WHEN I speak to you of Greek Science, of course I use the word in the old and proper sense to include all strict reasoning, especially of the deductive kind, particularly therefore pure Mathematics, and not merely the inferences from observation and experiment which now commonly assume and even monopolise the title of Science. I often see in educational programmes Science and Mathematics contrasted as distinct things, which indeed in this case they are, only because the Science so-called is often unworthy of the name. Sciences of observation were, I think, not formulated by the Greeks except in the case of Medicine, in which their results are still quoted with respect; in the case of Hydrostatics, as Heron’s great book shows; and in the case of Natural History, in which they made the first collection of facts that modern men of science can use; but we have lost what they said on their artistic observations, namely their minute observations of the anatomy of the human body, which, as I have told you, their sculptors learned to represent with such accuracy that no modern anatomist can find a flaw in their work. This was done by careful external observation, for the practice of dissecting the human body would have seemed to them impious and horrible. But, whenever it was possible, the Greeks went back to first principles and framed a theory from which they deduced the facts; and this it is which has made their science so valuable. It will not be hard to show you how in Logic—the Science of Reasoning,—in Arithmetic, and in Geometry—the science of the laws of lines, of figures, and of solid bodies in space—they are our teachers to the present day.

It is well to approach the subject of Logic through the avenue by which the Greeks approached it, through the analysis of ordinary language and as the natural expression of thinking. The early poets and great prose writers had so far perfected the use of language that the Greeks in the catalogue of human acquisitions came to put their speech on a very high pedestal. Delighted with it, and despising all other tongues as barbarous, they convinced themselves that the Greek word adequately expressed the nature of the thing it signified, and therefore that to understand their language properly was to understand the nature of things. ????? meant not only speech (oratio), but reason (ratio), and so, after first seeking to obtain clear conceptions of abstract ideas, they advanced to the structure of sentences and analysed speech in so accurate a way that their technical terms are our technical terms of to-day. When you talk of infinitives, or genitives, or participles, you are only using words borrowed from Latin translations, often mistranslations, of the Greek. You find these logical studies in their beginning, but by no means in their infancy, in the Dialogues of Plato. Whole conversations are employed in trying to fix the connotation of important moral terms, such as holiness, or valour, or temperance. And we also find in some of the dialogues an appreciation of the difficulties contained in the form of simple propositions, the meaning of affirmation or negation, and the nature of the deduction of one proposition from another.

But I need not detain you with particulars about these early preparations for science, when we have before us in Aristotle various treatises on the analysis of speech from its logical side, and the laying down of the laws of formal thinking with such accuracy and completeness that nothing of importance has ever been added to it. We hear it often said that a single man apprehended and systematised these laws. That is not true; there were plenty of tentative essays before his time. But if there be one achievement which has made his name and fame everlasting, it is his treatment of the theory of Reasoning.

The mediÆval universities knew this well, and so do the modern universities of Europe which are worthy of the name. I need not bear witness to the vast importance of common Logic by telling you that in my own youth nothing ever woke me up like having a good Logic put into my hands at the age of fourteen. For since that time I have been often teaching it and have watched its effects on hundreds of intelligent youths. Among all the subjects that we teach, not for the purpose of supplying mere facts, but for the purpose of training youth to judge facts and co-ordinate their knowledge, I know nothing that benefits the average student like the study of Aristotelian Logic. May I add that, so far as I know American education, the most serious defect I have observed in it is the small attention paid to this subject, and hence the vast number of your men and women who are unable to distinguish a sound from an unsound argument, still less to point out where the fallacy lies.

There are here present, I have no doubt, a large number of people, otherwise highly educated, who, were I to propose a stock example for their criticism, would feel at a loss how to deal with it. Let me give an illustration. “Every hen comes from an egg; every egg comes from a hen; therefore every egg comes from an egg.” Is this a correct argument? If not, where is it at fault? If you had all been trained in Whately’s Logic, or any other Logic of the kind, as we were in our youth, such a question would present no difficulty whatever.

But if you have failed to derive this lesson from the old Greeks, your English ancestors were better advised. All the subtlety of the mediÆval schools, all the disputations of their universities, were based on Greek Logic; and, if they often wasted their time on idle problems, it must always be remembered that by this means Europe was trained to accuracy and subtlety in argument, and hence to weigh vague and random theorising and to make men competent critics of any new dogma. We often remark from our side of the Atlantic how many wild theories in religion, how many sham theories in science, blossom and flourish in this country, inhabited though it may be by a most shrewd and intelligent population. The simplest answer is to point to their ignorance of common Logic, and hence their liability to be deceived by the most vulgar fallacies. It would be easy to mention a book popular in this country, the pages of which any logically trained people would only use to wrap sardines or to heat a stove.

The Greeks do not parade their logic in their writings, though we know they were fond of subtleties; there are indeed examples of it in the Sophist of Plato, where this sort of thing is ridiculed in his travesty of two professional educators. But there are two great and solid proofs of the power which strict Logic had upon their minds. The first comes out in their literature. Wherever they undertake to argue an issue, whether political, social, or religious, their reasoning is clear and easily followed. They of course often start from traditional beliefs, which may not now command assent, but they always reason from these with clear and sober thinking. There was no more important cause for the permanence of that great literature. Its sound thinking has kept it from all extravagance and made it acceptable to educated men of all ages and nations. The second proof is my chief subject to-day: it is the peculiarly logical character of Greek mathematics which has made this too the model of the scientific thinking of the world.

Let me go back to the infancy of Greek science and give you evidence for this statement. Setting aside for the present the metaphysical thinkers, who will occupy us in another chapter, we may safely say that the earliest mathematicians were the school of Pythagoras, and also that their work started (so far as they did not start from the highest of all—pure thinking) from Arithmetic. To this science Pythagoras and his school attached such importance that they were supposed to hold that numbers were the essence of the universe. If you think that such a theory is mere nonsense, I may tell you that I have often heard my colleagues, distinguished in modern science, discuss a theory, alive at the present day, that the so-called material universe consists of mere motion, without anything to be moved! At the root of these speculations lies the fundamental distinction of form and matter, of the definite and the indefinite; and the Pythagoreans had got a glimpse of the eternal truth that it is only through our intuitions of space and time, and through abstract concepts explicating these, that we can bring the myriad phenomena of nature under intelligible law. It was an early anticipation, so far as we can explain it, of the great theory of Descartes, that all the universe could be reduced to mathematical relations, and these handled by algebra, which is in its essence but a very abstract and generalised arithmetic. If therefore all parts of the world stand in mutual arithmetical relations, of which the chemical law of definite proportions is the most signal example, the science of numbers must be the capital of every scientific man.

And remember that in Greek parlance this was the strict meaning of their arithmetic—a pure science, while they used the term logistic (or computation) for the working of practical rules. At the basis of their theory of numbers lay of course the one great assumption which makes the science possible—I mean the absolute equality of the units of any number used for the purpose of calculation.

This is not merely the abstraction from all their differences, as when I say that the present audience consists of five hundred people, regardless of the countless variations existing between the units of this crowd. It is the assumption of an ideal and accurate identity between each of the units, as to magnitude, which makes the expression of geometrical truths arithmetically possible.

The truth that 3² + 4² = 5² applies not only to numbers but to lines, and probably suggested the geometrical proof to Euclid (1, 47). But it is only true if the units in the measurement of each line are exactly equal.

Starting from this first assumption, the Pythagoreans began to speculate on the peculiarities of the natural series of units in use among men, and to deduce from these general considerations various theorems, which they believed might solve the secrets of nature. At the very outset they were struck with the obvious contrast between odd and even, which Plato, following them, regarded as a fundamental distinction in nature. Had they been told that, thousands of years later, men of science would find that a most primitive and fundamental distinction among animals is founded on this difference, I mean that of artio-dactyle, and perisso-dactyle, actually called by the Greek words, they would have said that this caused them no surprise, as their arithmetic had long since laid down the distinction as a law of nature. As simple specimens of the sort of treatment that the science of numbers received from them, I may cite the following: The successive additions of the odd numbers produce the squares of the series of even and odd.[32] The series of even numbers when added give us no such result, but rather this—that the addition of even numbers gives us figures which are the products of successive numbers differing by only one, e.g. 2 + 4 = 3 × 2; 2 + 4 + 6 = 4 × 3, and so on. These latter numbers were regarded as rectangles, when expressed in lines. It was by the discovery of the relation of the sides to the base of a right-angled triangle that they, so to speak, stumbled upon irrational numbers. If the two sides are each equal to 1, the hypothenuse is equal to v2, which is no integral number, but a problem in itself.[33]

All the results of this Pythagorean research lived through into the days of Plato and Aristotle and then, as we know from Euclid and Theon, into the learning of Alexandria. The importance recognised by them in the numbers ten and twelve was shown by the general adoption of a decimal system of notation, and of the division of time on a duodecimal system.

You will ask me what symbols the Greeks had which could enable them to treat arithmetical figures of any complexity, and on this I could give you now a very definite reply, but the details would lead us away from our subject, seeing that this notation was lost in the Dark Ages and was ultimately replaced by the Arabic numerals. But we now know that they had a very practical system of decimal notation based on the use of the letters of the alphabet; and the fact that several letters obsolete in the alphabet of the fifth century B.C. appear as symbols, proves that it was current as early as Pythagorean days. The sign for 6 is the digamma, that for 90 is the koph of the Phoenician alphabet, which is still found in Locrian inscriptions; the Phoenician letter known as sampi is used for 900. We know the practical management of this easy notation perfectly from the mass of accounts both private and public found on Egyptian papyri. It can express large numbers far more compendiously than the Roman system, often more compendiously even than ours. Suppose you desire to express any large number, say 20,050, here it is /??; say 47,678, it is d/?????, and if there be small gain in simplicity here, I will give you 800,000 = 10,000 × 80 = p/?. But these are practical matters, though without an easy notation even the most scientific thinkers could not make large progress.[34]

The next great step was to pass from arithmetic to geometry as the science of space and to show how far the same laws governed both.

If we are not well informed upon the beginnings of arithmetic, we are more fortunate in the case of geometry, and here, if anywhere, the old Greeks have been the acknowledged teachers of modern Europe. For we have in the so-called Elements of Euclid, composed most probably at Alexandria about 300 B.C., a summary of all that had been discovered up to his day, doubtless with many new things of his own. He had distinctly built upon his predecessors; he has before him all through his book a problem discussed in Plato, that of the possible number of regular polyhedra, and its solution forms the climax of his work. But he begins from the very beginning and builds up his whole doctrine with such accuracy that a flaw in the demonstration is hard to be found.

How did this great master attain to such perfection? The form of his demonstrations does not suggest an intimacy with the logic of his immediate predecessor Aristotle; but from him he might easily have obtained the whole notion of a strictly deductive science, which, starting from the smallest possible number of primary data, proceeds to derive from these by strict demonstration proposition after proposition. Philosophers of our own time have often expressed wonder at the clearness with which these data are laid down. They are three in kind: first the common notions, which apply to all science and all practical life, such as “the whole is greater than its part”; secondly, the axioms peculiar to our intuition of space, such as “two right lines cannot enclose a space”; and thirdly the very simple postulates, which amount to the use of a ruler and compass with a pencil. There are besides very careful definitions, so careful that they are at first obscure, because they apply to the ideal construction of the mind in its intuition of pure space and do not concern themselves about the flaws of actual figures. Thus his “point which has no parts” is not nothing at all, but the minimum of definite place; his right line, “which lies in the same way (?a???) between any two points taken upon its length,” is simply unity of direction. Every other line varies in direction in some of its successive parts. This is a direct appeal to intuition, without which we can make no beginning in the science of space. Such also is the axiom about parallel lines. Such is also the proof by superposition, to show that two triangles, if some of their measurements be the same, must wholly coincide.

But I must not attempt to give you a lecture on the Elements of Euclid, of which some of you may have evil recollections. For it is the misfortune, as well as the glory, of a great work not only to be repeated for centuries, but to be parroted and travestied by those who merely accept its greatness from the voice of ages, and who come to think that the words of inspiration only require blind repetition to instruct men. So if Euclid has become in many classical schools a sort of amulet or fetish (which must for common decency be put in the programme but which may be learned by committing the proofs to memory without any intelligence) such a misfortune is not the fault of Euclid, but the most pathetic tribute to his genius. Let me also add, for the benefit of those of you who have never seen more than six books of the Elements, and who probably thought six more than enough, that these are but the introduction to the discussion of higher and more complex questions, which show the large advance made by the Greeks in this science, and which explain also how in other arts, such as architecture, there is no defect for want of scientific accuracy. Books VII-X are not on geometry, but on higher arithmetic, and even treat, as in Book X, of incommensurable or irrational quantities. With XI he begins to teach solid geometry, the measurement of pyramids, cones, spheres, and the like, ending (XIII) with the discussion of the five regular polyhedra, of which Plato had long since spoken.

From the great sequence of discoverers and teachers of pure mathematics, I need only here pick out three immortal names: Apollonius of Perga, living about 200 B.C., whose geometrical treatment of conic sections is, I am informed, a splendid monument of genius, which would still be the basis of modern study had not the treatment of these figures by analysis entirely superseded the geometrical method. Then there is Pappus in the second century A.D., who gives us in eight books a review of all the previous masters, with important additions of his own. The third name is Diophantus, who lived much later, perhaps in the fourth century, and whose work is considered the first great step toward the science of Algebra.

All these speculations were developed in the direction of mathematical physics by Archimedes, Heron, and other great men of the Alexandrian school. The triumphs of Archimedes in mechanics astonished the Romans, who, in the defence of Syracuse against their attack, found him equal to a host. But how little Archimedes confined himself to practical problems is shown by his famous method of determining the area of a circle by approximation, by inscribing and circumscribing polygons of a great number of sides, which can of course be treated and measured as a complex of triangles. This is still, I am told, the proof admitted by modern mathematicians as the best.

The works of Heron show not only an excellent practical knowledge of mechanics, but of hydrostatics, from which he deduces a number of most ingenious inventions, such as our penny in the slot, and even the construction of a whole scene acted by marionettes moving by a most elaborate hidden machinery. It[35] is a fine specimen of his ingenuity in using the ordinary mechanical contrivances. He postulates a tall hollow basis, adorned with pilasters, and having an architrave, with boards covering its upper surface. Over this stands a little round temple, visible from all sides, with six pillars. It is covered with a conical roof, and on the apex is a figure of Victory with outspread wings and holding in her right hand a garland. Under the centre of the roof stands a figure of Bacchus, holding a thyrsus in his left hand, and a cup in his right. At his feet lies a little stuffed panther. Before and behind Bacchus, and outside the temple, stands an altar with dry shavings of wood. Also on each side, outside the temple, a Bacchante, in a proper costume and attitude. The whole concern being set up at some suitable spot, the exhibitor will retire, and the automatic machine will presently move forward to a fixed spot. The moment it stops, the altar fire in front of Bacchus will light up, and from his thyrsus will flow milk or water, and from his cup wine will be poured out on the panther beneath him, the pilasters beneath will be adorned with garlands, the Bacchantes will dance round the temple; drums and cymbals will be heard. When this noise ceases, the figure of Bacchus will turn round to the other altar and all the movements be repeated in the other direction. As soon as this has happened the second time, the show is over, and the whole machine will return to its original place. We have felt bound, he adds, to make the measurements (which he gives) small, for if made large, the suspicion naturally arises in the audience that there is a man inside the machine producing all the movements. This precaution, then, should be observed in making any automatic machine.

He then proceeds to give in great detail the construction of this machine. It is as ingenious as any construction of the present day, but cannot be presented to you without a series of figures, which are given in his book. Any of you may read it in the Greek (Teubner text), to which is added an excellent German translation. It will be enough to mention that the lighting of the altar fires is done by concealing a lamp inside the altar immediately under the wood, and by withdrawing a metal plate which separates them. The flowing of milk and wine is produced by concealing two little reservoirs in the summit of the building, and leading the liquor by pipes down the inside of the pillars, and up the inside of the figure of Bacchus, so that, when the cocks are turned by machinery, the milk and wine flow and rise to the level of the thyrsus and the cup, which are set underneath the level of the cisterns. It is evident enough that people who could do these things were capable of inventing the sakia now in use throughout Egypt, where a horizontal wheel worked round a capstan by oxen moves another set perpendicularly, at right angles to it, furnished with jars, which get filled below and, when they pass over the highest point of their revolution, are emptied into a water course, and so irrigate a higher level. This is well known to have been the invention of these Alexandrian mechanicians, whose theory had long preceded their practice, and whose applications of science they never valued so highly as their pure speculations.

Perhaps before leaving the subject I should tell you what was the moving force in the automatic machinery. It was a weight suspended in the air by a rope over a pulley, which, as soon as it was allowed to sink from its support, made the rope, wrapped round the axle of a large wheel, move the wheel, that was in its turn connected with other wheels. With very great and ingenious contrivance, as the machinery was all carefully concealed, the exhibitor could take his seat among the spectators, and make the ignorant believe that the whole effect was produced by some magic.

Nor were the laws of optics and the correction of the illusions of sight neglected. Euclid wrote a work on the subject which is now lost; but the praise of it by competent men of the Alexandrian school shows that it was on a level with his other scientific productions. To our educated public, the work of the Greeks in most fields is known at least by hearsay; the great library of Greek mathematics, scores of volumes, some of which are only quite recently published, is, except for Euclid, absolutely unknown. Yet from it is derived not only the scanty knowledge of science that filtered through the Romans into Western Europe, but also that adopted by the Arabs, and which in translations from Arabic versions came from them into awakening Italy and Germany and France. But let me add that now, when their discoveries in pure mathematics are being weighed by the light of expert knowledge, we are assured by all those really competent to judge that in no field of learning have the old Greeks shown their amazing originality and acuteness more signally than in higher arithmetic and in higher geometry.

The great fathers of the exact sciences are therefore in arithmetic the Pythagoreans, whose history is too obscure to mention from it any single name before Archytas, Euclid, and Theon of Smyrna; in geometry, Euclid; in mechanics, Archimedes; in conic sections, Apollonius of Perga; in hydrostatics, Heron; in astronomy, Eudoxus and Hipparchus; last, but not least, in higher arithmetic and algebra, Diophantus; all of these were, moreover, men who did not confine themselves to any single department, but promoted accurate thinking in many. These, and others hardly less great, have left a record and a legacy to posterity second to none in its mighty consequences.

But among them all Aristotle stands out as the “master of those that knew”—the man who attained in the Middle Ages such celebrity and authority that he narrowly escaped being canonised as a saint in the Roman calendar. If that distinction really belonged to the benefactors of mankind, I know not that any man ever lived who had a better claim to it. For his life and activity mark an epoch not only in the progress of many sciences, but in the general culture of the human mind, to which I know no parallel. He was brought up under the influence of the Socratic method of inquiry as perfected by Plato, but, though in some popular works (now lost) he adopted the dialogue as the correct method of teaching, there can be no doubt that the sober and practical tone of his mind made him despise all the delays and delights of character-drawing, and of spinning out the subject, for what we have from him is pre-eminently plain and scientific in form. There is seldom an unnecessary sentence; if there be a metaphor, it is a mere flash of colour across the cold severity of his argument. He writes like a man who had no time to waste and a vast world of subjects to teach. If it was still an age when the sciences had not entered upon the path of observation and experiment, but were philosophical speculations, Aristotle did more than any man to establish a separation between philosophy and science, while fully recognising, what in our day most scientists ignore, that positive science without a sound knowledge of philosophy is apt to run into fatal mistakes.

Of course this immense programme which Aristotle set before him could not be carried out without large collaboration, and so we know that, as Plato seems to have underrated such collaboration, and thus have failed in fruitfulness among his pupils, Aristotle, who was not chosen as his successor by the school (I suppose as usual there were jealousies among the commonplace and docile pupils toward the great original thinker), formed and stimulated a band of helpers, who gathered special observations in botany, mineralogy, zoÖlogy, physics as the science of nature, and others who put into shape his views on rhetoric and on poetry, on ethics and on theology. We have, in my opinion, a new specimen of such delegated work in the now famous Constitution of Athens, which was known and quoted as Aristotle’s through later antiquity, but which is rather the work of a pupil and not a brilliant one. But then we know that Aristotle either wrote or brought out 158 of these tracts on Greek constitutions. To this I shall return in a subsequent lecture.

Theophrastus, Eudemus, and Aristoxenus are among the best-known names of these helpers, and from these we have valuable work extant. Physical geography was entrusted to DikÆarchus. All these researches were carried out in the same spirit, and with that unity of purpose that marks a school. There was apparently but one division of all the domain of science in which Aristotle did no original work, and yet his contribution to it is not to be underrated. This was the field of pure mathematics. For we know that he entrusted to his ablest pupil, Eudemus the Rhodian, the task of writing the history of what other men had done in this field. These books on the history of arithmetic, of geometry, and of astronomy (then called astrology) were well known and valued, and the modern critics declare that whatever is now known about the earlier development of mathematics was derived from this pure and rich source. Still more remarkable is it that this, the part of the edifice to which Aristotle himself did not contribute, should have been the only one that took root and flourished without any period of corruption or decay. As to Aristotle’s personal competence in this matter, I am assured by the best mathematicians that his not infrequent allusions to mathematics, by way of metaphor or illustration, show a clear and sound understanding of the subject. It is not, therefore, the vagary of an idle admirer, but the deliberate expression of a weighty judge, when we learn from him in his Discussion on Beauty—which he, being a Greek, of course seeks in form, symmetry, and proportion—that the highest and noblest examples of earthly beauty are to be found in mathematics.

Euclid was almost the contemporary of Aristotle, and so the Peripatetic Mathematics found at Alexandria a new home and a mighty development, which lasted for centuries and is not stayed to this day. But the rest of the vast system of Aristotle seems, after about two generations, to have fallen into incompetent hands. The activity of the Greek intellect passed into other channels and became again purely philosophical and ethical instead of scientific, as I shall show when I speak of the Stoic and Epicurean systems.

But there was another branch of practical science which, if not created by Aristotle, was certainly promoted by his studies in zoÖlogy and botany. We still regard these sciences as a necessary introduction to medicine, and we may be sure that in old days the order of such studies was not different. The distinction of being the father of rational medicine need not be added to the other crowns which adorn the great sage. Both Greeks and moderns are unanimous in awarding that honour to Hippocrates of Kos, where there was an old guild of physicians, of which he was neither the first nor the last of his name. Hence the works now known as those of Hippocrates may not all be the actual writing of one man; for as with Aristotle, so with Hippocrates, there was a school, and the pupils followed in the master’s path. But there is no doubt whatever as to the character and tone of his teaching. We find even a literary grandeur in his prose, that is not the writing of any but a great master. The famous opening of his Aphorisms is probably known to most of my hearers. But it is a puzzle to translate without dull amplification. Here is a paraphrase: “Life is brief, yet craft grows slowly; the right time is instantaneous, yet experience is treacherous, and decision burdensome.” As is the style, so is the thinking out of the problems before him. Starting from hygiene as the proper basis of medicine, he thinks those should be regarded as the earliest physicians who improved the food of primitive men by crushing grain, by cooking meat, and by selecting edible vegetables. From that time onward, there was growing up an experience of what was healthy and what the reverse. It is this experience which he seeks to systematise by careful observation and so to establish laws of hygiene, and the probable natural prophylactics or remedies afforded by air, water, and climate. He analyses with care the proper aspect for a town and decides (in the latitudes which he knew) for the eastern as the best and the western as the worst. He discusses the quality of the water supply, and lays great stress upon its altitude. He sets down careful clinical records of cases of fever—typhus, puerperal, malarious, and the like. The results of this rational treatment of disease were far-reaching and permanent. To cite to you the cloud of witnesses would be mere waste of time. But I will take one instance, closely related to the history of my great college and of medicine in Ireland.[36] The founder of the College of Physicians in Ireland under the Cromwellians and Charles II. was John Stearne, a grand-nephew of Archbishop Ussher, himself also a theologian and metaphysician. Driven out of Ireland by the stress of the Rebellion of 1641, and educated in all the medical learning of Cambridge, he returned with the Cromwellian restoration of order and became not only a Fellow of his college (along with some eminent Puritans from Harvard) but a distinguished practitioner in Dublin. By his influence was founded the Royal College of Physicians, once an adjunct to the University and ever since a great and dignified corporation, which has for many generations contributed eminent men to medical science.

But Stearne, like Hippocrates, not only practised; he wrote works on life and death; he was a theorist and a philosopher. This man, writing from the highest standpoint of Cambridge and of Dublin in the middle of the seventeenth century, tells us over and over again that the works of Hippocrates are wellnigh infallible, and are the only sure guide to medical science in his day.[37] The causes of this attitude are not far to seek. All mediÆval medicine had been ruined by the admission of supernatural influences, special interventions, the action of evil spirits, the conjunction of hostile constellations, and other rubbish at which we now smile, but which men of science then deplored. The first great feature in Hippocrates is the utter ignoring of any such influences as the special causes of disease or cure. He is afraid of no ghost or goblin, he never mentions an incantation. And here is a momentous passage, which probably few of you have ever read, that expresses the mental attitude of his school. He is speaking of a class of patients affected with impotence who are venerated among the Scythians and even worshipped, each man fearing for himself, as he attributes the sickness to a special visitation of his God. “Well now I also think that these diseases are of divine ordinance and so are all the rest, but not one of them more divine or human than the rest, but all are homogeneous, and all from the gods. Yet each of them has its nature, and nothing happens without a natural cause.” He then goes on to explain the disease from the practice of too much riding, and observing that it attacks the rich more usually than the poor, because the latter do not live on horseback, he argues:

This was the spirit that died out when the Greek world decayed, and Europe fell a victim to ignorance and superstition. Then came the heyday of miraculous images, of relics with power to cure, of pilgrimages, of intercessions, of all that mental degradation which the MediÆval Church, far from repudiating, used for its own purposes. And so the resurrection of medical science was connected with rebellion against the Church. Among every three physicians, are two atheists, was the word, and even the pious Stearne, whom I have mentioned, preaches a purely Stoic creed, and systematically ignores all the rites of his church.

Hippocrates and his school had in their day to combat similar superstitions, just as the scientific medicine of our day has to deal with Lourdes and with Christian Science. Within the last few years, we have recovered from oblivion the ruins of the temple and town of Epidauros, where the god Æsculapius had a famous shrine, and where hundreds of pilgrims assembled to seek cures for their several ailments. Their recreation was as well looked after as in any modern watering-place; the theatre was the most splendid thing of the kind in Greece, and there were porticoes, and baths, and groves to secure that comfort and idle amusement which have a great effect on health. But as we know from the ridicule of Aristophanes, corroborated by numbers of inscriptions commemorating cures, the method of these Asklepiads was far behind those of Kos; it was superstitious and not scientific. Dreams and omens, charms and ceremonial acts still stood in the way of sound hygiene and careful clinical observation. Not that I deny the occurrence of cures under such treatment. The most sceptical examination of the annals of Lourdes shows that mental influences will cure not only mental diseases, and diseases known as nervous, but even those that seemed absolutely physical. And what the Blessed Virgin does for the faithful of Lourdes may doubtless be done by the influence of more human and tangible causes. These admissions, which I make freely, will not change the opinion now held by every true man of science. It is the opinion of Hippocrates and his school, and that which he sought to enforce by his theory and his practice. The great truth that work is what exhausts the human frame, and that food supplies this waste, was laid down clearly in their practice. The equally important principle, that no organ will keep in health and vigour without exercise of its natural function and that if disused it will shrink or decay, was also clearly pronounced. They even guessed that the greatest problem of medicine (which they failed to solve) was the passage from inorganic into organic substances.

It is of course idle to say that these practitioners were not encumbered and shackled by many false guesses, many pretended discoveries, many groundless speculations of their predecessors. But as the famous oath, which every practitioner in the school of Kos took, expresses clearly the high moral aim with which even now the physician enters on his noble work, the solemn declaration that he will not abuse his influence or intimacy in any house for selfish or immoral purposes, so in their scientific aims these Greeks sought to advance human knowledge by recording honestly their observations, even by telling of their failures, and by seeking to leave behind them such clinical work as might enlighten not only successors but opponents. If we compare this truly modest and scientific attitude with that of the doctors whom MoliÈre scourged, and whose practice is but too well known to us from the minute account of their treatment of princely or even royal patients, we shall again come to the conclusion that where the Greeks failed to teach modern Europe it was not for want of rich suggestion and splendid anticipations of modern science.

I need hardly tell you (in conclusion) that I have not only confined myself to touching the fringes of these vast subjects; I have deliberately omitted large topics such as optics, and the correction of optical delusions, which the Greeks attained by a subtle use of curves, not merely sections of a large circle, but particularly by the use of the conic section still known by its Greek name of hyperbola. I have said nothing about their astronomy, with its prediction of eclipses, its application to the calendar, and its use as the basis of scientific geography. Had I attempted to weave all these matters into the present lecture, I must have given you a kaleidoscope and not a picture. The main fact to be impressed upon you is that the great triumphs of the Greeks in art and in literature were not attained without a strict education in hard thinking and close reasoning. Plato is said to have made it the first condition of entering on a course of philosophy that the pupil should have studied geometry.

It was in accordance with that principle that in our older universities every student, though he were a specialist in classics, must show an adequate knowledge of mathematics. No man in Trinity College, Dublin, can take the degree in languages without having been taught, and having qualified in, pure mathematics, physics, and astronomy. That was the kind of education given by the Greeks. So far as we have departed from it in our education; so far as we have substituted hurry for deliberation, quantity of facts for quality of knowledge, miscellaneous information for systematic thinking, so far we have rendered modern culture impotent to rival their excellence.