by our government and our parliament. I was speaking, at the beginning of my address, of the in- creasing division of labour and the improved organisation among scientific workers. In fact, men of science form, as it were, an organised army labouring on behalf of the whole nation, and generally under its direction and at its expense, to augment the btock of such knowledge as may serve to promote industrial enterprise, to increase wealth, to adorn life, to improve political and social relations, and to further the moral development of indivi- dual citizens. After the immediate practical results of their work we forbear to inquire ; that we leave to the uninstructed. We are convinced that whatever contributes to the knowledge of the forces of nature or the powers of the human mind is worth cherishing, and may, in its own due time, bear practical fruit, very often where we should least have expected it. Who, when Galvani touched the muscles of a frog with different metals, and noticed their contraction, could have dreamt that eighty years afterwards, in virtue of the self-same process, whose earliest manifestations attracted his attention in his anatomical researches, all Europe would be traversed with wii-es, flashing intelligence from Madrid to St. Petersburg with the speed of lightningl In the hands of Galvani, and at first even in Volta's, electrical currents were phenomena capable of exerting NATURAL SCIENCE TO GENEKal, SCIENCE. 25 only the feeblest forces, and could not be detected except by the most delicate apparatus. Had they been neglected, on the ground that the investigation of them promised no immediate practical result, we should now bo ignorant of the most import- ant and most interesting of the links between the various forces of nature. When young Galileo, then a student at Pisa, noticed one day during divine service a chandelier swinging backwards and forwards, and convinced himself, by counting his pulse, that the duration of the oscillations was independent of the arc thi-ough which it moved, who could know that this discovery would eventually put it in our power, by means of the pendulum, to attain an accuracy in the measurement of time tUl then deemed impossible, and would enable tlie storm-tossed seaman in the most distant oceans to determine in what degree of longi- tude he was sailing ? Whoever, in the pursuit of science, seeks after immediate practical utility, may generally rest assured that he will seek in vain. All that science can achieve is a perfect knowledge and a perfect understanding of the action of natural and moral forces. Each individual student must be content to find his reward in rejoicing over new discoveries, as over new victories of mind over reluctant matter, or in enjoying the aesthetic beauty of a well-ordered field of knowledge, where the connection and the filiation of every detail is clear to the mind, and where all denotes the presence of a ruling intellect ; he must rest satisfied with the consciousness that he too has contributed something to the increasing fund of knowledge on which the dominion of man over all the forces hostile to intelligence reposes. He wUl, indeed, not always be permitted to expect from his fellow-men appreciation and reward adequate to the value of his work. It is only too true that many a man to whom a monument has been erectedafter his death would have been delighted to receive during his lifetime a tenth part of the money spent in doing honour to his memory. Atthesame time, wemust acknowledge that the value of scientific discoveries is now far more fully recog- nised than formerly by public opLoion, and that instances of the authors of great advance in science starving in obscurity have 20 ON THE RELATION OF become rarer and rarer. On the contrary, the governments and peoples of Europe have, as a rule, admitted it to be their doty to recompense distinguished acliievements in science by appro' priate appointments or special rewards. The sciences have then, in this respect, all one common aim, to establish the supremacy of intelligence over the world : while the moral sciences aim directly at making the resources of intellectual life more abundant and more interesting, and seek to separate the pure gold of truth from alloy, the physical sciences are striving indirectly towards the same goal, inasmuch as they labour to make mankind more and more independent of the material restraints that fetter their activity. Each student works in his own department, he chooses for himself those tasks for which he is best fitted by his abilities and his training. But e,ach one must be convinced that it is only in connection with others that he can further the great work, and that therefore he is bound, not only to investigate, but to do his utmost to make the results of his investigation completely and easily accessible. If he does this, he will derive assistance from others, and will in his turn be able to render them his aid. The ajmals of science abound in evidence how such mutual services have been exchanged, even between departments of science apparently most remote. Historical chronology is essentially based on astronomical calculations of eclipses, accounts of which are pre- served in ancient histories. Conversely, many of the important data of astronomy — for instance, the invariability of the length of the day, and the periods of several comets — rest upon ancient historical notices. Of late years, physiologists, especially BrUcke, have actually undertaken to draw up a complete system of all the vocables that can be produced by the organs of speech, and to base upon it propositions for an universal alphabet, adapted to all human languages. Thus physiology has enteied the service of comparative philology, and has already succeeded in account- ing for many apparently anomalous substitutions, on the ground that they are governed, not as hitherto supposed, by the laws of euphony, but by similarity between the movements of the mouth that produce ihem. Again, comparative philology gives us NATURAL SCIENCE TO GENERAL SCIENCE. 27 information about tlie relationships, the separations, and the migrations of tribes in prehistoric times, and of the degree of civilisation which they had reached at the time when they parted. For the names of objects to which they had already learnt to give distinctive appellations reappear as words common to their later languages. So thatthe study of languages actually gives us historical data for periods respecting which no other historical evidence exists.' Yet again I may notice the help which not only the sculptor, but the archseologist, concerned with the investigation of ancient statues, derives from anatomy. And if I may be permittod to refer to my own most recent studies, I would mention that it is possible, by reference to physical acoustics and to the physiological theory of the sensation of hearing, to account for the elementary principles on which our musical system is constructed, a problem essentially within the sphere of esthetics. In fact, it is a general principle that the physiology of the organs of sense is most intimately connected with psychology, inasmuch as physiology traces in our sensations the results of mental processes which do not fall within the sphere of consciousness, and must therefore have remained inac- cessible to us. I have been able to quote only some of the most striking instances of this interdependence of different sciences, and such as could be exjilained in a few words. Naturally, too, I have tried to choose them from the most widely separated sciences. But far wider is of course the influence which allied sciences exert upon each other. Of that I need not speak, for each of you knows it from his own experience. In conclusion, I would say, let each of us think of himself, not as a man seeking to gratify his own thirst for knowledge, or to promote his own private advantage, or to shine by his own abiUties, but rather as a fellow-labourer in one great com- mon work bearing upon the highest interests of humanity. Then assuredly we shall not fail of our reward in the approval of our own conscience and the esteem of our fellow-citizens. ' See, for example, Mommsen's Rome, Book I. ch. U. — Tk, 28 ON THE RELATION OF NATURAL SCIENCE. To keep up these relations between all searchers after truth and all branches of knowledge, to animate them all to vigorous co- operation towards their common end, is the great office of the Universities. Therefore is it necessary that the four faculties should ever go hand in hand, and in this conviction will we strive, so far as in us lies, to press onward to the fulfilment of our great mission. 29 ON GOETHE'S SCIENTIFIC EISEAECHES. A Lecture delivered be/ore the German Society of Kinigsberg, in the Spring of 1853. It could not but be that Groethe, whose comprehensive genius was most strikingly apparent in that sober clearness with which he grasped and reproduced with lifelilie freshness the realities of nature and human life in their minutest details, should, by those very qualities of his mind, be drawn towards the study of physical science. And in that department, he was not content with acquiring what others could teach him, but he soon at- tempted, as so original a mind wag sure to do, to strike out an in- dependent and a very characteristic line of thought. He directed his energies not only to the descriptive but also to the experi- mental sciences ; the chief results being his botanical and osteological treatises on the one hand, and his theory of colour on the other. The first germs of these researches belong for the most part to the last decade of the eighteenth century, though some of them were not completed nor published till later. Since that time science has not only made great progress but has widely extended its range. It has a-ssumed in some respects an entirely new aspect, it has opened out new fields of research and undergone many changes in its theoretical views. I shall attempt in the following Lecture to sketch the rela- tion of Goethe's researches to the present standpoint of science, and to bring out the guiding idea that is common to them alL 30 ON Goethe's scientific RESEAEceES. The peculiar character of the descriptive sciences — botany, zoology, anatomy, and the like — is a necessary result of the work imposed upon them. They undertake to collect and sift an enormous mass of facts, and, above all, to bring them into a logical order or system. Up to this point their work is only the dry task of a lexicographer ; their system is nothing more than a muniment^room in which the accumulation of papers is so arranged that any one can find what he wants at any moment. The more intellectual part of their work and their real interest only begins when they attempt to feel after the scattered traces of law and order in the disjointed, heterogeneous mass, and out of it to construct for themselves an orderly system, accessible at a glance, in which every detail has its due place, and gains additional interest from its connection with the whole. In such studies, both the organising capacity and theinsighc of our poet found a congenial sphere — the epoch was moreover propitious to him. He found ready to his hand a sufficient store of logically arranged materials in botany and comparative anatomy, copious and systematic enough to admit of a compre- hensive view, and to indicate the way to some happy glimpse of an all-pervading law ; while his contemporaries, if they made any efforts in this direction, wandered without a compass, or else they were so absorbed in the dry registration of facts, that they scarcely ventured to think of anything beyond. It was reserved for Goethe to introduce two ideas of infinite fruit- fulness. The first was the conception that the differences in the anatomy of different animals are to be looked upon as variations from a common phase or type, induced by differences of habit, locality, or food. The observation which led him to this fertile conception was by no means a striking one ; it is to be found in a monograph on the intermaxillary bone, written as early as 1786. It was known that in most vertebi-ate animals (that is, mammalia, birds, amphibia, and fishes) the upper jaw consists of two bones, the upper jaw-bone and the intermaxillary bone. The former always contains in the mammalia the molar and the canine teeth, the latter the incisors. Man, who is dis- ON Goethe's scientific eesearciiks. 31 tinguislied from all other animals by the absence of the pi'ojecting snout, has, on the contrary, on each side only one bone, the upper jaw-bone, containing all the teeth. This being so, Goethe discovered in the human skull faint traces of the sutures which in animals unite the upper and middle jaw-bones, and concluded from it that man had originally possessed an intermaxillary bone, which had subsequently coalesced with the upper jaw-bone. This obscure fact opened up to him a source of the most intense interest in the field of osteology, generally so much decried as the driest of studies. That details of structure should be the same in man and in animals when the parts continue to perform similar functions had involved nothing extraordinary. In fact, Camper had already attempted, on this principle, to trace similarities of structure even between man and fishes. But the persistence of this similarity, at least in a rudimentary form, even in a case when it evidently does not correspond to any of the requirements of the complete human structure, and consequently needs to be adapted to them by the coalescence of two parts originally separate, was what struck Goethe's far-seeing eye, and suggested to him a far more comprehensive view than had hitherto been taken. Further studies soon convinced him of the univei-sality of his newly discovered principle, so that in 1795 and 1796 he was able to define more clearly the idea that had struck him in 1786, and to commit it to writing in his ' Sketch of a General Intro- duction to Comparative Anatomy.' He there lays down with the utmost confidence and precision that all differences in the structure of animals must be looked upon as variations of a single primitive type, induced by the coalescence, the alteration, the increase, the diminution, or even the complete removal of single parts of the structure ; the very principle, in fact, which has become the leading idea of comparative anatomy in its- present stage. Nowhere has it been better or more clearly ex- pressed than in Goethe's writings. Subsequent authorities have made but few essential alterations in his theory. The most important of these is, that we no longer undertake to construct Q common type for the whole animal kingdom, but are content 32 ON Goethe's scientific researches. vith one for each of Cuvier's great divisions. The industry of Goethe's successors has accumulated a well-sifted stock of facts, infinitely more copious than what he could command, and has followed up successfully into the minutest details what he could only indicate in a general way. The second leading conception which science owes to Goethe enunciated the existence of an analogy between the different parts of one and the same organic being, similar to that which we have just pointed out as subsisting between corresponding parts of different species. In most organisms we see a great repetition of single parts. This is most striking in the veget- able kingdom ; each plant has a great number of similar stem leaves, simUar petals, similar stamens, and so on. According to Goethe's own account, the idea first occurred to him while look- ing at a fan-palm at Padua. He was struck by the immense variety of changes of form which the successively developed stem-leaves exhibit, by the way in which the first simple root leaflets are replaced by a series of more and more divided leaves, till we come to the most complicated. He afterwards succeeded in discovering the transformation of stem-leaves into sepals and petals, and of sepals and petals into stamens, nectaries, and ovaries, and thus he was led to the doctrine of the metamorphosis of plants, which he published in 1790. Just as the anterior extremity of veitebrate animals takes different forms, becoming in man and in apes an arm, in other animals a paw with claws, or a forefoot with a hoof, or a fin, or a wing, but always retains the same divisions, the same position, and the same connection with the trunk, so the leaf appears as a cotyledon, stem-leaf, sepal, petal, stamen, nectary, ovary, &c., all resembling each other to a certain extent in origin and composition, and even capable, under certain unusual con- ditions, of passing from one form into the other, as, for example, may be seen by any one who looks carefully at a full-blown rose, where some of the stamens are completely, some of them partially, changed into petals. This view of Goethe's, like the other, ia now completely adopted into science, and enjoys the universal assent of botanists, though of course some details are stiU OT? GOETHE'S SCIENTIFIC RESEARCHES. 3.1 muttcTS of controversy, as, for instance, whether the bud is a aiugle leaf or a branch. In the animal kingdom, the composition of an individual out of several similar parts is very striking in the great sub- kingdomof thearticulata — forexample,ininsectsand worms. The I.irva of an insect, or the caterpillar of a butterflj', consists of a number of perfectly similar segments ; only the first and last of them differ, and that but slightly, from the others. After their transformation into perfect insects, they furnish clear and simple exemplifications of the view which Goethe had grasped in his doctrine of the metamorphosis of plants, the development, namely, of apparently very dissimilar forms from parts origin- ally alike. The posterior segments retain their original simple form ; those of the breastplate are drawn closely together, and develop feet and wings, while those of the head develop jaws and feelers ; so that in the perfect insect, the original segments are recognised only in the posterior part of the body. In the vertebrata, again, a repetition of similar parts is sugirested by tlie vertebral column, but has ceased to be observable in the ex- ternal form. A fortunate glance at a broken sheep's skull, which Goethe found by accident on the sand of the Lido at Venice, suggested to him that the skull itself consisted of a series of very much altered vertebrse. At first sight, no two things can be more unlike than the broad uniform cranial cavity of the mammalia, inclosed by smooth plates, and the narrow cylindrical tube of the spinal marrow, composed of short, massy, jagged bones. It was a bright idea to detect the transformation in the skull of a mammal ; the similarity is more striking in the amphibia and fishes. It should be added that Goethe left this idea unpublished for a long time, apparently because he was not quite sure how it would be received. Meantime, in 1806, the same idea occurred to Oken, who introduced it to the scientific world, and afterwards disputed with Goethe the priority of discovery. In fact, Goethe had waited till 1817, when the opinion had begun to find adherents, and then declared that he had had it in his mind for thirty years. Up to the present day the number and composition of the vertebrae of the skull are a I. D S4 ON Goethe's scientific researches. subject of controversy, but the principle has maintaiLeJ ita ground. Goethe's views, however, on the existence of a common type in the animal kingdom do not seem to have exercised any direct influence on the progress of science. The doctrine of the meta- morphosis of plants was introduced into botany as his distinct and recognised property ; but his views on osteology were at first disputed by anatomists, and only subsequently attracted attention when tho science had, apparently on independent grounds, found its way to the same discovery. He himself com- plains that his first ideas of a common type had encountered nothing but contradiction and scepticism at the time when he was working them out in his own mind, and that even men of the frashest and most original intellect, like the two Von Humboldts, had listened to them with something like impatience. But it is almost a matter of course that in any natural or physical science, theoretical ideas attract the attention of its cultivators only when they are advanced in connection with the whole of the evidence on which they rest, and thus justify their title to recognition. Be that as it may, Goethe is entitled to the credit of having caught the first glimpse of the guiding ideas to which the sciences of botany and anatomy were tending, and by which their present form is determined. But great as is the respect which Goethe has secured by his achievements in the descriptive natural sciences, the denuncia- tion heaped by all physicists on his researches in their depart- ment, and especially on his ' theory of colour,' is at least as uncom- promising. This is not the place to plunge into the controversy that raged on the subject, and so I shall only attempt to state clearly the points at issue, and to explain what principle was involved, and what is the latent significance of the dispute. To this end it is of some importance to go back to the history of the origin of the theory, and to its simplest form, because at that stage of the controversy the points at issue are obvious, and admit of easy and distinct statement, unincumbered by disputes about tho correctness of detached facts and complicated theories. Goethe himself describes very gracefully, in the confession a* ON GOETHE'S SCIENTinC RESEARCHES. 35 the end of his ' Tlieory of Colour,' how he came to feike up the Bubjf et. Finding liliuself unable to grasp the esthetic princi[ile3 involveil in eflVcts of colour, he resolved to resume the study of the physical theory, which he had baen taught at the university, and to repeat for himself the experiments connected with it. With that view he borrowed a prism of Hofrath Butter, of Jena, but was prevented by other occupations from carrying out his plan, and kejit it by him for a long time unused. The owner of the prism, a very orderly man, after several times asking in vain, sent a messenger with instructions to bring it back directly. Goethe took it out of the case, and thought he would take one more peep through it. To make certain of seeing something, he turned it towards a long white wall, under the impression that as there was plenty of light there he could not fail to see a brilliant example of the resolution of light into different coloura; a supposition, by the way, which shows how little Newton's theory of the phenomena was then present to his mind. Of cour.se he was disappointed. On the white wall he saw no colours ; they only appeared where it was bounded by darker objects. Accordingly he made the observation — which, it should be added, is fully accounted for by Newton's theory — that colour can only be seen through a prism where a dark object and a bright one have the same boundary. Struck by this observation, which was quite new to him, and convinced that it was irreconcilable with Newton's theory, he induced the owner of the prism to relent, and devoted himself to the question with the utmost zeal and interest. He prepared sheets of paper with black and white spaces, and studied the phenomenon under ev^ery variety of condition, until he thought he had sufficiently proved his rules. He next attempted to explain his supj)osed discovery to a neighbour, who was a physicist, and was dis- agreeably surprised to be assured by him that the experiments were well known, and fully accounted for in Newton's theory. Every other natural philosopher whom he consulted told him exactly the same, including even the brilliant Lichtenberg, whom he tried for a long time to convert, but in vain. He studied Newton's writings, and fancied he had found some 36 ON Goethe's scientific researches. faUacies in them which accounted for the error. Unable to con- vince any of his acquaintances, he at last resolved to appciir before the bar of puVjlic opinion, and in 1791 and 1792 published the first and second parts of his ' Contributions to Physical Optics.' In that work he describes the appearances presented by whit<» discs on a black ground, black discs on a white ground, and coloured discs on a black or white ground, when examined through a prism. As to the results of the experiments, there is no dispute whatever between him and the physicists. He de- scribes the phenomena he saw with great truth to nature ; the style is lively, and the arrangement such as to make a conspectus of them easy and inviting ; in short, in this as in all other cases where facts are to be described, he proves himself a master. At the same time he expresses his conviction that the facts he has adduced ai'e calculated to refute Newton's theory. There are two points especially which he considers fatal to it: first, that the centre of a broad white surface remains white when seen through a prism; and secondly, that even a bla<'k streak on a white ground can be entirely decomposed into colours. Newton's theory is based on the hypothesis that there exists light of different kinds, distinguished from one another by the sensation of colour which they produce in the eye. Thus there is red, orange, yellow, green, blue, and violet light, and light of all intermediate colours. Different kinds of light, or differently coloured lights, produce, when mixed, derived colours, which to a certain extent resemble the original coloure from which they are derived ; to a certain extent form new tints. White is ft mixture of all the before-named colours in certain definite pro- portions. But the primitive coloui-s can always be reproduced by analysis from derived colours, or from white, while themselves incapable of analysis or change. The cause of the colours of transparent and opaque bodies is, that when white light falls upon them they destroy some of its constituents and send to the eye other constituents, but no longer mixed in the rit'ht proportions to produce white Ught. Thus a piece of red glass looks led because it transmits only red rays. Consequently all ON Goethe's scientific researches. 37 colour is derived solely from a change in the proportions in which light is mixed, and is, therefore, a property of light, not of the coloured bodies, which only furnish an occasion for ita manifestation. A prism refract-s transmitted light; that is to say, deflects it BO that it makes a certain angle with its original direction ; the rays of simple light of different colours have, according to Newton, different refrangibilities, and therefore, after refraction in the prism, pursue different courses and separate from each other. Accordingly a luminous point of infinitely small dimen- sions appears, when seen through the prism, to be first displaced, and, secondly, extended into a coloured line, the so-called pris- matic spectrum, which shows what are called the primary colours iu the order above-named. If, however, you look at a broader luminous surface, the spectra of the points near the middle are superposed, a.s may be seen from a simple geometrical investigation, in such proportions as to give white light, except at the edges, where certain of the colours are free. This whit© surface appears displaced, as the luminous point did; but in- stead of being coloured throughout, it has on one side a margin of blue and violet, on the other a margin of red and yellow. A black patch between two bright surfaces may be entirely covered by their coloured edges; and when these spectra meet in the middle, the red of the one and the violet of the other combine to form purple. Thus the colours into which, at first sight, it seems as if the black were analysed ai-e in reality due, not to the black strip, but to the white on each side of it. It is evident that at the first moment Goethe did not recol- lect Newton's theory well enough to be able to find out the physical explanation of the facts I have just glanced at. It was afterwards laid before him again and again, and that iu a thoroughly intelligible form, for he speaks about it several times in terms that show he understood it quite correctly. But he is still so dissatisfied with it that he persists in his assertion that the facts just cited are of a nature to convince any one who observes them of the absolute incorrectness of Newton's theory. Neither here nor in his later controversial writings does he ever 38 ON Goethe's scientific keseaeches. clearly state in what he conceives the insufficiency of the ex- planation to consist. He merely repeats again and again that it is quite absurd. And yet I cannot see how any one, wliatever his views about colour, can deny that the theoiy is perfectly consistent with itself; and that if the hypothesis from which it ,6tarls be granted, it explains the observed facts completely and even simply. Newton himself mentions these spurious spectra in several passages of his optical works, without going into any special eluuiilation of the point, considering, of course, that the explanation follows at once from his hypothesis. And he seems to have had good reason to think so; for Goethe no sooner began to call the attention of his .scientific friends to the pheno- mena than all with one accord, as he himself tells us, met his difficulties with this explanation from Newton's principles, which, though not actually in his writings, instantly suggested itself to eveiy one who knew them. A leader who tries to realise attentively and thoroughly every step in this part of the controversy is ant to experience at this point an uncomfortable, almost a painful, feeling to fee a man of exti'iiordiniry abi iti&s persistently declaring that there is an obvious absurdity lurking in a few inferences apparently quite clear and simple. He searches and searches, and at List unable, with all his etTurts, to fiud any such aK-iurdity, or even the ap- pearance of it, he gets into a state of mind in which his own ideas are, so to speak, crystallis d. But it is just this obvious, flat contradiction that makes Goethe's point of view in 1792 so intere-.ting and so importiint. At this point he has not as yet developed any theory of his own; there is nothing under dis- cussion but a few easily giasped facts, as to the correctness of which l)oth parties are agreed, and yet both hold distinctly opposite views; neither of them even understands what his op|X)nent is driving at. On the one side are a rumlier of phy- sicists, who, by a long series of tlie ablest investigations, the mo.st elaborate cjilculatious, and the most ingenious inventions, have Drought optics to such perfection that it, and it alone, among the physcal sciences, was beginning almost to rival astiouomy in accuracy. Some of them have made the pheno- ON gokthe's scientific researches. 39 mena the sulyect of direct investigation ; all of them, thanks to the accuracy with which it is possible to calculate beforeliand the result of every variety in the construction and combination of instruments, have had the opportunity of putting the infer- ences deduced from Newton's views to the test of experiment, and all, without exception, agree in accepting them. On the other oide is a man whose remarkable mental endowments, and whose singular talent for seeing through whatever obscures reality, we have had occasion to recognise, not only in poetry, but also in the descriptive parts of the natural sciences ; and this man assures us with the utmost zeal that the physicists are wrong : he is so convinced of the correctness of his own view, that he cannot explain the contradiction except by assuming narrowness or malice on their part, and finally declares that he cannot help looking upon his own achievement in the theory of colour as far more valuable than anything he has accomplished in poetry.' So flat a contradiction leads us to suspect that there must be behind some deeper antagonism of principle, some difference of organisation between his mind and theirs, to prevent them from undarstanding each other. I will try to indicate in tho following pages what I conceive to be the grounds of this anta- gonism. Goethe, though he exercised his powers in many spheres of intellectual activity, is nevertheless, par excellence, a poet. Now in poetry, as in every other art, the essential thing is to make the material of the art, be it words, or music, or colour, the direct vehicle of an idea. In a perfect work of art, the idea must be present and dominate the whole, almost unknown to the poet himself, not as the result of a long intellectual process, but as inspired by a direct intuition of the inner eye, or by an outburst of excited feeling. An idea thus embodied in a work of art, and dressed in the garb of reality, does indeed make a vivid impression by appeal- ing directly to the senses, but loses, of course, that universality fiad that intelligibility which it would have had if pieseuted ia ^ See Eckermann's ConveTsatioia 40 ON Goethe's sciENTinc iiesearches. the form of an abstract notion. The poet, feeling how tho cbiirm of his works is involved in an intellectual process of this type, seeks to apply it to other materials. Instead of trying to arrange the phenomena of nature under definite conceptions, independent of intuition, he sits down to contemplate them as he would a work of art, complete in itself, and certain to yield up its central idea, sooner or later, to a sufficiently susceptible student. Accovdiagly, when he sees the skull on the Lido, which suggests to him the rei-tebral theory of the cranium, lie remarks that it serves to revive his old belief, already confirmed by experience, that Nature has no secrets from the attentive observer. So again in his first conversation with Schiller on the 'Metamorphosis of Plants.' To Schiller, as a follower of Kant, the idea is the goal, ever to be sought, but ever unattain- able, and therefore never to be exhibited as realised in a phe- nomenon. Goethe, on the other hand, as a genuine poet, couceive.s that he tinds in the phenomenon the direct expression of the idea. He himself tells us that nothing brought out more sharply the separation between himself and Schiller. Tills, too, is the secret of his affinity with the natural philosophy of Schelling and Hegel, which likevri-e proceeds from the assumption that Nature shows us by direct intuition the several steps by which a conception is developed. Hence too the ardour with which Hegel and his school defended Goethe's scientific views. Moreover, this view of Nature accounts for the war which Goethe continued to wage against complicated experi- mental researches. Just as a genuine work of art cannot bear retouching by a strange hand, so he would have us believe Nature resists the interference of the experimenter who torturea her and disturbs her ; and, in revenge, misleads the impertinent kill-joy by a distorted image of hei-self. Accordingly, in his attack upon Newton he often sneers at f pectra, tortured through a number of narrow slits and glasses, and commends the expeiiments that can be made in the ojien air tuider a bright sun, not merely as particularly easy and parti- cularly enchanting, but also as particulaily convincing ! The poetic turn of mind is very marked even in his morphological ON Goethe's scientific researches. 41 researches. If we only examine what has really been accom- plished by the help of the ideas which he contributed to science, we shall be struck by the very singular relation which they bear to it. No one will refuse to be convinced if you lay before him the series of transformations by which a leaf passes into a Btamen, an arm into a fin or a wing, a vertebra into the occipital bone. The idea that all the parts of a flower are modified leaves reveals a connecting law which surprises us into acquiescence. But now try and define the leaf-like organ, determine its essential characteristics, so as to include all the forms that we have named. You wUl find yourself in a difficulty, for all distinctive marks vanich, and you have nothing left, except that a leaf Ln the wider sense of the term is a lateral appendage of the axis of a plant. Try then to express the proposition ' the parts of the flower are modified leaves ' in the language of scientific defi- nition, and it reads, ' the parts of the flower are lateral appen- dages of the axis.' To see this does not require a Goethe. So again it has been objected, and not unjastly, to the vertebral theory, that it must extend the notion of a vertebra so much that nothing is left but the bare fact — a vertebra is a bone. We are equally perplexed if we try to express in clear scientific language what we mean by saying that such and such a part of one animal corresponds to such and such a part of another. We