1.1.

Kepler's Century: Prelude to Newton's I. BERNARD COHEN

Harvard University, Cambridge, Mass.

KEPLER'S century is bounded by Copernicus and by Newton) Since one of Kepler's greatest scientific achievements was his elaboration and major reform of the Coperni- can system of the world, it seems proper to set the beginning of Kepler's century at 1543 : the year when Copernicus' De Revolutionibus Orbium Coelestium was published. Kepler's century was a prelude to Newton's to the extent that Newton's Principia accomplished the dual goals of Kepler: to find the forces that produce the motions of the planets and their satellites, and to demonstrate thereby that the world must be conceived from a heliocentric rather than a geocentric standpoint. Kepler's goal transcended a mere defense of the Copernican system; his mission was the search for causes, for the forces that produce the Copernican planetary motions. Kepler's insistence that the celestial motions be explained by physical forces was perhaps conceptually more revolutionary than Copernicus's proposal of a heliostatic system; certainly, it was more innovatory and without precedent. Yet not until Newton's Principia was there in fact a proper demonstration of the Keplerian heliocentric system of the world, which is basically different from the Copernican heliostatic system. 2

Since Newton transformed the very nature of the exact physical sciences, historical logic demands that we set a pre-Newtonian termination to Kepler's century. And, indeed, the reckoning of years agrees with this judgment, for at the very end of

x See Notes section on pp. 29-36.

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the hundred years beginning with 1543 and the publication of Copernicus' treatise on the revolutions, Isaac Newton was born on Christmas Day, in 1642, the year (in the old Julian reckoning) in which Galileo died. a

For me, as historian of science, the happy conjunction of these two dates (1543, 1642) fits the concept of Kepler's century with a degree of conceptual propriety that the ordinary chronology of centuries would not permit. Since Kepler does not appear as a dominant figure in seventeenth-century science, it would be improper to refer to the 1600s as Kepler's century, as we might do in calling the seventeenth century the age of Galileo, or of Descartes, or of Newton. ~ The later 1600s, in fact, prove to be notably non-Keplerian, and even anti-Keplerian. As we shall see below, in certain of Kepler's concepts and principles and laws Newton could find the most powerful tools the mind might imagine for creating a wholly new level of discourse in the exact sciences o.f dynamics and celestial mechanics. But, while apparently realizing Kepler's goals for an exact celestial science on a foundation of dynamics, Newton himself conceived his Principia to be Galilean rather than Keplerian. For the most part, Kepler's major writing on dynamics and theoretical astronomy were unknown and unread, and his major contributions did not affect the advancement of science in a productive manner, save for Newton's Principia. 5

The sense in which the age of Newton, beginning in the latter part of the seventeenth century, was not truly Keplerian may be illustrated by many aspects of the science of that day and by the later testimony of writers on the history of science. A Keplerian or numerical argument may suffice to prove the point: comparison of the number of editions and translations of the writings of Galileo and of Kepler. Galileo's major works have been reprinted and translated into many languages ever since their original publication; whereas Kepler's major works have been reprinted only occasionally, and even now the number of translations has been regrettably small. Galileo's "Two Greatest Systems of the World" (the Dialogo), published in Italian in 1632, was reprinted in 1710; this work was speedily translated into Latin (1635) and the Latin text was published three more times in the seventeenth century, accompanied by a Latin version of the "Two New Sciences" (the 1699 edition Discorsi). Both works had been published in English translation by Thomas Salusbury in the 1660s; but they were hard to obtain, all but a bare handful of the English "Two New Sciences" having perished in the London fire of 1666. The "Two New Sciences" was reprinted in English twice in the eighteenth century, in two editions (or issues) of a revised version of Salusbury's seventeenth-century translation, made by Thomas Weston. In the 1890s, both this work and the "Two Greatest Systems of the World" came out in German, and twentieth-century translations have been published in Spanish (1946), Russian (1948), Polish (1953), Hungarian (1959), Japanese (1959, 1961), Romanian (1961), Slovak (1962). In the twentieth century, the "Two New Sciences" has appeared in numerous languages, including Italian (1958), 6 Japanese (1956) and French (1970), while yet another (the third)

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English translation by H. Crew and A. de Salvio has been reprinted again and again. A fourth translation has just been published by Stillman Drake. Galileo's "Two Greatest Systems of the World" has been issued in English in the twentieth century in two versions, one based on Salusbury's seventeenth-century translation. "The Sidereal Message" (or, as Kepler conceived it, Galileo's "Sidereal Messenger") was reprinted a number of times in the seventeenth century and has been translated into English at least twice. There have been many editions in various countries ever since its publication in 1610; translations have been published in English (1880, 1959), Italian (1948), French (1964), and Russian (1968).

What a contrast to Kepler! At the present time, not a single one of Kepler's greatest works has ever been completely translated into English, French, Russian, or Italian. 7 And only in recent years have any of Kepler's writings whatsoever been published in complete English versions. The latter include a little essay of a few pages on the snowflake, and Kepler's "Dream" and "Conversations with Galileo's Sidereal Messenger"; for the latter two, we are indebted to Edward Rosen (whose edition of the "Dream" is, however, the third English version of that work with which I am familiar). Even in German, there are at present no complete translations of Kepler's major optical writings; and the German versions of the Mysterium Cosmographicum, Astronomia Nova and Harmonice Mundi were made only in the twentieth century. 8 A small portion of the Harmonics is available in English, along with portions of the Epitome Astronomiae Copernicanae. The latter has never been fully translated into any vernacular language. Not a single one of Kepler's works is available in full in French, or--so far as I know--in Russian or in Italian.

This glimpse at the bibliographical record may give us some measure of the plain fact that over the centuries the development of science has not been directly influenced by Kepler's writings, which have been inaccessible to all save a handful of specialists. And yet, paradoxical as it may seem, Newtonian science--and all of modern exact science since Newton's day--is actually Keplerian. How this may be, in an apparently brazen contradiction of the bibliographical record, I shall explore in what follows.

Ever since the seventeenth century, there has been a continued world-wide interest in Galileo's science that seems aggrandized by the minimal attention paid to Kepler's astronomy and physics, with the exception of the famous three laws of planetary motion. 9 Until very recently, as a matter of fact, the scholarly world in general knew very little about Kepler's science as a whole. I find it curious that one of the best accounts of Kepler's physical astronomy, explaining in detail how Kepler built a new astronomy for the first time on physical rather than kinematical principles, written by David Gregory, is relatively unknown today to scholars doing research in either the history of astronomy or the history of seventeenth- century science, or to students of Kepler. 1° An index to the general level of ignorance

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concerning Kepler's pioneering work in physical science is provided for us by the account of dynamics by so good a scholar as Ernst Mach. Although Mach lived most of his creative life in Prague, where Kepler had done perhaps his greatest work, Mach did not once refer to Kepler's innovatory principles of physical mechanics. In Mach's often reprinted and revised survey of the development of the science of mechanics, there is no sign of an awareness of the fact that Kepler had introduced into the science of motion that most significant technical term, inertia, although Mach eventually learned that Kepler had conceived a kind of gravitation theory. But Mach did know of Kepler's work in optics, and devoted a chapter to Kepler in his last book, the posthumously published Principles of Physical Optics.

One may search in vain throughout most of the classical literature of mechanics for an accurate presentation of Kepler's contribution. The three published versions of Newton's Principia and the preliminary manuscript drafts contain no mention whatever of Kepler's magisterial contribution to the science of motion. Not only do the printed pages of Newton's great book fail to list Kepler among the inventors of dynamical principles and concepts; there is not even an attribution to Kepler of the discovery of the whole set of three major laws of planetary motion. Kepler appears in Newton's Principia only as an astronomer, primarily an observer of comets, and he is mentioned in passing as the admitted discoverer of only the third of the Keplerian laws of planetary motion, the harmonic law. n In an earlier draft of Book III of the Principia, Newton's "System of the World", Kepler is assigned one further role: he is said to have been an original inventor of-the Cartesian system of vortices. This is one point, I may add, on which Newton and Leibniz were in agreement, poles apart as they were on all other questions of priority, to say nothing of basic philosophy. Of course, when Newton called Kepler an inventor of Cartesian vortices, he was doing so in a pejorative manner, whereas Leibniz, who actually believed in a kind of vortex theory, was giving Kepler high praise.

I believe that the historical rejection of Kepler and the acclaim for Galileo has not been an accident, the result of mere chance. I see this aspect of history as part of a movement, begun in the seventeenth century and continuing to our own day, to establish a very special viewpoint towards science and scientific discovery: science conceived as a domain in which knowledge advances by the practice of what has been traditionally called the "scientific method". For at least three centuries this "method" has been described or referred to again and again, and is often said uncritically to have been invented by Galileo (or by Bacon), or to have been certified by Descartes. Sometimes, the "method" is actually called Galilean, and said to consist of varying one parameter at a time. It has even been alleged traditionally that Galileo not only invented this "scientific method", but thereby invented modern science itself. Thus Bertrand Russell echoed a common opinion when he said (in The Scientific Outlook, 1931), "Scientific method, as we understand it, comes into the world full-fledged with Gal i leo. . ." , adding that Kepler possessed the method "to a

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somewhat lesser degree". Russell was not equivocating; he insisted that Galileo knew "the scientific method in its completeness". Reminding his readers of the vast accumulation of scientific knowledge since Galileo's day, Russell nevertheless held that "nothing essential has been added to method".

Galileo's high place in this pseudo-history may be contrasted with the image of Kepler, whose writings would seem to abound with mystical references to the Trinity, and to the special hierarchical qualities of certain geometric figures and number relationships. Rather than varying one parameter at a time, Kepler is said to have tried extravagant hypothetical constructions under what he claimed was explicit divine guidance, since he fully believed that God communicated directly with him, even leading him along the path of scientific discovery and invention. This Kepler, who made bold and imaginative great leaps forward, was clearly not a patient classifier of facts, however experimental or observational, nor did he use a "scientific method" in a way which we might advise our students to emulate. Indeed, Kepler is all too often described as a mystic: a word which I personally dislike in the loose sense in which it is apt to be used even by outstanding members of my profession. 1~ Kepler's search for numerical and geometrical relationships tends not to be lauded in itself, but is called "number mysticism". Therefore, the only justification for allowing Kepler a place in the classical pantheon of science is that his "unscientific" method happened by chance to yield useful results for the later advance of true science by more orthodox practitioners. 13

Kepler made a never-ending search for number-relations of all sorts. Post- Keplerian science has rejected or ignored almost all of his geometrical and numerical "laws", and exclusively gives him credit for the three laws of planetary motion. But in order to quarry these three laws out of his "Epitome of Copernican Astronomy", it is necessary for us to be highly selective, and to deny most of what Kepler set forth as fundamental relationships or laws: such as those between the sizes or densities of planets and their speeds or their particular orientation in the universe. This reduction of Kepler's major planetary laws to a mere three in number requires that scientists and historians must discard what is often described by "positivist historians" as a "youthful" discovery of Kepler's (thus supposedly rejected in his maturity), that the orbits of the six planets in the Copernican system are separated by the five regular solids, arranged in a concentric nest of circumscribed and inscribed spheres in which these orbits are imbedded. It may come as a surprise to find that Kepler himself did not consider this as an early discovery that he disowned later on, but cherished it to the very end of his life as a fundamental law; it is presented proudly and prominently in the "Epitome". Kepler's search for quantitative or exact relations between astronomical quantities was fruitful in yielding the third law of planetary motion, that the cubes of the mean distances of the planets from the Sun are proportional to the squares of their sidereal periods. 14 But whereas Kepler's search for such a "harmonic" law may be lauded, his more purely numerological argument for the

I. Bernard Cohen

number of moons of Mars disturbs the image of Kepler as an early practiser of the "scientific method". For Kepler apparently so believed in the necessity of proper numerical sequences that he concluded from the position of Mars's orbit in the Copernican system (between the orbits of the Earth and Jupiter) that Mars must have two moons. His reasoning was based on the discovery of four moons of Jupiter. Since the Earth has one moon, the only way to have a proper sequence 1, 2, 4 , . . . is for two moons to be encircling Mars. 15

If Kepler is to be displaced from the positivist pantheon of great scientists because he dealt with queer stuff, practised scientific numerology, and alleged that he had made his discoveries by God's direct intervention and explicit guidance (rather than by a systematic application of the scientific method), what are we to do about Isaac Newton ? In the traditional, orthodox, and classic conception, according to the usage of scientists, Newton was as much a mystic as Kepler. Newton, in fact, wrote thousands and thousands of pages of quite obviously queer stuff on mystic philosophy, on the meaning of the prophetic books of the Bible, on alchemy, on prophecy in general, and on the wisdom of the ancients. Is there any basis, then, for possibly admitting Newton to the pantheon of acceptable great scientists, while rejecting Kepler ? There is one reason for treating Newton differently than Kepler; Newton did not initially introduce such extraneous or extra-scientific matters into the Principia or the Opticks, but only did so in the later editions of these two works, and then in supplements which are separate from the text proper. Thus Newton appears to have made a distinction between his science and his discussions of such topics as the Creation, divine providence, the existence of God, or morality. 16 Newton's contemporaries could easily read the purely scientific part of these two treatises without having to bother with the "sermon". Indeed, Newton's original scientific writings did seem so far removed from his concerns with these religious or mystic questions, that it was even possible to build up the fiction (as J.-B. Biot did in the nineteenth century) that Newton's intens~ devotion to these extra-scientific aspects or implications of science arose only in his old age (and so, presumably, could be attributed to senility).

The difference between Newton and Kepler is thus not primarily a matter of interest or of motivation or concern. Still less is this difference only a reflection of their distinct and individual personalities. There is a bold separation between Kepler's century and Newton's, as if a decision had been made between the "Harmonics" and the Principia that motivation and personal history should not be an integral part of the exposition of a scientific structure of concepts, laws, and the results of observation and experiment. Newton himself may have been a major force in effecting that decision, although it is certainly presaged in the writings of Galileo and Boyle. Kepler, however, in his Astronomia Nova and Harmonice Mundi, tends to publish almost every aspect of his failure, his success, his motivation, his moment of inspiration. This feature of Kepler's writings may possibly constitute a

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major reason why he personally never produced the full effect on science that was his due. None but the hardiest reader would ever wade through the prolixity of his account of his experience with the divine force, of his motivations, to say nothing of the detailed calculations based on hypotheses which he finally admits could not be made to accord with the facts of observation. The latter is part of the historical record of scientific discovery, but after Newton's day this kind of personal narrative became increasingly less common in ordinary scientific expositions, x7 But even in the seventeenth century, many scientists must have found it difficult to separate the useful astronomical laws and dynamical principles from the extra-scientific matrix in which Kepler had imbedded them. In our own times, some scholars have begun to recognize that an understanding of the creative personality of such men as Kepler and Newton and Leibniz cannot ignore those intellectual pursuits which are not scientific in the usual or orthodox sense, and which may be more mystical than purely rational. But scientists generally have tended to want history to reveal chronologies and priorities of discovery, and accordingly they have not been much concerned with such activities of their predecessors as seem to go counter to the usual canons of orthodox scientific beliefs and practices. The Royal Society, faced for at least a century and a half with the problem of what to do about the "queer stuff" that Newton wrote out so laboriously, has decided--just as the Prussian Academy has done in the case of Leibniz--to let it all stay in manuscript so far as they are concerned, on the grounds that such matters are not part of science, however much they may be part of a scientist's total creative life. At present, scholars have the greatest difficulty in gauging the extent of Newton's involvement in alchemy, mystical philosophy, prophecy, or theology, save by going to Newton's manuscripts, which are now widely dispersed, xs Kepler's case is different from Newton's. It is often impossible for a reader to separate Kepler's scientific and extra-scientific expressions because they are apt to occur together in the same "scientific treatise"; the Dioptrice and Astronomiae Pars Optica, however, are purely "scientific".

Despite his extensive writings, however, Kepler's life as a scientist does leave us with certain mysteries. He was, I believe, the last major astronomer who practised the art of astrology on an extensive scale: he used himself as subject as well as others, including his patrons. Did Kepler really believe in astrology ? Did his attitude toward astrology waver back and forth between belief and disbelief? x" It is easy enough to find quotations to show that Kepler held that astrology serves as a means of support for astronomy; but, contrariwise, there are extracts aplenty to indicate a true belief in astrological predictions. He even made a retrodiction, based on his own life history, assigning an exact moment to his own conception within his mother's womb. Kepler's attitude toward astrology can perhaps best be described by that grand Scottish verb "to swither", which is losing currency today, yet another sign of the continual impoverishment of our language. In this regard Kepler differs greatly from Tycho Brahe, who never had a moment's doubt about the aspects of the heavens in

I. Bernard Cohen

relation to his personal fate and who even conditioned his judgments as to proposed actions by casting his own horoscope. Galileo also cast a number of horoscopes; to do so was part of the job of a court astronomer of that age. But Galileo was not seriously interested in studying whether or not astrology might be a valid science, and there is no evidence that he ever applied astrology to guide his own life.

Astrology, in fact, may be one of the indices that enables us to separate Kepler's century from Newton's. There were practising astrologers in Newton's day, as there are in ours, and the almanacs of the seventeenth and eighteenth centuries carried astrological predictions (along with long-range weather forecasts), just as our newspapers do at present. But I do not know of any major astronomer (or other scientist) of Newton's day who believed in, or practised, astrology. Newton, as a young man, studied astronomy in books by Wing and Streete, both of whom wrote manuals of astrology and cast horoscopes, but these men were not astronomers of any note, in the class of Halley, Flamsteed, Hevelius, Huygens, Cassini, Romer, or Picard. John Conduitt (who married Newton's niece) held that Newton turned to mathematics through an interest in astrology, when still a Cambridge undergraduate. In a draft of a life of Newton, Conduitt wrote:

He [Newton] bought a book of Judicial Astrology out of curiosity (which Hobbes calls the mother of all Philosophy...) tosee what there was in that science & read in it till he came to a figure of the heavens which he could not understand for want of being acquainted with Trigonometry, & to understand the ground of that bought an English Euclid with an Index of all the problems at the end of i t . . . , & was soon convinced of the vanity & emptiness of the pretended science of Judicial astrology.

We may doubt the authenticity of the final sentence, but I believe the rest of the anecdote to be as reliable as any such tale that a scientist tells many decades later about his youth. We may especially note in this story that at that time it was proper to test the validity of astrology, and to see "what there was in that science". The final sentence must be understood as embodying Conduitt's judgment that this "science" was vain and empty, and his approval that on these grounds astrology had been absolutely and fully rejected by the young Newton.

The repudiation of astrology by Isaac Newton and his major scientific con- temporaries may seem all the more striking when we recall Newton's own passion for alchemy, which is sometimes held to be astrology's twin. Newton shared his belief in alchemy with Boyle and Locke. While Newton was concerned with alchemy and with mystic philosophy, and even with prophecy and biblical chronology, on which topics he left many pages of manuscript, he did not similarly leave us any sign whatever of an interest in astrology. This difference may indicate only that in the post- Keplerian world, astronomy had advanced to the point of disdaining astrology, whereas chemistry had not yet reached the stage where it could divorce itself from alchemy, z°

We cannot discuss the two centuries, Kepler's and Newton's, without asking how

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Kepler's science was transmitted to Newton and his contemporaries. There is no doubt that one work of Kepler's was widely read, the Dioptrice, printed in a handy edition together with Galileo's "Sidereal Message" and Gassendi's little treatise on the sphere (the Institutio Astronomica). Conduitt, in the account of Newton's life mentioned above, relates that Newton's " t u t o u r . . . told him he was going to read Kepler's Opticks to some gentlemen commoners & that he might come to those lectures. Sir I. immediately read it at home & when his tutour gave him notice of the lectures he told him he had already read that book through. ''21 The first thorough- going Keplerian in England was Jeremy Horrox, struck down before he had time to make the real contribution to astronomy of which his genius gave promise. When Horrox's papers were published posthumously in 1672, John Collins sent Newton a set. As a young man, Newton encountered Kepler's third law and the concept of elliptical orbits in Streete's Astronomia Carolina, and he found elliptical orbits dis- played also in Vincent Wing's treatise in astronomy. 22

Of all Newton's contemporaries, however, the major Keplerian was no doubt the Scots astronomer, David Gregory, who nosed out Edmond Halley for the Savilian chair at Oxford. Gregory's Astronomiae Physicae & Geometricae Elementa (Oxford, 1702), to which I have referred above, opens with a simple declaration:

My design in publishing this Book, was that the Celestial Physics, which the most sagacious Kepler had got the scent of, but the Prince of Geometers Sir Isaac Newton, brought to such a pitch as surprises all the World, might, by my care and pains in illustrating, become easier to such as are desirous of being acquainted with Philosophy and Astronomy.

Gregory's reference to "Celestial Physics" (which he later qualified by adding: "or Physical Astronomy") is taken directly out of Kepler's Astronomia Nova, which had a subtitle of "Physica Coelestis". Gregory was quite aware that Kepler's most fundamental contribution to physical science was his program of basing astronomical laws on physical causes. Gregory quite properly observed, however, that Kepler's planetary laws did not lead him to the correct causes, an assignment reserved for Newton.

Gregory was a staunch Newtonian; he had been recommended for the Oxford post by Newton himself, and he wrote out a lengthy commentary on Newton's Principia, which it was his hope might be published along with a new edition of the Principia, edited by himself. In these manuscript Notae in Isaaci Newtoni Principia Philosophiae, Gregory chided Newton for his failure to give sufficient credit to Kepler. For instance, in Book I of his Principia, Newton says (Scholium to Prop. 4) that the harmonic law "obtains in the heavenly bodies (as Hooke, Halley, and Wren have severally found out)". In Book III, however, Newton does admit (Hyp. 7, ed. 1; Phen. 4, eds. 2-3) that this relation was "first observed" by Kepler. 2s "It is remarkable", Gregory wrote in his Notae ("Mirum est . . . " ) , concerning the above reference by Newton to Hooke, Halley, and Wren,

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• . . that the Author does not mention Kepler, since in Hypothesis 7, Book III the Author mentions this observation as first made by Kepler and since Kepler was the first to discover that it obtains in the Celestial bodies. It is indeed true that the observations of later men prove this law more exactly observed in Celestial bodies than Kepler had thought. [Translated from the Latin MS.]

Gregory was not alone in believing Newton to have withheld just credit from Kepler. Edmond Halley, the great astronomer after whom the comet is named, who saw Newton's Principia through the press, was even more explicit about Newton's debt to Kepler. In a book review of the Principia published in the Philosophical Trans- actions of the Royal Society, Halley discussed the general laws of planetary motion, as expounded by Newton in Book I of the Principia. He observed, "All which being found to agree with the Phenomena of the Celestial Motions, as discovered by the great sagacity and Diligence of Kepler . . . " . Since Newton himself had omitted to mention Kepler at all in Book I, Halley's gentle reminder of Kepler's contribution must be read as a kind of public rebuke, however mild. ~4

I mentioned earlier that Leibniz alleged, as Newton did too, that Descartes had taken the concept of vortices from Kepler. Leibniz did this in his famous tract on motion, the Tentamen or "Essay on the Causes of the Motions of the Heavenly Bodies", published in the Acta Eruditorum in 1689. 25 In this essay, Leibniz referred to Kepler as "that incomparable man", whom "the fates had watched over that he might be the first among mortals to publish the laws of the heavens, the truth of things, and the principles of the gods"• Leibniz then stated briefly the three major planetary laws of Kepler, leaving the reader in no doubt that Kepler "discovered that each primary planet describes an elliptical orbit, with the sun in one focus, and with a motion according to the law that the areas swept out by radii drawn from the sun to the planet are always proportional to the times. He also found the several planets of the same system to have periodic times proportional to the 3/2 power of their mean distances from the sun . . . . " Although Leibniz then criticized Kepler for not being "yet able to assign the Causes to so many and so uniform truths, either because his mind was hampered by belief in Intelligences or inexplicable sympathetic radiations", or because the subjects of "geometry and science of motions were not yet as advanced in his time as they are now", he insisted that Kepler, nevertheless, had shown the way of inquiring into the reasons or causes:

For it is to him that we owe the first proof of the true cause of gravity and of the law of nature on which gravity depends, that rotating bodies tend to recede from their centers along the tangent, and thus if stems or bits of straws swim in water, and if the water, by the rotation of the vessel, moves in a vortex, the water, being denser than the stems, and therefore being forced away from the center more strongly than the stems, will push the stems toward the center, as he himself has eloquently explained in two--and more--places in his Epitome of Astronomy.

Leibniz held, however, that Kepler "was still somewhat in doubt, and ignorant of his own riches, and insufficiently aware of how many things follow therefrom, both

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in physics and (especially) in astronomy". This led Leibniz to his attack on Descartes:

But Descartes later used [Kepler's results] brilliantly, although, as is his custom, he concealed their author. Indeed, I have often been amazed that Descartes, as is well known, never undertook to provide the reasons of the celestial laws discovered by Kepler, either because he could not sufficiently reconcile them [Kepler's laws] with his own principles, or because he ignored the fruitfulness of the discovery, thinking Kepler's laws not to be so faithfully observed by nature.

Newton's reference to Kepler and vortices occurs in a preliminary version of Book III, known as "Newton's System of the World". 20 Here Newton discussed the ways in which "later philosophers" allege (or pretend) to account for the motion of the planets in "regular revolutions in curvilinear orbits", citing first the explanation "by the action of certain vortices", an explanation due to "Kepler and Descartes".

Leibniz's accusation of plagiarism in relation to the concept of planetary vortices is but one of a number of such charges raised against Descartes in the seventeenth century. Most readers are aware that one of the most famous of all Descartes' writings, his "Discourse on Method", was written as a preface to three famous books on science, all published together in 1637: a work on dioptrics, the treatise on analytic geometry, and a book entitled Les Mdtgores, which is not quite meteorology in the sense in which we use the word today for weather prediction, but possibly to be under- stood as the physics of the upper atmosphere, in the Aristotelian sense of describing all the phenomena that occur in the region between the surface of the Earth and the sphere of the Moon, and thus including comets, rainbows, and so forth. In the "Discourse on Method", Descartes explained how to make the great discoveries contained in the three treatises which were to follow. But Leibniz was implying that Descartes had a much simpler method of making discoveries, namely, by examining the writings of his predecessors. Christiaan Huygens, the great Dutch physicist who was a contemporary of Leibniz and Newton, suggested that Descartes had made one of his greatest discoveries, the law of sines or the law of refraction, not by the applica- tion of the method he had expounded, but by looking at the unpublished manuscripts of Snellius. Newton's contemporary John Wallis alleged that Descartes had not given full credit to certain British mathematicians for their discoveries, which he had utilized. There were charges that Descartes had taken much from Kepler's book on dioptrics without giving him credit, the work (to which we have referred earlier) which Newton may very well have read as a Cambridge undergraduate.

Did Newton's failure to give credit to Kepler for the first and second laws of planetary motion derive from ignorance ? Not at all. Throughout most of his life, Newton exhibited what must seem to us today to be an amazing ignorance of Kepler's writings, but at the time of writing his Principia he certainly knew that Kepler had been the first person to have stated the law of elliptical orbits and the law of areas. Newton even referred to these laws in relation to Kepler's name in some unpublished manuscripts, written just before the Principia. 27 I shall return to this subject in a

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moment. But first, let me indicate a true aspect of Newton's ignorance of Kepler's writings.

One of Newton's greatest achievements was the "Theory of the Moon", in the seventeenth-century sense of this expression ;~8 for Newton showed for the first time in history that the "inequalities" in the Moon's motion, or the apparent departures from a simple regularity, could be derived from physical principles (the effect of the Sun and the Earth on the physical body of the Moon), whereas until Newton's day, the "inequalities" in the Moon's motion had been investigated solely on the basis of complex geometric models. What is most interesting to us in the present context, however, is that Newton, relating the history of attempts to understand the Moon's motion, states expressly that Jeremiah Horrox "was the first person who advanced the theory of the Moon's moving in an ellipse, about the Earth placed in its lower focus". This statement comes from the Scholium to Prop. 35 in Book III of the Principia (ed. 2-3). But in a hitherto unpublished manuscript, Newton declared that Horrox wanted the Moon's motion to be so much like the Keplerian concept of planetary motion that he both introduced an orbit in the shape of an ellipse and postulated that the Moon moves along the ellipse according to the law of areas.

This statement, curiously enough, appears to be doubly wrong. Our colleague, Professor Edward Rosen, had recently shown (and there is much evidence to support his position: for instance, the Rudolphine Tables) that Kepler himself based his lunar theory on the concept of an elliptical orbit, a9 Horrox's innovation was not the elliptical orbit as such; he introduced a variable eccentricity, so as to produce a geometric model that accorded well with observations. As to Newton's assertion that Horrox conceived that the law of areas might apply to the Moon's motion, I may only say that I have looked through the published writings of Horrox several times, with- out finding this particular reference. Indeed, I have not found in Horrox even a statement of the law of areas with regard to the primary planets. I have asked Professor Wilbur Applebaum, the authority on Horrox, whether such a reference occurs in Horrox's writing, and he informs me that he too has never been able to find any text of Horrox's mentioning a law of area with regard to either the Moon or the primary planets.

Before going further into the question of the relations between Newton's ideas and Kepler's, let me add a word or two more about Newton's reading. The only book of Kepler's which Newton is said to have read is a work on optics which he supposedly studied as an undergraduate. 3° Does the fact that Newton apparently never read any of the other writing of Kepler imply a value judgment on his part ? Did he esteem Galileo the more by reading more fully in his works ? These questions may be answered quite simply: Newton honored Kepler and Galileo equally in his general ignorance of their writings. I believe he read Galileo's "Sidereal Message", at nearly the same time early in his youth when he would have read Kepler's book on optics. There is evidence that Newton had read parts of Salusbury's English translation

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of Galileo's Dialogo on the two "Systems of the World", but I am convinced (and there is much evidence to support me) that Newton had never read Galileo's Discorsi or the "Two New Sciences", at least not prior to writing the Principia. al If Newton had really been familiar with Galileo's work on motion, he would not have said that Galileo had known the first two laws of motion (as expounded by Newton in the Principia), or that Galileo had used the second law of motion in order to dis- cover the law of freely falling bodies. I think it fair to say, however, that very often the most creative scientists do not read the writings of other men fully and carefully. A great scientist of Newton's stamp, with a restless creative mind, would use other men's books as sources for concepts, facts of experiment, results of observation, and laws. Once such a man began to read, he would often find his own ideas coming to the fore and would rather quickly put down a book in favor of pen and paper, in order to record and work out the consequences of the thoughts aroused by his reading. We shall see a typical example, below, of the way in which Newton developed his own concept of inertia after encountering the Keplerian concept and its name in some published correspondence of Descartes.

Ever since the publication of Newton's Principia in 1687, there has been a general awareness among scientists of a kind of direct progression from Kepler to Newton. Kepler's science and Newton's thus appear linked in logic as firmly as those of Galileo and Newton. I have mentioned that Halley stressed this connection in his review of the Principia in the Phil. Trans., and that this link was featured in Gregory's textbook of astronomy. The Kepler-Newton theme was made clear even before the whole of the Principia had been composed by Newton. When the manuscript of Book I (of three) was presented to the Royal Society on 28 April 1686, it was described as a treatise in which Newton "gives a mathematical demonstration of the Copernican hypothesis as proposed by Kepler". From Halley's later reference to Kepler and Newton, in his book review of the Principia, we may suspect that this very appropriate description was due to Edmond Halley.

Newton's Principia is, in a sense, a more Keplerian book than he was aware. One way to discern this feature of the Principia is to examine the relation between the first and second of Kepler's laws as treated by Newton. I well remember how puzzled I was, when--as a graduate student, soon after I had made a shift in speciality from physics and astronomy to history of science--I was asked by a scientific colleague if Kepler could possibly have found the law of areas before the law of elliptical orbits. Like others who had not done any direct research on the question at that time, I had assumed that what we call Kepler's first law preceded what we call the second law in both a chronological and a logical sequence. After plotting a number of Mars's positions in place, I had supposed, Kepler then found the curve that gave the best fit, and so introduced the elliptiform path. Next, in order to regularize the changing orbital speed, he would have hit upon the area law by slicing up the orbit in various

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ways. Those who have studied this topic know better of course. Kepler first found a general area law, using certain principles of force and motion in relation to the Sun's influence on the planets, and he then applied the general area law to discover the actual shape of the orbit. Indeed, this is the sense in which Kepler described his "new astronomy" as a "celestial physics" based on "causes". Unlike Ptolemy or Copernicus, he was not merely tracing out geometric patterns that would result from one form or another of a heliostatic or geostatic model, but was rather deducing the shape of the orbit and the law of orbital speed from physical considerations of the nature of the solar force. 32 The planetary motions were thus studied in relation to the Sun itself, rather than a mean Sun (such as the center of the Earth's orbit in a pure Copernican system): a feature, as we have seen, that makes the Keplerian system differ from the Copernican in being truly heliocentric and not merely heliostatic.

Once I had grasped this sequence in Kepler's development of the first two laws of planetary motion, I recognized the existence of a Keplerian logic in Newton's Principia. For Newton too begins with the law of areas in general, and only then pro- ceeds to the shape of the orbit. The beginning propositions of Book I are devoted to the area law without reference to any particular shape of orbit. First Newton shows that whenever a body moves freely without any external force acting (so that its motion is purely inertial or uniformly rectilinear), a radius vector drawn from the body to any point not on the line of the motion will sweep out equal areas in equal times. Next he shows that if there is a force acting on a body with an initial component of inertial motion, then the law of areas is a necessary and sufficient condition that this force be directed toward a center, toward the point with regard to which the equal areas are reckoned. Thus was revealed for the first time the physical or causal significance of the area law in relation to the law of linear inertia and the concept of a centripetal force. It is only in the next section of the Principia, in Prop. 11, that Newton proceeds to the actual shape of the orbit. He proves that if the orbit of a moving body is elliptical, the centripetal, force directed toward a focus must vary inversely as the square of the distance. Succeeding propositions demonstrate that in a parabolic or a hyperbolic orbit, the same law of force will obtain, s3

This Keplero-Newtonian order of the first two planetary laws has a further logic that the customary facile presentations lack. Many historians and the writers of elementary textbooks seem to assume that it is possible to find the law of areas by actual computation on the basis of an elliptical orbit, or that one can use the area law to find planetary positions on an elliptical orbit. 34 But as Kepler knew, and as Newton stated specifically in the Principia : "There is no oval figure whose area, cut off by right lines at pleasure, can be universally found by means of equations of any number of finite terms and dimensions" (Lemma 28, Bk. I). Hence, "To find the place of a body moving in a given ellipse at any assigned time" (Prop. 31 and its Scholium, Bk. I), Newton introduced a "solution by approximation" and devised "a particular calculus. . , fitted for astronomical purposes". This aspect of the first

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Kepler's Century

two laws of Kepler has an additional importance in the development of mathematical and practical astronomy. Since the area law cannot be used in a simple and direct manner for computing orbital positions along an ellipse, it was necessary to introduce some other (and approximate) computing program. In Kepler's century, and on into Newton's, planetary positions were usually computed by means of a geometric model, in which a radius vector turned uniformly about the empty focus. In the simplest version, the planetary position was determined with a fair degree of accuracy by the intersection of this rotating radius vector and the ellipse. An even more accurate result (especially in the regions of the apsides) was gained when a correction factor was introduced by means of an auxiliary circle. These approximations, in their several variations, are associated with the names of Bullialdus, Seth Ward, and Mercator. In Streete's Astronomia Carolina, from which Newton first learned of Kepler's third law and in which elliptical orbits are introduced, there is no mention whatsoever of the law of areas; a method of approximation is used instead, of the sort described above. It appears now that Newton only learned of the law of areas in the late 1670s and almost at once he was able to solve the problem of elliptical orbits in relation to an inverse-square law of force--a solution impossible without the area law. 35

Book I of the Principia is devoted to the development of general or abstract principles and theorems concerning motion under the influence of various types of forces. Only in Book III does Newton apply these results to the realities of the "System of the World". Here Newton starts out by indicating that the first two laws of Kepler apply to the planets and to satellites of planets, and that the third law holds for both types of system. In this Book III, Kepler's name appears in the Principia for the first time, but only (as I have already mentioned) in relation to the third or harmonic law. Since Newton's failure to mention Kepler's name in relation to the law of areas and the law of elliptical orbits was not due to ignorance, we may ask why he refused to give credit to Kepler for the first two laws of planetary motion.

We have no direct evidence concerning Newton's decision, and we cannot even say whether the "refusal" was made consciously or unconsciously. But there are both printed and manuscript texts that may illuminate Newton's point of view. Newton apparently assumed that with respect to the law of areas Kepler had made a successful guess, since Kepler's approach was valid only in the region of the apsides ;ae furthermore, Kepler had found the elliptical orbit only in the case of a single planet, Mars, and had then guessed that this result could be generalized to all the planets. Newton seems to have believed, rightly or wrongly, that he himself deserved credit for the first two laws of Kepler. After all, the general validity of the law of areas could not be appreciated until it was shown how this law was related to the combination of intertial rectilinear motion and a force directed towards a central point. Furthermore, the elliptical orbit arose from these same conditions, when (and only when) this central force varies inversely as the square of the distance; but a full

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understanding must also include the consequence that any other conic section--a parabola or a hyperbola--may equally result from an inverse-square central force.

Newton's point of view reflects a general standard of credit for discoveries: in which "guesses" unsupported by solid proof are considered worthless, or only of some small or inspirational value. Newton, however, was not really concerned with the application of this principle to Kepler so much as he was with its possible applica- tion to Robert Hooke. Hooke wanted Newton to give him some credit for having suggested to Newton the possibility of an inverse-square law, but Newton refused on the grounds that he had conceived the possibility of this law without Hooke's suggestion, and that Hooke had only made an unsupported guess. In explaining his position to Halley, who was readying the Principia for the press, Newton compared the case of Hooke with Kepler. Newton held that even if he had received the concept of an inverse-square law from Hooke (but only "afterwards", that is, after he had thought of it himself), he nevertheless had "as great a right to it [the inverse-square law] as to the Ellipsis". His reasoning is as follows:

For as Kepler knew the Orb to be not circular but oval & guest it to be Elliptical, so Mr Hook without knowing what I have found since his letters to me, can know no more but that the proportion was duplicate quam proxim~ at great distances from the center, and only guest it to be so accurately & guest amiss in extending that proportion down to the very center, whereas Kepler guest right at the Ellipsis.

Whatever the merits of Newton's position with regard to Hooke, this statement leaves us in no doubt as to Newton's feeling that Kepler had only made a happy correct guess at the elliptical orbits. In fact, Newton continues, "And so Mr Hook found less of the Proportion [of the inverse-square] than Kepler of the Ellipsis". Newton was aware of the fact that Hooke really did not know fully, in the sense of all the conditions and consequences, the law of the inverse-square, because no one-- Hooke included--had been able to work out the proofs which today occur at the beginning of the Principia, and which I have described above. Furthermore, no one else had worked out how a sphere behaves gravitationally, that is, when its diameter is large enough to be a significant magnitude in relation to the distance over which the gravitating force acts. Newton was no doubt referring specifically to the mathe- matically difficult problem of the gravitational attraction of a sphere, when he wrote to Halley:

There is so strong an objection against the accurateness of this proportion [of the inverse- square], that without my Demonstrations, to which Mr Hook is yet a stranger, it cannot be beleived by a judicious Philosopher to be any where accurate. And so in stating this business I do pretend to have done as much for the proportion as for the Ellipsis & to have as much right to the one from Mr Hook & as to the other from Kepler. And therefore on this account also he must at least moderate his pretenses.

Although in stating this position about Kepler's having "guest right at the Ellipses", Newton did not refer specifically to the law of areas, I believe that he would have

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Kepler's Century

applied the same argument to the law of areas that he applied to the ellipses. The case is quite different for the harmonic law, however since this relation is purely numerical and merely depends on a simple comparison of the best values for the planetary distances and periods of revolution, both raised to appropriate powers.

There is one further aspect of Kepler's law which is important in considering the relations between Kepler and Newton. It is often said by modern historians of science, who are unknowingly repeating the statement made when Newton's manuscript was received at the Royal Society, that Newton gave a mathematical demonstration of the truth of the Copernican system as emended by Kepler. Such a statement would mean that Newton proved that Kepler's three laws are true, but this is not so. What he displayed was, first, the methematical or hypothetical conditions under which Kepler's laws may be valid; and he then indicated just how each law must be modified in the real world of our solar system, or of any physical system of one or more bodies moving mutually under the action of a mutual gravitational force.

In the beginning propositions in Book I of the Principia, Newton discusses the motion of a body moving about a center of force which is a mathematical point, which is a very different problem indeed from the determination of the trajectory of one physical body moving about another. Newton proves that Kepler's laws are true only under the strict mathematical conditions that such a body moves about a mathematical point, and that it may not be gravitationally affected by any other bodies in the system. If the above purely mathematical (or hypothetical) con- ditions do not obtain, then Kepler's laws are false. In the real world of the solar system, or the system of Jupiter and Saturn and their satellites, or the Earth-Moon system, Kepler's laws are no longer true, but must be modified. First of all, according to Newton's principles, each body moving in a planetary system or satellite system is acted upon gravitationally by more than one force--or, there is more than one center of gravitational force. The Earth's motion, for example, as Newton showed, cannot be considered only in relation to the attraction of the Sun; account must be taken also of the attraction of other planets, notably Jupiter. And in one of the most difficult problems of all, the motion of the Moon, Newton showed that it is necessary to take cognizance of the gravitational action of the Sun as well as of the Earth, if the actual or observed motions are to be considered in all their variations and departures from the simplest kinds of Keplerian regularities.

Newton showed, furthermore, that such perturbations were not the only cause of the difference between observed motions in the heavens and Kepler's laws. For even in a system of two bodies, without any outside perturbations, neither the law of elliptical orbits nor the law of areas can be applied simply, because of the effect of the mutuality of the gravitational force; each of the two bodies in such a system will move about their joint center of gravity. In the case of the Earth and the Sun, this new center is not very far removed from the geometric center of the Sun, but in a system like the Earth and Moon, where the sizes of the two bodies are significantly

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greater in relation to the distance between their centers and where the two masses do not differ by so great a factor, this effect is notable. Similar considerations apply to the third law as well. On this basis alone, the first two laws of planetary motion as stated by Kepler are strictly false for any pair of real bodies; at best, these laws are approximations requiring serious modificationY

Newton's Principia thus begins by specifying the conditions under which Kepler's laws are valid, but then demonstrates that in the real world (whether of the solar system or of any planetary satellite system) Kepler's laws must be modified. Newton did not stop there, but went on to derive the actual modifications that must be intro- duced into the harmonic law, the law of areas, and the elliptical orbits themselves, in the real universe of the solar system. As Newton said in Prop. 13 (Bk. III), " . . . if the sun were at rest, and the other planets did not act one upon another, their orbits would be ellipses, having the sun at their common focus; and they would describe areas proportional to the times of description". In practice, we find that "the actions of the planets one upon another are so very small, that they may be neglected", and in fact (as proved by Prop. 66, Bk. I), "they disturb the motion of the planets around the sun in motion, less than if those motions were performed about the sun at rest". Of course, as Newton showed, "the action of Jupiter upon Saturn is not to be neglected", because these two planets come quite close at conjunction, and because Jupiter's mass is so large. Newton computed that "the whole error" in the motion of Saturn about the Sun "may be almost avoided (except in the mean motion) by placing the lower focus of its orbit in the common center of gravity of Jupiter and the Sun (according to Prop. 67, Bk. I), and therefore that error, when it is greatest, scarcely exceeds two minutes; and the greatest error in the mean motion scarcely exceeds two minutes yearly".

I have stated above that the Copernican system as emended by Kepler was very different from the true Copernican system ;88 for not only did Kepler eliminate the circles which are so prominent in Copernicus's metaphysical hierarchy of values and are the basis of his models for computation, but he rejected the Copernican principle of uniformity of motion in favor of the area law. Above all, Kepler centered the system in the true Sun, rather than the Copernican mean Sun, so that the motions of the planets could be explained by physical causes, by the action of real forces emanating from the true Sun. In this sense, Newton modified the Keplerian system, since he altered the three laws of planetary motion that Kepler had announced, retaining only the Keplerian centering of the system upon the true Sun. ~9 But Newton did construct his own system of celestial mechanics upon a most significant Keplerian concept: that planetary motions are to be explained by the action of forces. Newton, possibly unwittingly, actually was Keplerian in introducing universal gravitation, since Kepler had suggested the concept of a kind of gravitating force. But I must repeat that Newton was most Keplerian in his general point of view that

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Kepler's Century

the motions of the heavenly bodies are to be derived from physical causes, and not be conceived merely in relation to geometric non-causal models (at least in the sense of a universal physical cause, rather than some kind of pseudo-mechanical constraint operating in a geometric model). This is the sense in which Kepler's century leads to Newton's, or in which Newton's century was truly Keplerian.

Before turning to the actual physical principles and concepts used by Kepler and by Newton, and the possible influence of Kepler upon Newton in this regard, let me say a word about one other aspect of the presentation of Kepler's laws in the Principia. I have mentioned the fact that Kepler's three laws occur at the beginning of Book III, where Newton presents the "System of the World" and applies the mathematical principles of natural philosophy which he has developed in the earlier books. In the second and third editions of the Principia, with which most of us are familiar, these laws of Kepler appear under the general rubric of "Phaenomena", but in the first edition, and in certain preliminary versions, they were called "Hypotheses". My presentation of Kepler's laws in relation to Newtonian principles may give us some insight into this particular designation, since, as we have just seen, in the real world, in our solar system or in any of the planetary systems, Kepler's three laws of plane- tary motion are not true but must be considered as approximations, or as Newton first called them "Hypotheses". Another way of stating this conclusion is that Kepler's three laws are true within the limits of observation, or hold in nature only to a certain specified degree of accuracy. Or, these laws are only phenomenologically valid; that is, they do not hold accurately in the sense of a mathematical relationship, but only within the limits of the numbers which we obtain by actual measurement or observation. And, in fact, in presenting Kepler's laws in Book III, Newton gave his readers the numerical data which set the degree to which these phenomenologi~- cally established laws are verifiable, the limits within which Kepler's laws may be considered phenomenologically "true". I believe that this aspect of Newton's analysis of Kepler's laws of planetary motion may explain why Newton could legitimately first have called these planetary relationships "Hypotheses", and then later "Phaenomena". This alteration of "Hypotheses" to "Phaenomena" would seem otherwise surprising, since Newton held that whatever is "neither a phenomenon" nor "deduced [or induced] from phenomena" is to be reckoned a hypothesis. 4°

Let me conclude this analysis by referring to a Keplerian concept that was of great significance for Newton's century, "inertia". There is no doubt that Kepler intro- duced into the language of physical science the technical term "inertia", but the meaning he gave to inertia was not the same as the one with which we are familiar. Kepler's inertia is a property of bodies that is related to the principle that matter is not self-animating or self-moving. This concept was very important in Kepler's program of destroying the traditional hierarchical view of space (which had been so important a component of Aristotelian physics) and the special position in space of our earth as an immovable center. Kepler held that matter is characterized by

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L Bernard Cohen

"inertia" or a fundamental kind of laziness or inert-ness; hence it cannot move unless there is a motive force to keep it going. If that force should cease acting, the body would stop moving--and would stop moving at once wherever it happened to be. Consequently, there could be no "proper place" for different kinds of matter, in the sense of the older physics and the older astronomy. Newton's inertia is somewhat different, for according to Newton inertia will keep a moving body in its uniform rectilinear motion after the external moving force has ceased to act. Inertia, in other words, keeps a body at rest if it is at rest, and keeps a body in motion if it is moving; this inertia causes a body to resist any change in its "state", whether that be a state of rest or of uniform rectilinear motion. Newton's concept in fact differs somewhat from that which is attributed to him in most elementary textbooks, because in the Principia he still thought of inertia as a "force", a "vis inertiae" or "vis insita materiae"; such a "force" was different in kind from those external forces which produce a change in state, rather than maintaining a state or resisting a change in state. 4x Thus the inertia of Newtonian physics is quite different from the inertia of Keplerian physics.

How did Newton arrive at his views concerning "inertia" and "vis inertiae" ? I have found that Newton came upon the actual expression "inertia" (in the form "natural inertia") in reading through one of the editions of the correspondence of Descartes. With the greatness of all men of genius, he seized upon this concept (without knowing it to be of Keplerian origin), and altered it by the addition of a principle which he had also found in Descartes: that motion, like rest, may be a "state". I have found some indications that Descartes may have derived his notion of a "state of motion" from Galileo, although indirectly. This process of taking concepts and expressions from the literature and using them in a wholly new fashion, as both Descartes and Newton did, seems to me to be characteristic of many of the greatest and most revolutionary innovations in science, and I have given it the general name of "transformation". 42 The development of the major lines of thought in the science of dynamics shows clearly what appears to be a universal process, in which the greatest men of science, inspired by their reading, do not merely adopt or transfer a concept or expression they may find in their reading, but rather transform it, the encounter thus becoming the occasion .(but not the cause) of the great intellectual leap forward which characterizes such great contributions as Newton's. In this light, we may find it especially interesting that Newton introduced into the language of physics a new concept which he had transformed from one of Kepler's, retaining Kepler's name "inertia"; later on, he modified this first version by the addition and transformation of yet other intellectual ingredients. What may seem most striking about Newton's introduction of "inertia" into our language of physics as a funda- mental or universal concept is that he probably did not even know the Keplerian origin of the technical term that he so transformed, and which he found not in reading Kepler, but in a discussion of "natural inertia" (in which Kepler's name was not mentioned) in the correspondence of Descartes. Many decades later, Newton did

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Kepler's Century

happen on a reference to Kepler's inertia in association with Kepler's name. This occurred while Newton was reading Leibniz's book, the Theodicy. He thereupon put a note in his own copy of the second edition of the Principia, intending it to be included in an eventual third edition, explaining that he did not have in mind Keplerian inertia which brings bodies to rest, but rather a somewhat different inertia which maintains a body in a state of rest if it is at rest, but will also maintain a body in a state of motion if the body is moving. This annotation did not, however, appear in the third edition of the Principia. 43

We may learn from this example how the influence of one man upon another transcends the boundaries or limitations of the reading of a man's actual works. Newton could draw upon the Keplerian physics of motion without even being aware that the concept which he transformed, and which was so central to Newtonian physics, had even originated with Kepler. And he did so, not by reading Kepler, but Descartes. In this sense, we must be cautious in evaluating the influence of Kepler in Newton's century.

Earlier, I mentioned the fact that Newton lauded Galileo in the Principia, but tended to ignore Kepler, and that Newton was almost as ignorant of the actual writings of Galileo as he was of Kepler's. Newton appears not to have read Galileo's "Two New Sciences" before writing the Principia. But Newton so admired Galileo, and held him to be so great a genius, that he believed (consciously or unconsciously) that Galileo's scientific thought must have been Newtonian. Thus he assigned to Galileo the discovery of the first two laws of motion, and said that Galileo had used these two laws to find that free fall is an example of uniformly accelerated motion and that the trajectories of projectiles are parabolas. This attribution to Galileo of the first two laws of motion is in striking contrast to Newton's denial to Kepler of the first two laws of planetary motion. It must have seemed "obvious" to Newton that Galileo would have recognized that a constant force produces a constant acceleration, so that in free fall from rest, as in other forms of uniform acceleration, V -- AT and S = ½AT 2. This great compliment has set a pattern for interpreting Galileo which we have followed ever since. Under the influence of Newton, it is all too often asserted that Galileo did know those first two laws of motion, and that he had discovered the laws of uniform acceleration or of free fall in the manner suggested by Newton in the Principia.

Although Newton knew only of Kepler's notion that the "inertia" of bodies tends to keep them at rest or to bring them to rest if there is no motive force acting upon them, Kepler was not always so limited as Newton supposed, and as many historians of science have assumed. In his Dream (or posthumously published Somnium), as Edward Rosen has shown, Kepler actually went beyond the original primitive concept, discussing how "finally the bodily mass proceeds towards its destination of its own accord". Rosen observes that this statement implies a situation in which "a motion, once initiated, continues as a result of something internal, and without the help of an external force, whether mechanical or not". In one of the notes

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or annotations (Note 75) on the Dream, Kepler introduces a situation in which there is a cancelling out of the external motive forces, under which circumstances he says that "the body itself as a whole propels its limbs". It is curious indeed, as Professor Rosen observes, that in this case "Kepler did not attach the label 'inertia' to this spontaneous continuation of motion", but discussed this possibility only in terms of the expression "sponte sua". I find this exceptionally noteworthy, since the words sponte sua occur a number of times in Lucretius's scientific poem De Natura Rerum, as an equivalent expression for quantum in se est, in specific relation to a kind of inertial motion of atoms which may continue of and by itself. It is this same expression, quantum in se est, which occurs in both Descartes's Principia and in Newton's Principia when they introduce the concept of inertia and the law of inertia. 44

By the end of the eighteenth century and early part of the nineteenth, some scientists were becoming aware of Kepler's contributions to astronomy and physics. Robert Small published a whole book in English on Kepler's astronomical dis- coveries, largely a paraphrase of the Astronomia Nova. Auguste Comte was only one of a number of writers who discovered Kepler's concept of inertia, but only Comte went so far as to suggest that Newton's laws of motion be renamed for Kepler. Delambre's account of Kepler in his monumental history of astronomy is of book length, and remains today a landmark in Kepler scholarship; but the low state of the then-current knowledge of Kepler is exhibited in Delambre's ignorance of the fact, so prominently displayed by Kepler, that the preface on hypotheses in De Revolutionibus was not written by Copernicus but by Osiander.

The close of the nineteenth century saw a great resurgence of historical scholar- ship concerning the science of Kepler's century. But whereas there was a huge outpouring of books and articles on Galileo's life and science, there was precious little on Kepler's. Antonio Favaro produced the magnificent national edition of Galileo's Opera, to replace the earlier edition prepared by Eugenio Alb~ri, but no one under- took a new edition of Kepler that would be fully worthy of his achievement. 4~ The Favaro edition of Galileo, first issued during the monarchy under the patronage of the King, has been twice reprinted, providing a mirror of the political history of Italy; for the second edition was published under the sign and seal of I1 Duce, and thc third under the name of the President of the Republic. But there still exists no adequate or full edition of Kepler, although there is a splendid edition of the Opera Omnia of Tycho Brahe, edited by J. L. E. Dreyer. At long last, happily, a truly great edition of Kepler, envisioned as occupying 22 volumes, begun in 1937, may possibly be completed in our lifetimes. Planned by Walther von Dyck and Max Caspar, and produced under the auspices of the Deutsche Forschungsgemeinschaft and the Bayerische Akademie der Wissenschaften, the editors have been successively Max Caspar and Franz Hammer. Caspar has written a full-length biography of Kepler, and he has also given us a valuable check-list of Kepler's writings and a guide to the secondary literature concerning him; an English version of this biography, prepared

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Kepler's Century

by C. Doris Hellman, contains valuable supplementary materials. Another major study on Kepler is Alexandre Koyr6's La R[volution Astronomique, containing extended quotations in translation from Kepler's own writings. And on a more popu- lar level, there is a book-length presentation of Kepler's life and personality, and his scientific accomplishment, in Arthur Koestler's The Sleepwalkers. 46

Bit by bit, Kepler's thought-processes and his life as a scientist are becoming known to historians and scientists at large. The realization is growing that the scientific revolution was characterized by other profound changes than those con- ceptual innovations and methodological procedures which we associate with Galileo (chiefly the Galilean art of combining experiments and critical observations with a theory based on mathematics). We know today that possibly the most significant development in the science of the seventeenth century may have been the recognition that the laws of nature are not only written in the language of mathematics, but of higher mathematics, and that such mathematical relations must express physical causes, whose nature and mode of action are to be elucidated by the study of phenomena in relation to such causes. This "Newtonian" aspect of modern science is now seen to have been initially Keplerian, even though Kepler himself did not always have as much success with the physical causes as with the mathematical relations to which they led him. We may find an affinity in our time, therefore, not only with Kepler's aims in science, but with the kind of science he produced. Even the atom exhibits a Keplerian set of orbits, and we may agree with Sir Arthur Eddington that in the twentieth century we have sought a Keplerian order within the atom, just as Kepler did in the skies.

In the German-speaking world of the late nineteenth and early twentieth century, Kepler began to be recognized as a major figure--in the full dimensions of his personality. Some examples will indicate a concern for Kepler: taken from philosophy, physics and literature. A strong reaction against the mechanistic philosophy led such men as Hegel and Fichte to laud Kepler and even to assign to him a more important place in history than Isaac Newton. In science, the image of Kepler became more and more commonly found. Otto Runge is reported to have said that the Balmer laws of atomic spectra were Kepler laws of the atom awaiting their Newton; in this case the Newton turned out to be Niels Bohr. Kepler even became a major figure in a novel, Tycho Brahes Weg zu Gott, written by Max Brod and pub- lished in 1915 (translated into English, 1928): the dedication reads (in translation) "To my Friend Franz Kafka". Max Brod's name is not generally known to astronomers or historians of science, but humanists will recognize him as a man who had to face one of the great decisions of the twentieth century. Brod was the literary executor of that Franz Kafka to whom he had dedicated his novel on Tycho; and Kafka had left strict instructions that all his manuscripts be burned. Brod, however, knowing that Kafka's unpublished novels and stories had a quality of greatness perhaps unmatched in modern literature, could not bear to destroy these

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I. Bernard Cohen

precious papers. And it is owing to Brod's intervention that we are able to read Kafka's writings today.

Max Brod is not a major novelist (in the sense of Joyce, Mann, Proust or Svevo), and I am not at all certain that Tycho Brahe's Redemption is a good novel, or even an accurate portrayal of Tycho's personality. It is a kind of "moral tale" about the sin of pride; but it has a happy ending when pride is finally overcome by the love of truth. Pride appears in the guise of Tycho's personal vanity and his conviction about the superiority of his own system of the world; the conflict arises from Tycho's belief that God had made him the world's greatest observer, which implied that the Tychonian planetary observations should be entrusted only to the greatest mathe- matical astronomer alive. Under such circumstances, does a vain man choose a sycophant who says he believes in the Tychonic system ? Or, does he turn over his tables of observations to a truly great creative mathematical scientist like Kepler, who was an admitted Copernican and no Tychonian ? Tycho's choice of Kepler was a good one for science, for without Kepler there would never have been the reforma- tion of astronomy that Kepler was able to base on Tycho's observations. Surely we may agree with J. L. E. Dreyer that "Longomontanus would doubtless have hoarded them [i.e. the observations] carefully as a great treasure, but he would most certainly not have discovered the laws of planetary mot ion . . . " .

Was Tycho Brahe redeemed ? I think not. But this alleged redemption is not the real source of our interest in a novel about Tycho and Kepler. What makes this novel by an Austrian from Bohemia so significant to us is the genesis of Brod's portrayal of Kepler. In the conclusion of the novel, Brod refers to the "encounter of the two great men, which we have sought to depict in these pages not without some freedom", but he does not tell his readers that Kepler's personality was partially drawn from the life, based on a scientist of Brod's own acquaintance. In describing the impression that young Kepler made on the inhabitants of Prague, and Kepler's personality and poirit of view, Max Brod apparently had in mind another brilliant German mathematical-physical scientist who had just come to Prague. We have it on the authority of Philipp Frank (the biographer of Einstein, and Einstein's successor in the Prague professorship), that it "was often asserted in Prague that in his por- trayal of Kepler, Brod was greatly influenced by the impression that Einstein's personality had made on him". Frank remarks that "the figure of Kepler is so vividly portrayed that readers of the book who knew Einstein well recognized him as Kepler". For instance, when W. Nernst, the German chemist (discoverer of the so- called fourth law of thermodynamics), had finished reading Tycho Brahes Weg zu Gott, he is reported to have said to Einstein, "You are this man Kepler". And so, in his biography of Einstein, Philipp Frank found it "appropriate to quote several passages where Brod characterizes his Kepler" in order to suggest "certain aspects of Einstein's personality". As a biographer, Frank found the "words of a poet" to be possibly "more impressive than the description of a scientist".

26

Kepler's Century

Through most of his life Einstein closely associated himself with Kepler, whom he admired for his gentle personality as much as for his scientific achievement. When Einstein talked about the fact that Galileo would not give Kepler credit for his discoveries, he seemed to be more than a mere litigant or advocate of Kepler's cause. Why did Einstein feel so close to Kepler ? He described Kepler as "a supreme and quiet man", as one "who reached the exalted goal he set himself in spite of all internal and external difficulties". Above all, his "admiration for this splendid man" was accompanied by a "feeling of admiration and reverence, the object of which i s . . . the mysterious harmony of nature into which we are born". He concluded:

It seems that the human mind has first to construct forms independently before we can find them in things. Kepler's marvelous achievement is a particularly fine example of the truth that knowledge cannot spring from experience alone but only from the comparison of the inventions of the intellect with observed fact.

Very likely, Einstein saw in Kepler a kindred spirit in the degree to which he held that "Kepler's lifework was possible only once he succeeded in freeing himself to a great extent of the intellectual traditions into which he was born". For Einstein this meant not only that Kepler had to free himself from "the religious tradition, based on the authority of the Church", but also from the "general concepts on the nature and limitations of action within the universe and the human sphere, as well as notions of the relative importance of thought and experience in science". So closely did Einstein feel a sense of identity with Kepler that in a conversation he once said, "You know it has always hurt me to think that Galileo did not acknowledge the work of Kepler". He thought that Galileo's lack of mention of Kepler's positive achievement in his book on the "Two Systems of the World" might have been akin to Newton's refusal to give Hooke "some mention" in the Preface to the Principia. "That, alas, is vanity", said Einstein, "You find it in so many scientists".

Scientists and historians are especially drawn to Kepler today because the qualities of his personality and his scientific life seem to strike so immediate a bond with ourselves. Kepler is always human, always evoking our sympathy. His life was dominated by a mother with a powerful personality. In fact, for a while Kepler even had to forego his scientific career in order to serve as his mother's advocate in her trial for allegedly practising witchcraft. His father was a more shadowy figure, appearing in intervals between his service as a mercenary and then disappearing from view once again.

Whereas Galileo sought and won many honors and favors of aristocratic patronage (until his trial by the Inquisition), Kepler was forever losing positions and finding his salary in arrears. He stands before us as an outstandingly great creative scientist, but also as a man who did not ever quite make it fully with the "establishment". We s e e

him as a man troubled in himself, lacking in that inner security and place in society that enabled a Galileo to become a fighter in the public arena. In Kepler's comparison

27

iT. Bernard Cohen

of himself to a poor dog beaten by a stick, we feel ourselves one with him~for we ourselves conceive our fate to be that of lone individuals lost in a world of mechanism. But nowadays Kepler's life seems especially notable because he did not seek worldly fame or public recognition; indeed, he never wavered in his devotion to the cause of truth and the need to see that truth might prevail.

In the cosmos and in the sub-microscopic world of molecules, atoms and funda- mental particles, we continually find Keplerian harmonies and we too may stand in awe before Nature's array of numerical relations. Thus today we may especially appreciate the way in which Kepler rejected the old physics, and praise him for so courageously emending the current concept of what was then considered to be the "proper" way of explaining natural phenomena. In our own revolutions of relativity and quantum theory, and in atomic physics and particle theory, we too have made emendations of a comparable quality. Today, we appreciate the extent to which the world itself may be Keplerian, and we are aware that advances in the sciences do not move ahead strictly by the application of a method which can be written out as a series of rules and precepts to be given to students--in the manner that the great physiologist Santiago Ram6n y Cajal wrote out his Censejos, so that his students might become able doctors, good scientists, and Nobel Prize winners. We have become sensitive to the effect of the creative personality in the advance of science, and we see that the great leap forward made by Kepler was a result of the kind of man he was. We cannot honor Keplerian science without honoring Kepler, and accepting him in all the full dimensions of his personality.

Einstein correctly described Kepler as "one of the few who are simply incapable of doing anything but stand up openly for their convictions in every field". We share Einstein's admiration for Kepler's honesty and sincerity, for his courage to assert the truth even when to do so might entail personal danger.

We esteem Kepler primarily for the magnitude of his creative gifts in science, and his great contributions to physics and astronomy; but at the same time we respect him for having been the kind of human being he was and for the unique personal quality of his science. Michael Polanyi called attention to that quality of Kepler's science when he stated that for Kepler "astronomic discovery was estatic communion". Quoting a famous passage from Kepler's "Harmonics", 47 Polanyi then felt obliged to comment, "What Kepler claimed here about the Platonic bodies was nonsense, and his exclamation about God's having waited for him for thousands of years was a literary fancy"; but Polanyi quite properly reminded us that Kepler's "outburst conveys a true idea of the scientific method and of the nature of science; an idea which has since been disfigured by the sustained attempt to remodel it in the likeness of a mistaken ideal of objectivity". A similar sentiment was expressed by W. Carl Rufus 48 when he wrote: "The chief glory of Kepler . . . is not fully revealed by his discoveries in the physical realm. It rests in the unity of his two-fold nature, scientific and religious, as he groped in the material universe to reveal the mind of the Maker".

28

Kepler's Century

The celebrations of the tercentenary of Kepler's birth have produced many studies of Kepler's life and work which will help to make better known the true character of Kepler's science and the qualities of his personality. We shall continue to honor him for his three laws of planetary motion, but our praise will not be diminished because of our awareness of the many other relations" which Kepler believed he had found and which he thought were just as significant as the three laws which later proved so important for the development of Newtonian science. As we begin to learn that Kepler's science was different from the narrow image we have of science today, our respect for this mighty creative scientist shall increase. When once we know the man Kepler in all his full dimensions, we shall honor him especially as one whose view of himself and nature has a special relevance for our own times. For us he shall be a fit companion of the mind: in his indomitable spirit, in his personality, and in his scientific achievement.

Notes

1. This article is based on research supported by the National Science Foundation (U.S.A.) grant no. GS-2063X3. For a guide to the essential literature relating to the subject of this article, see Supplementary Notes 1, 2.

2. We shall see below that when the manuscript of Newton's Prindpia was presented to the Royal Society, it was described in just such words as I have used: a demonstration of the Copernican hypothesis, as emended by Kepler.

The Keplerian system of the world differed from the Copernican in at least two fundamentals. Kepler placed the Sun, immobile, at the true center of the Universe, and accordingly reckoned planetary orbits with respect to the Sun itself; Copernicus reckoned planetary orbits with respect to a "mean Sun" or the center of the Earth's orbit, and hence a point in space different from the Sun's place in the heavens. Kepler's alteration is consonant with his views concerning forces and motions, and his conclusion therefrom that the solar force must cause planetary motions and must originate from the true Sun (and not a suppositious "mean Sun"), the center for reckoning planetary orbits. A second difference between the Keplerian and Copernican systems is the intro- duction by Kepler of the concept of non-circular orbits. Since Copernicus insisted, and at some length, that the nature of the planets requires that they must move only in pure circles or com- binations of circles, Kepler's introduction of elliptical orbits and his rejection of the Copernican circles cannot be held to have been but a minor modification of the Copernican system. Generally speaking, it is the Keplerian system that is meant when historians and scientists refer to the "Copernican system". It would be more correct to use the expression Keplero-Copernican, so as still to honor Copernicus while giving Kepler credit for his own radical innovation.

3. In Kepler's calendar, the reformed or Gregorian calendar, we would reckon the 100 years as ending in 1642. Newton's century would begin, in the new style Gregorian calendar, in January 1643, since Newton was born on 8 January 1643, in that new reckoning.

For those who may enjoy playing with numbers, as Kepler did, I may point out that the years marking the beginning and the end of the century I have called Kepler's have one property in common: if you add up the four numerals comprising either of the dates 1543 or 1642, the result is that incredible number 13.

4. It is only in the sense of being a "prelude" to Newton's century that we are justified in referring to the hundred years 1543-1642 as "Kepler's century".

5. It may be argued that to have had a significant influence on the formulation of Newtonian celestial dynamics is historically of far greater importance than to have conditioned the scientific

29

I. Bernard Cohen

thought of the whole century (or even the years 1611-87) in a more or less continuous fashion. But such considerations are irrelevant to the judgment as to whether or not, in any real sense, Kepler may have been a dominant figure in seventeenth-century science, or may even have exerted a continued and productive influence on the thinking of men of science (whether major or minor) during his own hundred years.

6. Galileo's Discorsi were written in Italian in the form of a dialogue; but major parts of a treatise are presented in Latin. The Italian edition of 1858, prepared by Adriano Carugo and Ludovico Geymonat, contained an announcement of the "traduzione dei brani in Latino".

7. I refer specifically to Kepler's Mysterium Cosmigraphicum, Harmonice Mundi, Astronomia Nova, Dioptrice, Astronomia Pars Optica, and Epitome Astronomiae Copernicanae.

8. For the editions and reprints of Kepler's major works, see Supplementary Note 1, below. 9. Not only have Galileo's works been printed and reprinted in many languages ever since the

seventeenth century, whereas "Kepler's works have been reprinted rather rarely"; the fact is, as Owen Gingerich has observed, "most of the reprintings [of Kepler's works] occurred in connec- tion with the greater interest in Galileo". Thus Kepler's Dioptrice was reprinted with Galileo's Sidereus Nuntius in London in 1633 and 1683; and Kepler's Dissertatio cum Nuncio Sidereo was reprinted together with this work of Galileo's in Modena in 1818, and in Florence in 1846 and in 1892. See Supplementary Note 1.

10. Published in two Latin editions and two English versions in the eighteenth century, Gregory's Elements of Physical and Geometrical Astronomy (1726) has just been reissued in facsimile, with an introduction by I. B. Cohen (New York, London: Johnson Reprint Corporation, 1972).

11. In an earlier tract, De Motu, as we shall see below, Newton gave Kepler credit for more than just the third planetary law, but not for any contribution to dynamics.

12. By a "mystic" I would understand an individual who found or acquired knowledge directly without the intervention of the reason. Kepler's scientific research may have been aided by what he considered divine assistance, but in his scientific work Kepler did not short-circuit the process of ratiocination, in the way that "true" or "proper" mystics have always done. (For a classic example of the receipt of mystical knowledge, see the autobiography of Sta Teresa de Jestis.) To believe that nature displays number relations or that in nature there is a special significance of geometry, as Kepler did, does not seem to me to be an exhibition of classical mysticism.

13. Although Bertrand Russell believed Kepler must have had some insight into the "scientific method" (for otherwise how could he have discovered his three laws ?), he criticized Kepler's Copemicanism in these words: "It would be doing Kepler more than justice to suggest that in adopting the Copernican hypothesis he was acting on purely scientific motives. It appears that, at any rate in youth, he was addicted to sun-worship, and thought the centre of the Universe the only place worthy of so great a deity." Need we comment ? Russell did, however, believe (in his naive and optimistic view of scientists, scientific discovery, and scientific method) that "None but scientific [ !] motives, however, could have led him [Kepler] to the discovery that the planetary orbits are ellipses and not circles".

Gerald Holton has called our attention to an example from recent physics in which the his- torical record seems to have been perverted by a desire (however unconscious) to have the advance of science based upon a method founded on a more empirical basis than the facts may warrant; see his article "Einstein, Michelson, and the 'Crucial Experiment'", Isis, 62, 133-97 (1969).

14. On this topic see O. Gingerich, "The origins of Kepler's third law", Vistas in Astronomy, Ed. A. Beer, vol. 18, pp. 595-601, 1974.

The reader wishing to obtain an authoritative general view of Kepler's life and scientific work may be referred to Gingerich's article in the Dictionary of Scientific Biography, edited by C. C. Gillispie, and currently being published by Charles Scribner's Sons.

15. Although such an argument is often ridiculed, it may be pointed out that Bode's "law" is based on similar reasoning and once served in the discovery of a new planet.

16. Tucked away in the third book of the Principia in the first edition there was a reference to the divine providence, but this was very minor and no more than an aside. The first edition ended

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Kepler's Century

with a discussion of comets; the famous concluding General Scholium appeared for the first time in the second edition (1713). Newton did write out the draft of a "Conclusio" which he never completed for publication, and also wrote out a draft of the Preface which contained much more speculative material than the one which was printed in the first edition (1687). The drafts of the "Conclusio" and of the Preface have been published by A. R. Hall and Marie Boas Hall in their edition of Unpublished Scientific Papers of Isaac Newton (Cambridge: at the University Press, 1962). Concerning Newton's reference to the divine providence in the first edition of the Principia, see I. B. Cohen, "Isaac Newton's Principia, the Scriptures, and the Divine Provi- dence", published on pp. 52348 of Essays in Honor of Ernest Nagel : Philosophy, Science, and Method, edited by Sidney Morgenbesser, Patrick Suppes, and Morton White (New York: St. Martin's Press, 1969).

17. In the nineteenth century some scientists, such as Michael Faraday, could still include in published scientific reports some account of the history of their investigation and discoveries. But such information W~s only secondary, and appeared primarily when it was relevant to the setting forth of a revolutionary new idea or the description of a sequence of experiments. In the eighteenth and nineteenth centuries, however, there was rarely if ever a scientific work as replete with autobiographical information as Kepler's, and I know of none in which so much space is given to a presentation of research which failed to yield the desired result, or of the kind of divine inspiration which Kepler alleged had guided his experimentation and theorizing.

18. In his published works and in manuscripts prepared for circulation, Newton generally left out references to his concern with non-orthodox scientific questions, although here and there he might mention such matters obliquely or give a hint as to his concerns (notably in the latter Queries of the Opticks). A few scholars, notably J. E. McGuire and P. M. Rattansi, have begun the serious study of Newton's alchemical manuscripts and others which relate to science in what then and now could be conceived as an unorthodox fashion.

19. Albert Einstein, in a draft preface to Kepler's letters, warned the reader to "watch out for remarks concerning astrology. They show that the anguished inner foe had been rendered harm- less, even though he was not yet altogether dead".

20. We must not forget that there have traditionally been two kinds of alchemy, or two alchemical traditions: extrinsic and intrinsic. In referring to the divorce of chemistry from alchemy, therefore, a distinction must be made between intrinsic and extrinsic alchemy. Boyle and Locke, like Newton, were concerned with intrinsic alchemy, that is, the actual chemical process of metallurgical transformation. Newton's extensive manuscript notes reveals that he was also interested in extrinsic alchemy, that is, he read works which were not necessarily purely alchemi- cal, but partook of a more mystical strain, including the mysteries of life and the ultimate nature and destiny of man.

21. Conduitt's note does not offer any evidence that Newton had read the Dioptrice rather than the Astronomiae Pars Optica. Since the latter was published in 1604 and not reprinted again until Frisch's edition of Kepler's Opera in the mid-nineteenth century, it would seem more probable that a tutor would have assigned the Dioptrice, which had just been reprinted in England. Fur- thermore, the form and length of the Dioptrice appear to be better adapted to an undergraduate's reading.

22. As shall be mentioned below, the law of areas was generally not mentioned in treatises on astronomy. Even Horrox apparently was either unaware of this law or thought it of insufficient importance to be mentioned anywhere in his writings.

On the dissemination of Kepler's three laws of planetary motion, see J. L. Russell, "Kepler's laws of planetary motion: 1609-1666", British Journal for the History of Science, 2, 1-24 (1964).

23. It will certainly seem odd that this relation should have been attributed by Newton to Kepler in Book III, whereas in Book I he said the relation had been observed in the motions of heavenly bodies by Halley, Hooke and Wren. In the reference to the three Englishmen, however, Newton was not indicating a first discovery so much as a discussion as to the cause of Kepler's laws. It

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L Bernard Cohen

was to this end that Halley had come to Cambridge to ask Newton's opinion: a visit which led to Newton's writing the Principia.

24. The concern for Kepler expressed in Halley's review of the Principia leads to the suggestion made below that Halley may have been responsible for the description of Newton's work as a demonstration of the Copernican system in the form emended by Kepler; it would be of interest to explore Halley's writings carefully to discover the extent of his knowledge of Kepler's actual treatises, and his familiarity with Kepler's laws and principles.

25. The Keplerian aspect of this essay is revealed in the title, which emphasizes the cause (in a physical sense) of the heavenly motions. Translation by E. J. Collins.

26. On the relation of this work to Book III of the Principia, see I. B. Cohen, Introduction to Newton's "Principia" (Cambridge, Mass. : Harvard University Press; Cambridge, England: at the Univer- sity Press, 1971).

27. The manuscripts in question are the several draft versions of the tract De Motu, published by W. W. Rouse Ball, by A. R. Hall and Marie Boas Hall, and by John Herivel; for further references by Newton to Kepler's laws, see Newton's autobiographical statements, collected in Appendix I to my Introduction (cited in note 26).

28. That is, by "theory of the moon", Newton and his contemporaries did not mean the physical cause of the actual motions, in the sense of gravitational perturbing forces, but rather the rules or geometric devices to make possible the prediction of the course of the Moon's motion.

29. See Edward Rosen, "The Moon's orbit in Kepler's Somnium", Centaurus, 11,217-21 (1967). In the Epitome, Liber Sextus, Pars Q.uarta ("De Inaequalitae Lunae Soluta"), Kepler asks how many circles are needed to solve the inequalities of the Moon, and replies : "Only one eccentric orbit, of a shape which is nearly circular, that is, elliptical . . . . "

30. Either the Dioptrice or the Astronomiae Pars Optica; see note 21. 31. See I. B. Cohen, "Newton's attribution of the first two laws of motion to Galileo", Atti del

Symposium Internazionale di Storia, Metodologia, Logica e Filosofia della Scienza "Galileo nella Storia e nella Filosofia della Scienza" (Florence: Gruppo Italiano di Storia della Scienza, "Collection des Travaux de l'Acad~mie Internationale d'Histoire de Sciences, N. 16", 1967), pp. xxv-xliv.

32. This is the same procedure we have seen Newton using in deriving "inequalities" in the Moon's motion from principles of force and motion, notably the perturbing effect of gravitational forces.

33. Newton proved, in other words, that a planet (considered as a point-mass) moving about a center of force (which could be at rest or in motion) in any one of the conic sections, according to the law of areas, would be combining an inertial motion with the continued accelerative effects of a central force varying inversely as the square of the distance. The converse case, also explored by Newton, namely, the orbit produced by a central force (varying inversely as the square of the distance) acting continuously on a body with an initial component of inertial motion, did not yield a unique answer unless a further specification of the initial conditions were made; the orbit could be any one of the conic sections, ellipse or parabola or hyperbola, or even a circle or a straight line.

34. The untrained and unsuspecting reader often supposes that for a specified elliptical orbit, one has only to know any two orbital positions separated by a period ofx days in order to predict any future position y days later. For it would seem that one has only to compute the area swept out during those x days by a radius vector drawn from the sun to the planet, and then find another area so swept out in the proportion ofy to x. As Kepler knew well, however, this problem cannot be solved by the methods of ordinary (finite) algebraic procedures. This is, in fact, the reason that astronomers in the age between Kepler and Newton did not use (or even refer to) the laws of areas, but introduced one form or another of approximation, as shall be discussed immediately below.

35. See D. T. Whiteside, "Newton's early thoughts on planetary motion: a fresh look", British Journal for the History of Science, 2, 117-37 (1964).

36. In the region of each apse, the mathematical problem is simpler than elsewhere in the orbit; there is a further technical aspect of planetary motion near the apsides, that there a line from the

32

Kepler's Century

Sun to the planet will very nearly coincide with a line drawn from the Sun perpendicularly to the tangent to the orbit drawn through the planet's position.

37. The logical connections between Galileo's and Kepler's laws and Newton's dynamics, and the possibility of deriving the Newtonian theory from Kepler's or Galileo's, has been discussed by Karl R. Popper, "The aim of science", Ratio, 1, 24--35 (I 957). A revised version, together with a "brief discussion of the correction of Galileo's and Kepler's results by Newton's theory", has been published in Popper's recent book, Objective Knowledge: An Evolutionary Approach (Oxford: at the Clarendon Press, 1972). I have written an extended discussion of Popper's article, currently in press in the Festschrift for A. Sambursky, edited by Yehuda Elkana, to be published by the Humanities Press, New York.

38. See note 2. 39. Whereas the changes introduced by Kepler into the Copernican system are so great as to alter

the foundations of the Copernican system, and so require the name Keplero-Copernican or Keplerian system, these Newtonian modifications do not require that we alter the name of the system itself. But it does seem to me that scientists and historians should be careful in making a distinction between the use of the expression "Kepler's laws" in the sense of a set of laws announced by Kepler and in the sense of a set of laws which we apply in astronomy today, with the modifications introduced by Newton. On this point, see the works cited in note 37. Incidentally, this analysis shows how misleading is the common statement of a Newtonian "synthesis"--in which supposedly Newton produced a general theory of celestial dynamics that incorporated laws announced by Kepler and also by Galileo.

40. The reader should not assume, however, that Newton always used the words "hypothesis" and "phenomenon" in so equivalent a sense.

41. An analysis of Newton's concepts of "force" and "inertia" (displaying the stages by which Newton's commitment to inertia is shown to have been the result of successive stages of revision, including certain changes in concept made just on the eve of the final version of the Principia) may be found in R. S. Westfall, Force in Newton's Physics (London: Macdonald; New York: American Elsevier, 1971). Another manner of conceiving the evolution of the concept of inertia is given in Chapter Two of the work cited in note 42.

42. The concept of "transformation" has been developed by me in the Wiles Lectures, given at Queen's University, Belfast; to be published under the title: The Newtonian Revolution in Science : with illustrations of the Transformation of Scientific Ideas (Cambridge: University Press, in preparation).

43. Concerning Newton's contrast of Kepler's concept of inertia and his own, see I. B. Cohen, "Newton and Keplerian inertia: an echo of Newton's controversy with Leibniz", pp. 199-211 of vol. 2 of Science, Medicine, and Society in the Renaissance : Essays to honor Walter Pagel, ed. by Allen G. Debus (New York: Science History Publications, 1972).

44. For Edward Rosen's analysis see his article : "Kepler's Harmonics and his concept of inertia", American Journal of Physics, 34, 610-13 (1966); also his edition of Kepler's Somnium, the Dream, or Posthumous Work on Lunar Astronomy, translated with a commentary (Madison, Milwaukee, London: The University of Wisconsin Press, 1967), Appendix I. My discussion of the use of the phrase from Lucretius by both Descartes and Newton may be found in an article: "Quantum in se est : Newton's concept of inertia in relation to Descartes and Lucretius", Notes and Records of the Royal Society of London, 19, 131-55 (1964).

45. While there were many editions and collections of Galileo's writings produced before the Favaro edition, there was no similar succession of editions of the writings of Kepler. In the middle of the nineteenth century there appeared an eight-volume edition of Kepler's Opera Omnia, edited by Frisch, which is very incomplete, particularly with regard to manuscript writings which were not published during Kepler's lifetime, including correspondence. In contrast to Favaro's edition of Galileo, which had many predecessors to draw upon (including the edition of Alb~ri), Frisch's edition of Kepler was a completely pioneering effort. On this topic see, further, Supplementary Note 1.

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I. Bernard Cohen

46. The Caspar biography (published in 1948 by W. Kohlhammer Verlag of Stuttgart) was published in an English version by Abelard-Schuman of New York, and has since been reprinted in paper- back. The Koyrg volume, long available in French, has been translated into English; and the English version, completed some time ago, was published in 1973. Koestler's general book on astronomy has aroused considerable criticism because of the author's unpleasant attitude with regard to Copernicus and Galileo, and a kind of hostility to science in general. The Kepler por- tion has been reprinted as a separate biographical volume in paperback, under the title The Watershed. In 1931 a tercentenary commemorative volume was published under the auspices of The History of Science Society (U.S.A.) under the title Johann Kepler 1571-1630, with contri- butions by Arthur S. Eddington, W. Carl Rufus, D. J. Struik, E. H. Johnson, and F. E. Brasch (who was the editor of this volume). Numerous articles and commemorative volumes have been or are being published on the basis of celebrations held in 1971 of the 300th anniversary of Kepler's birth. For an introduction to the secondary literature concerning Kepler, see Caspar's bibliography, cited in Supplementary Note I, and the article by Owen Gingerich in the D.S.B., cited in note 14.

47. Michael Polanyi: PersonalKnowledge (Chicago: The University of Chicago Press, 1958), pp. 6-7. The passage quoted is the famous one, given as follows: "What I prophesied two-and-twenty years ago, as soon as I discovered the five solids among the heavenly o r b i t s - - . . , what I had promised my friends in the title of this fifth book, which I named before I was sure of my dis- covery--what sixteen years ago I urged to be sought--that for which I have devoted the best part of my life to astronomical contemplations, for which I have joined Tycho Brahe . . . at last I have brought it to light, and recognized its truth beyond all my hopes . . . . So now since eighteen months ago the dawn, three months ago the proper light of day, and indeed a very few days ago the pure Sun itself of the most marvellous contemplation has shown forth--nothing holds me; I will indulge my sacre~t fury; I will taunt mankind with the candid confession that I have stolen the golden vases of the Egyptians, in order to build to them a tabernacle to my God . . . . If you forgive me, I shall rejoice; if you are angry, I shall bear it; the die is cast, the book is written, whether to be read now or by posterity I care not; it may wait a hundred years for its reader, as, God himself has waited six thousand years for a man to contemplate His work."

48. W. Carl Rufus, "Kepler as an astronomer", pp. 1-38.of The History of Science Society's volume Johann Kepler 1571-1630 (Baltimore: The Williams & Wilkins Company, 1931); esp. p. 35.

Supplementary Note 1

The contrast between the many editions and translations of Kepler's writings and those of Galileo's may be seen in a striking manner in three chronological lists. First, the major astronomical or physical writings published during Kepler's lifetime (and ending with the posthumously pub- lished "Dream"):

1596--Mysterium Cosmographicum (Tfibingen); reprinted 1621 (Frankfurt). 1604--Ad Vitellionem Paralipomena, quibus Astronomiae pars optica traditur (Frankfurt). 1606--De Stella Nova (Prague). 1609--Astronomia Nova (Heidelberg). 1610~Dissertatio cure Nuncio Sidereo (Prague); reprinted 1610 (Florence), 1611 (Frankfurt). 1611--Dioptrice (Augsburg). 1618-20-21--Epitome Astronomiae Copernicanae (Linz, Frankfurt). 1619--Harmonices Mundi Libri V (Linz). 1627--Tabulae Rudolphinae (Ulm). 1634--Somnium (Frankfurt).

In the next list, there are given those works reprinted between 1634 and 1900, again omitting extracts, minor works, correspondence, and mathematical tables. The gaps speak for themselves.

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Kepler's Century

(All of the works in this and in the preceding list were reprinted in the Frisch edition of Kepler's Opera Omnia, with the exception of the Rudolphine Tables.) 1635--Epitome Astronomiae Copernicanae (Frankfurt). 1650--Tabulae Rudolphinae [red. J. B. Morin] (Paris); reprinted 1657 (Paris); 1675 (London;

"digested into a most accurate and easie compendium"), 1676 (London; reprint of 1675 "compendium") plus other printings.

1653--Dioptrice (London, together with Galileo's Nuntius Sidereus and Gassendi's Institutio Astronomica); 1683 (London; a reprint of the 1653 collection).

1665--Dissertatio cum Nuncio Sidereo (Frankfurt); reprinted 1818 (Modena); 1846 (Firenze; in vol. 5, part 2, of E. Alb~ri's edition of Galileo); t892 (Firenze; in vol. 3 of A. Favaro's edition of Galileo).

1858-71--Opera Omnia ed. Ch. Frisch. 1898--Keplers Traum vom Mond (Leipzig; German trans, of the Somnium, by Ludwig Giinther).

In the third group, I give those of the above-listed works that have appeared since 1900. 1904--Dioptrik (Leipzig; German trans, by Ferdinand Plehn). 1905-11--Keplers Neue Astronomic (Freiburg; German trans., abridged, by Georg Baldauf). 1918--Die Zusammenkldnge der Welten (Jena; German trans, by Otto J. Bryk of portions of the

Harmonices Mundi Libri V, the Mysterium Cosmographicum, and of the Astronomia Nova and Dissertatio cum Nuncio Sidereo).

1920-21--"Joh. Keplers Behandlung des Sehens" (Zeitschr.f. ophthalmol. Optik, VIII, IX; German trans, of chap. V of Kepler's 1604 treatise, by F. Plehn).

1922--J. Keplers Grundlagen der Geometrischen Optik (im Anschluss an die Optik des Witelo) (Leipzig; trans, by F. Plehn of chaps. I I - IV of Kepler's 1604 treatise, revised and edited by Moritz von Rohr).

1923--Mysterium Cosmographicum = Das Weltgeheimnis (Augsburg; German trans, by Max Caspar); reprinted 1936.

1925--Johannes Keplers Kosmische Harmonie (Leipzig; trans, of major portions of chaps. I I I -V of Kepler's Harmonices Mundi Libri V, by W. Harburger).

1929--Neue Astronomie (Mfinchen-Berlin; trans, by Max Caspar). 1938 sqq.--Gesammelte Werke (Munich; ed. by Walther von Dyek and Max Caspar, and Franz

Hammer). Those volumes to date which contain works given on the first list are : I. Mysterium Cosmographicum; De Stella Nova, 1938; II. Astronomia Pars Optica, 1939; III. Astronomia Nova, 1937; IV. Dioptrice, 1941; VI. Harmonice Mundi, 1940; VII. Epitome Astronomiae Copernicanae, 1953.

1939--Weltharmonik (Mfinchen-Berlin; trans, by Max Caspar). 1958--Somnium sire Astronomia Lunaris (Physikalische Bldtter, XIV).

The foregoing lists are based primarily on Max Caspar, Bibliographia Kepleriana (M~inchen: C.H. Beck'sche Verlagsbuchhandlung, 1936), supplemented by C. Doris Hellman's edited trans- lation of Caspar's biography: Kepler (London and New York: Abelard-Schuman, 1959), pp. 397 sqq.; plus my own study of the sources. There may be a recent reprint or translation which may be missing from these lists, but I believe that there are few lacunae for the period up to 1936, for which the contrast with Galileo is most striking. See, further, F. E. Brasch, "Bibliography of the Works of Johann Kepler, 1571-1630", pp. 86-133 of the work cited in note 48. Both Caspar and Brasch give a list of secondary works (books and articles).

In the early eighteenth century M. G. Hanseh, who had bought Kepler's manuscripts, began an edition of Kepler, but only succeeded in publishing a first volume of correspondence (1718). This collection of manuscripts was purchased by the Empress Catherine of Russia and is at present in Leningrad; an inventory is given by O. Gingerich in his article on Kepler in the Dictionary of Scientific Biography, cited in note 14, an admirable introduction to Keplerian science, which may be supplemented (for biographical details) by Caspar's biography.

Frisch's edition of Kepler's Opera Omnia contains valuable new materials, from rare works and manuscripts. Kepler's major writing are generally reprinted, but without an apparatus criticus or

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I. Bernard Cohen

commentary. Of special value are the Kepterian items printed in Vol. VIII (notably "Collectanea ex Codicibus Pulkoviensibus" and "Judicium Matris Kepleri"), including some 450 pages of a documentary "Vita Johannis Kepleri" (together with a "Historia Astronomiae Seculo XVI").

Supplementary Note 2

A bibliographical study of the writings of Galileo is available in Dino Cinti, Biblioteca Galileiana, raccolta dal Principe Giampaolo Rocco di Torrepadula (Firenze: Sansoni Antiquariato, 1957).

Editions and translations of Galileo's writings, together with a list of books and articles relating to Galileo (or containing extracts from his writings), are listed in the following three works:

A. Carli and A. Favaro, Bibliografia Galileiana (1568-1895), raccolta ed. illustrata (Roma: Ministero della Pubblica Istruzione (Indici e Cataloghi, XVI), 1896).

Giuseppe Boffito, Bibliografia Galileiana 1896-1940, raccolta ed illustrata, Supplemento alia Bibliografia Galileiana di Alarico Carli e Antonio Favaro (Roma: La Libreria della Stato (Ministero della Educazione Nazionale), 1943).

Ernan McMullin, "Bibliografia Galileiana 1940-1964" plus "Addenda to the Carli-Fararo (1564-1895) and Boffito (1896-1940) Bibliografia Galileiana"; Appendices A and B (pp. i-xxxiii) of Ernan McMullin (ed.), Galileo, Man of Science (New York, London: Basis Books, 1967).

A guide to some recent literature is given in Elio Gentili, Bibliografia Galileiana fra i due Centenari (1942-1964) published by the Seminario Arcivescovile di Milano, Editrice "La Scuola Cattolica" of Venegono Inferiore (Varese) in 1966, in the series Hildephonsiana ("Collana di Studi Teologici e Religiosi a cura della Facolta Teologica di Milano").

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