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To MARGOT

" But that which relies on calculation and measurement will be the best element in the soul?"

" Of course."

11 Then that which opposes it will be one of the beggarly elements in us?

" Inevitably."

PLATO, Republic.

Christian Huygens

CHRISTIAN HUYGENS

AND

THE DEVELOPMENT OF SCIENCE IN THE SEVENTEENTH CENTURY

By

A. E. BELL. Ph.D., M.Sc.

Head of the Science Department, Sandhurst Formerly Head of the Science Department, Clifton College,

LONDON

EDWARD ARNOLD & CO.

COPYRIGHT

First published 1947 Reprinted 1950

Printed in Great Britain by

Sons Ltd., Guild ford and Es/ier

PREFACE

THERE can be no doubt that Christian Huygens was one of the greatest scientific geniuses of all time. A man who transformed the telescope from being a toy into a powerful instrument of in- vestigation, and this as a consequence of profound optical researches; who discovered Saturn's ring and the satellite Titan; who drew attention to the Nebula in Orion; who studied the prob- lem of gravity in a quantitative manner, arriving at correct ideas about the effects of centrifugal force and the shape of the earth; who, in the great work Horologium Oscillatorium, founded the dynamics of systems and cleared up the whole subject of the compound pendulum and the tautochrone; who solved the out- standing problems concerned with collision of elastic bodies and out of much intractable work developed the general notion of energy and work; who is rightly regarded as the founder of the wave theory in light, and thus of physical optics — such a man deserves memory with the names of Galileo and Newton, and only the accidents of history have so far prevented this. It might be argued that Robert Hooke, who like Huygens was influenced by Descartes 's teachings, is of equal stature and showed as much inventive genius and intuition. In the extraordinary range of their activities there is some similarity. The overwhelming difference lies in the fact that Huygens was a great mathema- tician and exponent of the quantitative method, whereas Hooke could never get beyond the first phase of a piece of work : that which led to the need of exact measurement and the discovery of mathematical relations.

Having made this claim for Huygens, it is natural to ask how he compares with Newton. It is a question which arises from time to time in these pages, and one to which there is no epigrammatic answer. In some senses it was Huygens's greatest misfortune to grow up under the powerful influence of Descartes, who was a grfeat friend of his father, a frequent visitor to the

5

6 THE LIFE OF CHRISTIAN HUYCENS

family, and master of at least one disciple who taught Huygens at the university. From Descartes too many of Huygens's hypotheses were taken, so much so that he might stand as the exact opposite of Newton, whose objection hypotheses non fingo he did so much to call forth. Looking at Huygens in this way it is easy to dismiss him as a " Cartesian ", one whose ideas were largely superseded after the publication of Newton's Principia. But this would be a serious mistake. If he could not so brilliantly see the way to extend the sphere of natural law to the heavens, perceiving that the task of science is not to disclose a mechanism so much as to arrive at laws, he neverthe- less did important work to prepare men of science for this modern attitude. If Newton owed nothing to Huygens, and he certainly owed exceedingly little, it is very probable that he was indebted in another way, for it may well have been the feeling of dissatisfaction with the position men like Huygens were reaching that drove Newton to make the new " instauration " Bacon had looked for — a renovation of natural philosophy. The progress of scientific explanation may then be seen to be a process of leaving out redundant elements, of emancipation from imaginary qualities, until one arrives at the really successful procedure of abstraction.

But Huygens was in all other senses an astoriishingly modern thinker, and he had the disposition which sets out to face things as they are which marks the man of science as much as does the possession of specialized knowledge. As a scientific researcher he was the first of a new profession, and this permanent occupa- tion with science brought its own characteristic attitude of mind. Colbert, Louis XIV's energetic and shrewd minister, subsidized scientific investigation for the first time in history when he obtained pensions for Huygens and the other scientists who formed the nucleus of the Academic Royale des Sciences. Of course Colbert had his eyes on commercial as much as on intellectual advances. Considering his jealousy of Dutch com- merce Colbert was indeed fortunate to get as an ally of French power the most noted Dutch scientist of the age. It has indeed been a puzzling feature of Huygens's life that, having embraced French manners, delighting in the freedom that his position at the Biblioth&jue du Roi gave him, he could even so remain in Paris in his official position during the years when Louis waged war on the Netherlands, determined if he could to break the

PREFACE 7

newly found independence of the Dutch for ever. More than this, Huygens in 1673 dedicated his magnum opus, the Horolo- gium Oscillatorium, to his royal patron.

Huygens possessed a delicate constitution and was, it should be admitted, not of the stuff of which fighters are made. Like Pascal he suffered from frequent illness, like Spinoza there was a certain effeminacy about him. Again it may be argued that war in those days never concerned more than the limited class of professional soldier. If Huygens had quitted Paris the best he could have done towards the defence of Holland would have been to work in a diplomatic capacity as did his brother Constantin, or decipher codes as did the mathematician John Wallis in the civil war in England, or be killed like any ordinary soldier as was Gascoigne at Marston Moor. Men of the profes- sional class in those days were not expected to give up their activities, and there can be little doubt that Huygens's scientific work benefited greatly from his life in Paris. At home at Voorburg, near the Hague, he lived the life of a recluse with only this stimulus of his correspondence with Paris and London. The investigation of the physical world appeared to Huygens and to nearly all men of science to be something of such moment that all events in the social and political world were merely so many inconvenient interruptions. That this was so in the seventeenth century is evident from the way in which the meetings which led to the foundation of the Royal Society were carried on during the civil war. From the very beginning the men of science felt them- selves to be advancing the real causes of humanity and this longer view may well have been the one at which Huygens looked when, in 1672, he decided to remain in Paris.

From birth Christian Huygens grew up under the strongest French influences. In Paris, as a young man, he evidently imbibed the fashionable ideas which in religion tended to agnosticism and in morals pointed the way to greater freedom. His seriousness forbade the lax immorality then current. " The beaux esprlts believed in God merely as a matter of courtesy and for reasons of state ", wrote Garasse, but while this might be true, the men of science, especially in England, kept their religion. Huygens stands in contrast with the other great scien- tists of his time and in closer resemblance with some of the encyclopaedists of the following century in that he turned away from Calvinism as from Catholicism.

8 THE LIFE OF CHRISTIAN HUYGENS

In spite of the evident growth of power politics and the existence of widespread corruption, the period of Huygens's life was one of extraordinary optimism among the men of science. Science was the last activity to come from the humanistic impulse and it was to its devotees the most dazzling discovery to be attributed to man's freedom. "... this is the age ", wrote Henry Power, " wherein all men's souls are in a kind of fermen- tation, and the spirit of wisdom and learning begins to mount and free itself from those drossie and terrene Impediments where-with it hath been so long clogg'd . . . This is the age wherein (methinks) philosophy comes in with a Spring-tide ..." The greater minds of the period were less confident over the in- evitability of progress; Huygens in particular was especially cautious when asked to compare his own times with the age of Pericles. But a cruder spirit came to be associated with the men of science of the eighteenth and nineteenth centuries.

At least one modern writer has, however, condemned the " false modern emphasis " on the bold confidence and rebellious energy of the Renaissance, and has pointed out the amount of pessimism in English seventeenth century literature. On the Continent the inroads on religious belief seem in fact to have been more rapid than they were in England. Bishop Sprat, writing a defence of the Royal Society in 1667, believed that science would never undermine the socially acceptable beliefs of his time. He never dreamed that a "Universal Inquiry into things hitherto unquestioned " could have the unending consequences it has in fact produced. He obviously supposed, as did Descartes, though not Huygens, that the complete scientific account of the universe would in its essentials require the labours of only one or two generations of gifted intelligences. In these labours the experimentalists would, thought Sprat, have always before their eyes the " Beauty, Contrivance and Order of God's works ". As the Master of Trinity College has written, " God was to be praised by studying the plan of His creation, but no further attempt was to be made to fit the findings of science into the scheme of theology, as the schoolmen of old had striven so long and painfully to do." This was Newton's position, it was Boyle's, but it was not Huygens's. He alone among the men of science of his day found the temper of scientific enquiry alien to orthodox religious faith. As it was, both in France and England I here were divines who supported the plan of organized enquiry

PREFACE 9

in natural philosophy. Liberal minded abbes and protestant bishops gave their approval to scientific research for the glory of God and the service of man. Occasionally the former tended to lose their nerve and clung then for stability to Descartes's " system ".

The particular feature of Huygens's thought which was at the same time his strength and weakness was his concern for particular problems and his distrust of all speculative general- izations. This distrust he no doubt acquired during his study of Descartes's writings. His attitude towards Spinoza's ideas may be explained in this way, for it would otherwise have been expected that these ideas would have gained his sympathy, for Spinoza, of all great religious writers, has come nearest to expressing the scientific attitude to the world. But Huygens distrusted the system which Spinoza elaborated and no doubt for the reason that Spinoza sought to apply the Cartesian method. This method, Huygens saw, is unable to give us an understanding of nature, and he himself made great contributions to the new scientific method. The fact that he personally despised Spinoza seems to be explained by a sense of superiority which rested on social rather than on intellectual considerations. It was not, of course, a democratic age.

In his scientific work Huygens was the greatest mechanist of the seventeenth century. He combined Galileo's mathematical treatment of phenomena with Descartes's vision of the ultimate design of nature. Beginning as an ardent Cartesian who sought to correct the more glaring errors of the system, he ended as one of its sharpest critics. The development in the seventeenth century of Dynamics and Astronomy beyond the stage of geometrical description demanded new inductive principles of correlation; the ideas of mass, weight, momentum, force, and work were finally clarified in Huygens's treatment of the phen- omena of impact, centripetal force and the first dynamical system ever studied — the compound pendulum. In Astronomy Huygens explained the appearances of Saturn, until 1656 the greatest anomaly of the Copernican system. His eminence as an observer was due to the high quality of his telescopes and this, in part, resulted from his thorough theoretical researches on the problems first attacked by Kepler, Snell and Descartes. It is well known that physical optics practically took its rise from Huvgens's Traite de la Lumi&re.

IO THE LIFE OF CHRISTIAN HUYCENS

The growth of interest in the history of science may be con- sidered to be in a sense an outcome of the increasing specializa- tion of science itself. So much is commonly ignored in concen- trating on the discipline of science, that for education in the broader sense, when once the demands of life are allowed to supersede merely professional ones, something more is needed. Many have felt that the history of science may provide an im- portant humanistic element. A protest may here be made against the practice of inserting historical notes in scientific textbooks without regard for the conflict of old and modern ideas. Once a subject has become well developed, the logical and not the histor- ical method is to be desired, for so much of the earlier science can be properly understood only with a really adequate study. The great scientist of the past tends soon to appear a distant and indeed thoroughly dead sort of figure. The modern scientist to a large extent accepts his reputation on trust and has little time and often less inclination to read the original work. How many now read Galileo's Discourses or Newton's Principiaf It is other- wise in "art and in literature. If science is to become a more widely accepted means of education (in the sense of a form of culture) there is need of more works on its history. A modern estimate can do much to revivify the past and present these great men, its creators, in a clearer light.

As an account in English of the work of Huygens this study is to be regarded as only a beginning. The Oeuvres Completes de Christiaan Huygens, published by the Societe Hollandaise des Sciences, comprise more than twenty magnificent volumes and contain all the material for a definitive work; beside them the present book must appear almost insignificant. It is greatly to be hoped that before long a large work on this great subject will be written by a scholar of the requisite stature. Writing as one whose training has been principally in chemistry the author has met with many difficulties in Huygens's works. It need hardly be said that they are properly to be studied by a mathematician, while the subject as a whole requires a combination of historian and Latin scholar, physicist and philosopher, which it must be rare to achieve.

A.E.B.

CLIFTON, 1947

CONTENTS

Page

PREFACE 5

PART I

NOTES ON THE LIFE OF CHRISTIAN HUYGENS . . . 13

PART II

I. THE STATE OF SCIENCE IN THE FIRST HALF OF THE

SEVENTEENTH CENTURY 97

II. WORK ON COLLISION BETWEEN ELASTIC BODIES . 109

III. CENTRIFUGAL FORCE 117

IV. STATICS 124

THE TREATISE ON THE PENDULUM CLOCK :

The Horologium Oscillatorium V. Part I. Construction and Use of the

Pendulum Clock . . . . 127

VI. Part II. Oscillation in a Cycloidal Arc . . 136

VII. Part III. Evolutes and the Measurement of

Curves 145

VIII. Part IV. The Centre of Oscillation of a Com- pound Pendulum . . . . 150

IX. THE CAUSE OF GRAVITY 161

X. HUYGENS'S OPTICAL STUDIES 165

XI. THE WAVE THEORY OF LIGHT . . . . 176

XII. SATURN 193

XIII. COSMOTHEOROS 2OO

XIV. THE PLACE OF HUYGENS IN THE HISTORY OF SCIENCE 203

PERSONS MENTIONED 213

BIBLIOGRAPHY 217

INDEX 219

ii

PLATES

Christian Huygens frontispiece

facing page I. Saturn — reproduced from Huygens's MS 32

II. One of Coster's clocks 38

III. Huygens's Clock as the centre feature of a design

showing scientific apparatus of 1671 56

IV. Members of the Academic Royalc dcs Sciences 58 V. Louis XIV at a meeting of the Academic 60

VI. Drawing by Huygens of his vacuum pump, 1668 162

PART I THE LIFE OF CHRISTIAN HUYGENS

CHRISTIAN HUYGENS has been a strangely neglected figure — apart from the study he has rightly received in his native Holland. A man of the greatest scientific genius without any doubt, he was one in whom great sagacity and mathematical power went side by side with a feeling for elegance and form in the interpretation we make of Nature, so much so, that it is with- out surprise that we find he was devoted to music and the arts ajid was by no means the type of narrow research worker that later scientific studies did for a time produce, and still produce in some measure. Huygens was a professional scientist in an age when the boundaries of Science were scarcely drawn, and his interest lies as much in his general outlook as in his specialized studies.

Huygens had not the religious feeling of a Spinoza or the sensitivity of a Pascal, nor was he a philosopher of the stature of Descartes or a mathematician of the rank of Leibnitz. In an age when the human mind was making great marches into the territory of natural philosophy, Huygens's energies were thrown now into the study of applied mathematics, now into optical researches or astronomy; and he managed somehow to pursue the most strikingly original researches in several subjects quite simultaneously, so that in his note-books matters of the most varied kind jostle one another in profusion, and a very large volume indeed would be needed to do justice to his labours. What is of chief significance to-day can be reduced to much smaller limits, and the reader who wishes for more must go to the great volumes published by the Societe Hollandaise des Sciences under the auspices of the Dutch Government.

Here we are concerned rather to look back for a space on that interesting period in Europe between the death of Galileo in

'3

14 THE LIFE OF CHRISTIAN HUYGENS

1642 and the rise to fame of Newton, a period in which Huygens, in fact, stood unchallenged as the greatest man of science of the age.

It has been remarked1 that " In 1600 the educated English- man's mind and world were more than half medieval; by 1660 they were more than half modern ". And this remark need not have been limited to Englishmen. On the Continent also, about the middle of the century, a certain profoundly important change was becoming visible. It was, perhaps, in the years following 1670 that the break-away from authoritative teachings — of Descartes as of the schoolmen — became the feature of the really important scientific theories. Galileo and Huygens both struggled to make use of teaching they received in their youth, and both failed; they were each forced in some degree to rely on their own powers. Indeed, underneath all successful scientific work there lies a great deal of experiment in failure.

One must read Dante, or toil over Thomas Aquinas, to get a picture of the universe as it was conceived by educated men in the Middle Ages. The sheer verbalism of all argument about the world repels and astonishes the modern reader, but there was an undeniable attractiveness in the notion of a Cosmos : the " idea of a hierarchically-ordered finite world structure ", a world in which all was made for man and consequently one in which clear and simple reasons existed why things are as they are. What we see as an appeal to objectivity must then have seemed to some to be pure obstinacy and blindness, for what the men of science really abolished was not so much an over-rational world structure as the appeal to feeling in the making of explana- tions. The new studies offered at first no more satisfaction than that which could be found in the agreement of theory with measurement. Nevertheless, scientific explanations did not get a reputation for their " inhuman " quality until the eighteenth century, when many physical theorems were generalized in abstract mathematical form.

Early in the century Descartes worked out an ingenious and even aesthetically satisfying system which welded natural science on to the structure of a philosophical theory about the nature of matter and of space, and some reference to this system must be made in later pages. The chief point about Descartes's teaching,

Douglas Bush : English Literature in the Earlier Seventeenth Century,

THE LIFE OF CHRISTIAN HUYGENS 15

if it were accepted, was that experiment and observation could soon be dispensed with and the human mind could rest satisfied with the knowledge it could gain through a rationale worked out by philosophers. So seductive was his reasoning, and so per- suasive the arrangement of the arguments, that both in France and England there were soon many ardent Cartesians who were distinguished by the ease with which they accounted (in a general way) for natural phenomena. Since space was supposed to be full of a " subtle matter " and this moved around each planet in a kind of vortex, it was easy to imagine various effects as resulting from the properties of this medium. And Huygens was himself for many years a Cartesian. The essays produced by Descartes were a flirtation with the mathematical treatment of observations begun by Galileo, only they went far further and cast the human mind in great voyages of imagina- tion— further, in fact, than it was yet ready to go. It is always an interesting question, therefore, how Huygens came to be a strong critic of Cartesianism, and on the other hand, why he rejected Newton's treatment of gravitation and even at the end of his life had not thrown overboard the whole Cartesian apparatus. Of all the events in Huygens's life when one would give much to know what happened, there is an occasion of which one gets only a faint glimpse: Huygens and Newton getting into a stage coach at seven o'clock on a July morning in 1689, to go from Cambridge to London, Huygens was then sixty and his zeal and lively curiosity were unabated; Newton was forty-seven, and every- where acclaimed as the author of the magnificent Principia — though it had to be confessed that only a handful of men really knew what it was all about. Huygens had left Holland in poor health in order to see Newton and to visit old friends among the English men of science. But all that can safely be connected with this meeting is the fact that Newton subsequently produced a further study of the Cartesian vortices and, on the other hand, Huygens began to object to Leibnitz's use of them. As the coach rolled on its way to London, it may be that Huygens was turn- ing over in his mind the final objections to any further develop- ments of Descartes's ideas. His own work had led far in this direction and the end of it all seemed to be that Descartes's ventures in physics had been pure romance, " un beau roman de physique " as Leibnitz himself concluded. Or is such conjecture too dangerous? Huygens, with his only moderate English and

16 THE LIFE OF CHRISTIAN HUYGENS

his weakness for a picturable sort of explanation may have made little of a taciturn Newton; he recorded nothing of interest from the meeting.

II

Unlike Newton, Christian Huygens came of a family which had already shown genius. His father, Constantin, was extra- ordinarily brilliant; a poet, student of natural philosophy, classical scholar and diplomat, he typified the conception of culture at its best at the beginning of the century. As secretary to the Prince of Orange, Frederick Henry, he must be considered important in the guiding of the country through difficult times. In this, however, his own father, an earlier Christian, stood as an example, for he had been secretary to William the Silent in the eventful years after 1578. This Christian was a native of the Southern Low Countries, while his wife, Susanna Hoefnagel, was of Antwerp, though at the time of her marriage a protestant refugee from Amsterdam. The two sons, Maurice and Constantin, were born in troubled times, the latter on September 4th, 1596, at the Hague.

The last quarter of the sixteenth century saw the indepen- dance of the seven northern provinces of the Netherlands regained after an eighty years' struggle with Spanish power. In the South, Spain and Catholicism continued to dominate; in the North, religious and political liberation occurred together and there grew up a deep mistrust of all hierarchial powers; even the doctrines of Luther were rejected because they acknowledged the authority of the State in religion. A new Calvinist common- wealth now existed, and its rise has been described in the pages of Motley's Rise of the Dutch Republic. The assassination of William the Silent, in 1584, came after he had accomplished his great task for he had, as Motley says, " planted a free common- wealth under the very battery of the Inquisition in defiance of the most powerful empire existing ".

It is interesting to look back at these important events which came close to the life of the Huygens family. When Maurice of Nassau was engaged in defeating the Spaniards in the open field, Constantin Huygens, father of the scientist, was receiving a care- ful and thorough education as a boy. This Huygens showed quite a distinction in mathematical work but all the influences

THE LIFE OF CHRISTIAN HUYGENS 17

of his life were in the direction of the courtier and diplomat. He was often at the court of Louise de Coligny, the widow of William the Silent, and he accordingly spoke French from boy- hood. He completed a course of Law at Leyden University and then was introduced at twenty-one to the life of diplomacy. This Huygens became by far the most well-known member of the family up to the mid-seventeenth century. His all-round culture has been mentioned, and he did in fact become known all over Holland, and in England, as a latinist and poet, as an amateur of music and painting, and as a student of philosophy. He was, besides, a close friend of Descartes and, at length, best known of the leaders of contemporary thought in the Republic : " no Dutchman commanded a more European culture; no Dutchman was more thoroughly Dutch ". After their first meeting, Descartes wrote of him " . . . despite what I heard of him, I could not believe that a single mind could occupy itself with so many things and acquit itself so well of them all ".

Christian Huygens's father, then, was a man of outstanding ability and brilliance and he was very well known in England. He studied at Oxford for a time and became an intimate friend of John Donne. He played the lute at the court of James I, and in 1622 received an English knighthood. Nor was this brilliance a mere glitter, the effect produced by a versatile and fashionable courtier. Constantin Huygens corresponded for years with Descartes, with Mersenne, the great intermediary of men of science of that time, with Diodati, a friend of Galileo, and with many well-known mathematicians, notably Schooten the elder. In his MSS. have been found notes on Euclid's propositions and records of his study of optics. When Golius succeeded Snell at Leyden, Constantin Huygens recommended him to apply him- self to optics. "The consequences of the law of refraction [formulated by Snell in 1621] have not been sufficiently studied by anyone," lie wrote. He himself is said to have attempted to grind lenses to the forms proposed by Descartes — the surfaces being of elliptical or hyperbolic section instead of spherical. Descartes had concluded that such lenses would be free from spherical aberration but Huygens (or the skilled mechanic employed by him) found the work impossible with the ordinary tools then used. His indirect influence in scientific work was undoubtedly of greater significance : without his encouragement Descartes might never have published his Dioptrique. The

18 THE LIFE OF CHRISTIAN HUYGENS

philosopher was induced to overcome his well-known hesitancy only through the efforts of Constantin Huygens and Mersenne.

This versatile man of letters and diplomat in 1627 married his cousin, Susanna van Baerle, daughter of a wealthy merchant of Amsterdam and by all accounts an intelligent and cultivated woman. The children of this marriage, which must interest geneticists, were Constantin (1628), Christian (1629), Louis and Philip, the last of whom died young, and Susanna. In 1637, after only ten years of married life, the mother of this family herself died. Another cousin took over the care of the family, which removed to a newly built country house at Voorburg, close to the Hague. Here, when he had recovered from the death of his wife, Constantin received officers of the French army, French diplomats and men of letters. Here Descartes himself made occasional visits and remarked on the prowess of young Christian in mathematics, a study in which he complained he saw no great progress.

Descartes spent a good deal of time in Holland and did much of his more important work in the quiet of the country. Even in Holland, however, he did not feel sufficiently secure to bring out his treatise Le Monde and it was not until 1637 that his Discourse on Method appeared. But it is easy to imagine the great influence of Descartes on the intellectual family at Voorburg in those years just succeeding the publication of the famous Discourse. The work itself shows the appeal of Descartes's mode of argu- ment and, to a generation who read and sympathized with Campanula's Defence of Galileo, it must have seemed that Descartes was indeed the apostle of intellectual freedom. Campanella's tract, composed in a Neapolitan dungeon in 1616, was printed at Frankfurt in 1622, and during the next thirty years it was widely read by educated men all over Europe. Its courageous stand for freedom of enquiry and for the truth of the Copernican theory was a source of inspiration. For it is clear that a generation which could revere Galileo did so because their minds were alreadly partly prepared by earlier critics of Aristotle: Benedetti, Stevinus and others. In Campanella there was a vigour and boldness which recalled Giordano Bruno. Bruno and Campanella held that there are an infinite number of worlds, and if in Descartes's writings this doctrine as well as that of Copernicus was taught with great caution there can be no doubt

THE LIFE OF CHRISTIAN HUYGENS 19

that this was through circumspection. Descartes was a cautious man but very probably in conversation he was bolder.

Constantin Huygens was extremely proud of his two eldest sons, who early showed intellectual brilliance. They were taught at home by a private tutor until Christian was sixteen. This education included singing, playing the lute, and the composi- tion of Latin verses. Like Newton, as a young boy Christian loved drawing and the making of mechanical models on which he spent much labour and ingenuity. So much so that his tutor felt misgivings; such practical work was after all an inferior and even a dubious sort of occupation for a young man of family and position. From the beginning, however, Christian showed promise of great skill in geometry while his brother, Constantin, excelled rather in literary compositions. Descartes was much impressed with some very early work of Christian's and he saw that great things might be expected from this rather serious boy with the rather pale face and the large dark eyes. Christian was rather delicate and by nature gentle, and his sensitivity seemed almost feminine to his father, who seems to have been fortunate in possessing an unflagging and exuberant vigour, quite different in character from his son.

Characteristically enough, the first experiments of the youth- ful Christian were in mathematics, and this is typical of him, for he rarely ventured publications on other than abstract and some- what theoretical subjects. But the influence of a cultured and enlightened society remained with him, and his interests, early determined, lasted unchanged all his life.

In 1645, when he was sixteen, Christian and his brother entered the University of Leyden. Here they studied Mathe- matics as well as Law, the younger Schooten, a protege of Descartes's, then being professor. Schooten was an able mathematician and Christian acquired the reputation of being his best pupil. Mathematics was a subject which included what we would now call mechanics and, for example, in Stevin's Hypomnemata, a work in six volumes, there are discussions of centres of gravity, levers, simple machines and hydrostatics. Christian's father was clear about the supreme importance of mathematical training. In 1644 Descartes had published his Principia, a bold attempt to reduce all the changes of Nature to mechanistic processes and he, it was well known, exalted the study of the subject. Radical changes were taking place in men's

2O THE LIFE OF CHRISTIAN HUYGENS

ideas and during his time at Leyden Christian lived in an atmosphere of intellectual ferment. The ideas of Descartes were hotly contested by the Aristotelians and to such an extent that in 1646 and 1647 the university almost became a battlefield. Un- fortunately, there are only scanty records of Huygens's reactions to these experiences. Regarding Descartes's Principia he many years later remembered the deep impression it made on him. " It seemed to me when I first read this book, the Principia, the first time," he wrote, " that everything in the world became clearer and I was sure that when I found some difficulty that it was my fault that I did not understand this thought. I was then only fifteen or sixteen years old/'

Descartes's ideas were strongly represented in Holland. Renier, one of his disciples, taught Cartesian philosophy at Leyden for a time and later went to Utrecht. Here 'he had great influence and was followed by Regius, one of his own pupils. Aristotelian philosophy was associated with the Jesuits and nowhere more than in northern Holland was their influence more strongly re- sisted. Nevertheless, even in Holland, freedom of thought was not absolute and only a few years previously the Aristotelians had scored notable victories by arousing suspicion as to the religious consequences of Descartes's teachings. Cartcsianism owed its wide appeal to the n£ed felt for a new celestial mechanics after the acceptance of the ideas of Copernicus. This, apparently, Descartes's theory supplied. Moreover, Aristotle's outlook in natural science was in the main teleological. It was felt that if the guiding principle of teleology were abandoned some way of expressing the determinism of events must be found. On this point Descartes's analysis proved less sound but his system as a whole was ingenious and even aesthetically satisfying.

In 1647, after two years at Leyden, Christian Huygens joined his brother at the College at Breda. This college, founded by Frederick Henry, seems to 'have achieved a temporary fame but it came to an end during the century. Descartes seems to have taken some interest in the place and certainly the forces of Aris- totelianism were there unable to challenge the new philosophy. John Pell, an Englishman, taught mathematics and was a man of quite high reputation. It was fortunate that, after Schooten, Huygens had so able a teacher.

As soon as Huygens's period at Breda was completed he made a number of journeys, first going to Denmark in the company of

THE LIFE OF CHRISTIAN HUYGENS 21

the Count of Nassau-Siegen and later, with Constantin, to Frisia, Spa and Rome. When in Denmark it was a great disappointment to him that the weather made it impossible to reach Stockholm for Descartes was then living at the court of Queen Christina.

Travel and a thorough education were, however, not the only elements which made up the pattern of Christian's early years. Most important, perhaps, of all was the correspondence he took up with Pere Mersenne, who was next in importance to Des- cartes among his father's acquaintance in the centre of the learned world. Duhem has described Mersenne as a man of in- satiable curiosity and the exuberant imagination of the artist. He was at this time the great intermediary for scientific com- munications between the chief centres of experiment. He popu- larized much of Galileo's work and did much to thrash out those fundamental notions on which seventeenth century mechanics was based. Men like Descartes, Gassendi, Fermat and Pascal met together at the cell of the Minorite father in Paris and this group has been described as the origin of the Academic Royale des Sciences. Mersenne was indeed a remarkable man, for he retained the esteem of both Church and the scientific world ; "... he did not believe all his religion," Pineau wrote to Rivet, " he was one of those who are glad enough to see church service done . . . he dared not often repeat his breviary for fear of spoiling his good Latin." He was not himself a great originator. Pascal possessed for mathematical and scientific work all the qualities which Mer- sennet lacked: a profound penetration, logical rigour, critical acuity, but Mersenne saw clearly which problems then mattered most and Huygens was indebted to him for many of the subjects of his early researches.

Aristotle, whose mechanics was the weakest part of his natural science, had supposed that heavy bodies fall towards the centre of the earth because this is their " natural " place. The heavier a body is, the faster it moves towards the earth. If it were to fall through a hole passing through the centre of the earth it would come to a standstill on reaching the centre. As early as 1585 Bene- detti had protested against this. He saw, in a general way, that the inertia of the mass would carry it past the midpoint and that it would in fact oscillate after the manner of a pendulum bob. Stevin, with greater certainty than in the case of Galileo, is known to have experimented by dropping large and small weights simultaneously and showing that they reached the

22 THE LIFE OF CHRISTIAN HUYGENS

ground together. Galileo made a more thorough examination of naturally accelerated motion and calculated the distances tra- velled in successive seconds by a freely falling body. Mersenne, in an early letter to Huygens, questioned if in fact the mass did not in some way determine the limit of the velocity which could be imparted. Huygens explained that his objections were all based on observations of air resistance and gave such an able ex- position of what is now termed Newton's first law of motion that Mersenne gave him ungrudging praise : " I assure you that I think so highly of your demonstration concerning falling bodies that I believe Galileo would have been delighted to have you as his follower/' Mersenne went on to set Huygens the problem of finding the form taken up by a rope hanging from its two ends which are fixed at the same height and some distance apart. Huy- gens did not solve this mathematical problem until he recurred to it late in life but he studied the disposition of weights along the rope which would give it a parabolic form. He also became interested in Mersenne's famous problem of determining the centre of percussion of suspended bodies. This most important problem was given its first general solution by Huygens many years later.

Young Huygens was delighted with these letters, which he received " with joy and avidity ". His father noted with approval the penetration with which young Christian, then only seven- teen, tackled problems then exercising the world's foremost men of science. In December 1646 Christian wrote that he was occu- pied with problems of centres of gravity and with modern de- monstrations of some of Archimedes' propositions on the sphere and cylinder — a remark which illuminates the nature of his early training — " but nothing yet concerning centres of percussion of which you recently wrote. However, I shall not fail to do all that I can to find the demonstration although, up to the present, it seems to me to surpass my ability . . ." Mersenne acknowledged that he also could not see how a single rule could satisfy the variety of figures for which the centre of percussion (or of oscil- lation) was required. The problem was that of finding a formula which would make it possible to calculate for any suspended body the length of the simple pendulum which would have the same period of oscillation. An experimental solution could, of course, be found but this was not acceptable as an answer. It is at first sight surprising that a grert deal of interest should be

THE LIFE OF CHRISTIAN HUYGENS 23

aroused by so academic a problem. This was because the prob- lem was one concerning a dynamical system (as opposed to a single mass) and it was obvious that a new approach was needed. Problems of this sort led to the development of the calculus by Newton and Leibnitz. Huygens, however, obtained a solution in advance of either of them, although it was without the use of their modern methods.

Some interesting matters are discussed in the correspondence of Mersenne and the elder Constantin Huygens. Christian, because of his precociousness, is sometimes referred to as a mod- ern " Archimedes ". Mersenne wrote about the new work of the young Pascal, then twenty-five, the problem of the nature of the vacuum, the development of the telescope and the most recent astronomical observations. There was a widely accepted belief that a true vacuum is contrary to nature and this made it very necessary to explain the well-known experimental results obtained by Viviani and Torricelli in 1643.

The followers of Descartes were in obvious difficulties because Descartes rejected the atomic doctrine and with it the notion of a void. Since Gassendi was reviving, at least in part, the atomic doctrine of Epicurus and considered it a profound philosophical necessity that a vacuum should be possible, this apparently recon- dite and academic matter aroused vigorous controversy. Galileo attributed the more or less constant height of the barometer to an equilibrium between the weight of the column of liquid and an attractive " force " acting upwards. This force was, of course, quite an illusion. Torricelli and Viviani verified that the relative heights of liquid which could be supported in a baro- meter tube varied inversely with the densities and in 1644 Torri- celli really gave the correct explanation based on the pressure of the atmosphere. Four years later Pascal's explanation of the behaviour of the barometer was put forward, after the experiment carried out for him on the Puy-de-D6me in September 1648, but his views were by no means universally accepted. Quite a litera- ture was produced in disproof of the existence of the vacuum and even Constantin Huygens, who confessed himself most anxi- ous to " penetrate all the mystery ", found the new explanation very contrary to his inclinations, which were all for Cartesianism.

It is important to realize the fascination which all but a few critical spirits found in Descartes's natural philosophy (see p. 109). Tn a sense, of course, Cartesianism was anti-scientific. At a time

24 THE LIFE OF CHRISTIAN HUYGENS

when the trend of natural philosophy was in the direction of empiricism, Descartes emphasized the great limitations of the empirical method. While he scorned scholastic logic he con- sidered that mere empiricism was futile and that his discovery of analytical geometry illustrated the true method by which physi- cal problems of all kinds involving motion in space could be attacked. He believed that the way was open to reduce all phe- nomena to the terms of geometrical description. From the pos- tulates of space and motion, without any assumptions as to the innate properties of matter, he hoped, by successive applications of his intuitive method to isolated problems, to build up an account of all the phenomena of the Cosmos. The a priorism of Descartes's method is thus anti-scientific. On the other hand it must be remembered that Aristotelian science was concerned with logical rather than spatial relations. Descartes, on the other hand, has been well described by the remark that he was " the author and prophet of mechanism". With Galileo he asserted the belief that the laws of Nature are both simple and open to dis- covery. The danger for a youthful student such as Huygens was that Descartes paid too little regard for what have been called " stubborn and irreducible facts " and that he strayed too far from the path of scientific work in undertaking to heal the schism between the natural and the revealed.

In the famous vortex theory of the Principia Philosophize (1644) Descartes supposed all space to be filled with a " subtle matter " which moved with the planets in their paths. He made brilliant play with this medium and used it to work out plausible explanations of gravity and magnetism as well as the action of the barometer. Light was treated as an action or as an inclination to move, possessed by the particles of the subtle matter. From this explanation, comparable with the idea of pressure in a liquid or of impact amongst panicles in motion, Descartes attempted to derive the laws of reflection and refraction. The same spirit was shown in the mechanical explanations offered in the Meteors : atmospheric phenomena and the rainbow were given explanations based on known — or partly known — scientific prin- ciples. In the Principia Philosophise Descartes dealt, among other things, with the nature of matter and the general laws of motion. The whole of this "system" rested on insecure foundations and there was a temptation to ignore small but " stubborn and irre- ducible facts " which did not fit in. Since a perfect vacuum was

THE LIFE OF CHRISTIAN HUYGENS 25

something to which Descartes denied existence the Torricellian space in a barometer tube was supposed to be filled with the Cartesian subtle matter which, like the ether of the nineteenth century scientists, penetrated almost everywhere. A crucial ex- periment was performed in which a sealed and empty bladder was placed in an evacuated tube. The fact that the bladder expanded was explained by Huygens as due to a small amount of residual air: Roberval, an original and controversial writer, also con- sidered the experiment disproved rather than supported the Cartesian theory.

Mersenne died in September 1648, but his influence on Huy- gens had been important. Although he was no great physicist or mathematician he stimulated the criticism of ideas; he was, for example, strongly opposed to Descartes's well-known treatment of animals as automata. In the years between 1648 and 1657 Huy- gens, from being a youthful admirer of Descartes's philosophy, became more and more critical. He wrote frequently to his old teacher Schooten and to the mathematician Slusius about Des- cartes 's demonstrably false laws of impact between elastic bodies. The laws, he wrote, did not agree with any experiments and the fifth law conflicted with the second. Before 1656 he had com- pleted his own important work on the subject (see p. 109) but some twelve years elapsed before he communicated his conclu- sions to contemporary men of science. The complete treatise, De Motu Corporum ex Percussione, was not published during his lifetime.

The first published work of Huygens came out, however, as early as 1651, when he was only twenty-two. This was his Cyclo- metrise, a treatise written to show up the fallacies of the mathe* matician Gregory de St. Vincent committed in a book of 1647 where Gregory had claimed to have developed no less than four different ways of " squaring the circle ". The task of replying to Huygens's serious objections was left to certain pupils, and notably to Ainscom. The result was considerable prestige for Huygens, for he was seen to have proved his case. The larger work, De Circuit Magnitudine Inventa. which appeared in 1654, it is safe to say, assured him of a place amongst the leading mathematicians of the day. He was hailed as the reborn Vieta and compared with Pappus and Apollonius, two giants of classical Greek geometry. The comparison was, in fact, not inept. In the years following 1652 Huygens spent a lot of time on re-

26 THE LIFE OF CHRISTIAN HUYGENS

ducing to algebraic analysis problems which Archimedes, Nicho- medes, and other Greek mathematicians had been able to solve only through geometry. Without these early studies it may be doubted if Huygens could have succeeded in the great problems he was later to tackle.

Before the death of Mersenne Christian had hopes of going to Paris in the company of his father, but the idea was post- poned. In 1649 came the first of two revolts by the nobility against the rule of Anne of Austria and Mazarin — during the minority of Louis XIV. Until 1653 t"ie situation continued to be uncertain; twice Mazarin was a fugitive, Anne was hunted from Paris and the monarchy was in jeopardy. The rebellious nobility were in league with Spain and the times were not propitious for the Huygens' visit. Not until 1655 was the long-projected visit made. The intervening five years were spent chiefly on Huygens's early researches, interrupted only by another journey to Den- mark and some time spent in the Low Countries. Huygens's important work on telescope construction dates from these days. The first telescopes were made in Holland early in the century, but they were very imperfect and it is remarkable that observa- tions such as those of Galileo were ever made with such instru- ments. The task of improving the telescope occupied Huygens throughout his life and in this he was encouraged by his father and had, from time to time, the skilful collaboration of his elder brother. By means of his own telescopes Huygens made his important observations on Saturn and a copy of a letter written at this time bears two rough sketches, one of Jupiter and the other of Saturn showing appendages. The contents of the letter do not relate to these matters and the date of the draw- ings is uncertain. The discovery of Saturn's ring cannot be put earlier than February or March 1656. Before he went to Paris in July 1655, however, Huygens had made the interesting discovery of a satellite of Saturn. The study of this anomalous planet whose irregular contour was such a mystery was continued by his brother Constantin in his absence.

The fertility of Huygens's mind at this period was truly astonishing and it can be matched only by comparison with Newton. Fundamental research in pure and applied mathema- tics, optical studies including important work on the theory of lens systems, the invention of an improved eye-piece for the astronomical telescope, and to crown the practical side of his

THE LIFE OF CHRISTIAN HUYGENS 27

work, the discovery of Titan, all belong to this period of his life. Yet there was a curious weakness in this energetic mind, a flaw implanted perhaps by Descartes's brilliant philosophizing. For the man of science who was himself a few months later to discover Saturn's ring seems to have concluded that, with the discovery of six planets and six satel- lites, the human mind had reached the limits of the solar system. This preoccupation with numbers reminds one of Kepler and shows how persistent were old currents of thought.

In 1655 Louis XIV was only seventeen and France continued to be governed by Mazarin. The second "Fronde" was at an end but this disorder and scramble for power left its results, abortive though it had been. The conditions were precisely those which could not but impress Louis with the need of becoming master and his reign from 1661 onwards was characterized by the great- est absolutism.

For a son of a noted Dutch diplomat and man of letters young Huygens remained extraordinarily aloof from the turmoil of events. His habits soon became those of a scholar and at twenty-six there was a marked vein of seriousness in his pursuits. During his five months in Paris, however, he revelled in the opportunities of pursuing the arts as well as the sciences. Music, the drama, and the society of intellectual and artistic people made life in the capital extremely interesting. At the country house of Conrart, the protestant secretary of the French Academy, he met Jean Chapelain, a mediocre but popular poet and a man of cultivated tastes, and Marie Perriquet, an attractive young woman who seems to have shown interest and some ability in scientific problems. The comic dramatist Scarron, the astron- omer Boulliau and the philosopher Gassendi were also among his new acquaintance.

Gassendi was at this time an old man. It is not clear how much Huygens could have been directly influenced by the philo- sopher on the occasions when they met, but his indirect influence on Huygens and several other men of science was considerable. Gassendi was at that time an important, perhaps the most im- portant, opponent to Cartesian teachings. His objections, more- over, reflected the influence of Galileo: logical deductions for

28 THE LIFE OF CHRISTIAN HUYGENS

him were useful only so long as they did not conflict with the physical facts. For Descartes mathematical and logical deduc- tions could be valid irrespective of verification from experience. The fact that this appears to us an impossible and irresponsible attitude must be attributed to the influence of Gassendi, Huygens and Leibnitz as well as of Newton in the history of thought. Even in a more detailed way, however, Gassendi had an im- portant influence on Huygens. He held an atomic theory which was later developed by Boyle and with this went a belief in scientific materialism. To Descartes's " cogito ergo sum " he objected that existence might be inferred from any other action besides thinking. Unfortunately Gassendi's name has become linked, not only with the revival of atomic doctrines, but also with the doctrine of mechanism. As a matter of fact Gassendi did not take up this extreme position. The atoms of bodies, he held, were not eternal or unproduced or moving of their own accord — a problem which he seems to have viewed with the same perplexity as we feel now for the rotation of nebulae. God, for Gassendi, was the creator and first cause, He was over and above the physical world.

From 1653 up to his death in October 1655 Gassendi lived at the house of Habert de Montmor, a wealthy amateur of the sciences, who gathered together at his house, 7 rue Vieille du Temple, many who had formerly met at the cell of Mersenne. This " Montmorian Academy " was an important forerunner of the Academic Royale des Sciences. As in London and in Florence, an informal gathering of men, free from the " systems " of the universities, committed to no philosophy save that of enquiry, founded the modern organization of scientific work. Besides en- quiring into new phenomena something was done to conserve the past. Gassendi wrote a life of Tycho Brahe and Copernicus. It is worth noting that he preferred the cosmology of the former to that of the latter. His pupil, the poet Chapelain, took a keen interest in the progress of scientific studies and formed a strong friendship with young Huygens. Chapelain knew little science or mathematics but his zeal was great and he assisted Sorbi&re, permanent secretary to the Montmorian Academy, to draw up its rules and maintain its foreign correspondence. Chapelain's letters to Huygens, after the latter's return to the Hague, show that he kept his master's atomic doctrines to the fore and con- scientiously maintained a critical attitude towards Cartesianism.

THE LIFE OF CHRISTIAN HUYGENS 19

After Gassendi's death in 1655, in fact, his place in Chape- Iain's life was taken by the newcomer Huygens. Unfortunately, the death of Gassendi was the beginning of a series of troubles for Montmor. First he lost his child and then his wife fell ill; finally, when she was recovering, his sister died. These misfor- tunes brought to an end, temporarily, the meetings held at his house. There may have been other reasons, for Gassendi's assist- ant, de la Poterie, and Huygens disliked each other, and Pierre Petit and Thevenot were hostile to Sorbiere. Numerous petty squabbles occurred and marred the work of the " Academy " for a period. Nor were other societies in Paris more successful. Thevenot later started discussions at his own house (in 1663) but these ended in 1664 because of the expense, part of which was incurred by keeping the mathematician, Bernard Frenicle de Bessy, and the anatomist, Steno, at his house. Groups supported for a time by Henri Justel or the Abbe Bourdelot suffered no better. It was through experience of this sort, as will be seen, that leading amateurs of science were brought to the conclusion that the Government should be responsible for the maintenance of a permanent academy.

At the time when Huygens first visited the Montmor group there was, as usual, little contact with the Sorbonne. Some of the university teachers attended meetings, but perhaps as much out of suspicion as out of sympathy. The ecclesiastical authority of the university colleges felt itself challenged by Cartesianism, and Gassendi's views were no more popular. Nevertheless, a rational- ist sect existed within the Church and this was not wholly opposed to new ideas in natural philosophy. Among its supporters the writings of Du Vair and Descartes were in- creasingly popular. But the support of neither the Jesuits nor their opponents the Jansenists was of any value for the cause of science.

Huygens enjoyed the meetings of the Montmor group and was anxious to prolong his stay in Paris. From the mathemati- cians he learned of problems on probability which occupied Fer- mat and Pascal about this time. It is of interest that his own little treatise on the subject, written after returning to Holland, became a classic. Before he left France he told Boulliau and Chapelain of his discovery of Saturn's satellite and the latter urged on him the importance of publishing the details. Huygens obviously wished to settle the problem of the ring first; he was

30 THE LIFE OF CHRISTIAN HUYGENS

pleased at the discovery that already his telescopes were as good as any that were to be had in Paris.

IV

In 1610 Galileo made a number of important telescopic observ- ations. In January he found that Jupiter had four satellites; in July he made out the appearance of Saturn as consisting of "three spheres which almost touch each other, which never change their relative positions, and are arranged in a row along the zodiac so that the middle sphere is three times as large as the others ". In the same year he distinguished separate stars in the Milky Way and saw the phases of Venus. His work left the Copernican theory in a much stronger position but certain unresolved doubts still remained. This " tri-spherical " form of Saturn for example was something completely anomalous. Were these outer spheres a peculiar type of moon? On the Copernican theory it appeared probable that other planets besides Jupiter would be found to possess satellites.

This is where Huygens's work commenced. At the age of twenty-six he made a search for satellites of Venus and Mars, but in vain. Turning his own twelve-foot telescope on Saturn, it appeared to him much as it did to Galileo. The nature of the lateral bodies or appendages could not be distinguished. Leaving this problem on one side, however, Huygens at eight o'clock in the evening 'of March -25th, 1655, noticed a small star very near the line passing through the planet and its appendages or " anses ". His suspicions that this would prove to be a satellite were strengthened during the following days, for the position of the star altered. After a few weeks Huygens decided that the period of the satellite (Titan) was sixteen days and four hours.

This discovery, as has been mentioned, was made before Huy- gens went to Paris in July. No doubt several of Montmor's group discussed with him the puzzling problem left by Galileo. Heve- lius, the noted astromer of Danzig, confirmed the planet's pecu- liarities, his telescope being not much better than that of Galileo. Huygens recognized that everything depended on improving the instrument. The diverging eyepiece of the Galilean telescope restricts the field of view and Scheiner, about 1630, successfully made the first instrument having two or three convex lenses. Telescopes of this type have a better field of view but are more

THE LIFE OF CHRISTIAN HUYGENS 31

subject to the defect of chromatic aberration, a matter not then understood. Huygens went to the lens maker Mocchi while he was in Paris and learnt all he could from him. When he returned to the Hague he worked continuously on lenses, trying amongst other things to produce a hyperbolic or elliptical surface, but both proved too difficult. He succeeded, however, in building a larger telescope having twice the magnifying power of his twelve-foot instrument and this enabled him to study Saturn more closely.

In the winter months of 1655—56 great progress was made to- wards solving the problem. Instead of the " tri-spherical " form he was able to distinguish a sort of band passing across the middle of the planet and drew it in the form :

A slightly later drawing of Saturn showed it in the form :

It is difficult to imagine what his conjectures were at this point. A new twenty-three foot telescope with the best lenses he could make was assembled with all speed and this was in use after Feb- ruary ipth, 1656. With this instrument the planet appeared much more distinctly and he at last made a drawing of it showing it surrounded by a ring :

The drawings he made show that he was struggling to gain a clearer image and only by degrees became certain about what he could see (cf. p. 194).

During an interval between June and October the planet was

32 THE LIFE OF CHRISTIAN HUYGENS

not clearly visible but Huygens already felt confident that his observations had only one interpretation: Saturn is sur- rounded by a thin ring of matter slightly inclined to the ecliptic. This idea was concealed in an anagram published in his De Satitrni luna abservatio nova, which came out in the spring of 1656. When disentangled the anagram reads "Annulo cingitur, tenui, piano, nusquam cohaerente, ad eclipticam inclinato," viz. : " It is encircled by a ring, thin, plane, nowhere attached, inclined to the ecliptic." From his correspondence it is clear that he was confident of his conclusions as early as February of that year.

The use of anagrams was common in those days. Huygens adopted the device so as to give an opportunity for other astron- omers to bring their own discoveries to the light of day " so that it may not be said that another has borrowed from us, or we from him ". The method was superseded with the growth of scientific periodicals. In this instance, Roberval, Hevelius and one Hodierna all came forward with their own announcements. Hevelius alone produced anything of importance. His Disser- tatio de Natura Saturna Facie (1656) contained in fact a complete theory for the observed periodicity in the phases of Saturn. He cannot have seen the planet clearly for he supposed it to be ellip- soidal and not spherical in form; also there were two appendages physically attached to its surface.

Roberval put forward the theory that Saturn is surrounded by a " torrid " zone. From this equatorial zone " exhalations " were ejected and these were supposed to be transparent except when present in great quantities. The periodicity in the phases was ignored. Even more remarkable was Hodierna's account of Saturn. His theory that the planet had the form of an egg or plum having two dark patches deserved careful verification, Huy- gens caustically remarked. Certainly such an appearance called for study by a better telescope than one of a magnification of five!

Bouliiau was unable to see the satellite Titan and this made Huygens suspect the quality of his telescope and for this reason to trouble little about Boulliau's criticism of the ring theory. It mattered rather more when Wallis, the English mathematician, wrote to say that the English had forestalled him. This, however, proved to be a practical joke by Wallis, who otherwise is known only for the seriousness of his pursuits.1 However, the details

1 See notes on Wallis and others (p. 212).

PLATE I

Saturn— Reproduced from Huygens's MS.

THE LIFE OF CHRISTIAN HUYGENS 33

of the ring continued to give Huygens, as he said, " no little trouble ". The difficulty was to fix the interval between the phases and calculate the future appearance of the planet. At the end of 1657 Huygens was able to inform Boulliau of the confirmation of his theory. " On the ifth of December I saw Saturn with my big telescope for the first time after it had passed the sun and was delighted to find it exactly in the form I had predicted according to my hypothesis." He went on to say that the ring appeared a good deal larger since its last occultation " so that now the sky can be seen through it ".

At the crowded assembly of Mommor's circle Chapelain pre- sented a detailed account of Huygens's studies of Saturn. The planet was in all other respects normal: it traversed an orbit around the sun and its axis of rotation was almost parallel with that of the earth. The axis was always perpendicular to the plane of the equatorial ring. The solid and permanent nature of the ring could be clearly perceived. Twice in thirty years — the sidereal period of the orbit — the ring appeared to vanish since it was viewed edge on. The company was a distinguished one and general praise was forthcoming for the young astrono- mer's discovery. Even Roberval paid him a generous tribute and retracted an earlier suggestion that Huygens was indebted to him for his ideas. He still maintained, however, that his own theory was to be preferred. Huygens wrote that the ring was without doubt a great novelty and one to which " in the rest of the universe there appears to be no parallel ". In June 1659 his book Systema Saturnium appeared.

Copies of the little treatise were sent to Paris and to Prince Leopold de Medici, to whom it was dedicated. The prince was a great supporter of science and founder of the Accademia del Cimento. Influenced by Boulliau, who sent him criticisms of the hypothesis, however, Leopold hesitated to express his opinion of Huygens's work and it was only after a considerable delay that he acknowledged its importance. Of the noted astronomers of the day, Hevelius, Boulliau and Riccioli did not accept Huy- gens's account of Saturn's ring. To this day no-one seems to have recognized the importance of Huygens's theory that the ring would be stable under uniform gravitational attraction — assum- ing mechanical resistance to fracture. He did not state that the gravitational force kept the ring in rotational stability but he did suggest that Saturn's gravity extended to the ring.

G

34 THE LIFE OF CHRISTIAN HUYGENS

It was as a comment on Copernicanism that Huygens intended his book to be read. The nature of gravity was, he insisted, the same for all the planets. A stationary ring of uniform thickness would, then, be in equilibrium. No further evidence could well be expected. There are other interesting matters in the work, but these will be discussed later. What concerns us here is that the severest attacks which were made on the Systema Saturnium were made for religious and not scientific reasons. It is curious that after a period of tolerance the Catholic Church became bitterly opposed to Copernicanism in the seventeenth century. In 1615 the Holy Congregation had declared all books of Coper- nican doctrine to be condemned and prohibited. Chapelain cer- tainly expected trouble and wrote that it was surprising that the hypothesis of the movement of the earth was allowed to pass in Holland. P£re Honori Fabri, a Jesuit, and an astronomer, Eustachio Divinis, were foremost in their antagonism to Huy- gens. These critics found it necessary to impugn not the argu- ments advanced by Huygens but his very observations. This drew a sharp reply from Huygens in his tract Antidivmis, but the controversy dragged on until Huygens was well established in Paris in 1666 and will need a further account later. The name of Fabri is obscure enough now. Nevertheless, under the name of his friend and pupil, Mousnier, appeared one or two inter- esting attempts to develop mechanics. The trouble was that Fabri possessed the outlook of an Aristotelian, for he wished to deduce the mathematical laws of dynamics from principles of natural philosophy. So deeply rooted was this habit of mind at this time that considerable feeling was frequently roused by ideas which rested on an entirely different attitude. In France the authorities of the theological college of Paris University tried to get decrees issued in defence of Aristotle's philosophy and against the new heresies as late as 167 1. This ridiculous situation was treated to a sarcastic burlesque by the playwright Boileau, who thereby did much to wreck the scheme. Later, a more eclectic outlook existed; Cartesianism entered the Sorbonne itself.

Between 1655 and 1660 Huygens spent much time on the invention of an accurate pendulum clock. The significance of

THE LIFE OF CHRISTIAN HUYGEN3 35

this invention in the history of science is that it marked the new interest taken in time as a dimension. We shall see that Huygens effectually began the study of dynamics. One reason why the history of mechanics up to his time was really the study of statics was undoubtedly the tendency resulting from the neo- Platonic revival of the sixteenth century which coincided with the decline in Aristotelianism. This tendency was to reduce most physical problems to geometry. But the absence of accurate time measurement was undoubtedly another reason. Galileo, it will be remembered, used a water clock in his experiments on acceler- ation over the inclined plane.

Very probably it was in the first place Huygens's early enthu- siasm for astronomy which led him to tackle the problem of the pendulum clock. Balance clocks existed, of course, from much earlier times, probably from the thirteenth century, but they were crude and unreliable machines. Tycho Brahe used one in conjunction with his mural quadrant and corrected for its errors by comparison with the sun. The measurement of the time of passage of a star across the meridian could be used to replace the measurement of its meridian altitude, this being a more difficult measurement and rendered uncertain through the absence of reliable corrections for the atmospheric refraction. Also, as a member of a seafaring nation, Huygens could not have failed to know that an accurate clock would afford the simplest method of determining longitudes at sea. This question seems to have interested him more after he had made his first clock.

His first publication, Horologium, a short treatise describing the application of the pendulum to the escapement, appeared in 1658 but the invention was known to his friends some two years earlier. Unfortunately a controversy arose through the claim made by Leopold de Medici that the priority for the in- vention belonged to Galileo. Roberval and a Paris clockmaker, Thuret, also claimed that they had anticipated Huygens. The whole history of the pendulum clock has in fact been obscured by various energetic contestants.

In 1598 the King of Spain offered a prize of one thousand crowns for a means of finding longitudes at sea and this was followed by an offer of ten thousand florins by the States General of the Netherlands. Now Galileo is said to have discovered the approximate isochronism of a simple pendulum in 158 1 . He him- self, in 1636, offered to the States General a method of determin-

36 THE LIFE OF CHRISTIAN HUYGENS

ing longitudes based on the telescopic observation of the occultations of the moons of Jupiter. It was proposed to publish an almanack of the eclipses of these moons and to use a " numeratore del tempo " to measure the time intervals. This instrument, from all accounts, was merely a simple pendulum maintained swinging by hand and fitted with a completely im- practicable mechanism for counting the swings. Admiral Read's committee did well to reject the " invention ". It is quite possible that in 1637 Galileo came across Leonardo da Vinci's drawing for a clock regulated by a pendulum. It was in this year that da Vinci's manuscripts were given to the Biblioteca Ambrosiana at Milan by Galeas Arconati and the donor is known to have been at pains to bring his treasure to the notice of contemporary men of science. Galileo in this year became blind after a long period in which his eyes were diseased but he had around him Viviani, Torricelli and his son Vincenzio. Viviani, writing to Leo- pold in 1659, described from memory how Galileo discussed with his son the construction of a pendulum clock. The date given was 1641. Whether Vincenzio ever completed its construction is not known. It is certain that Huygens knew nothing about the design until after the publication of his Horologium in 1658. A copy of this was sent to Leopold de Mediei, who replied guardedly, pointing out that Galileo had had the same idea.

As against the theory that Galileo was indebted in any way to da Vinci it needs to be mentioned that the design commonly attributed to Galileo differs somewhat from that shown (though rather imperfectly) in da Vinci's note-books. Huygens's design differs from that of Galileo and was, in fact, closer in prin- ciple to that of da Vinci.

It was in the records of the Accademia del Cimento of 1662 (published in 1667) that the implication of Huygens's plagiarism was really blazoned abroad. Here it was stated that Vincenzio had put his father's design into practice in 1649. No details were given and the illustration simply showed a drum-shaped clock mounted horizontally on a vertical pedestal. From the under- neath side of the drum hung something resembling a simple pendulum, the mode of attachment of which had to be imagined. It is obvious that a simple pendulum would be useless, since it is impossible to give an impulse to the thread and pre- sumably a thin iron rod was intended. Nevertheless, Matteo Campani stated that he saw the clock constructed by Vincenzio

THE LIFE OF CHRISTIAN HUYGENS 37

— " an antique and rusty machine not at all complete " — and Leopold's letters certainly suggest that such a clock was in existence, though whether it conformed to the diagram is not known. The clock was never forthcoming and it has generally been supposed that Viviani pressed the whole case for Galileo out of a desire to honour his master. Nevertheless, the evidence does seem to indicate that Galileo did precede Huygens in achieving the successful application of the pendulum to the escapement, but that the complete clock was constructed is exceedingly doubt- ful. Probably da Vinci was the first to have the idea and still more probably Huygens was the first to carry it through to fruition. In a later chapter it will be shown how astonishingly thorough in every particular Huygens's work was; so completely did he clear up the theoretical and practical problems that he is in a real sense the father of modern time-measurement. Samuel Coster, his clock-maker at the Hague, made a large number of clocks to his design and these were the first to be commercially available.

As has been mentioned, Huygens probably interested him- self in the longitude problem after he had made his first clock. He may have read the work Nieuwe Geographische Onder- wijsinge in Dutch by Metius (1614) which pointed out that it was only the irregularity of balance clocks which prevented them from supplying a means of finding longitudes at sea, but in any case the relation between local time, standard time and longitude was well known. The pendulum clock was a far better instrument but it was very easily disturbed. Huygens consistently under- estimated this problem of the movement of the ship. He thought that a pendulum whose period was independent of the amplitude of swing would enable this difficulty to be overcome. The idea was ingenious and led to the discovery that the period of oscillation of a cycloidal pendulum is independent of the amplitude, but the practical value of the discovery was strictly limited. A great deal of time was occupied by the investigation of this problem, conducted as the research was by elementary and tedious mathematical methods. In practice a cycloidal pendulum may be constructed by allowing a simple pendulum to swing between two curved metal plates along which the thread curves itself on each half of its swing. In applying the idea to the clock pendulum Huygens used a short ribbon attached to a rigid pendulum. These plates or " cheeks " were first tried in

38 THE LIFE OF CHRISTIAN HUYGENS

1657 or during the last days of 1656. Towards the end of 1659 Huygens showed that theoretically they should themselves possess the form of cycloid arcs. He was immensely pleased with this discovery and ranked the geometrical part of the work above all the rest.

About this time (1659) more detailed accounts of Galileo's escapement became available. Models of this escapement have since been made and it cannot be said to work satisfactorily. As Huygens pointed out at the time this escapement imparts a very uneven movement to the pendulum. His own clock remained therefore the only one in this field.

Continued efforts by other inventors, including the clock-maker Thuret, to profit from the invention drove him to the unwelcome decision that he should take out a patent or " privilege " to protect his rights. Much delay occurred before the French " privilege " was issued, but thereafter Huygens's priority was recognized and he made some profit from the construction of clocks to his design.

The story of the clock needs to be told with reference to certain of Huygens's mathematical researches. His first essay in this field had dealt (1651) with some fallacious work by Gregory de Saint Vincent on the rectification (or measurement) of certain curved lines. Huygens became interested in the rectification of curved lines known as conies and in the age-long problem of the rectification of the circle. When Boulliau sent him some problems by Pascal on the curve known as the cycloid in 1658, therefore, the subject was by no means a new one. These problems, to which Pascal had already obtained solutions, and which he set for the interest or exasperation of other mathematicians, were known as the " Dettonville " problems, this being the pseudonym under which they were issued. Huygens succeeded in solving some of the necessary preliminary problems but found the main ones so difficult that he declared himself unconvinced that they had ever been solved. When he later came across a rectification of the cycloid by Christopher Wren he expressed his admiration. It was, he commented, the first curved line known to be rectified, and he wondered if it were the only one which could be rectified. There was some correspondence between Huygens and Pascal on the " Dettonville " problems. Pascal praised Huygens's

R|,4

m

One

THE LIFE OF CHRISTIAN HUYGENS 39

penduhim clock very highly, but such was Huygens's esteem for Pascal as a mathematician that he deprecated such mechanical inventions. There was, he remarked, little science or subtlety in such things. About this time Pascal's adherence to the Jansenist sect was somewhat weakened but his periods of religious pre- occupation invariably interrupted his most interesting work — and his most promising friendships. So it was in his relations with Huygens. The latter was eager to collaborate but closer relations were frustrated.

It is clear that at some time between Septetnber 1659 anc* January 1660 Huygens discovered the theoretical form of the small plates or " cheeks " for his corrected pendulum. These dates may be fixed by an examination of his correspondence. From this it seems that he did not at first use the metal plates except for clocks in which a large swing was employed. Later, taking the view that a marine clock would benefit from having a pendulum swinging through a large arc, he felt that it was im- perative to discover the theoretical form of the restraining plates. His success in this problem gave him the pleasure of a mathe- matician with a pretty solution. He announced that the second edition of his Horologium would contain "a fine invention which I added to the clock a little while ago ". It appears prob- able that, although Pascal's problems were of a very different character, the interest of the cycloid led Huygens to make his investigations.

The improved clock was in use towards the end of 1669 and was adopted after that date as being the best time measurer then made. Earlier astronomers, notably the Landgrave of Hesse (who used balance clocks made by Byrgius in the sixteenth century), Tycho Brahe, and later, Hevelius and Mouton, recog- nized the importance of time measurements, but Roemer and Flamsteed, late in the seventeenth century, were really the first to use the clock systematically. Delambre, in his great Histoire de rAstronomie Moderne, states that Huygens " started the great revolution " in practical astronomy by the invention of the pendulum clock.

Curiously enough the cycloidal pendulum, in spite of its elegance, did not have a very long life. It was recognized by Huygens himself that small circular arcs were equally accurate and in his model of 1658 he was able to restrict the size of swing. After the application of the anchor escapement by a London

40 THE LIFE OF CHRISTIAN HUYGENS

clock-maker, Clement, in 1680, few cycloidal pendulum clocks appear to have been made. The anchor escapement causes the pendulum to describe small arcs of constant amplitude and this made the cycloidal pendulum — for all but marine clocks — super- fluous.

As for the marine clock or chronometer, although Huygens constantly considered himself near to success, it proved eventu- ally to be a failure. The pendulum seemed for many years to be the only means of controlling the going of the clock with sufficient accuracy. Huygens accordingly tried various forms of suspension and various forms of pendulum, all designed to with- stand the movement of the ship, but none proved to be a practical proposition. Such was the commercial rivalry of the various East India Companies, however, that he was encouraged to persevere, and persevere he did up to the last year of his life. How near he came to success will be described later.

Meanwhile the astronomers obtained their longitudes by Galileo's method of observing the recurrent eclipses of the satellites of Jupiter. Cassini, working at Paris, drew up the first tables for the observation of these satellites and, with Richer, in consequence of this work was able to make the first modern estimate of the distance of Mars. But astronomical methods were clearly unsuited to the determination of longitudes at sea.

Huygens's great essay, Horologium Oscillatorium, on the construction of the clock and all the relevant propositions on the cycloidal pendulum and on the centre of oscillation did not appear until 1673. Already, however, he had made notes for the work and even wrote to Chapelain in September 1660: "The treatise on the clock has been finished a long time but tnere is no means of having it printed before my journey ..." This refers to an extended edition of the original Horologium which included a treatment of the cycloid; much was yet to be added before the work reached its final form. In October Huygens left the Hague for Paris.

VI

In considering the encouragement given to literature and the arts in France during the seventeenth century, the credit belongs almost as much to Mazarin as it does to his successor Colbert.

THE LIFE OF CHRISTIAN HUYGENS 41

Mazarin it was who gave pensions to many of the great writers who made this the golden age of French literature. Molifcre, Balzac, Descartes, Pascal, Racine, Corneille, Boileau and others benefited from Mazarin's patronage and his example was followed by Colbert after 1661.

Nevertheless, the establishment of the Academic Royale des Sciences would never have been achieved if the men of science had waited for Colbert. Up to 1663 what progress there was in any regular pursuit of science was made by men who were associated with one or other of the amateur societies, Montmor's and Thevenot's being much the most important. But in this year there was a rather defeatist air about the correspondence on the subject of a permanent academy and Sorbiere summarized the difficulties in an account sent to Colbert. There had to be appeals by Sorbtere, Thevenot and the Abbe d'Aubignac, how- ever, before any impression was made. Finally Auzout publicly appealed to the king's pride (and vanity) and after the Peace of the Pyrenees things began to look more hopeful.

The scientific societies did indeed develop under difficult con- ditions. In England, for example, where the Royal Society was taking shape, there was in progress a stern struggle between king and parliament, a deep religious dissension and in the com- mercial sphere a rivalry with the Dutch which had become acute. In Holland, on the other hand, it was understood that the chief political problem of the time was the neutralizing of the grow- ing power of Louis XIV. Civilization was passing through a critical period and internal dissension as much as external danger made the times, one would have thought, unpropitious in most countries of Europe for the growth of societies with the calm in- terests of natural science as their pursuit. But perhaps these interests were all the greater attraction; as Sprat wrote after- wards, the members of the Royal Society wished simply for " the satisfaction of breathing a freer air, and of conversing in quiet with one another, without being engaged in the passions and madness of that dismal age ". Needless to say their work was not always taken seriously and both in Paris and London there were scoffers who doubted the worth if they did not mistrust the in- fluence of " natural philosophy ". Pepys recorded that Charles II " mightily laughed at Gresham College for spending time only in weighing of ayre and doing nothing else since they sat ". But Colbert certainly saw that there was more to those pursuits than

42 THE LIFE OF CHRISTIAN HUYGENS

met the eye. It may be doubted if Louis XIV, unaided, saw any- thing significant at all in what was going on.

In spite of the difficulties an extensive correspondence was carried on between the men of science. Paris was at first the chief centre of experiment, but London later rivalled and then surpassed it in activity. The meetings of the scientists seem to have been devoid of political motive; religious difference only rarely caused antipathy, national differences scarcely ever. As will be seen, Huygens spent many years in Paris under the patronage of Louis XIV, even though his family had a long association with the house of Orange and, after 1672, the young Prince of Orange headed the resistance to French invasion. It might have been thought that Huygens, a protestant Dutchman, would have been regarded as a spy but this was not the case. Not until 1683 did it become clear that, with Colbert's death, support for his continuance in Paris was gone. Colbert was succeeded by Louvois, and in 1685 the Revocation of the Edict of Nantes caused many protestants to leave the country. All this, however, lay in the future.

In 1658 Montmor charged Sorbiere with the task of drawing up rules for the meetings of the assembly which were held regularly at his house. The keynote of the rules, in the form finally adopted, was the need of restricting " the vain exercise of the mind in useless subtleties ". Mere philosophizing, it was agreed, was profitless. Unfortunately the assembly did not appreciate how their aim should be achieved : without a pro- gramme of experimental work directed to the solving of selected problems too many of their meetings continued to degenerate into philosophical combats.

Huygens returned to this gathering of scientific amateurs in 1660 and was introduced by Chapelain on November and. At Montmor's, he wrote to his brother, " there is a meeting every Tuesday where twenty or thirty illustrious men are found together. I never fail to go ... I have also been occasionally to the house of M. Rohault, who expounds the philosophy of M. Descartes and does very fine experiments with good reasoning on them ..." Rohault's meetings were held on Wednesdays and began about 1658. There is no doubt that he did a great deal to make science popular in Paris. Unauthorized editions of his lectures were published, so great was the popular interest. It is not surprising that Huygens approved of him, although no

THE LIFE OF CHRISTIAN HUYGENS 43

association between them seems to have occurred. Rohault was enlightened and modern in his attitude but he was an expositor and lecturer rather than an original thinker. Where he abandoned Aristotle he followed Descartes.

At Montmor's house Huygens noted a room "full of beautiful paintings ", a cabinet of curious inventions and mathe- matical instruments, and drawings by Albert Durer. With the astronomers he discussed his work on Saturn and the problems of lens grinding; with the mathematicians, as he noted, " my theories of the superficies of conoids and spheroids and the new properties of the cycloid for pendulums "; and with the clock- makers and telescope-makers Huygens also passed interesting hours. He met Conrart, Roberval, de Carcavy, Pascal, Pierre Petit, Sorbiere, Desargues and others. Some of these names will recur later.1 He corresponded with Fermat and with his friend Boulliau, then staying with Hevelius at Dantzig. With Robert Moray, a prominent member of the London group of " scientists ", he also began a correspondence. These men were all really amateurs and the title astronomer, in most cases, for example, simply indicates the kind of work for which a particular man showed especial interest and in which he spent his leisure time. Nevertheless, a man like Cassini, later invited to work at Paris, represents the new type of professional worker in that most of his time was in fact spent on genuine systematic work. Huygens also belongs to this class. Real specialization in the modern sense was quite unknown, of course. Like all the early scientific assem- blies of the mid-seventeenth century the Montmorian society cast its net almost too wide. Huygens's diary records dissections of human bodies, the examination of machines for which per- petual motion was claimed, the making of lenses and telescopes and many other matters. Too much time, Huygens considered, was spent in arguments of a purely philosophical nature. He felt that a sterner discipline, a greater application, was needed than could come out of the performance of merely curious ex- periments and the holding of discussions.

Nevertheless it must have been an interesting and stimulat- ing experience to have met so many natural philosophers, all of whom felt the common interest in the new study of nature. At the house of the Due de Roannes, Huygens, in December 1660, met Pascal. Eight days later the Duke, with Pascal, visited

1 Sec notes on Persons Mentioned, pp. 212-6.

44 THE LIFE OF CHRISTIAN HUYGENS

Huygens at his lodgings in rue Sainte Marguerite and, wrote Huygens, "... we talked of the force of water rarefied in cannons and of flying; I showed them my telescopes." Pascal was at this time a sick man. The writer of Provincial Letters had, in fact, by this date retired more or less completely from the world. Less than a year later he was dead.

The publication at this time of tracts against Huygens's account of Saturn shows that the orthodox Jesuits were not pre- pared to ignore the author's Copernican doctrines. Pere Fabri especially opposed what he called Huygens's "furtive insinua- tion" of the Copernican "error". In his Brevis Annotatio in Sy sterna Saturnium Christiani Eugenii (1660) he presented his own fantastic theory, although this work was published over the name of the astronomer Divinis. According to this theory the planet had two luminous bodies (lucidi) and three dark ones (obscuri) placed around it and the different relative positions of these bodies were the cause of its observed phases. This criticism drove Huygens to compose his Brevis Assertio Systematis Saturnii within the year. Hevelius is said to have been so favour- able to this reply that he abandoned his own theory in favour of the theory of the ring. Leopold, to whom both Divinis and Huygens dedicated their publications, remained reserved. In 1 66 1 he sent Huygens a further pamphlet by Divinis and Fabri but it did not seem to Huygens to deserve a reply. It is note- worthy that by January 1665 even Fabri recognized the truth of the ring theory, convinced at last by the excellent telescopes of Guiseppe Campani. Huygens was extremely pleased by this conversion of his critic. "No-one, 5n my opinion, could reason- ably reproach me " he wrote, " for having adapted my account of Saturn to the system of Copernicus . . . the truth of the matter can only be explained by following Copernicus, and indeed our system of Saturn corroborates his own strongly."

VII

One of the reasons for Huygens's visit to London in 1661 was undoubtedly his desire to obtain information of the society of men of science then meeting at Gresham College, the society which by charter became in 1662 the Royal Society. He arrived in London in March — just before the coronation of Charles II and left for the Hague at the end of May.

THE LIFE OF CHRISTIAN HUYGENS 45

The London which Huygens saw in 1661 was the London which was largely swept away by the Fire and he was not at all favourably impressed with the condition of the town. All, he found, was in marked contrast with Paris : the smoke from the furnaces of the brewers, soap boilers and dyers; and the stench of narrow alleys innocent of drainage and sanitation. Even Gresham College had been rendered malodorous. Monk's sol- diers had for a year used it as a barracks and it was, Bishop Wren wrote to a member of the society, " in such a nasty con- dition, so defiled, and smells so infernal, that if you should now come to make use of your tube [telescope] , it would be like Dives looking out of hell into heaven." This was in 1658 or the " fatal year 1659 ". With the " wonderful pacific year 1660 " meetings of the " invisible college " as Boyle called it, recommenced. By 1 66 1 the college was presumably cleaned up. Huygens, at any rate, had only admiration for the proceedings there. Brouncker, Moray, Oldenburg, Godard, Boyle, Wallis and many others were familiar figures at the meetings of the society and their activities seemed to him to surpass anything done in Paris. The observa- tion of stars was done in the garden of Whitehall Palace and there Huygens tried his own telescope lenses, sent over by his brother Constantin. These proved to be better than the English. The Duke and Duchess of York came out to observe the Moon and Saturn.

Huygens's meeting with Wallis is of especial interest. This great mathematician showed in his Mechanica sive de Motu (1669-71) that he had much to contribute to mechanics. The his- torian Duhem has given the opinion that this work was " the most complete and the most systematic which had been written since the time of Stevin ". In his work Wallis generalized the idea of force which up to his day was used only in connection with gravity. Huygens's English was at this time not at all good but he saw that it would be most valuable to keep in communi- cation with Wallis, as indeed with others of the Gresham College group. This was the begining of a life-long association with the English men of science. It is striking that, in spite of the official position Huygens came to have in the Academic Royale des Sciences, in 1670, when he feared that he had only a short time to live, he made arrangements to entrust his papers not to the Paris society but to members of the Royal Society. Through Oldenburg, the indefatigable secretary of the Royal Society, Huy-

46 THE LIFE OF CHRISTIAN HtJYGENS

gens was fortunately able to remain in close contact with the pro- gress of science in England.

There is good evidence that the outlook characteristic of the English men of science was less complicated by the consider- ations of a priori philosophies than that of the Paris group. Francis Bacon has, probably, always influenced literary men more than he has the men of science, but there is no denying his importance. Bacon was no scientist and his scientific "method " was the literary man's conception of science. He never advanced as far as Descartes into scientific studies. He foresaw, " he cast forth brilliant intuitions "; ridiculing Aristotle's natural philo- sophy he pointed to experiment and observations as the only means of discovering truth : " Nature to be commanded must be obeyed." With this spirit the English men of science, neverthe- less, were thoroughly imbued. Their opposition to Hobbes illustrated th£ir belief in empiricism. Hobbes's dictum " Experi- ence concludeth nothing universally " appeared to them mere philosophic wind; his excursions into physical science the sort of thing against which their motto Nullius in Verba was later aimed. It has to be admitted, of course, that most of the Eng- lish men of science were shocked by Hobbes's acceptance of the Epicurean philosophy. This appeared to them to be an approach to Nature which was neither scientific nor pious. Although he was not explicit about it, it was the more empirical attitude of the English men of science which impressed Huygens so favour- ably.

Before leaving London Huygens took part in a determination of the comparative sizes of the ring and globe of Saturn. He was pleased to find that his account of the planet was accepted with admiration. Huygens also saw a transit of Mercury from Long Acre, using one of Reeve's excellent telescopes.

After Huygens's return to the Hague his father and younger brother went on a diplomatic mission to Paris. The elder Con- stantin Huygens, a man of European repute, then made the acquaintance of some of his son's associates. Through him the Montmor group heard of Christian's latest experiments. The Dutch diplomat took the opportunity to present Louis XIV with one of his son's pendulum clocks. This gift was opportune, for it was at this time that Colbert was drawing up his schemes to excel all past achievements in making Paris the cultural capital of the world and Louis the pre-eminent monarch of the age.

THE LIFE OF CHRISTIAN HUYGENS 47

Louis, of course, became surrounded by an almost ridiculous cult which sought to elevate him above everyday existence, but even this had its merits ! The singling out of writers, poets and men of science was at any rate one of the better consequences. These were given rewards totalling many thousands of pounds and the inven- tor of the pendulum clock later came in for suitable appreciation. More important, however, was Huygens's subsequent invitation to Paris to assist in organizing a scientific society under royal patronage. There were delays in carrying out this project, which must be ranked high among Colbert's achievements, but in 1666 the societies which had been associated with the names of Montmor, Thevenot and others received this formal recognition of the importance of their work.

VIII

The early scientific societies exhibited an enthusiasm and universal interest which scarcely characterizes the professional societies into which they have developed. Specialization was vir- tually unknown and through Latin the members had a means of communication with foreign societies and with a learned world which had existed before the new studies had begun. It is not surprising that men like Huygens were acquainted with the works of some of the Greek writers, nor that it was the Greeks of the Alexandrian period that held the greatest attraction. Huy- gens was only following in the steps of Galileo when he studied the works of Archimedes, for they contained some of the funda- mental ideas used in mathematics and in statics. But it was clear that new ideas of a fundamental kind were needed in mechanics and it was equally necessary to clear away many plausible suppositions which had no basis in fact.

Huygens saw clearly that such simple machines as the lever, the pulley, and the wheel and axle, although thfcy gave a mechanical advantage, could in no way increase the energy avail- able. Machines for flying, for propelling boats by means of springs connected with trains of gears, strengthened his convic- tion that their limitations resulted from a simple mathematical identity of some kind. But it was many years before this idea could be expressed satisfactorily. Desargues seems to have tried to evolve a proof that perpetual motion is impossible but, proof or no proof, the impossibility was accepted as axiomatic within

48 THE LIFE OF CHRISTIAN HUYGENS

the realm of mechanics by Huygens. The search for a form of perpetual motion did in mechanics the sort of work that in chemistry was produced by the search for the philosopher's stone. In 1659 a book entitled Mechanica Hydraulico-Pneumatica^ by the Jesuit Schottus, reached Huygens. It was partly about perpetual motion but it also described Guericke's invention of the simple vacuum pump. In 1661, while in England, Huygens saw experiments performed at Gresham College using Boyle's pump, which was a great improvement on that of Guericke. After reading Boyle's book, New Experiments Physico-Mechanicall touching the Spring of the Air (1660) he had a copy of Boyle's pump constructed in November 1661. It is clear from his corre- spondence that he repeated many of Boyle's experiments, observ- ing for himself the boiling of water under reduced pressure, the absence of propagation of sound and the expiration of small birds in a vacuum. An important original discovery made during this work was that of the tensile strength of liquids, an effect which at that time baffled explanation and which led Huygens to make far-reaching conclusions on the existence of a subtle fluid or ether which later came into his theory of light.

The question constantly in view behind all work with vacuum pumps was whether a complete vacuum could really exist. Many scientists felt, with Hobbes, that empty space is " an imaginary space indeed ". A fundamental experiment was to fill a tube with water and invert it so that the open end was under water in an open vessel and then to place the apparatus in the receiver of the air pump. When the pressure was reduced the liquid fell inside the tube and with continued pumping was brought down to the level of the water in the vessel. With rather more difficulty the same result was obtained, approximately, using mercury in place of water. These results agreed well with Pascal's explanation of the barometer. However, the appearance of small air bubbles in water which was placed in the receiver of the pump raised serious doubts, for the descent of the water and mercury might be attributed to the dilatation of these bubbles and not to the evacuation of the upper space in the tube. Huygens, much to his astonishment, found that if air-free water was used no descent occurred. If a very small bubble of air was introduced the descent took place. Boyle's law, however, showed that the magnitude of the effect was far too great to be accounted for on the dilatation theory. Huygens's observation

THE LIFE OF CHRISTIAN HUYGENS 49

was confirmed in England, and, at Boyle's suggestion, the effect was obtained without the use of a pump at all Long barometer tubes of mercury were inverted and were found by Brouncker to give the effect if air bubbles were carefully excluded. A column of mercury 75 inches long failed to descend unless a minute air bubble was present and then the level fell to the normal position of about 30 inches.

For several years no explanation of this effect satisfied Huy- gens. But in 1668 he concluded that there must be a subtle fluid capable of penetrating glass where the contact of the liquid is not complete and that the height of the barometer is due to the combined pressures of this fluid and air. Wallis pointed out that if the subtle fluid were capable of penetrating glass it would penetrate the Torricellian space also. It is surprising if Huy- gens did not see the force of this criticism. Although he saw an analogy with the cohesion of two wet glass plates he missed the true explanation, which is that films of moisture (such as exist on mercury and glass) have considerable tensile strength. In his Traite de la Lumiere, written in 1678 and published in 1690, much was made of this ethereal fluid in explaining refrac- tion. In fact, very great importance must be attached to Huy- gens's experiments with the vacuum pump, for his conclusions profoundly affected his whole outlook. He became an admirer of Boyle, whom he supported against the criticism of Hobbes and Linus. The former, he saw, contributed nothing to natural philosophy; of the obscure ideas of Linus (Francis Hall) he thought just as little. Boyle's Skeptical Chymist was published in September 1661 and Oldenburg gave Huygens an account of its contents. Later Huygens received a copy of the book which he read with " great pleasure ". " It contains an infinity of use- ful and remarkable things," he commented, " and in my opinion it is worth twenty of these other books which are continually printed on the matters of Philosophy and Chemistry. This Carneades certainly speaks very truly, reasons acutely, and with- out doubt shows the true way to discover the truth of things. ..." In 1662 Huygens heard of Boyle's famous experiments on the alteration of the volume of a gas with the pressure and he read Boyle's retort to Hobbes and Linus (A Defence of the Doc- trine touching the Spring and Weight of the Air). The kinetic theory of the gaseous state which originates with this work was propounded by Hooke as well as by Boyle. Hooke spoke of his D

50 THE LIFE OF CHRISTIAN HUYGENS

theory as Epicurean after the Greek philosopher who, with Democritus, expounded an atomic doctrine. With the resuscita- tion of this doctrine in Europe Gassendi had a good deal to do. Hooke went into greater detail. The particles of air, he sug- gested, have " much the shape of a watch spring, or a coyle of wire " which, having rotatory motion, sweeps out a " potential sphere ", the volume of which varies with the closeness of the adjacent particles. Huygens was somewhat uncertain if this theory was in accord with the fact that at high pressures air retains its fluidity.

If Huygens gained an interest in experiments employing the air pump from his visit to London in 1661, the English philoso- phers gained for their part just as much although in a different direction. For Huygens, by 1661, had discovered the use of a particular axiom in mechanics which enabled him to solve problems which Wren, Wallis and others found especially difficult. This axiom is a simple one : the centre of gravity of a system of bodies cannot rise as a result of any motion of the bodies under gravity. Experiments on the ballistic pendulum, carried out in Huygens 's rooms in London, showed that he could by this means calculate the heights to which elastic pendulum bobs would ascend after collision. Another discovery which greatly intrigued English mathematicians was the theorem that oscillations of a body in cycloidal arc, occurring under gravity, are truly isochronous. At the time he was in London Huygens had not worked out a complete proof although his note-books show that the work was well advanced. Many mathematicians were consequently attracted to the problem in the hope of being first to provide a proof. Brouncker and Auzout both failed, the former ignominiously, in attempting this problem, which is difficult by the old geometrical methods but simple when treated by means of the differential calculus.

All of this work, which was of first-rate importance, was held up because of Huygens's attempts to construct a successful marine clock — a task which was obstructed more by the limita- tions of the artisan's resources than by theoretical difficulties. Alexander Bruce, Earl of Kincardine, then living at the Hague, collaborated with Huygens in this work. In January 1663 Bruce crossed to England with two pendulum clocks suspended from ball and socket anchorages in the ceiling of his cabin. The weather was so rough that one clock fell from its suspension and

THE LIFE OF CHRISTIAN HUYGENS 51

the other stopped also. In April of this year two similar clocks were taken on a voyage to Lisbon by Captain Holmes. One clock went fairly regularly, and the report on its behaviour is preserved in the British Museum. A filibustering expedition in 1664 to the west coast of Africa and Guinea gave Holmes another opportunity. On one occasion the clocks proved more accurate than the method of dead reckoning in use. Huygens was optimistic as a result of this report and quoted it in his Horologium Oscillatorium of 1673. In 1665 war broke out between Holland and Britain and this ended English collabora- tion.

Huygens rather resembles Hooke in the variety of his scientific interests, but he was far more thorough than his English contemporary and was besides a more " mathematical head ". Besides his work on the marine clock and in mechanics, his work on telescopes and the theory of optics was kept up. It is worth noticing, this dual activity — experimental and mathe- matical. Huygens used it — to obtain a guiding idea rather than a quantitative result. Very great obstacles then lay in the way of exact quantitative work except in Astronomy. Huygens thus knew experimentally what order of aperture was needed, in a telescope of given length and magnifying power, to produce a clear and sufficiently bright image. He saw that the building of longer and yet longer telescopes required improved methods of lens grinding so as to secure sufficient aperture. It also raised problems of a purely structural kind. Wooden tubes, suitably braced, were used for telescopes of about ao or 30 feet; for great lengths Huygens proposed using two short tubes, one at the objective and one at the eyepiece and with rings placed along the intervening space. This method was tried in Paris, but it was found to be very difficult to align the two lenses — as can be imagined. These " aerial telescopes " gave high magnification but poor definition. Many astronomers accordingly experi- mented on the grinding of lenses to forms suggested by Descartes. Many abortive attempts were made before the idea was abandoned. Huygens made some use of a machine for grinding lenses but it was not possible to make really large lenses by any method then known. His superior knowledge enabled him to see that the eyepiece could in certain ways be made to compensate for the defects of the objective. In 1662 he spoke of using two oculars instead of one as a " new manner " of en-

5$ THE LIFE OF CHRISTIAN HUYGENS

larging the field of view. The date of his well-known eyepiece is, however, not quite certain, but it probably was not invented much before 1662 and it may have been as late at 1666.

Huygens's theory of Saturn's phases was at this time so widely accepted, and was confirmed by observation as improved telescopes came more and more into use, that only more detailed matters remained to be settled. It was questioned, for example, if the periods of the phases agreed with the theory that the ring remained at a constant inclination to the ecliptic. Huygens showed how the phases could be calculated and succeeded in converting most of his critics. Wren wrote that " when . . . the Hypothesis of Huygens was sent over in writing, I confesse I was so fond of the neatness of it and the naturall simplicity of the contrivance, agreeing so well with the Physicall causes of the heavenly bodies that I loved the invention beyond my owne ..." And the accumulation of observations bore gradual witness to the success of Huygens's work.

Wren's hypothesis is now forgotten. He and Neile, in 1658, tried to reproduce the appearance of Saturn by fitting an ellipti- cal " corona " to the planetary globe, meeting it at two places. They suggested that this corona rotated with the planet once during its revolution round the sun, on an axis coinciding with the plane of revolution.

As a result of his work in astronomy and in mechanics Huygens's reputation was already high. Moreover, his scientific temper was in accord with that of the best spirits of his age. " I notice," he wrote to Boulliau (who was an ardent Pythagorean) on receiving a copy of his treatise on light " that in many places you dispute the opinions of Aristotle. That is always worth doing." His opposition to the Aristotelianism of the schools, his disregard of the Catholic opposition to Copernicanism, and the steadfastness of his belief in the new mathematical method brought him the esteem of modern spirits among his contempor- aries. It was, then, natural that in France, where Colbert was working to raise the achievements of art and learning above that of previous ages, Huygens should be considered as one of the more brilliant among notable foreigners who might be invited to take up a residence in Paris.

Just as we know little about Newton which is not a descrip- tion of his mental quality, so it is with Huygens. His corre- spondence speaks a mind of great intellectual power and clarity.

THE LIFE OF CHRISTIAN HUYGENS 53

and the singular absence of violence and prejudice in his com- ments on men and things is but a necessary concomitant of this mentality. Nevertheless, he was a very human creature and one can sense that the parental authority at times aroused irritation just as at other times the elderly Constantin's desire to show off his son caused amusement. The trouble was that old Huygens's attitude to his sons did not change as they grew up into men, and when he was forced to treat them no longer as children he regarded them as young diplomats who might conveniently do him services in different parts of Europe. Diplomacy was, how- ever, not much in Christian's line, and while he affected French elegance and a seriousness of bearing, at the same time he was impatient with those who were tedious and self-important.

IX

The vicissitudes which both the French and English societies experienced before receiving official support, and even after, were such that they might well have died in infancy. Meetings at Montmor's were discontinued in 1661, but in 1662 the society held meetings at the house of the Marquis de Sourdis and when Huygens made another short visit to Paris in 1663 the society had regained much of its former activity. After the foundation by charter of the Royal Society in 1662 it was inevitable that in Paris, where meetings had been held at Mersenne's and else- where as early as 1650, the idea of a similar institution should be discussed. Sorbiere, ignoring or ignorant of the early history of the Royal Society, considered that the early Paris societies had in fact led the way. But however this may be, he and Huygens seem to have been on a semi-official errand when they came to London in 1663 to study the organization of the new Royal Society. Writing to Boyle of Huygens's introduction to the Royal Society, Oldenburg said " we had no ordinary meeting; there were no less than foure strangers, two French and two Dutch gentlemen: ye French were, Monsieur de Sorbiere and Monsieur Monconis; ye Dutch, both the Zulichems,1 Father and Son, all foure inquisitive after you." Huygens evinced some surprise that no particular qualifications appeared to be necessary for election to the Royal Society at this time. Christian accompanied his

* Christian Huygens held the title of seigneur de Zulichem (in the province of Gueldre) up to the death of his father. He then inherited the title of seigneur de Zeelhem.

54 THE LIFE OF CHRISTIAN HUYGENS

father on a diplomatic mission on this occasion and was still in London when the news of his award from Louis XIV was made public. This necessitated a return to Paris.

During this short stay in England, however, he had occasion to see further into the character and customs of his hosts. Through his father's connections in this country he dined a good deal with the great, and met many personalities outside the scientific circle at Gresham College. Huygens and his brother Constantin both dabbled in art, and perhaps his chief interest on this occasion lay in his visits to the studio of Sir Peter Lely from whom he obtained a recipe for making pastels.

Soon after his return James Gregory arrived from England with some correspondence from Moray. Moray wrote of this young man that he had " a present to make you of a book of which he is the author, which he calls Optica Promota . . . " He suggested that Huygens should give his opinion of the work and its author but Huygens left no record that he did this. The work was interesting in that it contained a description of a reflecting telescope — some eight years before Newton's invention.

After wintering in Paris, Huygens returned to the Hague (1664) bent on the pursuit of more fundamental researches than could be carried out in Paris. Not until 1666, when he became an official member of the newly formed Academic Royale des Sciences, did he return. Although, therefore, Huygens's work for the new academy was very important and the prestige he con- ferred on it was especially advantageous, it fell to others to com- plete the details of the organization. A wealthy amateur named Thevenot gave hospitality to the society at this time and did a good deal of the preliminary organization. It was he who, doubt- less with Colbert's knowledge, approached Huygens in November 1664 with a suggestion that he should become a member of the reconstituted society. As will be seen, the offer finally carried with it an official position in Paris with facilities for scientific work.

Soon after his return to Holland, Huygens set about obtain- ing patents protecting his design of a pendulum clock for use at sea for determining longitudes. The news of this move not un- naturally aroused a good deal of excitement. The commercial value of a reliable method of finding longitudes at sea would be enormous and several others were after the prize. The members of the Royal Society, who knew of previous trials with marine

THE LIFE OF CHRISTIAN HUYGENS 55

clocks, were frankly sceptical about the use of a pendulum clock. As a result of full discussion, the society, with the national interest in view, resolved to investigate other methods. Of these some sort of spring-regulated clock appeared to be the most promising. It is not surprising, therefore, that Hooke, a most fertile experimenter, should have taken up the question of the isochronism of the oscillations of a loaded spring. In August 1665 Huygens heard of Hooke's successful experiments and his confidence that a spring-regulated clock would be the solution of the problem.

Huygens returned Hooke's scepticism. So long ago as 1660, he remarked, the Due de Roannes had tried the idea but without success. Temperature changes, he considered, would have a serious effect on the going of such a clock and sufficient accuracy would be impossible. Hooke, he concluded, spoke too confidently about this " as also of many other things ". Nevertheless, Huygens tried a spring-regulated clock in November 1665, but was hindered through the great delicacy of workmanship required. Brouncker, in England, found that Hooke's spring driven spring-regulated clock was not so accurate as a pendulum clock. The plague interrupted scientific work in London and Hooke's Potentia Restitutiva, on the properties of springs, did not appear until 1678. Huygens had to leave the Hague and retire into the country for a time.

There, at Voorburg, he returned to his work on the com- pound pendulum, in particular the problem of determining the centre of oscillation. Lacking a general method, he proceeded to study the problem inductively, starting with several simple examples. It was not long before, discarding the erroneous work of Descartes, he arrived at some " quite pleasant propositions ". The work aroused great interest in England and its technical nature will be explained later.

It should be mentioned that by this time (1665) there were two scientific journals of repute for the publication of new work. The publication of the Royal Society, Philosophical Transactions, was begun by the secretary, Oldenburg, on his own initiative in March 1665; in Paris the Journal des Savants was started, also as a private venture, by de Sallo in January of the same year. De Sallo's privilege was withdrawn after about a year because of his denunciation at Rome, but the Abb6 Gallois restarted the journal in January 1666. Neither the Journal nor the Transactions had

56 THE LIFE OF CHRISTIAN HUYCENS

the form of modern scientific periodicals: little original work was published and they were more of the nature of reports. The second number of the Transactions bore an account of some observations by Guiseppe Campani on Saturn's ring. These were of interest since Campani claimed to have distinguished the shadow thrown on the planet by its ring, the remarkable thing really being that his telescope was sufficiently good for such detail to be seen. It was said that Campani's lenses were ground and polished on a machine, but attempts so far made in this direction had been discouraging. Hooke published an account of a machine but it does not appear to have been well tested and he was castigated for publishing an account " upon a meer theory".

Cassini, using a telescope made by Campani, observed a per- manent mark upon the surface of Jupiter and from its return was able to give the period of revolution. This, Huygens affirmed, was " assuredly a very fine discovery ". He himself succeeded in observing the shadow of one of the satellites of Jupiter on the surface of the planet as predicted by Cassini. He also spent some time studying a comet which made its appearance at the end of 1664. As will be explained later, the paths of the comets, so far as these were known, were proving a great difficulty for Descartes's cosmology. Huygens was primarily interested in them as they concerned the Copernican theory. He was at first sceptical about the idea that they recur at long intervals of time. It is interesting that Horrox's defence of the Copernican theory, written about 1635 and resuscitated by members of the Royal Society, came to Huygens's notice through his correspondence with Moray. Horrox, although he died at the age of twenty-two, is generally agreed to have made his mark as an astronomer of a very high order.

The largest telescopes used at this time were of the type now known as Huygens's aerial telescopes, but it is not clear that he originated the idea or wished to claim it as his own. Auzout used an aerial telescope and devised his own method of aligning the lenses; in England the suggestion was widely attributed to Wren. An invention of greater importance and one to which Huygens made an interesting contribution was the micrometer eyepiece. It began to be realized that telescopes could be used for the determination of small quantities which were completely beyond the scope of ordinary instruments used up to that time

PLATE III

Huygens's Clock as the Centre Feature of a design showing Scientific Apparatus of 1671

THE LIFE OF CHRISTIAN HUYCENS 57

for quantitative work. The measurement of small angular separations, for example, required the use of a very large quadrant, but these large instruments became distorted under their own weight. Gascoigne first hit on the idea of using two fine hairs close together and situated in the focal plane of the objective as a means of converting the telescope to quantitative measurements. Auzout and Huygens did some measurements of planetary diameters in 1664 and 1665, but Huygens's micro- meter was a thin plate of metal in the form of a trapezium. It was inserted between the two lenses of his eyepiece where the real image was formed. The plate could be moved until the disc of the planet was just obscured. In this way, as early as December 1659, he obtained a good result for the diameter of Mars. Shortly after Huygens went to Paris in 1666 a micrometer consisting of moveable hairs was used. The modern form of micrometer was invented by Auzout and Picard. Curiously enough it was Picard who saw the value of the pendulum clock in astronomy rather than Huygens. Delambre remarks that Huygens " started the great revolution " in practical astronomy by his invention of the pendulum clock but it was Picard who did most to introduce regular time observations at the Paris observatory. Using Huygens's pendulum clock he used the times of meridian transit of stars to determine their differences in right ascension.

Huygens was not, in fact, a regular observer. His contribu- tion to astronomy lay rather through his work on optics, which had throughout a practical bias: the invention of his eyepiece and the study of conditions under which spherical aberrations may be reduced. In this period just preceding his departure for Paris, Huygens became deeply interested in two works sent over from England : Hooke's Micrographia (1665) aad Boyle's Experi- ments and Considerations touching Colours (1664). Hooke, indeed, was at his best in descriptive and experimental work in which mathematics was not required. The hypotheses which he and Boyle advanced regarding the nature of light and the cause of colours were extremely stimulating and aroused Huygens to the desire to carry out experiments on the subject. From these days some of his important work in physical optics may be dated. He was convinced that before the phenomena of colour could be explained it would be essential to understand the mechanism of refraction. This, he considered, Hooke and Boyle had omitted to study sufficiently. His own note-books show that he calculated

58 THE LIFE OF CHRISTIAN HUYGENS

the order of thickness of the air film involved in the production of colours by interference in the so-called Newton's rings experi- ment (November 1665). Boyle, while admitting that he knew of this experiment, wisely declined to be drawn into a discussion of its explanation.

In his views on the nature of light Huygens always showed a greater dependence on Descartes than in the rest of his work. This bias may explain his first scornful reception of Fermat's least-time principle, for Fermat was, of course, the great critic of Descartes 's work in optics. His principle — that a ray of light follows that path for which the time of transmission is less than for any alternative path — had also an Aristotelian flavour, or so it seemed to Huygens. He declared he found no satisfaction in the idea and considered it was a " pitiable axiom ". Nevertheless, he repeated Fermat's calculation of indices on this " obviously pre- carious " principle and, while retaining doubts as to its validity, began to be convinced more and more that the refractive index of a medium is in fact given by the ratio of the velocities of light in air and in the medium. It was necessary to suppose, with Fermat, that light has a finite velocity, whereas Descartes staked his scientific reputation, as he said, on the belief that its velocity is infinite. Roemer's famous calculations of 1676-7 were thus extremely important, for they showed that Fermat and Huygens were correct.

In the meantime, as has been mentioned, the men of science in Paris had not found it easy to get the project of a permanent academy of science properly launched. The intimations Huygens received of a position in such an academy were not for a time followed by any concrete offer. Nevertheless, his name was kept in front of Colbert. Moray wrote to Oldenburg in 1665 that "Colbert intends to sett up a Society lyke ours and make Huygens Director of the designe," but during this year Huygens began to feel far from confident about the statements which reached him from Chapelain. He bombarded Carcavy with anxious letters and his feelings had to be assuaged with a variety of excuses. No doubt official delays occurred and accommoda- tion had to be found. Huygens was, however, more concerned over the amount of his salary, clearly through anxiety to live in

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THE LIFE OF CHRISTIAN HUYGENS 59

the style to which his upbringing and habits had accustomed him. When he arrived in Paris in 1666, it was to find that no plans for the new society had been drawn up: The official found- ing of the Academic Royale des Sciences, on June ist, meant at first nothing by way of financial aid. It was simply agreed that Auzout, Roberval, CarcAvy, Frenicle, Picard, Buot and Huygens should be the nucleus. But, from a letter l written by Montmor to Alessandro Segni, the secretary of the Accademia del Crusca, it looks as if it was from the first intended that Huygens should have a prominent place. Then, too, writing to Hevelius in 1667, Boulliau said: "Chief of all is the renowned Christian Huygens . . . Next are Roberval . . . Auzout ..."

Huygens became a close friend of the Colberts and served on occasion as the minister's scientific adviser. Meetings were held at first in Colbert's library and the first co-operative undertaking, an observation of a lunar eclipse, June 16, 1666, was planned to take place at his house. Unfortunately, cloudy weather made observations impossible. But two weeks later the same group, Huygens, Carcavy, Roberval, Auzout, Frenicle and Buot met to observe a solar eclipse. Once more visibility was poor and results were disappointing. Micrometer measurements giving the rela- tive diameters of the sun, moon and planets were, however, made.

The appearance of the members at these early gatherings of the Academic Royale has been excellently recorded in the work of the skilful engraver Lfe Clerc. One of this artist's pictures, for example, shows an informal meeting of members and may well represent an hour spent in desultory discussion before the giving of an address. It has been suggested that the figure holding a lens and standing in the window is that of Huygens. When we look at the plate showing a meeting attended by Louis XIV (facing p. 60) it does not appear that Huygens was included. This is the opinion of E. C. Watson,* who points out that Huygens was away from Paris through illness early in 1671.

In August 1666 Huygens took over apartments at the Bibliothique du Roi after the headquarters of the Academic had been transferred there. On December M the society gathered officially for the first time to hear from Carcavy the decision of the king to protect the new institution.

i A. J. George. Annals of Science, III, 37*. * E. C. Watson, Osiris, VII, 556.

60 THE LIFE OF CHRISTIAN HUYGENS

Adherents of Descartes's philosophy, men, that is, who gave out their belief in vortices of subtle matter and who did not accept atoms or the existence of a vacuum, were not con- spicuous in the make-up of the Academic. Roberval was a noted critic of Descartes; later the Academic included Mariotte, who also was dubious about Cartesian theories. Frenicle resembled Mariotte in being prepared to accept resemblances between facts without feeling obliged to attribute them prematurely to a single cause. Huygens alone referred to the doctrines of Descartes's Principia when called on for explanations of such phenomena as gravity, and he and Charles Perrault for a time exerted a slight influence in favour of Descartes. In time, it is clear, Huygens became distinctly aware of the failure of such an experimen- talist as Rohault to maintain his Cartesian explanations without disingenuousness,and his work shows a progressive decline in his adherence to the great " system ". Yet he long remained in two minds and it only required some ignorant criticism of the great philosopher to rouse him to his defence. It is surprising too, to see how closely the form of some of his work (for example, that on impact) resembled that of Descartes1.

Unfortunately this period of Huygens's work in Paris was twice interrupted by serious illness, necessitating a return to his native air. One gains the impression that his position was thereby weakened in some degree, for his absences were prolonged. When he left for yet a third time to regain his health it was never to return. His protector Colbert died soon after and profound changes in the p critical situation militated against his regaining a position which all along had aroused a certain envy. Huygens's last years were consequently spent in comparative retirement. Mach says that Huygens " shares with Galileo a noble, unsur- passable and complete uprightness " and this is a true estimate. The manner in which his years at Paris came to an end can only be deplored. Huygens's scientific work throughout illustrates a readiness to make his personal reputation always subservient to larger interests. Nil actum reputans, si quid superesset agendum was, according to the historian PoggendorfF, his adopted device.

The presence of Huygens in Paris throughout the onslaughts

of the French armies against the Dutch Republic is the fact

which historians find hardest to explain. To a large extent wars

reflect nothing of individual feeling towards members of another

lCf. Mouy. Le Dtveloppement de la Physique Cartdsienne 1646-1712 (p. 197).

PLATE V

Louis XIV at a Meeting of the Academic

THE LIFE OF CHRISTIAN HUYGENS 6l

nation and in those days the instruments of propaganda necessary for whipping up appropriate hatreds did not exist. Nevertheless, in the shifting scene of the wars of Holland, now against England with France as ally, now against France, then against both, and later with England as an ally, the opposition to Louis XIV really remained the one permanent feature. Louis was bent on destroying the Dutch Republic and, with the treacherous help of Charles II, it looked in 1672 as if he would succeed. Huygens could have secured a position of eminence under the Prince of Orange at this time but he had a deep repugnance for political activity and remained in Paris, suspected by some but protected throughout by the minister Colbert. It is not surprising, therefore, that he came in for some criticism by his fellow-countrymen. This criticism was brought to a head in 1673 by the eulogistic dedication of his great Horologium Oscillatorium to Louis XIV. The explanation of these facts seems to be that, once having yielded to the cordial friendship of his associates at the Academic Royale and having decided to endure the war, he had to pursue a difficult and always depress- ing course. The dedication may be regarded as a piece of political wisdom, as justifying his continued patronage, in fact. As a friend of the Dutch ambassador van Beunigen, who during the short war of 1667-8 was suspected of a plot against Louis, it would have been easy for him to come under suspicion as a spy. For Huygens was by no means remote from the world of affairs. He was very well known at court and had many influential friends. After the rise of Louvois and the death of Colbert none of these things mattered; the feelings of Louis towards the house of Orange can scarcely be said to have improved after 1678.

But in 1666 Huygens was indisputably the one who chiefly guided the affairs of the Academic Royale des Sciences. Profiting from his knowledge of the Royal Society, Huygens emphasized in Paris the importance of Bacon's teaching. " Experiment and observation/' he wrote, " provide the only way of arriving at the knowledge of the causes of all that one sees in Nature." This attitude is the more striking when one reflects that Descartes had so long been his model. The point here is that while both Bacon and Descartes distrusted formal logic, Descartes scorned empiricism while Bacon apprehended its power. It is not clear that Huygens realized the shortcomings of Bacon's " method ". The great omission in Bacon's scheme of research was the recog-

62 THE LIFE OF CHRISTIAN HUYCENS

nition that measurements provide the key to the understanding of phenomena. Bacon ranged himself with Aristotle in saying classify when he should have said measure.

The attention paid to Chemistry should, in Huygens's view, be restricted to essential problems. He appears to have recognized that the old alchemy was decadent and that the beginnings of a true science lay in the work of Boyle and others. Problems such as that of combustion were obviously worth the closest study. Huygens was interested in Hooke's experiments at the Royal Society which, he held, agreed with the " bizarre hypo- thesis " of an " aerial saltpetre ". This hypothesis of an active constituent in the air he considered was " not ill conceived " but he tended towards Moray's empiricism. " We others/' wrote the latter, " look for the truth of existence and the nature of things as belongs to the true philosophy ".

There can be no doubt of the influence of the London group on Huygens 's views of the functions of the new Academy. This influence abroad was recognized by the English themselves, who were fully conscious of the unique importance of their work. " I hope our Society will in time ferment all Europe at least," wrote Oldenburg to Boyle. " Let envy snarl," he wrote, when the new societies excited opposition, " it cannot stop the wheels of active philosophy in no part of the known world."

The Academic at first made astronomy its special study, en- couraged, no doubt, by the occurrence of a partial eclipse of the sun in 1666. Huygens noted with dissatisfaction the paucity of astronomical observations in earlier years and this was to be remedied. New observatories were in the course of construction at Greenwich and Paris; Hevelius at Danzig had for some years applied himself to completing Tycho Brahe's observations and had, in 1661, made with Boulliau careful observations of a solar eclipse. In 1666 more was expected from eclipse observations, namely, to rectify the motion of the earth and the moon and to determine differences of meridian on the earth. In the course of the work, several telescopes were compared and micrometers were used for obtaining the relative diameters of the moon and sun.

In continuing his work on lenses at Paris, Huygens was hin- dered by the poor quality of the French glass, which was inferior to the Venetian. The material showed veins or striae and tended to extrude salts on cooling. Lens-making brought Huygens into contact with the work of Spinoza, who had then a greater reputa-

THE LIFE OF CHRISTIAN HUYGENS 63

tion as a lens-grinder than as a philosopher. Lenses were ground by hand in a hollow form or mould in which abrasives of increas- ing fineness were successively used. It was the impossibility of grinding any but small lenses in this way that put a limit to the power of telescopes. The appearance of colours in the image was considered by Huygens to be connected with the inclination of the lens surfaces. The error in this was recognized by Newton some years later but in the meantime a great deal of work was expended in the attempt to make lenses of other than spherical curvature.

Astronomy in Paris gained very greatly by the arrival of Cassini in 1669. His first observations were made at the new observatory in 1671. Here he continued his striking work on the rotation of certain of the planets. Huygens had observed the rotation of Mars in 1659 ^ut» true to his device, had not con- sidered the results sufficiently good for publication. Cassini was rewarded by the discovery of four satellites of Saturn and the division in Saturn's ring which is now known by his name.

Huygens was not a competitor with Cassini for the honours of new astronomical discoveries. After 1666 his interests lay more in the direction of terrestrial mechanics and, as the sequel shows, this preference was sound. " I am now starting experiments on circular motion," he told his brother in 1667. A few years later, when Richer's expedition to Cayenne returned to Paris it brought back interesting evidence which bore on the question of the earth's gravity, but the effect of circular motion of a medium was the question which at this time interested Huygens, for it was through this that he hoped for an explanation. In taking up the effects of rotation, Huygens was, from one standpoint, return- ing to work which he had put away ten years before. By 1659,

v2 it is thought, he had arrived at the expression — for the

acceleration towards the centre in the case of a body describing a circular path. In 1669, however, he chose to address the Academic Royale not on this but on an elaborate theory employing the vortex of subtle matter as the cause of gravity. Any easy con- victions we may have that Huygens had by this time rid himself of Cartesian influences must be profoundly shaken by a perusal of this discussion. The opposition with which his theory was greeted by Mariotte and Roberval on this occasion may have been highly beneficial, for the criticisms they made

64 THE LIFE OF CHRISTIAN HUYGENS

were entirely justified. It may be mentioned in passing that Huygens at this time believed that circular motion is a funda- mental form. Uniform rectilinear motion, he saw, had no effects on events which normally occur in an apparently stationary environment. Circular motion, howfever, introduced new effects. It was only after the appearance of Newton's Principia that Huygens retracted this statement of the absolute nature of circular motion. He then, more consistently, took a firm stand on the relative nature of all motion — and against the idea of any absolute space.

Mariotte was a French priest who joined the Academic Royale in the year of its foundation and thereafter played an important part. He must be reckoned among the lesser lights who at this time were attempting to make the important next step beyond the mechanics of Galileo. His TraiU de la percussion ou choc des corps (1677) shows that he and Huygens were work- ing on similar problems. When Oldenburg approached Huygens in 1668 with a request that he should contribute to the Royal Society some work on mechanics he replied by sending some work on impact. This, afterwards published in the posthumous Tractatus de Motu Corporum ex Percussions (1703), is really a study of various applications of the law of conservation of momentum. There can be no doubt that Newton profited from the work on impact which was carried out by Huygens, Mariotte, Wallis and Wren. The formulation of his relation between rate of change of momentum and external impressed force completed in a magnificent way this contemporary work. In regard to centri- fugal force Huygens forestalled Newton by many years. " What Mr. Huygens has published since about centrifbgal force I sup pose he had before me," wrote Newton with some chagrin.

The immediate result of the correspondence with Oldenburg was that Huygens learnt that Wren and Wallis had both com- municated papers on the subject of impact and momentum and at practically the same time as his own. More instances were to come in which Huygens felt himself to have been unfairly fore- stalled in publication and in some cases he gave vent to severe criticisms which were by no means justified. Oldenburg showed great fairness and removed much oif this feeling of resentment, but the outbreak of some acrimonious correspondence over some mathematical work by James Gregory shows that Huygens had become unduly nervous for his reputation. When Mercator put

THE LIFE OF CHRISTIAN HUYGENS 65

forward a method of determining longitude by means of a pen- dulum clock he roundly condemned his intrusion. It was for- tunate that when Barrow's Lectiones Opticae came out in 1669 it was evident that the work did not overlap with Huygens's pro- longed researches in optics. Huygens was surprisingly slow to learn the consequences of his own attitude towards publication.

It was not customary in those days to isolate a particular problem and to study it exclusively for a considerable time. The seventeenth century men of science were nearly all capable of turning their attention to a wide range of subjects and they fre- quently were engaged on a variety of topics. Huygens indeed must be considered one of the most versatile men of the age, for he excelled Hooke in the quantitive nature of his work while at the same time he showed as wide a range of activity. Hooke's Micfogrophia stimulated Huygens at this time to attack the problems of constructing microscopes, employing the theoretical advances he had achieved in his work on the telescope. Spinoza was interested in similar problems. Galileo was described as having constructed " an occhiale which magnifies ... so that one sees a fly as large as a hen ". This was a compound microscope. Hooke improved the instrument as regards its mounting and the illumination used. Optical improvements were seriously needed. Huygens's own microscopic observations will be mentioned later; they belong to the years after his translation of Leeuwenhoek's work into French in 1677 or 1678.

As has been mentioned, Huygens's health was never robust. From early youth he was from time to time subject to a certain kind of debility, later accompanied by severe headaches. The illness of 1670 brought about his complete prostration in Paris and he clearly believed himself to be at the point of death. In these circumstances he concluded that he should bequeath his more important unpublished work in mechanics to someone capable of appreciating its importance and he decided to send it to London in the hands of Francis Vernon, secretary to the Eng- lish ambassador. This action is sufficiently interesting in view of Huygens's official position in Paris for Vernon's account to be given at length. In a letter to Oldenburg he described Huygens's condition "... I saw the condition hee was in which was none of the most lively, that his weaknesse & palenesse did sufficiently declare how great a destruction his sicknesse had wrought in his health and vigour & that though all was bad, which I saw, yet

£

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there was something worse which the eye could not perceive nor sense discover, which was a great dejection in his vital spirits, an incredible want of sleep, which neither hee, nor those who coun- celd and assisted him in his sicknesse knew how to remedie & that hee did not know what the end of these things would bee, butt his fancy was ready to suggest the worst ..." This mood Vernon did his best to dispel. He accepted his mission to England should the worst befall. Then, he wrote, " hee fell into a discourse concerning the Royal Society in England wich hee said was an assembly of the Choicest Witts in Christendome & of the finest Parts: hee said hee chose rather to depositt those little labours of his which God had blest and those pledges which to him were dearest of anything in this world, in their hands sooner than in any else. Sooner then of those into whose Society hee was here incorporated & from whom hee had received all demonstrations of a most affectionate civilitie because hee judged the Seat of Science to bee fixed there & that the members of it did embrace & promote Philosophy not for interest, not through ambition or a vanity of excelling others not through fancy or a variable curiosity, butt out of naturall principles of generosity, inclina- tion to Learning & a sincere Respect and love for the truth. . . . Whereas hee said hee did foresee the dissolution .of this academic because it was mixt with tinctures of Envy because it was sup- ported upon suppositions of proffitt because it wholly depended upon the Humour of a Prince & the favour of a minister, either of wich coming toe relent in their Passions the whole frame & Project of their assembly cometh to Perdition/'

It is clear that so early as 1670 differences had arisen between Huygens and certain members of the Paris Academy. This fact will be of interest later when the circumstances of the rupture of his official connection are considered.

Huygens's illness lasted in acute form for several weeks during which great anxiety was felt by his friends in Paris and London. In June there were signs of recovery and three months later the convalescent was able to return to the Hague. In October he resumed correspondence with Oldenburg.

XI

Apart from this winter in Holland, 1670-71, the five years from 1670 to 1675 were spent by Huygens in Paris. And they were stirring years in the scientific world. Huygens as chief of the

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Paris Academic was at the centre of things on the Continent, while he was well informed of what passed in England. In 167 1 Picard's M&ure de la Terre came out, a work of interest from the technical aspect as well as for a general discussion of current theories concerning the shape of the earth. Picard, for example, was well aware in 1671 that the length of a seconds pendulum was different at London, Lyons and Boulogne, but while he admitted that the results might be in conformity with the rota- tion of the earth, he did not think there was sufficient confirma- tion of the results, as yet, to justify any conclusion. Very probably he was acquainted with the notion of centrifugal force through his relationship with Huygens, for the latter had arrived at his important theorems as early as 1659. I*1 lfy* news came from England of Newton's work on the solar spectrum; from Holland in the same year came interesting mathematical work by Slusius on the drawing of tangents to curves. 1673 was the year of Huy- gens's Horologium Oscillatorium, his magnum opus. In 1674 Hooke issued a work giving his views on evidence for the motion of the earth.

During this period Huygens worked with Denis Papin on the use of gunpowder as a source of useful energy, and, more important, with Leibnitz at Mathematics. In 1675 Leibnitz brought out his calculus differentialis. And to these busy years belong also the invention of the spiral-spring regulator and balance wheel which are essential parts of the watch and chrono- meter.

Yet they were not altogether happy years for Huygens. After the invasion of the Low Countries, by the armies of Louis XIV in 1672, he may frequently have asked himself why he had re- turned to Paris in 1671, and immersed himself in work as the only outlet for his despair at his situation. Huygens felt keenly the wrong done to his country and it required much tact and consideration from his friends in Paris to preserve the calm rela- tionship in which he had been accustomed to live. Huygens followed the course of the war with anxiety, but it must be remembered that at forty-three he was by upbringing and experi- ence almost as much a citizen of the French capital as he was of Holland. Paris was indeed the centre of the cultivated world and the prospects for the man of science who should be cut off from the activity of one or other of the two flourishing societies would be poor indeed.

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Huygens seems to have worked even when quite ill; certainly he was struggling to regain his old activity in October 1670 when he received some interesting work on mechanics from Wallis. Yet he agreed that his recovery (" for which I thank God ") was too recent for him to do other than attempt very little.

We shall see that Huygens's work in theoretical optics, for example, rivals that in mechanics, but in 1670 he considered the latter subject more important. Though overlooked nowadays, the ideas he contributed to mechanics were as fundamental as his contributions to physical optics. His Horologium Oscilla- torium was practically completed and had grown from a treatise on the construction and regulation of the clock to a work on centres of oscillation, the tautochrone, the theory of evolutes and centrifugal force. As an examination of this treatise will show, it contains a great deal which was made more explicit in Newton's Principia (1687) although discovered by Huygens independently. The law known as Newton's First Law was known and used by Galileo and Huygens; Huygens, in addition, must have employed the Second Law in arriving at his propositions on centrifugal force as early as 1659. He also saw the necessity of distinguishing between mass and weight at about the same time (see p. 119). The greater merit of Newton's work, in fact, was that he gave a clearer presentation of these ideas and made them more useful by means of simple mathematical relations.

When the Horologium Oscillatorium came out in 1673, after Huygens's return to Paris, it showed the extent to which his thought had developed. The work was singularly free from Car- tesian influences. Huygens himself hoped that it would be in direct line with the great work of Galileo and his hopes were not disappointed. Newton wrote to Oldenburg of his " great satis- faction " with the work and said he found it " full of very subtile and usefull speculations very worthy of ye Author ". Newton especially admired Huygens's mathematical style and con- sidered him the " most elegant writer of modern times ". This remark starts some interesting reflections. Newton regretted that he had not applied himself to geometry before proceeding to algebraic analysis. It was Huygens's predominantly geometrical methods, employed in the Horologium Oscillatorium, which aroused his admiration. At this time Newton was well advanced in his work on fluxions and, as w-e know, Leibnitz took up similar

THE LIFE OF CHRISTIAN HUYGENS 69

problems after 1672. The central idea of the differential calculus owes a great deal to the study of motion, for this study intro- duced the notion of a continuously varying quantity. Huygens 's work in this connection was of the greatest importance for, as Leibnitz admitted, it was Huygens who had dispelled the rnys tery attaching to the study of motion.

The two mathematicians, Huygens and Leibnitz, met in Paris in 1672 and Leibnitz became a regular visitor at the Bibliotheque du Roi. Under Huygens's guidance Leibnitz's ideas developed rapidly, for up to this date, as he himself admitted, he had been only an amateur in such studies. In 1674 Huygens was able to present to the Academic Royale Leibnitz's first paper on the differential calculus. Whether Huygens gave Leibnitz an inkling of Newton's work on fluxions will always remain an in- teresting speculation. Newton's own ideas date from about 1665 or 1666 and there is no doubt that after 1669 these were well known to his friends in England. Wallis especially must have known about them. Huygens himself was not happy in the use of analytical methods. He was, in Newton's words, " the most just imitator of the ancients " and it is a striking fact that the classical geometrical method was used by Newton himself in writing the Principia. This fact, which has always troubled historians in some degree, must be explained by the prestige of Huygens at this time and the fact that proofs by the newer methods were not everywhere accepted. The ideas of both the Principia and the Horolofnum Oscillatorium were later cast in analytical form by the mathematicians of the eighteenth century.

The Horologium Oscillatorium made a great impression on contemporary men of science. The propositions on centrifugal force, given at the end, were of course important in the develop- ment of planetary theory, and the conical pendulum interested those who, like Hooke, concerned themselves with the problem of time measurement. It is certain that Huygens employed the conical pendulum in clocks in 1659 and again in 1667, when he had more fully investigated the laws of motion involved. Con- troverting Hooke's claims to the invention of such a clock, he pointed out, what Hooke certainly did not know, that the conical pendulum should be so designed that all revolutions of the bob describe horizontal circles in the surface of a paraboloid of revolu- tion with the axis vertical. Only then would all revolutions be isochronous.

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Huygens showed considerable dislike for quarrels such as the one of 1674 in which he became involved with Hooke and others. In 1675 he had yet another such experience. This was over his invention of the first successful spring regulator for the clock. Huygens's design of a spiral spring combined with a balance wheel is the one which is still used in watches and its distinction lies in the fact that the centre of gravity of the oscillating part bears a fixed relation to the stationary parts. This meant that the influence of gravity was eliminated. A quarrel with the clock- maker Thuret and the Abbe de Hautefeuille was settled by the Academic Royale on these grounds in Huygens's favour, for Hautefeuille used a straight spring and not a spiral. Hooke was, however, a more tedious antagonist in connection with the same invention and he was made more bitter by the support given by some members of the Royal Society for Huygens's priority. "Zulichem's spring not worth a farthing," he wrote in his diary. When Huygens, for a quiet life, gave Oldenburg the rights to the English patent, he drew from Hooke a full and free ex- pression of his long dislike of the secretary. Oldenburg, he averred, was Huygens's spy. " Saw the Lying Dog Oldenburg's Transactions," he noted eight months later, " Resolved to quit all employment and to seek my health." Oldenburg, he said angrily, was a "trafficker in intelligence". He would hear nothing favour- able about Huygens's marine clocks. " Seamen knew their way already to any Port," he somewhat childishly stated. Altogether the complaints of Hooke appeared in print over a considerable period tut they hold little interest now.

A more famous result of Huygens's correspondence with the English scientists during his years in Paris was that the French became aware in 1672 for the first time of the work of Newton. On January 1 1 of that year Oldenburg wrote to Huygens of the " invention of a new sort of telescope by Monsieur Isaac Newton, Professor of Mathematics at Cambridge ". His next letter gave a full description and this was utilized by Huygens for an account published in the Journal des Savants of the following month. It should be mentioned that Gregory's design for a reflecting tele- scope was never put into practice and the new invention was based on his ideas. Huygens found it *' beautiful and ingenious " and he thanked Oldenburg for the news of " the marvellous tele- scope of Monsieur Newton ". The problem of making the con- cave mirror, though difficult, did not appear to be insuperable.

THE LIFE OF CHRISTIAN HUYGENS 71

He supposed that Newton had come to despair, as he had him- self, of overcoming spherical aberration but did not refer to the fact that it was this consideration which had led Gregory to his idea nine years before. Up to this date Huygens had not heard of Newton's experiments on the composition of white light and certainly underestimated the defect of chromaticism.

It is consequently surprising, after this initial enthusiasm, to find that Huygens soon abandoned the reflecting telescope. The trials which he himself immediately carried out proved dis- appointing owing to the imperfect polish given to the mirror. Newton's first telescope was hardly more than a model and when the construction of larger telescopes was attempted in England, the most expert glass worker in London, Cox, found the task of grinding the mirrors too difficult. Reflecting telescopes of a large and useful size were in fact not made for more than fifty years. Huygens found that metal jnirrors were unsuitable since the polish was unequal to that given to glass and it was not perman- ent. He found himself compelled to return to the refracting tele- scope but realizing that a new difficulty beside that of spherical aberration now required to be overcome.

For in March 1672 Oldenburg sent Huygens a copy of the Philosophical Transactions in which, he said, Huygens would find " a new theory of Monsieur Newton (the inventor of the cata-dioptric telescope) touching light and colours : where he maintains that light is not uniform but a mixture of rays of different refrangibility, as you will see fully in the same dis- course. . . " This copy of the Transactions contained, of course, an account of Newton's famous experiment on the spectrum. The Royal Society, on receipt of this, Newton's first published scientific paper, sent it to Huygens as the one whose opinions would carry the most weight. Huygens's reply was that the con- clusions drawn and the theory put forward seemed "very ingenious ". But, he went on, " it must be seen if it is compatible with all the experiments ". Three months later he wrote that he considered the compound nature of white light had been proved by Newton's experimcntum crucis, in which it was shown that the separate coloured rays emerging from the prism could not be further decompounded. Huygens went on, however, to make observations which disappoint the modern reader almost as much as they disappointed the young Newton. He questioned if it would not suffice to base an explanation " on the nature of move-

72 THE LIFE OF CHUISTIAN HUYGENS

ment " for the two colours yellow and blue only. Until the essential difference of these two colours was understood " he [Newton] will not have taught us what the nature and difference of colours consists of, but only this accident (which assuredly is very considerable) of their different refrangibility ". Failing to see the distinction between an impression of colour and the different rays of the spectrum, Huygens suggested that Newton would find that yellow and blue would be sufficient to produce white light. The other colours he regarded as " degrees of yellow and blue more or less deep ".

These criticisms were an easy prey to Newton who, far from rushing prematurely into publication, had kept the work by him for at least five years. Oldenburg warned Huygens that Newton, then thirty, was not a man who spoke lightly about anything he advanced. Newton flatly denied that all colours could be " de- rived out of the Yellow and Blew . . . none of all those colours which I defined to be Original " could be so obtained. " Nor is it easier,." he insisted, " to frame an Hypothesis by assuming only two Original colours rather than an indefinit variety; unless it be easier to suppose, that there are but two figures, sizes and de- grees of velocity or force of the ^Ethereal corpuscles or pulses, rather than indefinit variety; which certainly would be a harsh supposition." It would be indeed, he remarked, " a very puzzling phenomenon ", "... But to examine how Colors may be ex- plained hy pot helically is besides my purpose. I never intended to shew, wherein consists the Nature and Difference of colors, but only to shew, that de facto they are Original and Immutable qualities of the Rays which exhibit them; and to leave it to others to explicate by Mechanical Hypotheses the Nature and Difference of those qualities: which I take to be no difficult matter ". It was unimportant if two colours in the spectrum could be combined to give an appearance of white. Such light was different in its physical nature from ordinary white light and could not be resolved by the prism into more than the two components. Clearly Newton was deeply disappointed, at the outset of his career, to receive so little appreciation of the true nature of this work from one so eminent as Huygens. He wished, he said, in future " to be no further solicitous about matters of Philosophy ". His rather summary answers to Huy- gens's remarks disposed at the same time of certain criticisms put forward by Hooke. For once Huygens and Hooke were in

THE LIFE OF CHRISTIAN HUYGENS 73

alliance, both opposed to what was essentially a new attitude to scientific problems; both, moreover, found the new facts difficult to reconcile with their respective wave or pulse theories of light. This first occasion for the comparison of Huy- gens and Newton raises, it will be seen, a question on which these two men of science consistently differed. This was the place of hypothesis in scientific method, a subject for which a later chap- ter must be reserved.

It is unfortunate that the two greatest scientists of this period did not achieve harmony in their attitude to problems of com- mon interest. For their divergence was not particularly fruitful although it extended from optics into the realm of mechanics. Huygens greatly admired the Principia after its appearance in 1687 and he met Newton in 1689. By rhis time, however, the dif- ference of outlook had become too ingrained and Huygens at sixty had become less amenable to new persuasions. And yet this difference is certainly not so great as some writers have sug- gested. One biographer of Newton, Louis Trenchard More, con- siders that men like Hooke and Huygens relied on an inward sentiment of knowledge and in opposing Newton " were merely opposing theory by hypothesis ". Whatever the significance of this distinction, this is a question which can be dealt with only after a careful survey of Huygens's work as a whole. It will be seen that it is a profound mistake to treat Huygens as merely another Cartesian, for all his life he vacillated between the Car- tesian view that the objects of scientific calculation are products of thought and the materialism which regards them as external realities. Not only is there much to say in Huygens's favour with regard to the status of scientific concepts, but in methodology also Huygens perceived as well as Newton the end of scientific investigation. " I do not believe we know anything with com- plete certainty," he wrote to Perrault, " but everything probably and to different degrees of probability ... as 100,000 to i as in geometrical demonstrations/* The latter he considered were in a category by themselves. " In the matter of Physics there are no certain demonstrations and one can only know causes through the effects in making suppositions founded on experiments or known phenomena and trying afterwards if other effects agree with these same suppositions." These remarks should make clear the difference between Huygens and Descartes. For Descartes the intuitional method, to which More refers, did undoubtedly

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take precedence over the experimental. For Huygens, a life-long experimentalist, there was no way to final certainty.

In the period we are considering Huygens continued his studies in optics but it is difficult to estimate his progress. This work began as early as 1652. By 1653 he had completed a first Tractatus de refractione et telescopiis of 108 pages. This was sub- sequently amplified but remained unpublished. As Huygens found, Cavalieri had independently obtained some of his results and published them in the Exercitationes Geometrical Sex. The only other previous writers of originality were Alhazen (nth century) and Kepler, whose Paralipomena was published in 1604 and Dioptrice in 161 i . In England the most important work was done by Barrow and by Halley. The latter drew attention to the advantages of algebraic formulae; up to this time the relations used in optics were expressed in the most cumbersome geometri- cal form. Many of the problems to which Alhazen had given prominence were definitely geometrical in character and these continued to be studied. A new interest was injected into these somewhat academic studies by Bartholinus's discovery of double refraction in i66g. This was described in a short Latin treatise, Experiinenta Cryslalli Islandici Disdiaclastici . . . , which was widely read. Huygens obtained a specimen of Iceland Spar and a considerable part of his Traite de la Lumiere, completed in 1678 (published 1690), deals with experiments he then carried out. Huygens had developed a pulse theory of light and the effort he made to reconcile his theory with the new and peculiar optical properties of Iceland Spar was a masterly one. Curiously enough there is little reference to this work in his correspondence.

About this time Huygens had as his assistant Denis Papin, a Frenchman who later worked with Boyle in England. With Papin, Huygens in 1673 experimented on gunpowder as a source of mechanical energy. There is a possibility that Huygens had considered some kind of atmospheric engine as early as 1660 when he talked with Pascal about " the force of water rarefied in cannons ". In thfcse experiments of 1673 we can see the fore- runner of Papin's atmospheric engine, which did in fact employ steam in place of gunpowder. Papin was later, through the in- terest of the Landgrave of Hesse, appointed professor at the university of Marbourg and it was here that he developed the atmospheric engine which gave Newcomen his clue.

In exchange for Papin, as one might say, Oldenburg sent over

THE LIFE OF CHRISTIAN HUYGENS 75

to Huygcns the wealthy young amateur Walter von Tschirn- haus, a friend of Spinoza and Leibnitz. He belonged to a class which had early supported the new scientific societies but he was exceptional in that his interest in science did not quickly flag and in that he made himself something more than a mere dilettante. Through Tschirnhaus Huygens undoubtedly learned more of Spinoza's philosophical ideas but he showed himself little inter- ested in them. Unlike many of the seventeenth century men of science Huygens did not occupy himself with philosophical or theological questions and neither he nor Leibnitz seems fully to have grasped the nature of Spinoza's thought.

XII

Early in 1676 Huygens was again ill. There is no doubt that the illness of 1670 had recurred and this time he showed greater caution in meeting the danger. In March 1676 he set out to return home to the Hague while he was yet able, but the journey was slow and very uncomfortable. To his brother he confessed his doubts whether he would return to a life in Paris which seemed to be injurious, and even when he had recovered, a year later, he procrastinated under the pretext of uncertain health. Colbert gave permission for his remaining at the Hague for the winter of 1677-78 and the return journey to Paris took place in June 1678.

During these two years at home he pushed on with his re- searches. To these years belongs a great deal of work on the double refraction of Iceland Spar and the development of his wave theory of light. On November 122, 1676, Roemer read a paper to the Academic Roy ale in which he gave the first calcula- tion of the velocity of light. Huygens was immediately interested on receiving a copy of the paper and an interesting cor- respondence with Roemer was begun. The assumption that light travelled with a finite speed was fundamental in Huygens's work and on this assumption, he wrote to Colbert, he had " demon- strated the properties of refraction and, a little while since, that of Iceland crystal which is no small marvel of nature nor one which it is easy to understand ". It was consequently gratifying that this assumption should receive confirmation and that the speed of light should be approximately known. There was some similarity of outlook between Roemer and Huygens for Roemer supposed, like Huygens, that the passage of light through cry*

76 THE LIFE OF CHRISTIAN HUYGENS

tals (thrown into prominence by the Iceland Spar phenomena) was analogous to the transmission of impulses through con- tiguous spheres. The explanation of double refraction along these lines would, he considered, establish the truth of the theory of light which for some years had been associated with Huy gens'? name.

It is well known that Huygens was led to his theory of trans- mission of light through his work on impact. The transmission of longitudinal, compressional, vibrations through perfectly elastic spheres seemed to him to have applications in light, since crystals and other transparent media might be supposed to be composed of assemblages of atoms. And even though he was unable to suppose the atoms of the elements were the actual medium — since all substances are not transparent — he found a mechanism which reduced light to a form of motion and brought it within the treatment of the " true Philosophy ". In this philo- sophy " one conceives the causes of all material effects in terms of mechanical motions. This, in my opinion, we must necessar- ily do, or else renounce all hopes of ever comprehending any- thing in Physics/1 This quotation is taken from the beginning of Huygens's Traite de la Lumiere. To explain the transmission of light through the Torricellian space and all manner of trans- parent substances, however, some pervading subtle medium was assumed. We must remember that Huygens was led to conclude that such a medium existed from his vacuum experiments. The ether was, however, not a continuous medium but was composed of very light particles in contact. These, on impact with the heavy vibrating atoms of incandescent bodies, transmitted their vibrations in all directions according to the laws of impact. The elasticity of air, Huygens thought, " seems to show " that it is made up of particles which are " agitated very rapidly in the ethereal matter composed of much smaller parts ". It was im- portant that slight impulses travelled as fast as strong ones, a fact which was readily explained by applying Hooke's law of elasticity to the particles of ether. Also, individual wave- lets by themselves were too weak to produce effects of light, which only arose when the wavelets combined to form a wave- front according to the well-known Huygens construction now given in all text-books on light.

Huygens's theory is better described as a pulse theory rather than a wave theory but in the Traite he made the remark that

THE LIFE OF CHRISTIAN HUYGENS 77

the vibratory motion "... is successive and . . . spreads as sound does, by spherical surfaces and waves ", Hooke developed a wave theory also — largely in relation to his observations of colours produced by thin films. The difference between his ideas and those of Huygens was mainly that Hooke did not consider the formation of a wave-front by the innumerable individual wavelets.

Not all scientists, however, were prepared to accept Roemer's estimate of the velocity of light. Descartes had been so con- vinced of the instantaneous transmission of light that he un- wisely said he would stake all his system of philosophy on its truth. Unlike Huygens there were many who remained under his spell. In the Traite, therefore, Huygens went to some pains to demonstrate the error of Descartes's reasoning. Cassini was opposed to Roemer's explanation of the apparent advance and retardation of the occultations of Jupiter's satellite, but mainly because only the innermost satellite had been studied. When the Academic had to decide on the dispute which arose over the work they came to the conclusion that Roemer was right; as he explained, the occultations of the outer satellites were less fre- quent and less sharply observable for obvious reasons. While the method he had put forward was the best one available for finding the velocity of light, he hoped that surface marks on Jupiter would prove of use, and later in the year observation of a spot on the planet gave the period of revolution of the planet on its axis. Observation of this spot could then be relied on in place of occultations for measurement of the velocity of light. Clearly Roemer was a man of the same outlook and ingenuity as Huy- gens. At the time when Huygens was at the Hague, Roemer was attempting to determine what effect the motion of the earth should have on the apparent positions of the heavenly bodies when this motion was transverse to the direction of the light rays. It scarcely matters that Roemer conceived the problem in terms of the Cartesian vortices; the point was that the circular motion of the terrestrial vortex should produce an apparent cur- vature of the path of light. In its modern form the problem was propounded and explained by Bradley, who discovered the effect of " aberration" in 1728.

Huygens made the journey back to Paris in the middle of the summer of 1678. With him went Nicholas Hartsoeker, later known as a maker of lenses. Once more Huygens settled down to

78 THE LIFE OF CHRISTIAN HUYGENS

his old occupations. The period to which we have come was, unhappily, one during which he was not for long well. He was ill again in 1679 and although he recovered he was compelled again to return to the Hague in 168 1 . From this last convalescence he never returned to Paris. We are consequently faced with the fact that this was Huygens's last stay in Paris, and one which was seriously interrupted by illness.

Curiously enough, in view of the swift reverse which was in store, Huygens's prestige seems never to have been higher than it was at this time. It is clear that he was widely regarded as in a real sense the head of the Academic Royale des Sciences, the position of which seemed even more assured than that of the Royal Society at this time. The Royal Society in fact suffered from the political upheavals of the time and from the defection of some of its members. 1678 was the year of the Popish Plot, which, according to Titus Dates, aimed at the conquest of the kingdom by the Jesuits. As late as November it was held that " there hath been and still is a damnable and hellish plot, con- trived and carried on by popish recusants, for the assassinating and murdering of the King and rooting out and destroying the Protestant religion ". With the death of Oldenburg in this year, Huygens's relations with the society were practically at an end. The Academic Royale had on the other hand increased in vigour after its slow development in the first few years. Thanks to Colbert, Huygens and Auzout had been able to equip the Academic with all the laboratory and astronomical apparatus required and each year saw improvements in scientific technique. The society had begun to undertake enterprises such as the ex- pedition of Richer to Cayenne in 1672 and this had led to impor- tant information concerning the shape of the earth.

Nevertheless, in France as in England there were jealous opponents of the new learning. The universities always feared an undermining of their authority if the scientific societies be- came too strong or too serious in their tasks, the Jesuits wished to have a monopoly of the new knowledge, and there were some who stirred the popular mind against investigations which seemed to a less and less degree to aim at the production of new inventions or the amelioration of life. In France, Paul Pelisson, who was writing a history of Louis's reign, gave Huygens space to deal with current criticisms and to enlighten the public on the aims and work of the Academic.

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In this review Huygens limited himself to the particular field in which he was an authority. He began by alluding to the need of astronomical studies and the great importance of the new observatory. The use of pendulum clocks and improved tele- scopes had made possible observations incomparably more exact and more easy than they were in the time of Tycho Brahe. The discovery of new stars, the confirmation of the ring of Saturn and the discovery of its satellites, a full study of the moon's surface and the description of comets and sunspots were among modern achievements. The discovery and measurement of the velocity of light were adduced as a consequence of such observations. Nor was such work without practical value : the occultations of Jupiter's satellites provided a method of determining longitudes, a problem for which the pendulum clocks might soon provide a better answer. The great appeal of the work of the Academic, however, lay in the steady expansion of man's knowledge and understand- ing of the world. Expeditions had been sent to Cayenne and to Hveen; more exact star catalogues and ephemerides were to be prepared so that the theories of the universe might accord more exactly with observation. The Earth itself had been made the object of scientific measurement. Geometry had been applied " in the study of causes in the field of Physics, it being accepted by almost all philosophers of today that the figure and movement of the corpuscles of which everything is composed are alone re- sponsible for all the wonderful effects which we see in nature ". This is really a statement of the new mechanistic philosophy to which the physical researches of the men of science had led. The world had come more and more to be regarded as a perfect machine and, says Burtt1, "first in Huygens and (in a more philo- sophical form) in Leibnitz we have this opinion unequivocally proclaimed ". Huygens clearly feared that this summary might seem to be written from the standpoint of the vortex theory of Descartes and he went on: " which opinion having been greatly supported through the philosophy of Descartes, they neverthe- less adhere neither to his sentiments nor to those of any other philosopher in order to gain authority ". Descartes, he pointed out, was mistaken in many things through lack of experiment and in particular he had sacrificed the accurate definitions of con- cepts which Galileo had begun to clarify. Truer ideas were now held regarding motion and force and momentum, the nature of

1E. Burtt: The Metaphysical Foundations of Modern Science (193*).

8o THE LIFE OF CHRISTIAN HUYCENS

meteors and other celestial phenomena, and the nature and effects of light. Microscopes, telescopes, the air pump and many other machines had been brought into use and had extended man's knowledge and led to the advancement of the sciences.

Nevertheless, while Huygens was an enthusiast for the new world of the seventeenth century science, he displayed caution in comparing his own age with that of classical antiquity. His friend Charles Perrault frankly regarded the seventeenth cen- tury as superior to all other ages and considered Huygens him- self an example of this superiority. To such praise and to that of the younger Fermat, who compared him with Descartes, he returned a modest reply. " I am one of those who have profited from the wisdom of that great man," he wrote.

That Huygens was not everywhere so popular and that there were factions in the Academic at this time can scarcely be doubted. The eminence of Huygens, in whose honour a medal was struck in 1679, was not agreeable to Cassini and de la Hire and the latter is known to have led an opposition to the entry of all foreigners — and especially the friends of Huygens — into the academy. In France just as in England religious differences were being exploited for political ends. The greatest division within the Academic Royale seems to have resulted not from national- istic or religious partisanship but arose between members who, like the original Montmorians, were eminently followers of Des- cartes, and those who, like Huygens and Mariotte, showed an increasing scepticism towards the Cartesian system. In these cir- cumstances Huygens seems to have felt more affinity with men of science who were not involved in the dispute and with Leibnitz in particular there grew up an interesting correspondence.

It will be remembered that Leibnitz had studied mathematics with Huygens in 1672. During the subsequent years the German mathematician had pursued his researches along new paths. In 1676 he had been in correspondence with Newton about methods of expansion in series. Newton mentioned his binomial theorem and the method of fluxions but did not describe the latter, although he added some illustrations of its use. By 1675 Leibnitz was employing his own form of differential calculus but was un- able to involve Newton in discussing anything which might arouse controversy. Newton's method of fluxions was, in fact, not published until 1693. In correspondence with Huygens, Leib- nitz claimed to have developed the calculus into a method by

THE LIFE OF CHRISTIAN HUYGENS 8l

means of which he had successfully treated a variety of prob- lems. Huygens, however, would not abandon geometry for the differential calculus and never gained any facility in its use. Leib- nitz wrote at length also about the subject of symbolic logic, of which he was an originator, but his ideas were not appreciated by Huygens or anyone else at that time and they wer6 not taken up until the following century. Leibnitz was anxious to secure nomination to the Academic Royale as a foreign member but this Huygens seems to have been unable to obtain. Not until 1700 was Leibnitz — and in the same year Newton — admitted as a foreign member. It was in 1700 that Leibnitz organized the Berlin Academy of Sciences.

At the Academic Royale Huygens's chief activity at this time was the presentation of his work in geometrical optics in a series of lectures lasting from May to August. The whole sum- mer of 1679 was spent in editing the work of many years before and with special problems concerning Iceland spar. Much of the work on the optical properties of conic sections which comes at the end of the Traite de la Lumiere was completed about this time. Fermat's least-time principle, also, he succeeded in de- ducing for refraction on the assumption that light travels more slowly in glass or water than in air. As for Descartes, both Huygens and Leibnitz had scant regard for the greater part of his work in this field. His " pretence of a demonstration " of the laws of refraction was replaced by the well-known treatment which employs Huygens's secondary wavelets. Huygens's work in optics may in fact be regarded as standing in relation to previous studies by Kepler, Snell, Descartes, and Fermat much as Newton's mechanics stands in relation to the mechanics of Galileo and Huygens : Huygens achieved the same union of the physical and mathematical aspects of the subject. His mastery of geometry of course equipped him in a unique way for this task. The subject of colour was, however, left on one side; Huygens seems always to have held that a mathematical ex- planation of this was not possible. Nevertheless, he appreciated the practical outcome of Newton's work in this subject: the discovery of chromatic aberration of lenses showed, he saw, that this effect may be no less important in telescopes than spherical aberration. It followed that the search for the achromatic lens might be more profitable than the attempt to obtain lenses with non-spherical surfaces had been. He would probably have had to

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admit by this time that the idea of the reflecting telescope was by no means " extravagant ".

The interest aroused in microscopic work by Hooke's Micro- graphia and the translation from Dutch into French of Leeuwenhoek's work by Huygens about 1677 led many at this time to take up such studies. The whole world of infusoria awaited discovery. The imperfections of the compound micro- scope were still considerable, however, and Leeuwenhoek, as is well known, preferred to use a single lens of short focal length in his observations, which perhaps included the discovery of bac- teria. Huygens used very small lenses of glass, some of which he made hollow and filled with alcohol. Locke, who was in Paris in 1678, wrote to Boyle of the " extraordinary goodness " of Huygens's microscopes. In devising a mount for his very small lenses Huygens introduced a method of altering the intensity of illumination of the object. Later, in 1692, he introduced dark ground illumination. These were the contributions of a prac- tical microscopist. After 1676, in fact, Huygens was very interested in making observations of infusoria in rain water.

Ill-health no doubt accounts for a diminution of the mathe- matical and more abstract studies of Huygens after 1680. He left Paris at the end of the summer of this year for a short stay at Viry, where the country air restored him for a time. He returned to the capital in time to take part in observations of a comet and as a recreation started the construction of a planetary machine which would reproduce by means of clockwork the relative motions in the solar system. Early in 1681 he was again ill, but not until September was his return to Holland practicable.

XIII

The convalescence after this last illness was slow. Letters arrived bearing the good wishes of men of science in Paris and London. Even de la Hire, only recently elected but before long a prominent member of the Academic, sent the good wishes of " all the company ". It is evident from his letter that de la Hire hoped for the position which Huygens had left at least tempor- arily vacant; there is a strong presumption that he did in fact work hard to prevent Huygens from having much opportunity to return to Paris. Huygens for his part was at first in no hurry to leave Holland even when, in 1682, he had practically

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recovered. Later in the year the Dutch East Indies Company showed interest in the latest pattern of marine clock and this was a further incentive to remain. By taking up the summer of 1683, the work on the new marine clock really decided his future, for Colbert died in September of this year and without his patron's support the opposition to Huygens's return began to be really formidable. Not only this but the political horizon was dark with the uncertainties caused by the renewal of Louis's activities abroad. By 1686 the situation in Europe was not unlike that of 1673. The Revocation of the Edict of Nantes (1685) roused all Protestant countries. To Holland fled a large number of exiled Frenchmen. It was a time of rapidly diminishing free- dom in France and Huygens's experience well illustrates the fact. For when he renewed his application to return the appeal fell on deaf ears. Whether anti-Protestant feeling was the sole reason is not altogether clear. Huygens's friend Roemer left Paris a few months earlier, and it was four years later that the Edict was repealed. Quite as much as anti-Protestantism, probably, per- sonal jealousies spoiled the work of the Academie; the years after 1681 seem indeed to have been years of retrogression

It is a striking illustration of the hostility which the Cartesians had come to feel for Huygens at this time that the Abb£ Catelan should, nine years after the publication of the Horologium Oscillatorium, attack the fundamental principles employed by Huygens in his treatment of the compound pendulum. There is nothing of scientific interest in Catelan's criticisms and they were designed to discredit Huygens's work in the eyes of those who were comparatively ignorant of mathe matics and mechanics. The mathematician James Bernoulli came forward to champion Huygens's ideas in 1684.

In the middle of 1684 Huygens was visited by Thomas Molyneux, a contemporary and acquaintance of Flamsteed and Hooke. Molyneux wrote to his brother that he was received " extraordinarily civilly ". Huygens, he said, " beyond my ex- pectations talked to me in my own language, and pretty well ". He was shown Huygens's planetary machine which he decided was " nothing more than an ingenious curiosity " for, he said, " I asked him could he by help of it exactly determine an eclipse, and I observed that he could not give me a positive answer, as being loath to confess the imperfections of his contrivance to me that seemed to admire it so much as I did ". Huygens had in fact

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come to the end of his great period of scientific activity, but some profound ideas were yet to be developed. The news of the death of Picard (1682), who had done notable work at the Paris observatory, caused Huygens to ponder the uncertainty of life and to think of publishing the " many good and useful things which I have written or found, to complete which I desire only peace and the continuance of my health ". As events turned out his retirement held more of solitariness than he desired. The death of his father at a great age in 1687, and the departure of his brother Constantin for England in 1688, when William of Orange became King of England, left him alone in the isolated residence at Voorburg in the summer. The winters he spent at the Hague. In his letters he lamented the absence of any with whom he could discuss scientific topics. Owing to financial worries he began to consider the possibility of securing a position as counsellor to William III, but this only embarrassed the King, who perceived that Huygens had " higher ideas than to loiter with administrators ".

The idea of a position in England seems to have occurred to Huygens after a short visit to this country in 1689. He was in London from June to August of this year, but only brief records remain. He met Flamsteed at Greenwich and attended a meet- ing of the Royal Society at Gresham College. In company with Fatio de Duillier, a Swiss mathematician, he met Newton for the first time. Little is known about this or of another occasion when, in July, Huygens, de Duillier, and Newton travelled from Cambridge together on the occasion of Newton's application for the position of Provost of King's College. Huygens also met Boyle on several occasions and witnessed some chemical experi- ments. He left London with many regrets for the isolation in which he then lived.

It would, of course, be extremely interesting to know what discussions took place between Newton and Huygens on the occasions when they met. It is clear that in mechanics the two scientists held certain divergent views, notably on the subject of the conservation of energy and on the existence of absolute space and time. For Huygens, after reading the Principle, became strongly critical not only of Newton's postulate of universal gravity but also of his belief in the existence of absolute space and motion. He had early perceived that a body, moving uni- formly in a straight line with respect to one observer, might be

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accelerated with respect to another. And while he first made a distinction in favour of the absolute nature of motion in a circle which was accompanied by the existence of a centrifugal force, he abandoned this also after reading the Principia. This was in contrast with Newton's acceptance of an absolute space and time according to which all motion possessed an absolute character. Whether they discussed such differences of view and whether they compared notes on the subject of resisted motion and other matters in which they were both interested at this time is not known.

Over the question of the cause of gravitational attraction there was, of course, a complete divergence of view between Newton and Huygens, for while the latter speculated for some time on the subject it was one for which Newton felt no interest. Huygens went out of his way to expound his views in such a way that they would not give Newton any offence. He seems to have been a little nervous about Newton's reception of yet another hypothesis. It may be remarked here that Huygens's theory grew out of his work on the nature of light and was an attempt to explain gravity as due to the action of an ether or fluid matter which, owing to rotation, seeks to travel away from the centre and thus, as he thought, forces slower moving bodies together. Even at this time, however, the difficulties of such a theory were becoming clearer. A fluid which could permeate matter could scarcely exert a reaction on it and de Duillier, who had gone to England for the purpose of studying Newton's works, pointed out to Huygens that the absence of any apparent resistance to the motion of planets and comets argued that the ether must be excessively attenuated. As is now known, however, Newton was not so thoroughly opposed to the ether theory as was generally supposed. Although he condemned the idea (as expressed by Hooke) in 1675, he returned to the question in the " Queries " to his Optics.

The inverse-square law of gravitational force posed great difficulties for Huygens's mechanistic theories. It was, he said, " a new and very remarkable property of gravity of which it was very necessary to search out the reason ". He could not see that the cause could be given on the principles of mechanics or of the rules of motion. The view that gravity was an inherent property of matter, he said, "takes us very far from the principles of mathematics or mechanics ". Leibnitz also was

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against Newton's view of gravity as innate. If it was to be regarded as a " law of God who brings about this effect without using any intelligible means, then it is -a senseless occult property, which is so very occult that it can never be cleared up, even though a Spirit, not to say God himself, were endeavouring to explain it," he wrote to Hartsoeker.

The importance of Newton's work was not, however, lost on Huygens, who perceived that the Principia utterly destroyed the Cartesian vortices. Writing to Leibnitz about the elliptical orbits of the planets Huygens said he would like to know if he could continue to hold to Descartes's vortices after reading the Principia since these " in my view are superfluous if one accepts the system of Mr. Newton in which the movement of the planets is explained by the gravity towards the Sun and the vis centri- fuga which balances it ... ".

The extreme Cartesian view of gravity was expounded (1690) by Regis in a book on Richer's observations at Cayenne. The explanations put forward were closely similar to the ideas ex- pressed by Huygens in 1669 on the occasion of the discussion at the Acad&nie Royale. Regis made no mention of Newton in his book. In 1690 Huygens felt a good deal of uncertainty and wavered between his original ideas and the view expressed in his letter to Leibnitz. The appearance of the tract on the cause of gravity at the end of the Traitf de la Lumtire, published in this year, cannot be held to represent Huygens's final views, about which more will be said later. In England the effect of the Principia was more profound. Fatio de Duillier said that some of the Royal Society were "extremely prepossessed" in the book's favour and reproached those who were not under its spell as being too Cartesian. " They . . . have led me to understand that after the meditations of their author all Physics has been much changed " lie wrote to Huygens. There can be no doubt that on the Continent the criticisms made by Huygens and Leibnitz strengthened the position of the Cartesian philosophy for a good many more years. And yet Huygens's own work was, at its best, as opposed as Newton's to the Cartesian frame of mind and he did a great deal to dispose of the errors of Descartes's physical ideas, llie last five years of Huygens's life were in fact to be years of crisis for the Cartesian philosophy. Leibnitz and Huygens would have developed an alternative analysis which freed itself from Descartes's errors while at the

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same time rejecting Newton's conception of matter, time and space but this project was never carried through. In the event their effect was to delay the acceptance of Newton's work while at the same time weakening the supports on which Descartes's physical teaching rested.

In the meantime the more orthodox Cartesians were driven to great lengths to show that the new results of scientific research were fundamentally in accord with Descartes's ideas. Even the differential calculus was claimed by Catelan to be derivable from Descartes's geometry. The faulty treatise which he produced to support his view led to a dispute with the mathematician de I'Hdpital. The latter, regarding Huygens as a natural ally, gave violent support to the latter's mechanics, also criticized by Catelan. This somewhat embarrassed Huygens, who was by no means sure of some of de I'Hopital's ideas on this subject. For de l'H6pital tried to obtain some sort of proof of the principle that the centre of gravity of a system of connected bodies cannot rise under the sole action of gravity. Huygens preferred to regard this principle as self-evident. Pascal and Torricelli, he pointed out, had used the same idea though limiting it to statics.

Of a different character was Huygens's correspondence with Pierre Bayle about this time. This famous French sceptic was appointed professor of philosophy at Rotterdam in 1681, so that he arrived in Holland in the year that Huygens returned from Paris. Under the conditions of Catholic intolerance the intellec- tual ferment, once concentrated in Paris, was becoming diffused into the freer but less educated provinces and into Holland. In 1684 Bayle started a periodical entitled Nouvelles de la r^publique de lettres, the first number of which he sent to Huygens. The latter became interested in Bayle's aims and received him at his house, where he enlightened him on the subject of scientific studies. His correspondence with Bayle came to an end, however, after the philosopher was condemned as an atheist in 1693. Bayle's view was that religious dogma is of its nature irrational and that there is no merit in Relieving that which is merely consonant with reason. This outlook of credo quia absurdum was one which could not appeal strongly to Huygens.

Rather more interesting was Huygens's correspondence with Pierre Daniel Huet, another sceptic whose avowed purpose was

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to discredit reason in the realm of religious belief. Both Huet and Bayle actually influenced thought in the opposite direction to that which was intended, that is, towards scepticism. Huet in addition was strongly opposed to the rationalism of Descartes and strongly in favour of empiricism. In October 1689 he sent Huygens a copy of his Censures on the Cartesian philosophy. In reply Huygens said that he also had meted out rough treatment to Descartes, and that he hoped that his scientific work had replaced Descartes's doctrines with truer ideas. He agreed with Huet that while Descartes had overthrown the older philosophies he had borrowed from them their dogmatic spirit. He had had the ambition to be the author of a new philosophy and in his haste had been led to maintain ideas even against disproof. To Huygens this philosophy appeared as the successor of Aristotel- ianism. Nevertheless, when Martin van Helden, a Cartesian and professor of mathematics at Louvain, was threatened with im- prisonment for his criticisms of scholastic philosophy, Huygens assisted him so that he should not become "a martyr to Cartesianism ". He did not feel very strongly over this matter, for the battle of experimental science against the a priori philoso- phies seemed to him to be won. " It seems to me " Leibnitz was able to say, " that the Cartesians have very much declined and that they have not too many able men ".

XIV

In 1685 Huygens was still negotiating over his return to Paris and there were endless letters, many of them unanswered* sent off from Holland. Nevertheless, it is not really certain that he wanted to go back, and he may well have been deterred by know- ledge of the changed conditions at the Academic. Up to 1688 he stayed on at the Hague, and in the spring of that year he settled at Hofwijk, a property in the neighbourhood of the city which had belonged to his father. After his father's death in March 1687, the house was lent to Christian by his brother Constantin, who left with William III on his memorable expedi- tion to England in the following year.

In these last years (1685-95) Leibnitz was solicitous about Huygens's unpublished works and recommended him to con- serve his strength, for, he wrote, " I do not know anyone who could replace you ". Huygens's old age was a lonely one and he

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was troubled with ill-health, but, he replied, " I see that one becomes accustomed to all these things ". He was not quite for- gotten, for Charles Perrault drew public attention to the great scientist's work in his Parnllele des Anciens et des Modernes and when Varignon was about to publish a book on mathematics he felt that he must take the opportunity, as he said, of paying homage to " the greatest mathematician of our age ".

The pattern of Huygens 's life remained much the same right up to the end. He continued to work on the improvement of lenses, on the spring-regulated clock and the marine clock, and the writing of his last work, the Cosmotheoros. Undaunted by the unpromising performance of the various marine clocks he had constructed since 1663 he continued, with characteristic patience, to labour at this still urgent problem of the marine chronometer. In 1685 he went himself on a short trial (the only one) on the Zuyder Zee. In 1686 and 1690, clocks fitted with bifilar pendulums were sent in charge of the captains. All these trials were unsuccessful. The failure of the bifilar pendulum was the greatest disappointment, for work on this type of clock dates as far back as 1673 at least, since it was described in the Horologium Oscillatorium. After 1690 Huygens experimented with a new type of regulator and reverted to the spring drive which he had tried at the beginning and then abandoned. The new clock went well in laboratory trials and in 1694 Huygens hoped that the Dutch East Indies Company would take it up. He died before anything further could be done.

The fact that Huygens could not accept the chief conclusions of Newton's Principia is the most interesting fact that comes out of his correspondence at this time. Five years after its appear- ance he wrote of Newton, " I esteem his understanding and subtlety highly, but I consider that they have been put to ill use in the greater part of this work, where the author studies things of little use or when he builds on the improbable principle of attraction." The idea of universal gravitation " appears to me absurd " he wrote. Yet he felt compelled to admit that Newton's explanation of comets was incomparably better than anything imagined by Descartes. It was difficult to see how comets could cut across the vortices imagined by Descartes, or to explain the eccentricity of the planetary orbits and the real accelerations and retardations of the planets in their orbits except on the lines laid down by Newton. Over the shape of the Earth, also, Huygens

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was in accord with Newton. He did not deny that if the gravita- tion of the planets towards the sun were taken as inversely proportional to the square of their distances " this, with the cen- trifiigal virtue gives the Eccentric Elliptics of Kepler ". But he and Leibnitz, far from feeling that this reduced the solar system to order, felt that it raised an insistent question of how gravita- tion arose. Leibnitz thought he could perceive an analogy with the intensity of light which, as a simple geometrical deduction, also obeyed the inverse-square law. Rays of attraction might be imagined which caused bodies to descend if their centrifugal force diminished. These rays were dismissed by Huygens, how- ever, as incompatible with his theory of a circulating medium. It almost seemed as if a return might be made to Kepler's identi- fication of gravity with a kind of magnetic attraction. Leibnitz, at least, inclined not a little to this view. Both he and Huygens insisted on attributing the effects of gravity to the medium which they believed pervaded the universe. Consequently they were both interested in the study of motion in a resisting medium, for they no doubt perceived that this was the Achilles' heel of their system. If the medium had mechanical properties exhibiting themselves as gravitational force, magnetic force and in other ways, what influence must it have on the orbital motions of the planets and on terrestrial motions? Newton's Principia had dealt with this problem and much of the work was deliber- ately aimed at the overthrow of the Cartesian vortices. Huygens considered Newton's treatment to be not without fault but he agreed with him as against Leibnitz over the definition of resist- ance, " for you," he wrote " call the resistance the velocity lost or the loss of velocity caused by the medium . . . For Mr. Newton and myself, however, the resistance is the pressure of the medium against the surface of the moving body . . . " It is really astonishing to us now that Huygens did not see that Newton's study of resisted motion completely disproved the vortex theory, but we must remember that the elastic fluid theory was held in the nineteenth century under even greater difficul- ties. Furthermore, a comparison of Huygens and Leibnitz at this date leads to a decision in favour of Huygens's notions. In 1692 Leibnitz still supported vortices, while accepting Kepler's laws; Huygens had at least got to the point of seeing the over- whelming force of the quantitative work of Newton even while he rebelled against innate gravity. As he finally left them, the

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vortices were considerably attenuated affairs, suitable only for popular exposition of the sort found in the Cosmotheoros. Leibnitz, on the other hand, converted the subtle matter of Descartes into a production of his own : the materia ambiens.

A good deal of what we should term pure mathematics crops up in Huygens's and Leibnitz's letters. Leibnitz took up several of the problems studied by Huygens and gave them new form. " My design has been " he wrote, " to give a little trouble to these good Cartesians who, through having read the Elements of Bartholin or Malebranche, believe they can do all in Analysis." There followed a series of letters in which Leibnitz gave Huygens an account of the differential calculus and its uses. He was able to investigate the properties of a curve like the cycloid, he said, from a purely analytical treatment and without any recourse to the figure. In regard to the calculus, Leibnitz was not a clear expositor. It is clear that from one aspect the new method was regarded not so much as a development of pure mathematics as an instrument for physical research. The union of mathematics with experiment is what Sir William Dampier has called the " new mathematical method ". For Huygens, as for Galileo and indeed for Newton, experiment had not achieved the position it later held in certain branches of science. From a comparatively few observations, by the aid of " geometry " one could advance far into new realms, a fact which is well illustrated by Huygens's work on impact and on the compound pendulum. " It must be admitted " wrote Huygens, " that geometry is not made for all sorts of minds."

From being sceptical Huygens soon became envious of the calculus differentialis. Finding Liebnitz's accounts rather obscure he wished that either he or Bernoulli could be there to assist him. Some collaboration did indeed spring up with Fatio de Duillier, and Huygens's note-books contain many pages of working on the new lines. The great change of outlook was a difficult one for the great geometer and he did not attain facility in the use of the calculus. The new calculus, Leibnitz emphasized, gave its results by a kind of analysis without any effort of the imagination, " and it gives us over Archimedes all the advantages which Vieta and Descartes have given us over Apollonius ".

Fatio's work on the calculus is important in the history of the subject, for it was through him that the dispute between the

92 THE LIFE OF CHRISTIAN HUYGENS

followers of Newton and Leibnitz sprang up. More's Isaac Newton (1934) gives a good account of the episode. Fatio seems to have become resentful of Leibnitz's rather superior criticism of his work, which was of an undistinguished nature, and it is considered that Fatio smarted under a sense of grievance. After returning from England, where he had been in contact with Newton, Fatio wrote to Huygens, saying that priority for the invention of the differential calculus certainly belonged to Newton. He suggested that Leibnitz's ideas were in fact obtained from Newton's letters which went back to 1676 and 1677. The publication of these, he hinted, would embarrass Leibnitz. Actually, these dates were beside the point since both mathe- maticians seem to have used the calculus much earlier. Leibnitz, at any rate, affected to be unimpressed by news of Newton's advances and hinted to Huygens that he had done a number of things of which Newton knew nothing. Huygens's part in the quarrel which ensued was small but noteworthy for it was through him that Leibnitz first learned of the charges made by de Duillier.

About this time an interesting comparison in mathematical methods was made through the study of the same problem by Leibnitz, Huygens and James Bernoulli. This problem was the one propounded by Mersenne many years before; to find the theoretical form of a chain suspended from its two ends which are at the same height, so that a curved line hangs between them. The publication of the results showed a fair agreement between the three mathematicians but showed up the advantages of the calculus, which was more and more applied, not only to new problems but also to others already solved by classical methods. Huygens was not altogether pieased by some of the new methods, notably that adopted by James Bernoulli in solving the problem of the centre of oscillation. But the truth is that the form of Huygens's work in mathematics had always been some- Wjhat reactionary and was