Pioneers of Science — Lecture VI: Descartes and his Theory of Vortices

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 Brahé, 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.

_René 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 Ælia Lælia 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 formulæ 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 _Encyclopædia 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, René 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 æsthetic 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.

[Illustration: FIG. 53. --Descartes.

] 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°.

The equation _x_ = 2_y_ 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.

[Illustration: FIG. 54. --The eye diagram.

[From Descartes' _Principia_.

] 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.

[Illustration: FIG. 55. --Descartes's diagram of vortices, from his _Principia_.

] 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.