These were the tender mercies of the Inquisition; and this was the kind of meaning lurking behind many of their well-sounding and merciful phrases. For instance, what they call "rigorous examination," we call "torture." Let us, however, remember in our horror at this mode of compelling a prisoner to say anything they wished, that they were a legally constituted tribunal; that they acted with well established rules, and not in passion; and that torture was a recognized mode of extracting evidence, not only in ecclesiastical but in civil courts, at that date.

All this, however, was but poor solace to the pitiable old philosopher, thus ruthlessly haled up and down, questioned and threatened, threatened and questioned, receiving agonizing letters from his daughter week by week, and trying to keep up a little spirit to reply as happily and hopefully as he could.

This condition of things could not go on. From February to June the suspense lasted. On the 20th of June he was summoned again, and told he would be wanted all next day for a rigorous examination. Early in the morning of the 21st he repaired thither, and the doors were shut. Out of those chambers of horror he did not reappear till the 24th. What went on all those three days no one knows. He himself was bound to secrecy. No outsider was present. The records of the Inquisition are jealously guarded. That he was technically tortured is certain; that he actually underwent the torment of the rack is doubtful. Much learning has been expended upon the question, especially in Germany. Several eminent scholars have held the fact of actual torture to be indisputable (geometrically certain, one says), and they confirm it by the hernia from which he afterwards suffered, this being a well-known and frequent consequence.

Other equally learned commentators, however, deny that the last stage was reached. For there are five stages all laid down in the rules of the Inquisition, and steadily adhered to in a rigorous examination, at each stage an opportunity being given for recantation, every utterance, groan, or sigh being strictly recorded. The recantation so given has to be confirmed a day or two later, under pain of a precisely similar ordeal.

The five stages are:—1st. The official threat in the court. 2nd. The taking to the door of the torture chamber and renewing the official threat. 3rd. The taking inside and showing the instruments. 4th. Undressing and binding upon the rack. 5th. Territio realis.

Through how many of these ghastly acts Galileo passed I do not know. I hope and believe not the last.

There are those who lament that he did not hold out, and accept the crown of martyrdom thus offered to him. Had he done so we know his fate—a few years' languishing in the dungeons, and then the flames.

Whatever he ought to have done, he did not hold out—he gave way. At one stage or another of the dread ordeal he said: "I am in your hands. I will say whatever you wish." Then was he removed to a cell while his special form of perjury was drawn up.

The next day, clothed as a penitent, the venerable old man was taken to the Convent of Minerva, where the Cardinals and prelates were assembled for the purpose of passing judgment upon him.

The text of the judgment I have here, but it is too long to read. It sentences him—1st. To the abjuration. 2nd. To formal imprisonment for life. 3rd. To recite the seven penitential psalms every week.

Ten Cardinals were present; but, to their honour be it said, three refused to sign; and this blasphemous record of intolerance and bigoted folly goes down the ages with the names of seven Cardinals immortalized upon it.

This having been read, he next had to read word for word the abjuration which had been drawn up for him, and then sign it.

THE ABJURATION OF GALILEO.

"I, Galileo Galilei, son of the late Vincenzo Galilei, of Florence, aged seventy years, being brought personally to judgment, and kneeling before you Most Eminent and Most Reverend Lords Cardinals, General Inquisitors of the universal Christian republic against heretical depravity, having before my eyes the Holy Gospels, which I touch with my own hands, swear that I have always believed, and now believe, and with the help of God will in future believe, every article which the Holy Catholic and Apostolic Church of Rome holds, teaches, and preaches. But because I have been enjoined by this Holy Office altogether to abandon the false opinion which maintains that the sun is the centre and immovable, and forbidden to hold, defend, or teach the said false doctrine in any manner, and after it hath been signified to me that the said doctrine is repugnant with the Holy Scripture, I have written and printed a book, in which I treat of the same doctrine now condemned, and adduce reasons with great force in support of the same, without giving any solution, and therefore have been judged grievously suspected of heresy; that is to say, that I held and believed that the sun is the centre of the universe and is immovable, and that the earth is not the centre and is movable; willing, therefore, to remove from the minds of your Eminences, and of every Catholic Christian, this vehement suspicion rightfully entertained towards me, with a sincere heart and unfeigned faith, I abjure, curse, and detest the said errors and heresies, and generally every other error and sect contrary to Holy Church; and I swear that I will never more in future say or assert anything verbally, or in writing, which may give rise to a similar suspicion of me; but if I shall know any heretic, or any one suspected of heresy, that I will denounce him to this Holy Office, or to the Inquisitor or Ordinary of the place where I may be; I swear, moreover, and promise, that I will fulfil and observe fully, all the penances which have been or shall be laid on me by this Holy Office. But if it shall happen that I violate any of my said promises, oaths, and protestations (which God avert!), I subject myself to all the pains and punishments which have been decreed and promulgated by the sacred canons, and other general and particular constitutions, against delinquents of this description. So may God help me, and his Holy Gospels which I touch with my own hands. I, the above-named Galileo Galilei, have abjured, sworn, promised, and bound myself as above, and in witness thereof with my own hand have subscribed this present writing of my abjuration, which I have recited word for word. At Rome, in the Convent of Minerva, 22nd June, 1633. I, Galileo Galilei, have abjured as above with my own hand."

Those who believe the story about his muttering to a friend, as he rose from his knees, "e pur si muove," do not realize the scene.

1st. There was no friend in the place.

2nd. It would have been fatally dangerous to mutter anything before such an assemblage.

3rd. He was by this time an utterly broken and disgraced old man; wishful, of all things, to get away and hide himself and his miseries from the public gaze; probably with his senses deadened and stupefied by the mental sufferings he had undergone, and no longer able to think or care about anything—except perhaps his daughter,—certainly not about any motion of this wretched earth.

Far and wide the news of the recantation spread. Copies of the abjuration were immediately sent to all Universities, with instructions to the professors to read it publicly.

At Florence, his home, it was read out in the Cathedral church, all his friends and adherents being specially summoned to hear it.

For a short time more he was imprisoned in Rome; but at length was permitted to depart, never more of his own will to return.

He was allowed to go to Siena. Here his daughter wrote consolingly, rejoicing at his escape, and saying how joyfully she already recited the penitential psalms for him, and so relieved him of that part of his sentence.

But the poor girl was herself, by this time, ill—thoroughly worn out with anxiety and terror; she lay, in fact, on what proved to be her death-bed. Her one wish was to see her dearest lord and father, so she calls him, once more. The wish was granted. His prison was changed, by orders from Rome, from Siena to Arcetri, and once more father and daughter embraced. Six days after this she died.

The broken-hearted old man now asks for permission to go to live in Florence, but is met with the stern answer that he is to stay at Arcetri, is not to go out of the house, is not to receive visitors, and that if he asks for more favours, or transgresses the commands laid upon him, he is liable to be haled back to Rome and cast into a dungeon. These harsh measures were dictated, not by cruelty, but by the fear of his still spreading heresy by conversation, and so he was to be kept isolated.

Idle, however, he was not and could not be. He often complains that his head is too busy for his body. In the enforced solitude of Arcetri he was composing those dialogues on motion which are now reckoned his greatest and most solid achievement. In these the true laws of motion are set forth for the first time (see page 167). One more astronomical discovery also he was to make—that of the moon's libration.

And then there came one more crushing blow. His eyes became inflamed and painful—the sight of one of them failed, the other soon went; he became totally blind. But this, being a heaven-sent infliction, he could bear with resignation, though it must have been keenly painful to a solitary man of his activity. "Alas!" says he, in one of his letters, "your dear friend and servant is totally blind. Henceforth this heaven, this universe, which by wonderful observations I had enlarged a hundred and a thousand times beyond the conception of former ages, is shrunk for me into the narrow space which I myself fill in it. So it pleases God; it shall therefore please me also."

He was now allowed an amanuensis, and the help of his pupils Torricelli, Castelli, and Viviani, all devotedly attached to him, and Torricelli very famous after him. Visitors also were permitted, after approval by a Jesuit supervisor; and under these circumstances many visited him, among them a man as immortal as himself—John Milton, then only twenty-nine, travelling in Italy. Surely a pathetic incident, this meeting of these two great men—the one already blind, the other destined to become so. No wonder that, as in his old age he dictated his masterpiece, the thoughts of the English poet should run on the blind sage of Tuscany, and the reminiscence of their conversation should lend colour to the poem.

Well, it were tedious to follow the petty annoyances and troubles to which Galileo was still subject—how his own son was set to see that no unauthorized procedure took place, and that no heretic visitors were admitted; how it was impossible to get his new book printed till long afterwards; and how one form of illness after another took possession of him. The merciful end came at last, and at the age of seventy-eight he was released from the Inquisition.

They wanted to deny him burial—they did deny him a monument; they threatened to cart his bones away from Florence if his friends attempted one. And so they hoped that he and his work might be forgotten.

Poor schemers! Before the year was out an infant was born in Lincolnshire, whose destiny it was to round and complete and carry forward the work of their victim, so that, until man shall cease from the planet, neither the work nor its author shall have need of a monument.

* * * * *

Here might I end, were it not that the same kind of struggle as went on fiercely in the seventeenth century is still smouldering even now. Not in astronomy indeed, as then; nor yet in geology, as some fifty years ago; but in biology mainly—perhaps in other subjects. I myself have heard Charles Darwin spoken of as an atheist and an infidel, the theory of evolution assailed as unscriptural, and the doctrine of the ascent of man from a lower state of being, as opposed to the fall of man from some higher condition, denied as impious and un-Christian.

Men will not learn by the past; still they brandish their feeble weapons against the truths of Nature, as if assertions one way or another could alter fact, or make the thing other than it really is. As Galileo said before his spirit was broken, "In these and other positions certainly no man doubts but His Holiness the Pope hath always an absolute power of admitting or condemning them; but it is not in the power of any creature to make them to be true or false, or otherwise than of their own nature and in fact they are."

I know nothing of the views of any here present; but I have met educated persons who, while they might laugh at the men who refused to look through a telescope lest they should learn something they did not like, yet also themselves commit the very same folly. I have met persons who utterly refuse to listen to any view concerning the origin of man other than that of a perfect primaeval pair in a garden, and I am constrained to say this much: Take heed lest some prophet, after having excited your indignation at the follies and bigotry of a bygone generation, does not turn upon you with the sentence, "Thou art the man."



SUMMARY OF FACTS FOR LECTURE VI

Science before Newton

Dr. Gilbert, of Colchester, Physician to Queen Elizabeth, was an excellent experimenter, and made many discoveries in magnetism and electricity. He was contemporary with Tycho Brahe, and lived from 1540 to 1603.

Francis Bacon, Lord Verulam, 1561-1626, though a brilliant writer, is not specially important as regards science. He was not a scientific man, and his rules for making discoveries, or methods of induction, have never been consciously, nor often indeed unconsciously, followed by discoverers. They are not in fact practical rules at all, though they were so intended. His really strong doctrines are that phenomena must be studied direct, and that variations in the ordinary course of nature must be induced by aid of experiment; but he lacked the scientific instinct for pursuing these great truths into detail and special cases. He sneered at the work and methods of both Gilbert and Galileo, and rejected the Copernican theory as absurd. His literary gifts have conferred on him an artificially high scientific reputation, especially in England; at the same time his writings undoubtedly helped to make popular the idea of there being new methods for investigating Nature, and, by insisting on the necessity for freedom from preconceived ideas and opinions, they did much to release men from the bondage of Aristotelian authority and scholastic tradition.

The greatest name between Galileo and Newton is that of Descartes.

Rene Descartes was born at La Haye in Touraine, 1596, and died at Stockholm in 1650. He did important work in mathematics, physics, anatomy, and philosophy. Was greatest as a philosopher and mathematician. At the age of twenty-one he served as a volunteer under Prince Maurice of Nassau, but spent most of his later life in Holland. His famous Discourse on Method appeared at Leyden in 1637, and his Principia at Amsterdam in 1644; great pains being taken to avoid the condemnation of the Church.

Descartes's main scientific achievement was the application of algebra to geometry; his most famous speculation was the "theory of vortices," invented to account for the motion of planets. He also made many discoveries in optics and physiology. His best known immediate pupils were the Princess Elizabeth of Bohemia, and Christina, Queen of Sweden.

He founded a distinct school of thought (the Cartesian), and was the precursor of the modern mathematical method of investigating science, just as Galileo and Gilbert were the originators of the modern experimental method.



LECTURE VI

DESCARTES AND HIS THEORY OF VORTICES

After the dramatic life we have been considering in the last two lectures, it is well to have a breathing space, to look round on what has been accomplished, and to review the state of scientific thought, before proceeding to the next great era. For we are still in the early morning of scientific discovery: the dawn of the modern period, faintly heralded by Copernicus, brought nearer by the work of Tycho and Kepler, and introduced by the discoveries of Galileo—the dawn has occurred, but the sun is not yet visible. It is hidden by the clouds and mists of the long night of ignorance and prejudice. The light is sufficient, indeed, to render these earth-born vapours more visible: it is not sufficient to dispel them. A generation of slow and doubtful progress must pass, before the first ray of sunlight can break through the eastern clouds and the full orb of day itself appear.

It is this period of hesitating progress and slow leavening of men's ideas that we have to pass through in this week's lecture. It always happens thus: the assimilation of great and new ideas is always a slow and gradual process: there is no haste either here or in any other department of Nature. Die Zeit ist unendlich lang. Steadily the forces work, sometimes seeming to accomplish nothing; sometimes even the motion appears retrograde; but in the long run the destined end is reached, and the course, whether of a planet or of men's thoughts about the universe, is permanently altered. Then, the controversy was about the earth's place in the universe; now, if there be any controversy of the same kind, it is about man's place in the universe; but the process is the same: a startling statement by a great genius or prophet, general disbelief, and, it may be, an attitude of hostility, gradual acceptance by a few, slow spreading among the many, ending in universal acceptance and faith often as unquestioning and unreasoning as the old state of unfaith had been. Now the process is comparatively speedy: twenty years accomplishes a great deal: then it was tediously slow, and a century seemed to accomplish very little. Periodical literature may be responsible for some waste of time, but it certainly assists the rapid spread of ideas. The rate with which ideas are assimilated by the general public cannot even now be considered excessive, but how much faster it is than it was a few centuries ago may be illustrated by the attitude of the public to Darwinism now, twenty-five years after The Origin of Species, as compared with their attitude to the Copernican system a century after De Revolutionibus. By the way, it is, I know, presumptuous for me to have an opinion, but I cannot hear Darwin compared to or mentioned along with Newton without a shudder. The stage in which he found biology seems to me far more comparable with the Ptolemaic era in astronomy, and he himself to be quite fairly comparable to Copernicus.

Let us proceed to summarize the stage at which the human race had arrived at the epoch with which we are now dealing.

The Copernican view of the solar system had been stated, restated, fought, and insisted on; a chain of brilliant telescopic discoveries had made it popular and accessible to all men of any intelligence: henceforth it must be left to slowly percolate and sink into the minds of the people. For the nations were waking up now, and were accessible to new ideas. England especially was, in some sort, at the zenith of its glory; or, if not at the zenith, was in that full flush of youth and expectation and hope which is stronger and more prolific of great deeds and thoughts than a maturer period.

A common cause against a common and detested enemy had roused in the hearts of Englishmen a passion of enthusiasm and patriotism; so that the mean elements of trade, their cheating yard-wands, were forgotten for a time; the Armada was defeated, and the nation's true and conscious adult life began. Commerce was now no mere struggle for profit and hard bargains; it was full of the spirit of adventure and discovery; a new world had been opened up; who could tell what more remained unexplored? Men awoke to the splendour of their inheritance, and away sailed Drake and Frobisher and Raleigh into the lands of the West.

For literature, you know what a time it was. The author of Hamlet and Othello was alive: it is needless to say more. And what about science? The atmosphere of science is a more quiet and less stirring one; it thrives best when the fever of excitement is allayed; it is necessarily a later growth than literature. Already, however, our second great man of science was at work in a quiet country town—second in point of time, I mean, Roger Bacon being the first. Dr. Gilbert, of Colchester, was the second in point of time, and the age was ripening for the time when England was to be honoured with such a galaxy of scientific luminaries—Hooke and Boyle and Newton—as the world had not yet known.

Yes, the nations were awake. "In all directions," as Draper says, "Nature was investigated: in all directions new methods of examination were yielding unexpected and beautiful results. On the ruins of its ivy-grown cathedrals Ecclesiasticism [or Scholasticism], surprised and blinded by the breaking day, sat solemnly blinking at the light and life about it, absorbed in the recollection of the night that had passed, dreaming of new phantoms and delusions in its wished-for return, and vindictively striking its talons at any derisive assailant who incautiously approached too near."

Of the work of Gilbert there is much to say; so there is also of Roger Bacon, whose life I am by no means sure I did right in omitting. But neither of them had much to do with astronomy, and since it is in astronomy that the most startling progress was during these centuries being made, I have judged it wiser to adhere mainly to the pioneers in this particular department.

Only for this reason do I pass Gilbert with but slight mention. He knew of the Copernican theory and thoroughly accepted it (it is convenient to speak of it as the Copernican theory, though you know that it had been considerably improved in detail since the first crude statement by Copernicus), but he made in it no changes. He was a cultivated scientific man, and an acute experimental philosopher; his main work lay in the domain of magnetism and electricity. The phenomena connected with the mariner's compass had been studied somewhat by Roger Bacon; and they were now examined still more thoroughly by Gilbert, whose treatise De Magnete, marks the beginning of the science of magnetism.

As an appendix to that work he studied the phenomenon of amber, which had been mentioned by Thales. He resuscitated this little fact after its burial of 2,200 years, and greatly extended it. He it was who invented the name electricity—I wish it had been a shorter one. Mankind invents names much better than do philosophers. What can be better than "heat," "light," "sound"? How favourably they compare with electricity, magnetism, galvanism, electro-magnetism, and magneto-electricity! The only long-established monosyllabic name I know invented by a philosopher is "gas"—an excellent attempt, which ought to be imitated.[12]

Of Lord Bacon, who flourished about the same time (a little later), it is necessary to say something, because many persons are under the impression that to him and his Novum Organon the reawakening of the world, and the overthrow of Aristotelian tradition, are mainly due. His influence, however, has been exaggerated. I am not going to enter into a discussion of the Novum Organon, and the mechanical methods which he propounded as certain to evolve truth if patiently pursued; for this is what he thought he was doing—giving to the world an infallible recipe for discovering truth, with which any ordinarily industrious man could make discoveries by means of collection and discrimination of instances. You will take my statement for what it is worth, but I assert this: that many of the methods which Bacon lays down are not those which the experience of mankind has found to be serviceable; nor are they such as a scientific man would have thought of devising.

True it is that a real love and faculty for science are born in a man, and that to the man of scientific capacity rules of procedure are unnecessary; his own intuition is sufficient, or he has mistaken his vocation,—but that is not my point. It is not that Bacon's methods are useless because the best men do not need them; if they had been founded on a careful study of the methods actually employed, though it might be unconsciously employed, by scientific men—as the methods of induction, stated long after by John Stuart Mill, were founded—then, no doubt, their statement would have been a valuable service and a great thing to accomplish. But they were not this. They are the ideas of a brilliant man of letters, writing in an age when scientific research was almost unknown, about a subject in which he was an amateur. I confess I do not see how he, or John Stuart Mill, or any one else, writing in that age, could have formulated the true rules of philosophizing; because the materials and information were scarcely to hand. Science and its methods were only beginning to grow. No doubt it was a brilliant attempt. No doubt also there are many good and true points in the statement, especially in his insistence on the attitude of free and open candour with which the investigation of Nature should be approached. No doubt there was much beauty in his allegories of the errors into which men were apt to fall—the idola of the market-place, of the tribe, of the theatre, and of the den; but all this is literature, and on the solid progress of science may be said to have had little or no effect. Descartes's Discourse on Method was a much more solid production.

You will understand that I speak of Bacon purely as a scientific man. As a man of letters, as a lawyer, a man of the world, and a statesman, he is beyond any criticism of mine. I speak only of the purely scientific aspect of the Novum Organon. The Essays and The Advancement of Learning are masterly productions; and as a literary man he takes high rank.

The over-praise which, in the British Isles, has been lavished upon his scientific importance is being followed abroad by what may be an unnecessary amount of detraction. This is always the worst of setting up a man on too high a pinnacle; some one has to undertake the ungrateful task of pulling him down again. Justus von Liebig addressed himself to this task with some vigour in his Reden und Abhandlung (Leipzig, 1874), where he quotes from Bacon a number of suggestions for absurd experimentation.[13]

The next paragraph I read, not because I endorse it, but because it is always well to hear both sides of a question. You have probably been long accustomed to read over-estimates of Bacon's importance, and extravagant laudation of his writings as making an epoch in science; hear what Draper says on the opposite side:—[14]

"The more closely we examine the writings of Lord Bacon, the more unworthy does he seem to have been of the great reputation which has been awarded to him. The popular delusion to which he owes so much originated at a time when the history of science was unknown. They who first brought him into notice knew nothing of the old school of Alexandria. This boasted founder of a new philosophy could not comprehend, and would not accept, the greatest of all scientific doctrines when it was plainly set before his eyes.

"It has been represented that the invention of the true method of physical science was an amusement of Bacon's hours of relaxation from the more laborious studies of law, and duties of a Court.

"His chief admirers have been persons of a literary turn, who have an idea that scientific discoveries are accomplished by a mechanico-mental operation. Bacon never produced any great practical result himself, no great physicist has ever made any use of his method. He has had the same to do with the development of modern science that the inventor of the orrery has had to do with the discovery of the mechanism of the world. Of all the important physical discoveries, there is not one which shows that its author made it by the Baconian instrument.

"Newton never seems to have been aware that he was under any obligation to Bacon. Archimedes, and the Alexandrians, and the Arabians, and Leonardo da Vinci did very well before he was born; the discovery of America by Columbus and the circumnavigation by Magellan can hardly be attributed to him, yet they were the consequences of a truly philosophical reasoning. But the investigation of Nature is an affair of genius, not of rules. No man can invent an organon for writing tragedies and epic poems. Bacon's system is, in its own terms, an idol of the theatre. It would scarcely guide a man to a solution of the riddle of AElia Laelia Crispis, or to that of the charade of Sir Hilary.

"Few scientific pretenders have made more mistakes than Lord Bacon. He rejected the Copernican system, and spoke insolently of its great author; he undertook to criticize adversely Gilbert's treatise De Magnete; he was occupied in the condemnation of any investigation of final causes, while Harvey was deducing the circulation of the blood from Aquapendente's discovery of the valves in the veins; he was doubtful whether instruments were of any advantage, while Galileo was investigating the heavens with the telescope. Ignorant himself of every branch of mathematics, he presumed that they were useless in science but a few years before Newton achieved by their aid his immortal discoveries.

"It is time that the sacred name of philosophy should be severed from its long connection with that of one who was a pretender in science, a time-serving politician, an insidious lawyer, a corrupt judge, a treacherous friend, a bad man."

This seems to me a depreciation as excessive as are the eulogies commonly current. The truth probably lies somewhere between the two extremes. It is unfair to judge Bacon's methods by thinking of physical science in its present stage. To realise his position we must think of a subject still in its very early infancy, one in which the advisability of applying experimental methods is still doubted; one which has been studied by means of books and words and discussion of normal instances, instead of by collection and observation of the unusual and irregular, and by experimental production of variety. If we think of a subject still in this infantile and almost pre-scientific stage, Bacon's words and formulae are far from inapplicable; they are, within their limitations, quite necessary and wholesome. A subject in this stage, strange to say, exists,—psychology; now hesitatingly beginning to assume its experimental weapons amid a stifling atmosphere of distrust and suspicion. Bacon's lack of the modern scientific instinct must be admitted, but he rendered humanity a powerful service in directing it from books to nature herself, and his genius is indubitable. A judicious account of his life and work is given by Prof. Adamson, in the Encyclopaedia Britannica, and to this article I now refer you.

* * * * *

Who, then, was the man of first magnitude filling up the gap in scientific history between the death of Galileo and the maturity of Newton? Unknown and mysterious are the laws regulating the appearance of genius. We have passed in review a Pole, a Dane, a German, and an Italian,—the great man is now a Frenchman, Rene Descartes, born in Touraine, on the 31st of March, 1596.

His mother died at his birth; the father was of no importance, save as the owner of some landed property. The boy was reared luxuriously, and inherited a fair fortune. Nearly all the men of first rank, you notice, were born well off. Genius born to poverty might, indeed, even then achieve name and fame—as we see in the case of Kepler—but it was terribly handicapped. Handicapped it is still, but far less than of old; and we may hope it will become gradually still less so as enlightenment proceeds, and the tremendous moment of great men to a nation is more clearly and actively perceived.

It is possible for genius, when combined with strong character, to overcome all obstacles, and reach the highest eminence, but the struggle must be severe; and the absence of early training and refinement during the receptive years of youth must be a lifelong drawback.

Descartes had none of these drawbacks; life came easily to him, and, as a consequence perhaps, he never seems to have taken it quite seriously. Great movements and stirring events were to him opportunities for the study of men and manners; he was not the man to court persecution, nor to show enthusiasm for a losing or struggling cause.

In this, as in many other things, he was imbued with a very modern spirit, a cynical and sceptical spirit, which, to an outside and superficial observer like myself, seems rather rife just now.

He was also imbued with a phase of scientific spirit which you sometimes still meet with, though I believe it is passing away, viz. an uncultured absorption in his own pursuits, and some feeling of contempt for classical and literary and aesthetic studies.

In politics, art, and history he seems to have had no interest. He was a spectator rather than an actor on the stage of the world; and though he joined the army of that great military commander Prince Maurice of Nassau, he did it not as a man with a cause at heart worth fighting for, but precisely in the spirit in which one of our own gilded youths would volunteer in a similar case, as a good opportunity for frolic and for seeing life.

He soon tired of it and withdrew—at first to gay society in Paris. Here he might naturally have sunk into the gutter with his companions, but for a great mental shock which became the main epoch and turning-point of his life, the crisis which diverted him from frivolity to seriousness. It was a purely intellectual emotion, not excited by anything in the visible or tangible world; nor could it be called conversion in the common acceptation of that term. He tells us that on the 10th of November, 1619, at the age of twenty-four, a brilliant idea flashed upon him—the first idea, namely, of his great and powerful mathematical method, of which I will speak directly; and in the flush of it he foresaw that just as geometers, starting with a few simple and evident propositions or axioms, ascend by a long and intricate ladder of reasoning to propositions more and more abstruse, so it might be possible to ascend from a few data, to all the secrets and facts of the universe, by a process of mathematical reasoning.

"Comparing the mysteries of Nature with the laws of mathematics, he dared to hope that the secrets of both could be unlocked with the same key."

That night he lapsed gradually into a state of enthusiasm, in which he saw three dreams or visions, which he interpreted at the time, even before waking, to be revelations from the Spirit of Truth to direct his future course, as well as to warn him from the sins he had already committed.

His account of the dreams is on record, but is not very easy to follow; nor is it likely that a man should be able to convey to others any adequate idea of the deepest spiritual or mental agitation which has shaken him to his foundations.

His associates in Paris were now abandoned, and he withdrew, after some wanderings, to Holland, where he abode the best part of his life and did his real work.

Even now, however, he took life easily. He recommends idleness as necessary to the production of good mental work. He worked and meditated but a few hours a day: and most of those in bed. He used to think best in bed, he said. The afternoon he devoted to society and recreation. After supper he wrote letters to various persons, all plainly intended for publication, and scrupulously preserved. He kept himself free from care, and was most cautious about his health, regarding himself, no doubt, as a subject of experiment, and wishful to see how long he could prolong his life. At one time he writes to a friend that he shall be seriously disappointed if he does not manage to see 100 years.



This plan of not over-working himself, and limiting the hours devoted to serious thought, is one that might perhaps advantageously be followed by some over-laborious students of the present day. At any rate it conveys a lesson; for the amount of ground covered by Descartes, in a life not very long, is extraordinary. He must, however, have had a singular aptitude for scientific work; and the judicious leaven of selfishness whereby he was able to keep himself free from care and embarrassments must have been a great help to him.

And what did his versatile genius accomplish during his fifty-four years of life?

In philosophy, using the term as meaning mental or moral philosophy and metaphysics, as opposed to natural philosophy or physics, he takes a very high rank, and it is on this that perhaps his greatest fame rests. (He is the author, you may remember, of the famous aphorism, "Cogito, ergo sum.")

In biology I believe he may be considered almost equally great: certainly he spent a great deal of time in dissecting, and he made out a good deal of what is now known of the structure of the body, and of the theory of vision. He eagerly accepted the doctrine of the circulation of the blood, then being taught by Harvey, and was an excellent anatomist.

You doubtless know Professor Huxley's article on Descartes in the Lay Sermons, and you perceive in what high estimation he is there held.

He originated the hypothesis that animals are automata, for which indeed there is much to be said from some points of view; but he unfortunately believed that they were unconscious and non-sentient automata, and this belief led his disciples into acts of abominable cruelty. Professor Huxley lectured on this hypothesis and partially upheld it not many years since. The article is included in his volume called Science and Culture.

Concerning his work in mathematics and physics I can speak with more confidence. He is the author of the Cartesian system of algebraic or analytic geometry, which has been so powerful an engine of research, far easier to wield than the old synthetic geometry. Without it Newton could never have written the Principia, or made his greatest discoveries. He might indeed have invented it for himself, but it would have consumed some of his life to have brought it to the necessary perfection.

The principle of it is the specification of the position of a point in a plane by two numbers, indicating say its distance from two lines of reference in the plane; like the latitude and longitude of a place on the globe. For instance, the two lines of reference might be the bottom edge and the left-hand vertical edge of a wall; then a point on the wall, stated as being for instance 6 feet along and 2 feet up, is precisely determined. These two distances are called co-ordinates; horizontal ones are usually denoted by x, and vertical ones by y.

If, instead of specifying two things, only one statement is made, such as y = 2, it is satisfied by a whole row of points, all the points in a horizontal line 2 feet above the ground. Hence y = 2 may be said to represent that straight line, and is called the equation to that straight line. Similarly x = 6 represents a vertical straight line 6 feet (or inches or some other unit) from the left-hand edge. If it is asserted that x = 6 and y = 2, only one point can be found to satisfy both conditions, viz. the crossing point of the above two straight lines.

Suppose an equation such as x = y to be given. This also is satisfied by a row of points, viz. by all those that are equidistant from bottom and left-hand edges. In other words, x = y represents a straight line slanting upwards at 45 deg.. The equation x = 2y represents another straight line with a different angle of slope, and so on. The equation x^2 + y^2 = 36 represents a circle of radius 6. The equation 3x^2 + 4y^2 = 25 represents an ellipse; and in general every algebraic equation that can be written down, provided it involve only two variables, x and y, represents some curve in a plane; a curve moreover that can be drawn, or its properties completely investigated without drawing, from the equation. Thus algebra is wedded to geometry, and the investigation of geometric relations by means of algebraic equations is called analytical geometry, as opposed to the old Euclidian or synthetic mode of treating the subject by reasoning consciously directed to the subject by help of figures.

If there be three variables—x, y, and z,—instead of only two, an equation among them represents not a curve in a plane but a surface in space; the three variables corresponding to the three dimensions of space: length, breadth, and thickness.

An equation with four variables usually requires space of four dimensions for its geometrical interpretation, and so on.

Thus geometry can not only be reasoned about in a more mechanical and therefore much easier, manner, but it can be extended into regions of which we have and can have no direct conception, because we are deficient in sense organs for accumulating any kind of experience in connexion with such ideas.

Three external points are shown depicted on the retina: the image being appreciated by a representation of the brain.]

In physics proper Descartes' tract on optics is of considerable historical interest. He treats all the subjects he takes up in an able and original manner.

In Astronomy he is the author of that famous and long upheld theory, the doctrine of vortices.

He regarded space as a plenum full of an all-pervading fluid. Certain portions of this fluid were in a state of whirling motion, as in a whirlpool or eddy of water; and each planet had its own eddy, in which it was whirled round and round, as a straw is caught and whirled in a common whirlpool. This idea he works out and elaborates very fully, applying it to the system of the world, and to the explanation of all the motions of the planets.



This system evidently supplied a void in men's minds, left vacant by the overthrow of the Ptolemaic system, and it was rapidly accepted. In the English Universities it held for a long time almost undisputed sway; it was in this faith that Newton was brought up.

Something was felt to be necessary to keep the planets moving on their endless round; the primum mobile of Ptolemy had been stopped; an angel was sometimes assigned to each planet to carry it round, but though a widely diffused belief, this was a fantastic and not a serious scientific one. Descartes's vortices seemed to do exactly what was wanted.

It is true they had no connexion with the laws of Kepler. I doubt whether he knew about the laws of Kepler; he had not much opinion of other people's work; he read very little—found it easier to think. (He travelled through Florence once when Galileo was at the height of his renown without calling upon or seeing him.) In so far as the motion of a planet was not circular, it had to be accounted for by the jostling and crowding and distortion of the vortices.

Gravitation he explained by a settling down of bodies toward the centre of each vortex; and cohesion by an absence of relative motion tending to separate particles of matter. He "can imagine no stronger cement."

The vortices, as Descartes imagined them, are not now believed in. Are we then to regard the system as absurd and wholly false? I do not see how we can do this, when to this day philosophers are agreed in believing space to be completely full of fluid, which fluid is certainly capable of vortex motion, and perhaps everywhere does possess that motion. True, the now imagined vortices are not the large whirls of planetary size, they are rather infinitesimal whirls of less than atomic dimensions; still a whirling fluid is believed in to this day, and many are seeking to deduce all the properties of matter (rigidity, elasticity, cohesion gravitation, and the rest) from it.

Further, although we talk glibly about gravitation and magnetism, and so on, we do not really know what they are. Progress is being made, but we do not yet properly know. Much, overwhelmingly much, remains to be discovered, and it ill-behoves us to reject any well-founded and long-held theory as utterly and intrinsically false and absurd. The more one gets to know, the more one perceives a kernel of truth even in the most singular statements; and scientific men have learned by experience to be very careful how they lop off any branch of the tree of knowledge, lest as they cut away the dead wood they lose also some green shoot, some healthy bud of unperceived truth.

However, it may be admitted that the idea of a Cartesian vortex in connexion with the solar system applies, if at all, rather to an earlier—its nebulous—stage, when the whole thing was one great whirl, ready to split or shrink off planetary rings at their appropriate distances.

Soon after he had written his great work, the Principia Mathematica, and before he printed it, news reached him of the persecution and recantation of Galileo. "He seems to have been quite thunderstruck at the tidings," says Mr. Mahaffy, in his Life of Descartes.[15] "He had started on his scientific journeys with the firm determination to enter into no conflict with the Church, and to carry out his system of pure mathematics and physics without ever meddling with matters of faith. He was rudely disillusioned as to the possibility of this severance. He wrote at once—apparently, November 20th, 1633—to Mersenne to say he would on no account publish his work—nay, that he had at first resolved to burn all his papers, for that he would never prosecute philosophy at the risk of being censured by his Church. 'I could hardly have believed,' he says, 'that an Italian, and in favour with the Pope as I hear, could be considered criminal for nothing else than for seeking to establish the earth's motion; though I know it has formerly been censured by some Cardinals. But I thought I had heard that since then it was constantly being taught, even at Rome; and I confess that if the opinion of the earth's movement is false, all the foundations of my philosophy are so also, because it is demonstrated clearly by them. It is so bound up with every part of my treatise that I could not sever it without making the remainder faulty; and although I consider all my conclusions based on very certain and clear demonstrations, I would not for all the world sustain them against the authority of the Church.'"

Ten years later, however, he did publish the book, for he had by this time hit on an ingenious compromise. He formally denied that the earth moved, and only asserted that it was carried along with its water and air in one of those larger motions of the celestial ether which produce the diurnal and annual revolutions of the solar system. So, just as a passenger on the deck of a ship might be called stationary, so was the earth. He gives himself out therefore as a follower of Tycho rather than of Copernicus, and says if the Church won't accept this compromise he must return to the Ptolemaic system; but he hopes they won't compel him to do that, seeing that it is manifestly untrue.

This elaborate deference to the powers that be did not indeed save the work from being ultimately placed upon the forbidden list by the Church, but it saved himself, at any rate, from annoying persecution. He was not, indeed, at all willing to be persecuted, and would no doubt have at once withdrawn anything they wished. I should be sorry to call him a time-server, but he certainly had plenty of that worldly wisdom in which some of his predecessors had been so lamentably deficient. Moreover, he was really a sceptic, and cared nothing at all about the Church or its dogmas. He knew the Church's power, however, and the advisability of standing well with it: he therefore professed himself a Catholic, and studiously kept his science and his Christianity distinct.

In saying that he was a sceptic you must not understand that he was in the least an atheist. Very few men are; certainly Descartes never thought of being one. The term is indeed ludicrously inapplicable to him, for a great part of his philosophy is occupied with what he considers a rigorous proof of the existence of the Deity.

At the age of fifty-three he was sent for to Stockholm by Christina, Queen of Sweden, a young lady enthusiastically devoted to study of all kinds and determined to surround her Court with all that was most famous in literature and science. Thither, after hesitation, Descartes went. He greatly liked royalty, but he dreaded the cold climate. Born in Touraine, a Swedish winter was peculiarly trying to him, especially as the energetic Queen would have lessons given her at five o'clock in the morning. She intended to treat him well, and was immensely taken with him; but this getting up at five o'clock on a November morning, to a man accustomed all his life to lie in bed till eleven, was a cruel hardship. He was too much of a courtier, however, to murmur, and the early morning audience continued. His health began to break down: he thought of retreating, but suddenly he gave way and became delirious. The Queen's physician attended him, and of course wanted to bleed him. This, knowing all he knew of physiology, sent him furious, and they could do nothing with him. After some days he became quiet, was bled twice, and gradually sank, discoursing with great calmness on his approaching death, and duly fortified with all the rites of the Catholic Church.

His general method of research was as nearly as possible a purely deductive one:—i.e., after the manner of Euclid he starts with a few simple principles, and then, by a chain of reasoning, endeavours to deduce from them their consequences, and so to build up bit by bit an edifice of connected knowledge. In this he was the precursor of Newton. This method, when rigorously pursued, is the most powerful and satisfactory of all, and results in an ordered province of science far superior to the fragmentary conquests of experiment. But few indeed are the men who can handle it safely and satisfactorily: and none without continual appeals to experiment for verification. It was through not perceiving the necessity for verification that he erred. His importance to science lies not so much in what he actually discovered as in his anticipation of the right conditions for the solution of problems in physical science. He in fact made the discovery that Nature could after all be interrogated mathematically—a fact that was in great danger of remaining unknown. For, observe, that the mathematical study of Nature, the discovery of truth with a piece of paper and a pen, has a perilous similarity at first sight to the straw-thrashing subtleties of the Greeks, whose methods of investigating nature by discussing the meaning of words and the usage of language and the necessities of thought, had proved to be so futile and unproductive.

A reaction had set in, led by Galileo, Gilbert, and the whole modern school of experimental philosophers, lasting down to the present day:—men who teach that the only right way of investigating Nature is by experiment and observation.

It is indeed a very right and an absolutely necessary way; but it is not the only way. A foundation of experimental fact there must be; but upon this a great structure of theoretical deduction can be based, all rigidly connected together by pure reasoning, and all necessarily as true as the premises, provided no mistake is made. To guard against the possibility of mistake and oversight, especially oversight, all conclusions must sooner or later be brought to the test of experiment; and if disagreeing therewith, the theory itself must be re-examined, and the flaw discovered, or else the theory must be abandoned.

Of this grand method, quite different from the gropings in the dark of Kepler—this method, which, in combination with experiment, has made science what it now is—this which in the hands of Newton was to lead to such stupendous results, we owe the beginning and early stages to Rene Descartes.



SUMMARY OF FACTS FOR LECTURES VII AND VIII

Otto Guericke 1602-1686 Hon. Robert Boyle 1626-1691 Huyghens 1629-1695 Christopher Wren 1632-1723 Robert Hooke 1635-1702 NEWTON 1642-1727 Edmund Halley 1656-1742 James Bradley 1692-1762

Chronology of Newton's Life.

Isaac Newton was born at Woolsthorpe, near Grantham, Lincolnshire, on Christmas Day, 1642. His father, a small freehold farmer, also named Isaac, died before his birth. His mother, nee Hannah Ayscough, in two years married a Mr. Smith, rector of North Witham, but was again left a widow in 1656. His uncle, W. Ayscough, was rector of a near parish and a graduate of Trinity College, Cambridge. At the age of fifteen Isaac was removed from school at Grantham to be made a farmer of, but as it seemed he would not make a good one his uncle arranged for him to return to school and thence to Cambridge, where he entered Trinity College as a sub-sizar in 1661. Studied Descartes's geometry. Found out a method of infinite series in 1665, and began the invention of Fluxions. In the same year and the next he was driven from Cambridge by the plague. In 1666, at Woolsthorpe, the apple fell. In 1667 he was elected a fellow of his college, and in 1669 was specially noted as possessing an unparalleled genius by Dr. Barrow, first Lucasian Professor of Mathematics. The same year Dr. Barrow retired from his chair in favour of Newton, who was thus elected at the age of twenty-six. He lectured first on optics with great success. Early in 1672 he was elected a Fellow of the Royal Society, and communicated his researches in optics, his reflecting telescope, and his discovery of the compound nature of white light. Annoying controversies arose; but he nevertheless contributed a good many other most important papers in optics, including observations in diffraction, and colours of thin plates. He also invented the modern sextant. In 1672 a letter from Paris was read at the Royal Society concerning a new and accurate determination of the size of the earth by Picard. When Newton heard of it he began the Principia, working in silence. In 1684 arose a discussion between Wren, Hooke, and Halley concerning the law of inverse square as applied to gravity and the path it would cause the planets to describe. Hooke asserted that he had a solution, but he would not produce it. After waiting some time for it Halley went to Cambridge to consult Newton on the subject, and thus discovered the existence of the first part of the Principia, wherein all this and much more was thoroughly worked out. On his representations to the Royal Society the manuscript was asked for, and when complete was printed and published in 1687 at Halley's expense. While it was being completed Newton and seven others were sent to uphold the dignity of the University, before the Court of High Commission and Judge Jeffreys, against a high-handed action of James II. In 1682 he was sent to Parliament, and was present at the coronation of William and Mary. Made friends with Locke. In 1694 Montague, Lord Halifax, made him Warden, and in 1697 Master, of the Mint. Whiston succeeded him as Lucasian Professor. In 1693 the method of fluxions was published. In 1703 Newton was made President of the Royal Society, and held the office to the end of his life. In 1705 he was knighted by Anne. In 1713 Cotes helped him to bring out a new edition of the Principia, completed as we now have it. On the 20th of March 1727, he died: having lived from Charles I. to George II.

THE LAWS OF MOTION, DISCOVERED BY GALILEO, STATED BY NEWTON.

Law 1.—If no force acts on a body in motion, it continues to move uniformly in a straight line.

Law 2.—If force acts on a body, it produces a change of motion proportional to the force and in the same direction.

Law 3.—When one body exerts force on another, that other reacts with equal force upon the one.



LECTURE VII

SIR ISAAC NEWTON

The little hamlet of Woolsthorpe lies close to the village of Colsterworth, about six miles south of Grantham, in the county of Lincoln. In the manor house of Woolsthorpe, on Christmas Day, 1642, was born to a widowed mother a sickly infant who seemed not long for this world. Two women who were sent to North Witham to get some medicine for him scarcely expected to find him alive on their return. However, the child lived, became fairly robust, and was named Isaac, after his father. What sort of a man this father was we do not know. He was what we may call a yeoman, that most wholesome and natural of all classes. He owned the soil he tilled, and his little estate had already been in the family for some hundred years. He was thirty-six when he died, and had only been married a few months.

Of the mother, unfortunately, we know almost as little. We hear that she was recommended by a parishioner to the Rev. Barnabas Smith, an old bachelor in search of a wife, as "the widow Newton—an extraordinary good woman:" and so I expect she was, a thoroughly sensible, practical, homely, industrious, middle-class, Mill-on-the-Floss sort of woman. However, on her second marriage she went to live at North Witham, and her mother, old Mrs. Ayscough, came to superintend the farm at Woolsthorpe, and take care of young Isaac.

By her second marriage his mother acquired another piece of land, which she settled on her first son; so Isaac found himself heir to two little properties, bringing in a rental of about L80 a year.



He had been sent to a couple of village schools to acquire the ordinary accomplishments taught at those places, and for three years to the grammar school at Grantham, then conducted by an old gentleman named Mr. Stokes. He had not been very industrious at school, nor did he feel keenly the fascinations of the Latin Grammar, for he tells us that he was the last boy in the lowest class but one. He used to pay much more attention to the construction of kites and windmills and waterwheels, all of which he made to work very well. He also used to tie paper lanterns to the tail of his kite, so as to make the country folk fancy they saw a comet, and in general to disport himself as a boy should.

It so happened, however, that he succeeded in thrashing, in fair fight, a bigger boy who was higher in the school, and who had given him a kick. His success awakened a spirit of emulation in other things than boxing, and young Newton speedily rose to be top of the school.

Under these circumstances, at the age of fifteen, his mother, who had now returned to Woolsthorpe, which had been rebuilt, thought it was time to train him for the management of his land, and to make a farmer and grazier of him. The boy was doubtless glad to get away from school, but he did not take kindly to the farm—especially not to the marketing at Grantham. He and an old servant were sent to Grantham every week to buy and sell produce, but young Isaac used to leave his old mentor to do all the business, and himself retire to an attic in the house he had lodged in when at school, and there bury himself in books.

After a time he didn't even go through the farce of visiting Grantham at all; but stopped on the road and sat under a hedge, reading or making some model, until his companion returned.

We hear of him now in the great storm of 1658, the storm on the day Cromwell died, measuring the force of the wind by seeing how far he could jump with it and against it. He also made a water-clock and set it up in the house at Grantham, where it kept fairly good time so long as he was in the neighbourhood to look after it occasionally.

At his own home he made a couple of sundials on the side of the wall (he began by marking the position of the sun by the shadow of a peg driven into the wall, but this gradually developed into a regular dial) one of which remained of use for some time; and was still to be seen in the same place during the first half of the present century, only with the gnomon gone. In 1844 the stone on which it was carved was carefully extracted and presented to the Royal Society, who preserve it in their library. The letters WTON roughly carved on it are barely visible.

All these pursuits must have been rather trying to his poor mother, and she probably complained to her brother, the rector of Burton Coggles: at any rate this gentleman found master Newton one morning under a hedge when he ought to have been farming. But as he found him working away at mathematics, like a wise man he persuaded his sister to send the boy back to school for a short time, and then to Cambridge. On the day of his finally leaving school old Mr. Stokes assembled the boys, made them a speech in praise of Newton's character and ability, and then dismissed him to Cambridge.

At Trinity College a new world opened out before the country-bred lad. He knew his classics passably, but of mathematics and science he was ignorant, except through the smatterings he had picked up for himself. He devoured a book on logic, and another on Kepler's Optics, so fast that his attendance at lectures on these subjects became unnecessary. He also got hold of a Euclid and of Descartes's Geometry. The Euclid seemed childishly easy, and was thrown aside, but the Descartes baffled him for a time. However, he set to it again and again and before long mastered it. He threw himself heart and soul into mathematics, and very soon made some remarkable discoveries. First he discovered the binomial theorem: familiar now to all who have done any algebra, unintelligible to others, and therefore I say nothing about it. By the age of twenty-one or two he had begun his great mathematical discovery of infinite series and fluxions—now known by the name of the Differential Calculus. He wrote these things out and must have been quite absorbed in them, but it never seems to have occurred to him to publish them or tell any one about them.

In 1664 he noticed some halos round the moon, and, as his manner was, he measured their angles—the small ones 3 and 5 degrees each, the larger one 22 deg..35. Later he gave their theory.

Small coloured halos round the moon are often seen, and are said to be a sign of rain. They are produced by the action of minute globules of water or cloud particles upon light, and are brightest when the particles are nearly equal in size. They are not like the rainbow, every part of which is due to light that has entered a raindrop, and been refracted and reflected with prismatic separation of colours; a halo is caused by particles so small as to be almost comparable with the size of waves of light, in a way which is explained in optics under the head "diffraction." It may be easily imitated by dusting an ordinary piece of window-glass over with lycopodium, placing a candle near it, and then looking at the candle-flame through the dusty glass from a fair distance. Or you may look at the image of a candle in a dusted looking-glass. Lycopodium dust is specially suitable, for its granules are remarkably equal in size. The large halo, more rarely seen, of angular radius 22 deg..35, is due to another cause again, and is a prismatic effect, although it exhibits hardly any colour. The angle 22-1/2 deg. is characteristic of refraction in crystals with angles of 60 deg. and refractive index about the same as water; in other words this halo is caused by ice crystals in the higher regions of the atmosphere.

He also the same year observed a comet, and sat up so late watching it that he made himself ill. By the end of the year he was elected to a scholarship and took his B.A. degree. The order of merit for that year never existed or has not been kept. It would have been interesting, not as a testimony to Newton, but to the sense or non-sense of the examiners. The oldest Professorship of Mathematics at the University of Cambridge, the Lucasian, had not then been long founded, and its first occupant was Dr. Isaac Barrow, an eminent mathematician, and a kind old man. With him Newton made good friends, and was helpful in preparing a treatise on optics for the press. His help is acknowledged by Dr. Barrow in the preface, which states that he had corrected several errors and made some capital additions of his own. Thus we see that, although the chief part of his time was devoted to mathematics, his attention was already directed to both optics and astronomy. (Kepler, Descartes, Galileo, all combined some optics with astronomy. Tycho and the old ones combined alchemy; Newton dabbled in this also.)

Newton reached the age of twenty-three in 1665, the year of the Great Plague. The plague broke out in Cambridge as well as in London, and the whole college was sent down. Newton went back to Woolsthorpe, his mind teeming with ideas, and spent the rest of this year and part of the next in quiet pondering. Somehow or other he had got hold of the notion of centrifugal force. It was six years before Huyghens discovered and published the laws of centrifugal force, but in some quiet way of his own Newton knew about it and applied the idea to the motion of the planets.

We can almost follow the course of his thoughts as he brooded and meditated on the great problem which had taxed so many previous thinkers,—What makes the planets move round the sun? Kepler had discovered how they moved, but why did they so move, what urged them?

Even the "how" took a long time—all the time of the Greeks, through Ptolemy, the Arabs, Copernicus, Tycho: circular motion, epicycles, and excentrics had been the prevailing theory. Kepler, with his marvellous industry, had wrested from Tycho's observations the secret of their orbits. They moved in ellipses with the sun in one focus. Their rate of description of area, not their speed, was uniform and proportional to time.

Yes, and a third law, a mysterious law of unintelligible import, had also yielded itself to his penetrating industry—a law the discovery of which had given him the keenest delight, and excited an outburst of rapture—viz. that there was a relation between the distances and the periodic times of the several planets. The cubes of the distances were proportional to the squares of the times for the whole system. This law, first found true for the six primary planets, he had also extended, after Galileo's discovery, to the four secondary planets, or satellites of Jupiter (p. 81).

But all this was working in the dark—it was only the first step—this empirical discovery of facts; the facts were so, but how came they so? What made the planets move in this particular way? Descartes's vortices was an attempt, a poor and imperfect attempt, at an explanation. It had been hailed and adopted throughout Europe for want of a better, but it did not satisfy Newton. No, it proceeded on a wrong tack, and Kepler had proceeded on a wrong tack in imagining spokes or rays sticking out from the sun and driving the planets round like a piece of mechanism or mill work. For, note that all these theories are based on a wrong idea—the idea, viz., that some force is necessary to maintain a body in motion. But this was contrary to the laws of motion as discovered by Galileo. You know that during his last years of blind helplessness at Arcetri, Galileo had pondered and written much on the laws of motion, the foundation of mechanics. In his early youth, at Pisa, he had been similarly occupied; he had discovered the pendulum, he had refuted the Aristotelians by dropping weights from the leaning tower (which we must rejoice that no earthquake has yet injured), and he had returned to mechanics at intervals all his life; and now, when his eyes were useless for astronomy, when the outer world has become to him only a prison to be broken by death, he returns once more to the laws of motion, and produces the most solid and substantial work of his life.

For this is Galileo's main glory—not his brilliant exposition of the Copernican system, not his flashes of wit at the expense of a moribund philosophy, not his experiments on floating bodies, not even his telescope and astronomical discoveries—though these are the most taking and dazzling at first sight. No; his main glory and title to immortality consists in this, that he first laid the foundation of mechanics on a firm and secure basis of experiment, reasoning, and observation. He first discovered the true Laws of Motion.

I said little of this achievement in my lecture on him; for the work was written towards the end of his life, and I had no time then. But I knew I should have to return to it before we came to Newton, and here we are.

You may wonder how the work got published when so many of his manuscripts were destroyed. Horrible to say, Galileo's own son destroyed a great bundle of his father's manuscripts, thinking, no doubt, thereby to save his own soul. This book on mechanics was not burnt, however. The fact is it was rescued by one or other of his pupils, Toricelli or Viviani, who were allowed to visit him in his last two or three years; it was kept by them for some time, and then published surreptitiously in Holland. Not that there is anything in it bearing in any visible way on any theological controversy; but it is unlikely that the Inquisition would have suffered it to pass notwithstanding.

I have appended to the summary preceding this lecture (p. 160) the three axioms or laws of motion discovered by Galileo. They are stated by Newton with unexampled clearness and accuracy, and are hence known as Newton's laws, but they are based on Galileo's work. The first is the simplest; though ignorance of it gave the ancients a deal of trouble. It is simply a statement that force is needed to change the motion of a body; i.e. that if no force act on a body it will continue to move uniformly both in speed and direction—in other words, steadily, in a straight line. The old idea had been that some force was needed to maintain motion. On the contrary, the first law asserts, some force is needed to destroy it. Leave a body alone, free from all friction or other retarding forces, and it will go on for ever. The planetary motion through empty space therefore wants no keeping up; it is not the motion that demands a force to maintain it, it is the curvature of the path that needs a force to produce it continually. The motion of a planet is approximately uniform so far as speed is concerned, but it is not constant in direction; it is nearly a circle. The real force needed is not a propelling but a deflecting force.

The second law asserts that when a force acts, the motion changes, either in speed or in direction, or both, at a pace proportional to the magnitude of the force, and in the same direction as that in which the force acts. Now since it is almost solely in direction that planetary motion alters, a deflecting force only is needed; a force at right angles to the direction of motion, a force normal to the path. Considering the motion as circular, a force along the radius, a radial or centripetal force, must be acting continually. Whirl a weight round and round by a bit of elastic, the elastic is stretched; whirl it faster, it is stretched more. The moving mass pulls at the elastic—that is its centrifugal force; the hand at the centre pulls also—that is centripetal force.

The third law asserts that these two forces are equal, and together constitute the tension in the elastic. It is impossible to have one force alone, there must be a pair. You can't push hard against a body that offers no resistance. Whatever force you exert upon a body, with that same force the body must react upon you. Action and reaction are always equal and opposite.

Sometimes an absurd difficulty is felt with respect to this, even by engineers. They say, "If the cart pulls against the horse with precisely the same force as the horse pulls the cart, why should the cart move?" Why on earth not? The cart moves because the horse pulls it, and because nothing else is pulling it back. "Yes," they say, "the cart is pulling back." But what is it pulling back? Not itself, surely? "No, the horse." Yes, certainly the cart is pulling at the horse; if the cart offered no resistance what would be the good of the horse? That is what he is for, to overcome the pull-back of the cart; but nothing is pulling the cart back (except, of course, a little friction), and the horse is pulling it forward, hence it goes forward. There is no puzzle at all when once you realise that there are two bodies and two forces acting, and that one force acts on each body.[16]

If, indeed, two balanced forces acted on one body that would be in equilibrium, but the two equal forces contemplated in the third law act on two different bodies, and neither is in equilibrium.

So much for the third law, which is extremely simple, though it has extraordinarily far-reaching consequences, and when combined with a denial of "action at a distance," is precisely the principle of the Conservation of Energy. Attempts at perpetual motion may all be regarded as attempts to get round this "third law."



On the subject of the second law a great deal more has to be said before it can be in any proper sense even partially appreciated, but a complete discussion of it would involve a treatise on mechanics. It is the law of mechanics. One aspect of it we must attend to now in order to deal with the motion of the planets, and that is the fact that the change of motion of a body depends solely and simply on the force acting, and not at all upon what the body happens to be doing at the time it acts. It may be stationary, or it may be moving in any direction; that makes no difference.

Thus, referring back to the summary preceding Lecture IV, it is there stated that a dropped body falls 16 feet in the first second, that in two seconds it falls 64 feet, and so on, in proportion to the square of the time. So also will it be the case with a thrown body, but the drop must be reckoned from its line of motion—the straight line which, but for gravity, it would describe.

Thus a stone thrown from O with the velocity OA would in one second find itself at A, in two seconds at B, in three seconds at C, and so on, in accordance with the first law of motion, if no force acted. But if gravity acts it will have fallen 16 feet by the time it would have got to A, and so will find itself at P. In two seconds it will be at Q, having fallen a vertical height of 64 feet; in three seconds it will be at R, 144 feet below C; and so on. Its actual path will be a curve, which in this case is a parabola. (Fig. 57.)

If a cannon is pointed horizontally over a level plain, the cannon ball will be just as much affected by gravity as if it were dropped, and so will strike the plain at the same instant as another which was simply dropped where it started. One ball may have gone a mile and the other only dropped a hundred feet or so, but the time needed by both for the vertical drop will be the same. The horizontal motion of one is an extra, and is due to the powder.

As a matter of fact the path of a projectile in vacuo is only approximately a parabola. It is instructive to remember that it is really an ellipse with one focus very distant, but not at infinity. One of its foci is the centre of the earth. A projectile is really a minute satellite of the earth's, and in vacuo it accurately obeys all Kepler's laws. It happens not to be able to complete its orbit, because it was started inconveniently close to the earth, whose bulk gets in its way; but in that respect the earth is to be reckoned as a gratuitous obstruction, like a target, but a target that differs from most targets in being hard to miss.



Now consider circular motion in the same way, say a ball whirled round by a string. (Fig. 58.)

Attending to the body at O, it is for an instant moving towards A, and if no force acted it would get to A in a time which for brevity we may call a second. But a force, the pull of the string, is continually drawing it towards S, and so it really finds itself at P, having described the circular arc OP, which may be considered to be compounded of, and analyzable into the rectilinear motion OA and the drop AP. At P it is for an instant moving towards B, and the same process therefore carries it to Q; in the third second it gets to R; and so on: always falling, so to speak, from its natural rectilinear path, towards the centre, but never getting any nearer to the centre.

The force with which it has thus to be constantly pulled in towards the centre, or, which is the same thing, the force with which it is tugging at whatever constraint it is that holds it in, is mv^2/r; where m is the mass of the particle, v its velocity, and r the radius of its circle of movement. This is the formula first given by Huyghens for centrifugal force.

We shall find it convenient to express it in terms of the time of one revolution, say T. It is easily done, since plainly T = circumference/speed = 2[pi]r/v; so the above expression for centrifugal force becomes 4[pi]^2mr/T^2.

As to the fall of the body towards the centre every microscopic unit of time, it is easily reckoned. For by Euclid III. 36, and Fig. 58, AP.AA' = AO^2. Take A very near O, then OA = vt, and AA' = 2r; so AP = v^2t^2/2r = 2[pi]^2r t^2/T^2; or the fall per second is 2[pi]^2r/T^2, r being its distance from the centre, and T its time of going once round.

In the case of the moon for instance, r is 60 earth radii; more exactly 60.2; and T is a lunar month, or more precisely 27 days, 7 hours, 43 minutes, and 11-1/2 seconds. Hence the moon's deflection from the tangential or rectilinear path every minute comes out as very closely 16 feet (the true size of the earth being used).

Returning now to the case of a small body revolving round a big one, and assuming a force directly proportional to the mass of both bodies, and inversely proportional to the square of the distance between them: i.e. assuming the known force of gravity, it is

V Mm/r^2

where V is a constant, called the gravitation constant, to be determined by experiment.

If this is the centripetal force pulling a planet or satellite in, it must be equal to the centrifugal force of this latter, viz. (see above).

_4[pi]^2mr/T^2

Equate the two together, and at once we get

r^3/T^2 = V/4[pi]^2M;

or, in words, the cube of the distance divided by the square of the periodic time for every planet or satellite of the system under consideration, will be constant and proportional to the mass of the central body.

This is Kepler's third law, with a notable addition. It is stated above for circular motion only, so as to avoid geometrical difficulties, but even so it is very instructive. The reason of the proportion between r^3 and T^2 is at once manifest; and as soon as the constant V became known, the mass of the central body, the sun in the case of a planet, the earth in the case of the moon, Jupiter in the case of his satellites, was at once determined.

Newton's reasoning at this time might, however, be better displayed perhaps by altering the order of the steps a little, as thus:—

The centrifugal force of a body is proportional to r^3/T^2, but by Kepler's third law r^3/T^2 is constant for all the planets, reckoning r from the sun. Hence the centripetal force needed to hold in all the planets will be a single force emanating from the sun and varying inversely with the square of the distance from that body.

Such a force is at once necessary and sufficient. Such a force would explain the motion of the planets.

But then all this proceeds on a wrong assumption—that the planetary motion is circular. Will it hold for elliptic orbits? Will an inverse square law of force keep a body moving in an elliptic orbit about the sun in one focus? This is a far more difficult question. Newton solved it, but I do not believe that even he could have solved it, except that he had at his disposal two mathematical engines of great power—the Cartesian method of treating geometry, and his own method of Fluxions. One can explain the elliptic motion now mathematically, but hardly otherwise; and I must be content to state that the double fact is true—viz., that an inverse square law will move the body in an ellipse or other conic section with the sun in one focus, and that if a body so moves it must be acted on by an inverse square law.



This then is the meaning of the first and third laws of Kepler. What about the second? What is the meaning of the equable description of areas? Well, that rigorously proves that a planet is acted on by a force directed to the centre about which the rate of description of areas is equable. It proves, in fact, that the sun is the attracting body, and that no other force acts.

For first of all if the first law of motion is obeyed, i.e. if no force acts, and if the path be equally subdivided to represent equal times, and straight lines be drawn from the divisions to any point whatever, all these areas thus enclosed will be equal, because they are triangles on equal base and of the same height (Euclid, I). See Fig. 59; S being any point whatever, and A, B, C, successive positions of a body.

Now at each of the successive instants let the body receive a sudden blow in the direction of that same point S, sufficient to carry it from A to D in the same time as it would have got to B if left alone. The result will be that there will be a compromise, and it will really arrive at P, travelling along the diagonal of the parallelogram AP. The area its radius vector sweeps out is therefore SAP, instead of what it would have been, SAB. But then these two areas are equal, because they are triangles on the same base AS, and between the same parallels BP, AS; for by the parallelogram law BP is parallel to AD. Hence the area that would have been described is described, and as all the areas were equal in the case of no force, they remain equal when the body receives a blow at the end of every equal interval of time, provided that every blow is actually directed to S, the point to which radii vectores are drawn.



It is instructive to see that it does not hold if the blow is any otherwise directed; for instance, as in Fig. 61, when the blow is along AE, the body finds itself at P at the end of the second interval, but the area SAP is by no means equal to SAB, and therefore not equal to SOA, the area swept out in the first interval.

In order to modify Fig. 60 so as to represent continuous motion and steady forces, we have to take the sides of the polygon OAPQ, &c., very numerous and very small; in the limit, infinitely numerous and infinitely small. The path then becomes a curve, and the series of blows becomes a steady force directed towards S. About whatever point therefore the rate of description of areas is uniform, that point and no other must be the centre of all the force there is. If there be no force, as in Fig. 59, well and good, but if there be any force however small not directed towards S, then the rate of description of areas about S cannot be uniform. Kepler, however, says that the rate of description of areas of each planet about the sun is, by Tycho's observations, uniform; hence the sun is the centre of all the force that acts on them, and there is no other force, not even friction. That is the moral of Kepler's second law.

We may also see from it that gravity does not travel like light, so as to take time on its journey from sun to planet; for, if it did, there would be a sort of aberration, and the force on its arrival could no longer be accurately directed to the centre of the sun. (See Nature, vol. xlvi., p. 497.) It is a matter for accuracy of observation, therefore, to decide whether the minutest trace of such deviation can be detected, i.e. within what limits of accuracy Kepler's second law is now known to be obeyed.

I will content myself by saying that the limits are extremely narrow. [Reference may be made also to p. 208.]

Thus then it became clear to Newton that the whole solar system depended on a central force emanating from the sun, and varying inversely with the square of the distance from him: for by that hypothesis all the laws of Kepler concerning these motions were completely accounted for; and, in fact, the laws necessitated the hypothesis and established it as a theory.

Similarly the satellites of Jupiter were controlled by a force emanating from Jupiter and varying according to the same law. And again our moon must be controlled by a force from the earth, decreasing with the distance according to the same law.

Grant this hypothetical attracting force pulling the planets towards the sun, pulling the moon towards the earth, and the whole mechanism of the solar system is beautifully explained.

If only one could be sure there was such a force! It was one thing to calculate out what the effects of such a force would be: it was another to be able to put one's finger upon it and say, this is the force that actually exists and is known to exist. We must picture him meditating in his garden on this want—an attractive force towards the earth.

If only such an attractive force pulling down bodies to the earth existed. An apple falls from a tree. Why, it does exist! There is gravitation, common gravity that makes bodies fall and gives them their weight.

Wanted, a force tending towards the centre of the earth. It is to hand!

It is common old gravity that had been known so long, that was perfectly familiar to Galileo, and probably to Archimedes. Gravity that regulates the motion of projectiles. Why should it only pull stones and apples? Why should it not reach as high as the moon? Why should it not be the gravitation of the sun that is the central force acting on all the planets?

Surely the secret of the universe is discovered! But, wait a bit; is it discovered? Is this force of gravity sufficient for the purpose? It must vary inversely with the square of the distance from the centre of the earth. How far is the moon away? Sixty earth's radii. Hence the force of gravity at the moon's distance can only be 1/3600 of what it is on the earth's surface. So, instead of pulling it 16 ft. per second, it should pull it 16/3600 ft. per second, or 16 ft. a minute.[17] How can one decide whether such a force is able to pull the moon the actual amount required? To Newton this would seem only like a sum in arithmetic. Out with a pencil and paper and reckon how much the moon falls toward the earth in every second of its motion. Is it 16/3600? That is what it ought to be: but is it? The size of the earth comes into the calculation. Sixty miles make a degree, 360 degrees a circumference. This gives as the earth's diameter 6,873 miles; work it out.

The answer is not 16 feet a minute, it is 13.9 feet.

Surely a mistake of calculation?

No, it is no mistake: there is something wrong in the theory, gravity is too strong.

Instead of falling toward the earth 5-1/3 hundredths of an inch every second, as it would under gravity, the moon only falls 4-2/3 hundredths of an inch per second.

With such a discovery in his grasp at the age of twenty-three he is disappointed—the figures do not agree, and he cannot make them agree. Either gravity is not the force in action, or else something interferes with it. Possibly, gravity does part of the work, and the vortices of Descartes interfere with it.

He must abandon the fascinating idea for the time. In his own words, "he laid aside at that time any further thought of the matter."

So far as is known, he never mentioned his disappointment to a soul. He might, perhaps, if he had been at Cambridge, but he was a shy and solitary youth, and just as likely he might not. Up in Lincolnshire, in the seventeenth century, who was there for him to consult?

True, he might have rushed into premature publication, after our nineteenth century fashion, but that was not his method. Publication never seemed to have occurred to him.

His reticence now is noteworthy, but later on it is perfectly astonishing. He is so absorbed in making discoveries that he actually has to be reminded to tell any one about them, and some one else always has to see to the printing and publishing for him.

I have entered thus fully into what I conjecture to be the stages of this early discovery of the law of gravitation, as applicable to the heavenly bodies, because it is frequently and commonly misunderstood. It is sometimes thought that he discovered the force of gravity; I hope I have made it clear that he did no such thing. Every educated man long before his time, if asked why bodies fell, would reply just as glibly as they do now, "Because the earth attracts them," or "because of the force of gravity."

His discovery was that the motions of the solar system were due to the action of a central force, directed to the body at the centre of the system, and varying inversely with the square of the distance from it. This discovery was based upon Kepler's laws, and was clear and certain. It might have been published had he so chosen.

But he did not like hypothetical and unknown forces; he tried to see whether the known force of gravity would serve. This discovery at that time he failed to make, owing to a wrong numerical datum. The size of the earth he only knew from the common doctrine of sailors that 60 miles make a degree; and that threw him out. Instead of falling 16 feet a minute, as it ought under gravity, it only fell 13.9 feet, so he abandoned the idea. We do not find that he returned to it for sixteen years.



LECTURE VIII

NEWTON AND THE LAW OF GRAVITATION

We left Newton at the age of twenty-three on the verge of discovering the mechanism of the solar system, deterred therefrom only by an error in the then imagined size of the earth. He had proved from Kepler's laws that a centripetal force directed to the sun, and varying as the inverse square of the distance from that body, would account for the observed planetary motions, and that a similar force directed to the earth would account for the lunar motion; and it had struck him that this force might be the very same as the familiar force of gravitation which gave to bodies their weight: but in attempting a numerical verification of this idea in the case of the moon he was led by the then received notion that sixty miles made a degree on the earth's surface into an erroneous estimate of the size of the moon's orbit. Being thus baffled in obtaining such verification, he laid the matter aside for a time.

The anecdote of the apple we learn from Voltaire, who had it from Newton's favourite niece, who with her husband lived and kept house for him all his later life. It is very like one of those anecdotes which are easily invented and believed in, and very often turn out on scrutiny to have no foundation. Fortunately this anecdote is well authenticated, and moreover is intrinsically probable; I say fortunately, because it is always painful to have to give up these child-learnt anecdotes, like Alfred and the cakes and so on. This anecdote of the apple we need not resign. The tree was blown down in 1820 and part of its wood is preserved.

I have mentioned Voltaire in connection with Newton's philosophy. This acute critic at a later stage did a good deal to popularise it throughout Europe and to overturn that of his own countryman Descartes. Cambridge rapidly became Newtonian, but Oxford remained Cartesian for fifty years or more. It is curious what little hold science and mathematics have ever secured in the older and more ecclesiastical University. The pride of possessing Newton has however no doubt been the main stimulus to the special pursuits of Cambridge.

He now began to turn his attention to optics, and, as was usual with him, his whole mind became absorbed in this subject as if nothing else had ever occupied him. His cash-book for this time has been discovered, and the entries show that he is buying prisms and lenses and polishing powder at the beginning of 1667. He was anxious to improve telescopes by making more perfect lenses than had ever been used before. Accordingly he calculated out their proper curves, just as Descartes had also done, and then proceeded to grind them as near as he could to those figures. But the images did not please him; they were always blurred and rather indistinct.

At length, it struck him that perhaps it was not the lenses but the light which was at fault. Perhaps light was so composed that it could not be focused accurately to a sharp and definite point. Perhaps the law of refraction was not quite accurate, but only an approximation. So he bought a prism to try the law. He let in sunlight through a small round hole in a window shutter, inserted the prism in the light, and received the deflected beam on a white screen; turning the prism about till it was deviated as little as possible. The patch on the screen was not a round disk, as it would have been without the prism, but was an elongated oval and was coloured at its extremities. Evidently refraction was not a simple geometrical deflection of a ray, there was a spreading out as well.