Meanest Foundations and Nobler Superstructures: Hooke, Newton and ''the Compounding of the Celestiall Motions of the Planetts'' (Boston Studies in the Philosophy of Science)

BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE

Editors ROBERT S. COHEN, Boston University JURGEN RENN, Max-Planck-Institute for the History of Science KOSTAS GAVROGLU, University ofAthens

Editorial Advisory Board THOMAS F. GLICK, Boston University ADOLF GRUNBAUM, University ofPittsburgh SYLVAN S. SCHWEBER, Brandeis University JOHN J. STACHEL, Boston University MARX W. WARTOFSKYt, (Editor 1960-1997)

MEANEST FOUNDATIONS AND NOBLER SUPERSTRUCTURES Hooke, Newton and the "Compounding of the Celestiall Motions of the Planetts"

by

OFERGAL Ben-Gurian University a/the Negev, Beer-Sheva, Israel

1iIl...

A ClP. Catalogue record for this book is available from the Library of Congress.

ISBN 1-4020-0732-9

Published by Kluwer Academic Publishers, .P.O. Box 17,3300 AA Dordrecht, The Netherlands. Sold and distributed in North, Central and South America by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers, P.O. Box 322, 3300 AH Dordrecht, The Netherlands.

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For Yi and Hagar

TABLE OF CONTENTS PREFACE

ix

INTRODUCTION Part A: The Historical Question I. Gallileo's Challenge 2. The Correspondence 3. Hooke's Programme Part B: The Historiographic Difficulty 4. Hooke vs. Newton 5. The Genius vs. The Mechanic

1 1 1 2 10 12 12 14

CHAPTER 1: INFLECTION Introduction: The Bad Ending Part A: The Novelty I. Hooke's Programme 2. Setting the Question Right Part B: Employing Inflection 3. Inflection 4. Application as Manipulation Part C: Producing Inflection in the Workshop 5. Construction 6. Implementation 7. Tentative Conclusion

17 17 19 19 22

34

35 42 44

53 57

1ST INTERLUDE: PRACTICE 1. Introduction - Methodological Lessons 2. Hacking 3. The Realism Snare

59 59 63

CHAPTER 2: POWER Part A 1. Introduction 2. De Potentia Restitutiva, or: Of Spring

83 83 83

69

86

CONTENTS

viii

Part B 3. 4. 5. Part C 6. 7. 8. 9.

102 Horology The Spring Watch Springs and Forces The Origins of the Vibration Theory Of Spring again Springs as a Topos A Clockwork Theory of Matter and Power

102 108

121 127 127 131 137 140

2ND INTERLUDE: REPRESENTAnON 1. Rorty 2. 'Knowledge Of' and 'Knowledge That' 3. Hacking and Rorty

143 143 152 159

CHAPTER 3: NEWTON'S SYNTHESIS 1. Introduction 2. Newton Before and After 3. Hooke's Programme Revisited

165 165 168 200

NOTES Introduction Chapter 1: Inflection 1,I Interlude: Practice Chapter 2: Clocks, Pendulums and Springs 2nd Interlude: Representation Chapter 3: Newton's Synthesis

207 207 207 211 213 214

BIBLIOGRAPY

219

INDEX

233

210

PREFACE

This book is a historical-epistemological study of one of the most consequential breakthroughs in the history of celestial mechanics: Robert Hooke's (1635-1703) proposal to "compoun[d] the celestial motions of the planets of a direct motion by the tangent & an attractive motion towards a central body" (Newton, The Correspondence II, 297. Henceforth: Corre:>pondence). This is the challenge Hooke presented to Isaac Newton (1642-1727) in a short but intense correspondence in the winter of 1679-80, which set Newton on course for his 1687 Principia, transforming the very concept of "the planetary heavens" in the process (Herivel, 301: De Motu, Version Ill). l It is difficult to overstate the novelty of Hooke's Programme • The celestial motions, it suggested, those proverbial symbols of stability and immutability, were in fact a process of continuous change: a deflection of the planets from original rectilinear paths by "a centrall attractive power" (Correspondence, II, 313). There was nothing necessary or essential in the Already known to be "not circular nor shape of planetary orbits. concentricall" (ibid.), Hooke claimed that these apparently closed "curve Line[s]" should be understood and calculated as mere effects of rectilinear motions and rectilinear attraction. And as Newton was quick to realize, this also implied that "the planets neither move exactly in ellipse nor revolve twice in the same orbit, so that there are as many orbits to a planet as it has revolutions" (Herivel, 301: De Motu, Version III). Far from "being exceedingly well ordered in heaven," as Kepler was still very much certain they were (New Astronomy, ·115), the planetary trajectories, according to Hooke's Programme, represented nothing but a precarious balance between conflicting tendencies. Culminating in this paragon of abstract celestial mechanics, however, the traces of Hooke's construction of his Programme lead through his investigations in such practical, earthly disciplines as microscopy, practical optics and horology. Similarly, the mathematical tools Newton developed to

I

Hooke's Programme is a modern title, coined, to the best of my knowledge, by S. I. Wawilow in 1951: "Die Prinzipien konnte im 17. lahrhundert niemand ausser Newton schreiben. Aber man kann nicht bestreiten, dass das Program, der Plan der Prinzipien, zum erstenmal von Hooke entworfen wurde" (cited by Lohne, 42).

x

PREFACE

realize Hooke's Programme appear no less crafted and goal-oriented than Hooke's lenses and springs. This transgression of the boundaries between the theoretical, experimental and technological realms lends philosophical significance to Hooke's free excursions in and out of the circles occupied by gentlemen-philosophers, university mathematicians, instrument makers, technicians and servants. Tracking these forays thus becomes more than just a survey of the epistemic activities of late seventeenth century English savants. Rather, it presents an opportunity to examine the epistemological categories embodied by Hooke and Newton, and the suspicion that much of these categories is nothing but a reflection of the social divisions, relations and hierarchies that separated Hooke's diverse acquaintances and collaborators. This examination is undertaken in three historical chapters with two philosophical interludes in between. The book opens with the correspondence between Hooke and Newton in 1679-80. The Introduction suggests a reading of the correspondence as one continuous text with two authors. It explores the manner in which communication was established, common grounds for exchange were laid down, and complex working relations were created, relations whose fruitfulness was a product of suspicion and careful positioning no less than of polite collaboration. The Introduction then proceeds to question the historiographical and epistemological merit of the common practice among historians of seventeenth century science to juxtapose Hooke, the "mechanic of genius, rather than a scientist" (Hall, "Robert Hooke and Horology," 175) with "the genius of Sit Isaac Newton" (Westman, in Lindberg and Westman, 170). Chapter i is dedicated to Hooke's depiction of planetary trajectories as curved from rectilinear paths into closed orbits due to an external, rectilinear 'power' (Hooke's term). References to Kepler, Descartes and Borelli highlight the surprising originality of this portrayal, which Hooke first introduced in his 1666 Address to the Royal Society, further developed in his 1674 Attempt to Prove the Motion of the Earth, and brought into fruition in the correspondence with Newton. Two tools used by Hooke in his 1666 Address hint at the motivations underlying his reformulation of the question of planetary motions and the means by which he achieved it. The first is a new theoretical term-'inflection'-signifying the gradual curving of a rectilinear trajectory. The other is an experimental design: a conical pendulum mechanically embodying the hypothetical configuration of motions and attractions in order to demonstrate its basic feasibility. The chapter follows these clues to reveal Hooke's techniques and procedures of knowledge production, in which material and theoretical artifacts are closely intertwined. Chapter 2 focuses on the unique concept of 'power' with its relations to motion that Hooke brings to the correspondence. This chapter offers an

PREFACE

xi

interpretation of Hooke's 1674 Cutlerian Lecture Of Spring, the locus of his celebrated Spring Law-the single one of Hooke's accomplishments that still carries his name. It explicates the original oscillatory theory of matter that Hooke constructs in this lecture, and analyzes the complex relations between Hooke's Law, the theory in which it is embedded, and Hooke's work on springs-work that sought to develop a spring watch for marine navigation. If the first chapter reveals Hooke's use of theoretical artifacts in the production of material ones, this chapter uncovers his use of material objects for linguistic-theoretical purposes. It demonstrates, among other things, that not only is Hooke's law far from being the paradig!TI of 'empirical generalization' that it is generally held to be, but its import within Hooke's theoretical apparatus defies the commonly assumed distinctions and relations between the empirical and the theoretical. Chapter 3 examines Hooke's Programme through the difference it made to the work of Isaac Newton. The new knowledge that arose from the correspondence between Hooke and Newton-the Programme as it came to function in Newton's 1680s manuscripts on celestial mechanics-is analyzed as a product of both men's skills, tools and techniques. The treatment of planetary motion that characterizes Newton's Kepler Motion Papers and De Motu is compared to his own early (1660s) formulations of the question, as well as to those of Huygens, and its main novelties are crystallized and traced back to the correspondence. This allows a reevaluation of Newton's indebtedness to Hooke. The historiography of the relations between the two protagonists has been dominated by the question of the credit Hooke deserved for such notions as universal gravitation and the replacement of centrifugal force with centripetal force, and, primarily, for the discovery of the inverse square law of gravitation. The comparison in .this chapter reveals that such questions of credit and priority are badly misleading, not least because none of these concepts constitutes the breakthrough enabling the Principia. What distinguishes Newton's later work is not the introduction of a new concept or the discovery of a particular universal constant. Rather, it is a new image of the "planetary heavens" coupled with a new task for celestial mechanics: the analysis of the forces produced by given orbits in Newton's (and Huygens') early work is replaced, following his correspondence with Hooke, with a calculation of the parameters of the rectilinear motions and rectilinear attractions by which precariously closed and stable orbits are created. The three historical chapters attempt to account for the production of each ~d every facet of Hooke's Programme-theoretical or experimental, Wllthematical no less than technological-through reference to the art and c~aft of Hooke, Newton and their contemporaries. This goal gives rise to S0qJe grave epistemological challenges, which are partially addressed in two ~hort interludes between the chapters. Pretending to be neither a survey of

xii

PREFACE

contemporary epistemology, nor a coherent alternative, these discussions critically examine the adequacy of available epistemological categories for the task. The presentation in the first and second chapters of the problem concerning the distinction and relations between thcoretical and experimental knowledge is linked by an account of one important attempt to address this tension; Ian Hacking's 1983 Representing and Intervening. The second and third chapters highlight the peculiarity of the historiographic categories by which Hooke and Newton are traditionally judged and compared, and are linked to one another by a discussion of Richard Rorty's critique of the epistemology supporting these categories as developed in his 1979 Philosophy and the Mirror of Nature. This book is the product of an attempt to write a history and philosophy of science as though it were a single discipline with a coherent set of norms, issues, rules of conduct and standards of integrity. Some ten or fifteen years ago, this integration seemcd just around the corner. The very fact that I had to separate historical chapters from philosophical interludes testifies that it never happened. In this sense, the book may have become old-fashioned even as it was attempting to be avant-garde, which should explain the relative intellectual isolation in which it was written. This makes me all the more grateful to those people and institutions that offered me their generous help during my years of research and writing. The project began as research for a dissertation in the Department of History and Philosophy of Science at the University of PIttsburgh, under the instruction of J. E. McGuire, a scholarly role model and friend, to whom lowe special debt of thanks. Peter Machamer, Friz Ringer, Robert Olby and Bob Brandom were the other members or" an encouraging dissertation committee. I had the important benefit of participating in seminars given by other members of the department: John Earman, Bernie Goldstein, Jim Lennox, John Norton and Merrilee Salmon, and of invaluable discussions with my colleague students, especially Jonathan Simon, Michel Janssen and Bill Sutherland. The administrative staff, headed by Rita Levine, always provided a cheerful and supportive environment. The research for Chapter 3 was conducted in the Max-Planck-Institut fUr Wissenschaftsgeschichte in Berlin, where I benefited greatly from taking part in a reading group on the history of mechanics led by Wolfgang Lefevre, Peter Damerow and Jtirgen Renn. I am especially grateful to Professor Renn, the Rector of the Institute, who was the one to suggest that I turn my research into a book and submit it for publication with Kluwer. My debt to my friends and colleagues there, Serafina Cuomo, Cristoph Luethy and Sophy Roux, is clear to both them and me. The library staff of the Institute, and especially its head, Urs Schoeplin, was enormously helpful, even after I left the Institute, and I cannot overstate my thanks. I conducted most of the final research, editing and preparation for publication in the particularly pleasant and enlightening atmosphere of

PREFACE

xiii

the Philosophy Department in Ben-Gurion University of the Negev in Isra~l, first as a Kreitman postdoctoral fellow and then as a lecturer and Alon fellow. Thanks go to Yehuda Elkana for his enduring support, to Rivka Feldhay, Gideon Freudental, Raz Chen, Shaul Katzir and Hanan Yoran for their attentive ear, to Ruth Freedman, who edited the style and language of the final manuscript, and also to the anonymous Kluwer reader for important comments. A version of Chapter 1 was published in Studies in the History and Philosophy of Science 27.2 (1996), and I am thankful to Elsevier Science Ltd for their permission to use it.

INTRODUCTION Part A: The Historical Question 1. GALILEO'S CHALLENGE On November 24, 1679, Robert Hooke wrote a friendly letter to Isaac Newton in Cambridge. It was partly ex-officio: Hooke has just been nominated to be the secretary of the Royal Society, succeeding his recentlydeceased nemesis Henry Oldenburg, and in his new capacity was responsible for the Society's correspondence. But it was not all formal; he was clearly glad of the opportunity. Hooke had long suspected Oldenburg of inciting Newton, among others, against him, and the relations with Newton were important to him. Still bitter, perhaps, over the outcome of the reflecting telescope dispute·, Hooke nevertheless required Newton's already-famous mathematical savvy in order to help him realize an idea he had been nurturing for over thirteen years, an idea which he had published and submitted to other mathematicians with so far no avail (Nauenberg, "Hooke," 336; Lohne, "Hooke versus Newton," 13-15). Hooke had every reason to be both proud and frustrated. His idea provided a clear and straightforward path towards solving a fifty-year old challenge: to account for the heavenly motions in the terms Calileo used in his treatment of terrestrial mechanics. Without overlooking Kepler's first valiant attempts at Physica Cadestis, this challenge was posed by Galileo himself, in the Fourth Day of his Discorsi (Galileo, Dialogues Concerning Two New Sciences. Henceforth: Discorsi). Evidently, Galileo had only a vague notion of how to solve this problem, for he refrained from letting his hero, Saliviati, reflect on it. Instead, in the midst ofa discussion on the subject of gravity and violent motion combining to produce a parabolic path, he placed in Sagredo's mouth a remark concerning the beautiful agreement between this thought of the Author and the views of Plato concerning the origins of the various speeds with which the heavenly bodies revolve. 2 (Viscorsi,261)

2

JNTRO/)UCTION

While we can judge the importance and difficulty of unpacking this "beautiful agreement" by the number and eminence of the scholars entranced by it, the sheer variety of approaches suggests that none were deemed satisfactory. Thus, in approaching Newton, Hooke wasted little space on the social niceties before presenting his request. "1 shall take it as a great favour" he wrote, if you will let me know your thought~ of that [hypothesis of minel of compounding the ceJe~tiall molions of the planetts of a direct motion by the tangent & an attractive motion towards a central body (Newton, The Correspondence II, 297. Henceforth: Correspondence).

This is the essence of "Hooke's Programme," as it later became known: to account for the revolutions of the planets as a rectilinear motion encurved by an attraction to the center about which they revolve.

2. THE CORRESPONDENCE 2.1.

November 24, 1679

Hooke may have thought that this succinct presentation, combined with his previous publications on the subject, would suffice Newton to grasp his Programme. The Programme indeed makes stringent demands regarding the theoretical tools it prescribes; but one might have thought that after Descartes, such austerity would not appear inordinate. Still, as 1 will show in Chapter 1, none of those whose fingerprints appear on Hooke's Programme has actually considered the planetary orbits as the outcome of curving rectilinear motions. For Kepler as well as Galileo, for Descartes himself, as well as for Gassendi and the Cartesians Mersenne and Huygens, for that venerable departed genius Horrox as well as for Newton's own favorite Borelli, the explication of the planetary motions had always included rotation as a primary cause. And Newton indeed failed, on first sight, to appreciate either this particular trait of Hooke's Programme or its general potential.

INTRODUCTION

3

Yet he did not snub Hooke's advances, and the ensuing correspondence, which spanned eight weeks during the winter of 1679/80, adds up to a fascinating document. It is compact--comprised of four letters by Hooke and two by Newton-and intense-the intervals between them are just enough for the London mail to reach to Cambridge (and vice versa). It is embedded in a well-defined social context; the network of public correspondence established by the late Oldenburg and revolving around the flourishing Royal Society, but it also registers a charged and intense encounter between two people with complex personal relations. It has a clear and explicit epistemic end; to enlist Newton's "excellent method" to solve "the celestial motions of the planets" as it was captured in Hooke's workshop, but the conjunction of Hooke's and Newton's complimentary skills and talents is more than simple collaboration. The communication between the reclusive Newton and the suspicious Hooke entails crafted structures of personal trust and intellectual respect beside subtle means of fending off the open and entrepreneurial social setting. The creation of common grounds for their differing, indeed almost incompatible conceptions of matter, force and motion, does not exclude rhetorical maneuvers of careful positioning towards future disputes over credit and authority. The correspondence is indeed a prime example of a "social process of negotiation situated in time and space" (Knorr-Cetina, The Manufacture of Knowledge, 152).

2.2. November 28, 1679 Here, however, I shall have to suffice it with brief consideration of those parts of the correspondence pertaining directly to the Programme 3• As mentioned, its first reception by Newton was lukewarm. Genuinely or not, he replied on November 28 by denying that he had ever "so much as heare (yt I remember) of [Hooke's] Hypothesis of compounding ye celestial motions of ye planets, of a direct motion by the tangt [sic.] to ye curve" (Correspondence n, 300). Yet, since Hooke discusses planetary motion and

4

INTRODUCTION

mentioned a demonstration of the annual motion of the earth, Newton contributes to the discussion a suggestion for an experiment to demonstrate its diurnal, i.e. west to east motion. One of the traditional anti-Copernican arguments had been that if the earth rotates around its axis (from west to east, or from B towards G in Figure 1), then objects detached from the earth-projectiles, clouds, birds-should be 'left behind' and fall to the west of their point of departure. On the contrary, suggests Newton: if one was to release a stone from a high enough tower BA, it would always fall to the east of the tower-towards point D in the diagram he includes. At point A at the top of the tower the stone is further from the center C of the earth rotation than at the bottom of the tower B is, hence its motion to the east is quicker. Since. as taught by Galileo. the motion downwards does not affect the motion eastward, the stone would continue traveling east as it falls down and would meet the ground "quite contrary to the opinion of ye vulgar" (Correspondence II, 301), at point D to the east of the tower.

fA '. "

I

"

Figure 1: Newton's diagram from his November 28, 1679 letter to Hooke (Lohne, "Hooke Versus Newton,· 9). The stone at the top of the tower (A) falls to the east (D) of the bottom of the tower (B). If allowed to continue through the earth, it will spiral through E until reaching the center of the earth

,".',

I

. ,

I

I

,

--/

(C).

INTRODUCTION

2.3.

5

December 9, 1679

Hooke responded, almost as promptly, on December 9. Not only did he like the experiment very much and promised to carry it out-he was, after all, the curator of experiments for the Royal Society-but a note in Newton's letter allowed him to redirect the discussion to his Programme. The diagram which Newton appended to his experimental suggestion (Figure 1) had a little speculative addendum to it, describing the hypothetical motion of the falling stone if it were to continue. resistancefree, through the earth: in this case, suggested Newton, it would fall through point E and spiral around its center C a few times, until coming to rest in C. This alluded exactly to the point Hooke was trying to make-the compounding of motion along the tangent with attraction to a center-and he was only too happy to set Newton right: "supposing then ye earth were cast into two half globes in the plane of the equinox and those sides separated at a yard Distance" (Correspondence II, 305), so that the stone could fall through it while still experiencing the attraction towards the center, it would not describe a spiral, but an "Elleptueid." Namely: like the planets, "the line in which this body would move would resemble an Ellipse" (ibid.) such as AFGHA in the diagram Hooke provides (Figure 2). This planetary orbit-like ellipse will collapse into spiral AIKL etc.terminating in the center C--only if the stone encounters a resisting medium as it falls. Again, these are the most basic elements of Hooke's "Theory of Circular motions compounded by a Direct motion and an attractive one to a center" (op. cit., 306).

INTRODUCTION

6

E

B

2.4.

Figure 2: Hooke's diagram from his December 9, 1679 letter to Newton (Correspondence II, 305). The stone falling through the 'sliced' earth orbits center C in the ellipse AFGHA, unless it is impeded by a medium.

December 13, 1679

Being corrected finally got Newton's attention. Once again, it took him only four days to receive Hooke's letter and compose a reply, which was mailed on December 13. Historians have always stressed the less friendly tone Newton's writing assumed after he was 'shown up' by Hooke, and his attempt to amend the humiliation by demonstrating his superiority over Hooke with geometrical control of the curves of motion. The resentment is difficult to deny, but should not be over stated either. There is a clear participatory side to Newton's reply, an admittance of the importance of the proposal and a request for further insights from Hooke. Newton's comments, seemingly curt, disguise the foHowing question: let us accept that the tangential, orbiting motion is not cancelled by the attraction towards the center, and that therefore the stone would never reach that center. But why, on the other hand, should it describe a 'clean' elliptical curve, with fixed apsides, analogical to a planetary orbit? In fact, argues Newton, it is far more reasonable to suppose that the stone would not acquire a planetary-like orbit (see also Chapter I, Section 2.2). Thus, he writes, let "gravity be supposed uniform." Since due to this

INTRODUCTION

7

constant attraction the stone will continually accelerate towards the center C. it will be closer Lo it in the second 'quarter' of its orbit, between F and Q in the enclosed diagram (Figure 3), than in the first, between A and F. This means that, "by reason of ye longer journey & slower motion," the stone will spend more time in the first quarter than in the second, and will receive more of the "innumerable and infinitely little moLions ... continually

A

:0 Figure 3: Newton's diagram from his December 13, 1679 letter to Hooke (the original, on the left, from Lohne, "Hooke versus Newton,« 27; transcription, on the right, from Pelseneer, 244). The stone falling through the earth from A along FOG etc. changes its apsides with every orbit.

generated by gravity in its passage" (Correspondence II, 308) in the first quarter. Hence, it will subject to more 'inclination downward' in the first quarter than compensating 'inclination upward' in the second. From this follows that by the time the stone reaches the point exactly opposite the starting point-namely, by the time it crosses the line connecting the original point of departure and the center, it would still be inclined 'downwards'. In other words, under the assumption of distance-independent gravity, the stone would not redirect itself opposite and parallel to its original motion at precisely the point that it cuts what would have been, for

8

INTRODUCTION

a planet, the line of apsides, but further on along its "journey." This also means that the point on the orbit closest to the center (its perigee) will not be on the a single line through the furthest point (apogee) and the center, nor will it be congruent with the point where the stone's motion is opposite and parallel to its motion in the apogee. In short: there will not be a single of apsides, and the stone will oscillate-reaching different apogees and perigees with each revolution.

2.5. January 6,1680 Hooke took this objection in his stride; it was precisely the mathematical question he had been trying to entice Newton into helping him solve. Once there was agreement-that only straight-line motions and attractions would be used to explain orbital motion-how exactly is the resulting curve to be calculated? Had Hooke known how to perform the calculation, he would not have bothered seeking Newton's assistance. He did, however, have some ideas, which he explained in his next letter, dated January 6, 1680. The main difficulty in 'compounding' rectilinear motions and attractions into planetary-like orbits. Newton was in effect suggesting, was balance. How could changing velocities and distances be balanced to produce a more-or-less stable, closed curve, one in which "the auges will unite at the same part of the Circle and that the neerest point of accesse to the center will be opposite to the furthest Distant" (Correspondence II, 309)? Hooke's idea was that this balancing could be achieved through the application of Kepler's 'law' of inverse proportion between distance and velocit/. This proportionality would hopefully ensure that the acceleration of the revolving body would regularly compensate for the diminishing distance between that body and the center of attraction. The 'law' could be derived, suggested Hooke, if (i) the attraction is not "supposed uniform" but rather inversely proportional to the square of the distance; "that the Attraction," in his own words, "always is in subduplicate proportion from the Center Reciprocal" (Correspondence n, 309). Then, if it were assumed that (ii) the velocity of a

INTRODUCTION

9

body is proportional to the square root of the attraction, the desired inverse proportion between distance and velocity would be obtained. These assumptions were not outrageous. By the late 1660s, the first assumption-the inverse proportion between gravity and the square of distance-was rather cornmon and had been advanced by a number of different people for a number of different reasons, some of which will be discussed in Chapter 3. The second assumption-"that the Velocity will be in subduplicate proportion to the Attraction" (Correspondence II, 309)seems, for its part, to have stemmed from an interpretation of Galileo's treatment of free fall. According to this interpretation, if the falling body is perceived as being accelerated by the continuous operation of external power ("Attraction"), its velocity can be understood as the outcome of the "sums of the powers," as Hooke calls it in Of Spring (see Chapter 2), powers that the body acquires as it falls. Since the power is constant-the weight of the body-the "sums" will depend on the length of the fall alone. Thus, from the famous theorem of the proportion between distance and the square of velocity follows a proportion between the "powers" and the square of velocity. Whatever was its source, this was for Hooke a "General Rule of Mechanicks," which he attempted to demonstrate numerous times, and which was closely tied in with his and Huygens' work on springs and pendulums 5. Other savants found this law of motion even more widely applicable: on November 26, 1674, William Petti read to the Royal Society a lengthy tract on the "Duplicate and Subduplicate Ratio or Proportion" between power and velocity (Petty, "A discourse"), which he applied to everything from the size of sails to human longevity.

2.6.

January 17,1680

To make it completely clear that the model of a stone rotating inside a sliced earth was more than an exercise for the imagination, Hooke added a paragraph indicating his awareness of the shortcomings of the analogy between this model and the real planets. Whereas in the case of the planets

to

INTRODUCTION

the attraction increased as the revolving body approached the center, in the model's case (as with pendulums or balls rolling inside spheres), the attraction increases with distance (Correspondence II, 309). This, however, was enough for Newton. He neither answered this nor the next letter, dated January 17, where Hooke happily announced the success of the experiment Newton had suggested, and submitted the final formulation of his Programme: It now remains to know the proprietys of a curve Line (not circular nor concentricall) made by a centrall attractive power which makes the velocitys of Descent from the tangent Line or equall straight motion at all Distances in a Duplicate proportion to the Distances Reciprocally taken. 1 doubt not but that by your excellent method you will easily find out what that Curve must be, and its proprietys, and suggest physicall Reason of this proportion. (Corre.'pondence, II, 313)

3. HOOKE'S PROGRAMME This, then, is the core of Hooke's Programme: to treat planetary orbits as a contingent effect of rectilinear motions and forces. It is, indeed, a fitting response to Galileo's challenge, an application of the terrestrial mechanics of the Discorsi to the heavens. Galileo had suggested that rectilinear motions-free-fall and projection-can be 'compounded' to create curved motion. Hooke suggests that the paradigm of curved motion-the motion of the planets-is actually compounded of projectionlike rectilinear motion and gravity-like rectilinear attraction. That the reasoning is inverted is not the most novel part of this application: the essential element Hooke borrows from Galileo is one that the latter never ventured to apply to heavenly motions. To wit, Hooke's Programme makes use solely of rectilinear motions and tendencies. Albeit pertaining to celestial mechanics, the Programme contains no motion which is originally curved and no cause which is rotating or revolving. The curved, orbital motion of the planets. Hooke would insist, consisted of uniform rectilinear motion ('inertial', as we would call it) along the tangent of the orbit, being

INTRODUCTION

11

continuously encurved or bent as the result of rectilinear attraction from a central body-:-presumably the sun. In the following pages I will attempt to tell the story of Hooke's Programme. What interests me is how this crucial piece of seventeenth century knowledge was produced and used: the material used, the skills, tools and techniques that shaped this material, its purposes, the difficulties that Hooke encountered while working on and with it, and the strategies he used to overcome these difficulties.

12

INTRODUCTION

Part B: the Historiographic Difficulty 4. HOOKE VS. NEWTON

There are a number of reasons for beginning the story of Hooke's Programme with the correspondence between Hooke and Newton. The following portrayal of Hooke epitomizes the most troubling of these reasons: "Whatever was his judgment of himself, he was not a Newton unrecognized" (Westfall, Introduction to The Posthumous Works, xxvii). Waller's biography of Hooke prefacing The Posthumous Works dates from l70S-two years after his death. It was the first such biography, and the last complete biography until 'Espinasse's. It may seem peculiar that the author, in an introduction to the biography of one historical figure should choose to compare the subject of his inquiry with another, and unfavorably at that. This cannot, however, simply be dismissed as strange. Even Margaret 'Espinasse, the most ardent apologist for Hooke's place in the history of science, dedicates the opening two chapters of her still-definitive biography of Hooke to Newton, concluding by citing Herschel's comment to the effect that Hooke was "the great contemporary and almost a worthy rival of Newton" CEspinasse, 15. Italics mine)-"almost," because, as she adds later, "Newton was, of course, the greater mind" (32). It is a commonplace of hermeneutics that the relations between the historiography and the philosophy of science are reciprocal. The historian's choice of exemplary episodes and heroes enacts and supports a more or less explicit epistemology, as do the particular roles these heroes are assigned, the relations that develop between them, and the choice and staging of the secondary cast. Thus, while there is no need to expand on Newton's eventual role in our conceptions of science, knowledge, rationality and modernity, it is in these depictions of Hooke that we find the most revealing, and amusingly vicious, examples of this 'hermeneutic circle'. The curator of experiments for the Royal Society for some forty years and later its secretary, during which time he was the most professional and prolific of all its members and affiliates, Hooke is by no means an obscure

INTRODUCTION

13

figure. It was inevitable he would be noticed by the historians of science, if only as the inventor of Boyle's air pump, the universal joint and the spring watch, to name just a few of his devices. As formulator of the spring law, properly named after him, of the pressure law, less properly named after his employer Boyle, and of course, of Hooke's Programme, Hooke could definitely not have been unattended, even by the most theory-oriented of historians. This notwithstanding, historians have only rather recently acquired an interest in Robert Hooke, and forty five years ago 'Espinasse could still complain that During the forty years of his work for the Royal Society and for forty years after his death Hooke was regarded as one of the greatest of English scientists; during the next two centuries he was almost unknown. ('Espinasse, I)

'Espinasse (Hooke's most recent biographer) and others convincingly credit this curious historiographic lapse to the great influence that "the genius of Sir Isaac Newton" (Westman, in Lindberg and Westman, 170) had on the historiography of that period. This influence was wielded by Newton personally and deliberately as President of the Royal Society, and also indirectly, through his unchallenged status as the hero of the scientific revolution. Thus, to quote 'Espinasse, "to make an enemy of Newton was fatal," which, unfortunately, was exactly what Hooke did. The cooperative tone of the 1679/80 correspondence proves the exception, rather than the rule, in Newton and Hooke's relations. So, although Hooke is by no means "almost unknown" anymore, he has become known in a very particular way. The role he has come to play in the historiogry of science in general and of his period in particular is expressed not only in those unflattering comparisons to Newton, but even more so in seemingly unbiased assessments of his work like the following: whereas Huygens had approached horologica] invention through his studies in pure mechanics, and left the work of construction to professional clock-makers, Hooke's attitude is that of a mechanic of genius, rather than a scientist. (Hall, "Robert Hooke and Horology," 175. Italics mine.)

Hooke, then, was "a mechanic," and it is as mechanic, be it one of

14

INTRODUCTION

genius, that he failed to have 'an attitude of a scientist'. It is interesting to note that the epithet of 'genius' is applied whenever these comparisons and adjudications are made. It is usually ascribed to Newton, "because Newton was the greatest scientist of his time, perhaps of all time" ('Espinasse, 40), amplifying Hooke's shortcomings. Occasionally, however, it is Hooke who is adorned with the title. Sometimes cautiously and somewhat ironically, as by Hall in the above quotation, and sometimes earnestly and enthusiastically, as by Allen T. Drake, whose book title anoints Hooke Restless Genius. An even more interesting facet of this typecasting, is that it does not fall far from the way Hooke himself was content to be remembered: As for my part, / have obtained my end, if these my small Labours shall be thought fit to take up some place in the large stock of natural Observations, which so many hands are busie in providing. If/have contributed the meanest foundations whereon olhers may raise nobler Superstructures, / am abundantly satisfied; and all my ambition is, that / may serve 10 the great Philosophers of Ihis Age, as the makers and grinders of my Glasses did to me; Ihal / may prepare and furnish Ihem with some Materials, which they may afterwards order and manage wilh beller skill, and 10 far greater advantage. (Micrographia, "Preface," xii·,dii)6

5, THE GENlliS VS. THE MECHANIC

That the historian's portrayal of a certain figure coincides with that person's professed self-image (whether this be a true expression of personal identity or an attempt to humor the powers that be-a very likely scenario in Hooke's case) does not mean, however, that either is correct. The only conclusion that may be drawn with some certainty from Hooke's autoportrait is that the same categories used to describe him in the twentieth century were available in the seventeenth. And clearly, both the categories of manually skilled 'mechanic' and mentally skilled 'scientist', and the clear-cut differences in their ranking and the knowledge claims they may aspire to, are at least as old as Plato's dialogues. The question is whether the categories of scientist, mechanic and genius are indeed appropriate to the story of Hooke's Programme. This question is a key one; and one I have no

INTRODUCTION

15

intention of shirking. First, however, let us begin by examining the main story of Hooke's Programme.

CHAPTER 1: INFLECTION Introduction: The Bad Ending The significance of the correspondence between Hooke and Newton was not to be denied, even when their relationships soured again. In the midst of their last and most bitter priority dispute-the one concerning the discovery of the inverse square ratio between gravity and distance-Newton was forced, albeit half-heartedly, to acknowledge at least some debt to Hooke: lbis is true, that his Letters occasioned my findings the method of detennining Figures.

He was of course quick to down-play it, adding when I had tried [the methodl in ye Ellipsis, I threw the calculation by being upon other studies & so it rested for 5 years till upon your [Halley'sl request I sought for yt paper, & not finding it did it again & reduced it into ye Propositions shewed you by Mr Paget,

and underscoring: but for ye duplicate ratio I can affirm yt I gathered it from Keplers Theorem about 20 years ago. (Correspondence, II, 444-5: Newton to Halley, 14 July 1686)

Hooke, of course, found this hard to stomach, and never forgave Newton for taking what he had no doubt was his, namely: ... those proprietys of Gravity which I myself first discovered and shewed to this Society many years since, which of late Mr. Newton has done me the favour to print and Publish as his own inventions, (Hall, 'Two Unpublisbed lectures," 224: Address to the Royal Society, 1690)

What stands out very clearly is that the adversaries saw "ye duplicate ratio"-the inverse square ratio between distance and gravity-as the crux of their 1679/80 correspondence, at least in terms of the prestige it was to draw: of all the "proprietys of Gravity," it was the discovery of this ratio for which they were most adamant in their pursuit of credit. To understand why, out of every thing, Newton and Hooke found the numerical constant worth fighting over, we would probably be well advised to consider the situation from Newton's perspective. "The definition of the stake of the struggle is a stake in the struggle (even in sciences where the apparent consensus regarding the stakes is very strong)" (Bourdieu, 14); and as in all

18

CHAPTER 1

their disputes, Newton seems to have had much more control over events than Hooke. Newton undoubtedly suspected that even if Hooke did have a case concerning the mathematical issue in question, it was a relatively weak one. First, there was Halley's word that Hooke could not prove the inverse square law (c./. Correspondence, II, 441-3: Halley to Newton, 29 June 1686). Secondly, whether he shared Huygens' low estimate of Hooke's mathematical abilities or not, Newton surely felt very secure with his advantage over Hooke where geometrical demonstrations were concerned. It was thus a reasonable step for Newton (to the extent that reason played any part in this struggle) to focus the debate on the 'duplicate ratio' and its The other aspects of the correspondence, concerning which proof. Newton's debt to Hooke was far harder to obscure, could then be neutralized with the dubious acknowledgment "occasioned my findings" (see above), which avoids conceding anymore than is absolutely necessary. As will be discussed at length in Chapter 3, the inverse square ratio had a long and winding career, in which Newton's proof "from Keplers Theorem" and Hooke's 1680 proclamation were just two stops. And whereas neither Hooke nor Newton deserve credit for being the first who "discovered and shewed" the famous ratio, it was Hooke who first suggested the combination of inertial motion and centripetal force. This he did as early as 1666, when Newton was still pursuing the issue of planetary motions in terms of centrifugal force. l But I do not intend to succumb to the temptation of belated adjudication of old priority disputes. Determining who indeed "first discovered" the "proprieties" may seem like the historians' core task, and the challenge definitely arouses one's detective instincts, but it also presents a clear trap: The image of a competition entails a definite finishing line, and obscures the work and struggle involved in the very shaping of the sought "findings." In attempting to referee such disputes in hindsight one adopts the framework of the debate, instead of analyzing the establishment of the framework, creating a patina of necessity around the claim for which the credit was sought, as though it is, or was, self evident that this claim was the issue. In our case in particular, there was much more to "those proprietys of Gravity which" discussed by Hooke and Newton than the concentration on the inverse square law allows one to notice.

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19

Part A: The Novelty 1. HOOKE'S PROGRAMME 1.1

Early Versions

His correspondence with Newton was not the first time that Hooke had aired his Programme; he had done this publicly on two earlier occasions. As a two-page finale to his 1674 Cutlerian Lecture Attempt to Prove the Motion of the Earth (henceforth: Motion of the Earth, Hooke presented a draft of "a System of the World ... answering in all things to the common Rules of Mechanics:" This depends on three Suppositions. Pirst, That all Crelestial Bodies Whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts ... but ... also ... all the other Crelestial Bodies that are within the sphere of their activity; and consequently that not only the Sun and the Moon have an influence upon the body and motion of the Earth, and the Earth upon them, but that [all the planets], by their attractive powers, have a considerable influence upon its motion as in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The Second Supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipsis, or some other more compound Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers. (Motion of/he Earth, 27-8)

This appendix to the Motion of the Earth was Hooke's most elaborate and explicit presentation of his Programme. It was also his last public one: as was often the case with Hooke, he never made good on his promise to "hereafter more at large describe" these ideas and the "foregoing observations" leading to them (ibid.). But the 1674 presentation was not Hooke's first lecture on his ideas; his earliest and the most basic statement of them was presented in an Address to the Royal Society eight years earlier: [A]II the celestial bodies, being regular solid bodies, and moved in a fluid, and yet moved in circular or elliptical lines, and not straight, must have some other cause, besides the first impressed impulse, that must bend their motion into that curve. And for the performance of this effect I cannot imagine any other likely cause besides these two: The first may be from an unequal density of the medium, thro'- which the planetary body is to be moved ... But the second cause of inflecting a direct motion into a curve may be from an attractive property of the body placed in the center; whereby it continually endeavours to attract or draw it to itself. (Birch II, 91: May 23,

1666)

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CHAPTER I

The constituents of the "System of the World," which Hooke promised in 1674, were rectilinear attraction between all celestial bodies declining with distance, and inertial motion which that attraction curved. "Inflecting a direct motion into a curve" already comprised the centerpiece of the 1666 Royal Society Address. Not so, however, the "attractive property of the body placed in the center." In the earlier version it was still only one of two possible causes that Hooke hypothesized for inflection. It would have been a real challenge to attempt a 'complete' story of Hooke's Programme, following its gradual nurturing by Hooke and ending with the final version laid before Newton. My aspirations are much more modest and fragmented, however, concentrating on Hooke's formation of the two concepts-curving rectilinear celestial motion and all-operating attraction-their final shaping in the correspondence with Newton; and Newton's assimilation of them. This chapter begins by exploring Hooke's development of the notion of curving planetary motion; Chapter 2 follows with a discussion of the concept of "power," and Chapter 3 concludes with Newton's adoption and utilization of these ideas. Credits and priorities aside, a few words first about the significance of the notions presented in Hooke's Programme

1.2. What Was at Stake A good indication for how difficult it was for Hooke's notions to be embraced is the amount of persuasion it took Newton to even consider them. The pressure did not begin with Hooke's letter; Newton was in fact familiar with the 1674 version of Hooke's Programme, in spite his repeated avowal to Hooke of being "unhappy as to be unacquainted with your Hypotheses" (Correspondence II, 302). His kind remark "I am glad to heare that so considerable a discovery as you made of ye earth's annual paralax is seconded by Mr Flamstead's observations" (301), gives Newton away; the "considerable discovery" he refers to was the parallax observations published as the Attempt to Prove the Motion of the World, in the last pages of which Hooke sketches his "System of the World." It hardly matters whether it was a bare-faced lie on the part of Newton, whether he had heard of Hooke's observations only second hand, or whether his little parenthesized qualification of claimed ignorance, viz. "(yt I remember)" (300) should be taken seriously. What matters is that whatever he had read or heard about Hooke's Programme had failed to make enough impression to stir him to accept the challenge and attempt to solve the riddle of

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21

planetary motion according to its prescriptions. It is therefore hardly a surprise that recruiting Newton required Hooke's obstinate pursuit. His succinctly introduced Programme implied and demanded a host of difficult concessions from his reader. The model to which Newton was invited to apply his "excellent method" (Correspondence, n, 313) in order to describe the "celestiall motions of the planetts" was of a uniform rectilinear motion which an acceleration-eausing power, operating in the manner of gravity from a (non-rotating) center, turns into a trajectory around that center. This model portrays the planetary orbit as an effect-the outcome of independent, seemingly contingent physical processes. It embeds an uninhibited commitment to treating heavenly bodies just like "all bodies whatsoever," and presents devastating metaphysical and religious ramifications. We need not however delve into these in order to understand Newton's reluctance. Accepting that "celestial bodies [are] regular solid bodies" (my italics) and imagining a "first impressed impulse," by which they are "put into a direct and simple motion," meant abandoning the conception of the orbit as a given curve. The notion that "the matter of heaven, in which the planets are situated, unceasingly revolves" because "God, in the beginning ... caused them all to begin to move with equal force ... around certain other centers" (Descartes, Principia Philosophi(E, Part Ill, Articles 30 and 46) was not just a self-evident presumption. It was also one of the most basic tools of the burgeoning celestial mechanics. For example, the evident stability of the God-created orbit implied equilibrium between inward and outward tendencies, which allowed Newton and Huygens to investigate gravity by calculating centrifugal forces. Hooke's Programme replaced celestial equilibrium with a continuous dynamic-active process of mutual balancing between motion along the tangent and attraction towards the center. In order to adopt this conception, Newton needed to relinquish another self-evident conviction; that continuous attraction towards a center results in the acceleration of the attracted body towards, and final collision with the attracting central body. According to Hooke's model, the attracted planet was expected instead to revolve around the attracting sun. This meant in tum that the stability of the revolution of the planet, e.g. the earth, was both unremarkable and possibly less than perfect, especially if "[all the planets], by their attractive powers, have a considerable influence upon its motion as in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also." In other words Hooke's Programme implies that the planetary orbits may not be exactly closed; one does not

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CHAPTER I

need to assume perfect, divine accuracy of design, suggests Hooke, in order to avoid complete havoc. This was a major change in the conception of planetary motion embedded in celestial mechanics. As I shall demonstrate in Chapter 3, it came with a new explanatory strategy, in which the parameters of attraction and velocity-among them the inverse square law-acquired new significance. No longer reflections of pre-established heavenly harmonies, to be inferred from astronomical observations, these parameters became explanatory measures for phenomena consisting of (Kepler's) generalizations regarding the motion of all planets. Moreover, the new approach, which was initiated by Hooke and perfected by Newton, endowed Kepler's 'second (area) law' with new import. A laborious approximation device in its original conception and employment, the area law now came to capture an actual process of compensation between the change in centripetal force according to (the square of) the distance from the center, and the change in centrifugal tendency according to the tangential velocity. With its new import, the area law called for a universal proof, which Newton indeed constructed and used as a basic building block in each of the texts leading up to the Principia. In what remains of this chapter, I shall endeavor to trace some of the steps taken by Hooke in developing one of the two main ingredients of his Programme-the notion that the planets move in rectilinear trajectories that are continuously 'encurved' by an external cause. The steps are characteristic of Hooke; they begin with a very simple laboratory device, barely relat~d to either mechanics or cosmology, continue with numerous ingenious ti'ansformations and manipulations, and end, as we have seen, with bad feelings. The story that emerges is, nevertheless, of considerable philosophical significance: it provides tangible testimony to the actual process in which a piece of knowledge of major importance was produced. It also contains a number of important historical details that, perhaps due to Hooke's ambiguous historical status, have been completely overlooked.

2. SETTING THE QUESTION RIGHT 2.1. Hooke It now remains to know the proprietys of a curve Line (not circular nor concentricall) made by a centrall attractive power which makes the velocitys of Descent from the tangent Line or equall straight motion at all Distances in a Duplicate proportion to the

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23

Distances Reciprocally taken. I doubt not but that by your excellent method you will easily find out what that Curve must be, and its proprietys, and suggest physicall Reason of this proportion. (Correspondence, II, 313)

This was Hooke's question to Newton on January 17 1680. It is clearly formulated in terms of centripetal force-"attraction or gravitating power" (see the quotation from Motion a/the Earth above. 10 Years later, worried about priority and on the defense, Hooke would stress: "Vis Centripeta ... (what I calld gravity),,2). This differs from his earliest presentation, in that Address to the Royal Society 14 years earlier, of this world picture as a project of inquiry: I have often wondered, why the planets should move about the sun according to Copernicus's supposition, being not included in any solid orbs ... nor tied to it, as their center. by any visible strings; and neither depart from it by such a degree. nor yet move in a straight line, as all bodies, that have but one single impulse, ought to do. . (Birch II. 91: May 23,1666).

Given that this represents the first clear formulation of the question of planetary motion in terms of "descent from the tangent line," it is surprising that the paragraph above has not attracted more historiographic attention. 3 Perhaps this formulation seems so self-evident from a post-Principia vantage point, that it is transparent to historians' gaze. Another possible explanation is that historians, drawn as they were into the priority dispute, were after the earliest references to the celebrated 'duplicate ratio', which is not to be found here, and neglected the more general and fundamental issue-that of constructing the question. Speculations aside, in some ways the May 1666 Address reveals the particular power of Hooke's innovation even more than the January 1680 letter. It is not difficult to recognize that this earlier version, unlike the later letter, contains no reference to the 'duplicate ratio'. Clearly, in 1666 Hooke had yet to develop any mathematical solution to his query. But it is equally clear that the solution was not (yet) Hooke's main concern; his major effort lay in seeking to engage his audience (his Royal Society employers) with his novel approach to framing this question. It is worth citing again: [A]ll the celestial bodies, being regular solid bodies, and moved in a fluid, and yet moved in circular or elliptical lines, and not straight, must have some other cause, besides the first impressed impulse, that must bend their motion into that curve. And for the performance of this effect I cannot imagine any other likely cause besides these two: The first may be from an unequal density of the medium, thro' which the planetary body is to be moved ... But the second cause of inflecting a direct motion into a curve may be from an attractive property of the body placed in the center; whereby it continually endeavours to attract or draw it to itself. (Birch II, 91)

Hooke can merely speculate about the answer: the cause might be the

24

CHAPTER I

medium, in a Cartesian fashion, or attraction, in a Keplerian mode. The question he asks, however, the phenomenon whose cause he seeks, is quite different from that which engaged either Kepler or Descartes. 4

2.2.

Other Candidates

The difference in the question, which is where Hooke's novelty lies, is not simply the notion of compounding motions. Such compounding, which Aristotle had ruled out, had ceased being regarded as heresy at least since the time of Giovanni Battista Benedetti (1530-1590), and was transformed into a rudimentary tool of mechanics by Galileo. Both Kepler and Descartes mobilized this idea. In Kepler's system the cause of planetary revolution is the magnetic attraction of the rotating sun along the radius vector. Since such a mechanism would produce a circular heliocentric motion and leave all irregularities unexplained, Kepler introduced a quasi-maguetic force internal to the planet, with a different polarity than the sun's attractive force. The planet is attracted to or repelled by the sun, depending on the angle between the two magnetic forces. Its distance from the sun is thus made dependent upon its position in its orbit, and is indeed a consequence of a combination of forces s. Descartes was not only acquainted with the compounding of motions, but incorporated it as a central pillar in his system. Proclaiming "that all movement is, of itself, along straight lines" and "that each part of matter, considered individually, tends to continue its movement .along straight lines, and never along curved ones," (Principia Philosophire, Part II, Article 39-the second law of motion) he insisted that restricted curvilinear motion- such as that of a sling, or a planet, for that matter-would continue in a straight line along the tangent if the restriction were removed6 • Yet in both Kepler and Descartes' writings the trajectory of the planet's motion is essentially curvilinear. Neither of them points to the planets' curved trajectory as the phenomenon in need of explanation; neither sees this trajectory as a deviation from a rectilinear path that had to have a cause. Roth Kepler and Descartes, though helping themselves to the compounding of motions, do not use this theoretical tool to explain the curving itself. According to both, the planets rotate because their movers rotate. Hooke's Address to the Royal Society on May 23, 1666 is the first record of a scholar seeking causes for the bending of planetary motion, i.e., an explanation of the curved motion of the planets in terms of forces and motions operating along straight lines.

INFLECTION

2.2.1

25

Kepler

This claim may seem rather strong, but at least in Kepler's case it can be substantiated rather straightforwardly. The rotation of the planets around the sun is undoubtedly caused, in Kepler's account, by the rotation of the sun about itself: Since the species [the power emanating from the sun] is moved in circular course. in order thereby to confer motion upon the planets, the body of the sun, or source, must move with it, not, of course, from space to space in the world-for I have said, with Copernicus, that the body of the sun remains in the centre of the world-but upon its centre of axis, both immobile, its parts moving from place to place, while the whole body remains in the same place. (Aslronomia Nova, Part UI, Chapter 34, 386)'

It is worth noting the "must" ("necesse") Kepler attaches to the rotation of the sun. Even though he was the one to break the commitment to circularity in astronomy, and despite his admiration to Galileo, Kepler never doubted the strict distinction between straight and curved motion, at least in the celestial realm. Since the planets rotate, their mover, the sun, necessarily rotates; and if the sun has to move, it is, "of course" ("quidem") a rotation-the motion appropriate for eternal bodies. The ancient pairing of rotation with the eternal was not just an unconscious presupposition for Kepler, but an important working hypothesis, which applied, for example, in his theory of comets: With the difference between everlasting and transitory bodies, there should follow a similar difference in their motion; circular motions (and hence revolutions) will belong to the everlasting bodies, whether the Sun moves, or-in its place-the Earth moves; rectilinear motions certainly [will belong] to evanescent bodies: for both types of bodies have their own constitution which attaches to their state of arising from their respective form; [the constitution of] eternity for the circle, and that of mortality for the straight line which certainly cannot be infinite. (Kepler, De Comelis, translated and cited by Ruffner, 181)8

The "difference" between the motions appropriate for the "everlasting" as opposed to the "transitory bodies" is the main consideration of this reasoning. What is yet more striking, is that this difference holds "whether the Sun moves, or-in its place-the Earth moves;" Kepler is explicitly committing himself to the distinction between the curved and the straight over and above his commitment to Copernicanism. Adhering to this distinction, he is as distant as can be from seeing the planetary rotation of the planets as a cosmological query to be solved by means of rectilinear motion.

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CHAPTER I

2.2.2.

Descartes

As regards Descartes, the claim-that he has stopped short of attempting an explanation of the planets' closed orbits by means of rectilinear motions--definitely calls for careful qualification and justification. Clearly, Descartes had all the theoretical tools needed for such an attempt, as well as the theoretical motivation. If his laws of collision (Principia Philosophire, Part II, Articles 45-52) were to serve as the basis for all future physical theorizing, then it is only reasonable to expect that Descartes would have been first to advocate their application to planetary motion. Surprisingly, however, this does not happen; nowhere in Descartes' writing is this line of thought explicitly developed, and in no place does he suggest that inertial, rectilinear motion should play the primary role in analyzing planetary motion. The planets, according to Descartes, revolve because the whirling motion of the surrounding 'boules'-particles of the second element. carries them along: ... the matter of heaven, in which the planets are situated, unceasingly revolves, like a vortex having the sun as its center, and all the Planets '" always remain suspended among the parts of this heavenly matter Thus, if some straws are Iloating in ... a vortex ... we can see that it carries them along and makes them move in circles. (Principia Philosophi"" Part III, Article 30)

Nor does Descartes reserve anything similar to Hooke's planetary model for the boules themselves. The explanation he suggests for their orbital motion makes it very hard to believe that he ever considered that curving rectilinear motion might produce such trajectories: God, in the beginning, divided all the matter of which He formed the visible world into parts as equal as possible and of medium size ... [andl caused them all to begin to move with equal force, each one separately around its own center ... and also several together around certain other centers ... (op. cit., Article 46).

Now it is true that after establishing his epistemology in Part I of the Pricipia Philosophi(1? and then 'deducing' his ontology from it in Part II, Descartes reverts in Parts III and IV to 'the language of the vulgar' and helps himself to terminology which he supposedly analyzed away in the earlier parts. He may have meant some of the expressions used in his later Articles to be read as abbreviations for more careful formulations founded the theory developed earlier. One may therefore hypothesize that Descartes intended the last paragraph to be interpreted in light of his most stern assertion of the primacy of rectilinear motion (Article 39 of Part II), partly cited above:

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each part of matter, considered individually, tends to continue its movement along straight lines, and never along curved ones; even though many of these parts are frequently forced to move aside because they encounter others in their path, and even though ... in any movement, a circle of matter which moves together is always in some way formed. (Op. cit., Part II, Article 39)

However, the phrase "parts are frequently forced to move aside" is by far the closest Descartes ever comes to presenting curvilinear motion as rectilinear motion that has been forcibly curved, and he never makes clear how this notion should be applied to heavenly bodies. Moreover; all the models, thought experiments and diagrams that Descartes uses to illustrate his second law of motion, including the celebrated sling argument, which is first referred to already in this Article (39), stress the rectilinear tendency as abstracted away from a preexisting circular motion rather than causal factor in producing the curved trajectory. In the sling model, for example, the hand can only be perceived as whirling the sling and the stone-as supplying a motion which is originally circular-and the primacy of motion along straight lines appears only as a tendency to recede from the center. Moreover, the hand not only provides the motion, but is also responsible for restraining the stone (through the sling) from flying away. It is not surprising, then, that Descartes found himself grappling with two kinds of centrifugal force (as is was to be called by Huygens)--tangential and radial (Part III, Articles 57-59). The latter, which historians found somewhat baffling9, may simply be an artifact of the construction of the thought experiment; an over-estimation of the siguificance of the outward 'pull' felt by the arm in addition to the tangential tendency evident from the stone's trajectory when released from the sling. Occasionally Descartes moves still further from basing his mechanics on his second law. This happens when he explicitly insists that all application of rectilinear motions to rotating bodies should be understood as an entirely analytic exercise: ... the curved line described by a point of the wheel depends on the straight and circular movements. Accordingly, a1thoogh it is often useful to divide a movement into several parts, in order to understand it more easily, nonetheless, strictly speaking, we must never attribute more than one movement to each body. (Op. cit., Part II, Article 32)

Again, this hierarchy between straight and curved motions-with the straight motion secondary to the curved-is further underscored when Descartes applies this line of thought to celestial motions: 10 a hard and opaque sphere ... rotates with the matter of [aJ vortex in such a way that it will be driven by that matter toward the center of this rotation, as long as it has less agitation than that matter which surround it. (Op. cit., Part III, Article 119)

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Agitation, like centrifugal tendencies, is produced by motion around a given center. It is The force which tal star acquires from its motion around the center S with the matter of heaven. (Op. cit.• Article 121)

And indeed, as McGuire and Tamny have shown J I, Newton himself, on reading the Latin version of the Principia Philosophia! in around 1664, "misses the full thrust of Descartes' use of the term conatus in the context of his vortical theory" (McGuire and Tamny, 171). Of course, recognizing this thrust was difficult without benefit of hindsight: from Newton's perspective it was completely reasonable to interpret Descartes as suggesting that rectilinear motion is only an abstraction from actual curvilinear motion and the cause of centrifugal tendency. This is the way it functions in Descartes' vortical theory, where it is used to account for the formation of the sun and the fixed stars. As Newton's Waste Book of 1666 testifies l2 , Newton's understanding of Descartes' treatment of orbital motion was arrived at from such sentences as "it is a law of nature that all bodies which are moved circularly attempt to recede from the centers around which they revolve" (Principia Philosophia!, Part m, Article 54). Hooke's far more radical idea, that orbital motion is secondary and caused 'by more elementary rectilinear motions, is simply not part of the Principia Philosophia!.

2.2.3.

Borelli

Newton, then, could neither have been introduced to the notion of encurved celestial motion through his (extensive) readings of Descartes, nor through his (scantier) knowledge of Kepler laws 13• This might partially explain his early difficulties in understanding the import of Hooke's suggestions. It also means that Hooke himself must have had other resources to draw upon, and when their priority dispute finally deteriorated into a sheer exchange of insults, Newton was only too happy to suggest what these might have been. "[H]e has published Borell's [sic.] Hypothesis in his own name" he wrote to Halley on July 20, 1686 (Correspondence, n, 437). Newton was referring to the following from Giovanni Alfonso Borelli's 1666 Theorica! Mediceorum Planetarum ex Causis Phsysicis Deducta!, a copy of which was in his library: the planets have a certain natural desire to unite with the globe about which they revolve in the Universe and which they tend to approaCh with all their power ... Furthermore, it is certain, that the circular motion confers on the moving body an

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29

impelus to move away from the centre of revolution. We shall assume, therefore, that the planet tends to approach the sun, whilst at the same time it acquires the impetus 10 move away from the solar centre through the impetus of circular motion: then, so long as the opposing forces remain equal (the one is in fact compensated by the other), [the planet] cannot come closer to, nor move away for, the Sun. (Cited in Koyn!, The Astronomical Revolution, 480)

There is indeed some resemblance between Borelli's and Hooke's hypotheses. Both appear to construct a picture of the planets retained in their orbits thanks to equilibrium between a tendency towards the sun and a tendency away from it. But this is as far as the resemblance goes. Borelli does not take the final step taken by Hooke; he does not present the planets' curved motion as an effect. It is this step that distinguishes Hooke's formulation of the question from Descartes' and Kepler's speculations, and transforms his hypothesis into a Progr,amme for celestial mechanics. For Borelli, on the other hand, celestial curvilinear motion remained one of the original causes: In the first place, we shall imagine the planet to move under two motions, the one, circular, the other, on the contrary, linear, and we shall show that from these two (Koyre, The motions [taken] as elements, an elliptical motion can result. Astronomical Revolution, 476)

The question troubling Borelli is not how rectilinear motion is curved, but how circular motion becomes elliptical. Highly impressed by Kepler's hypothesis, he endeavors to demonstrate its geometrical possibility within a Galilean framework (as developed by Ismael Boulliau), retaining Kepler's rotation of the sun asa cardinal explanatory element, and helping himself to the notion of circular inertia (Koyre The Astronomical Revolution, 473-8). Koyre argues that Borelli's hypothesis is an important step towards "assimilation of celestial mechanics to terrestrial mechanics" (op, cit., 480), and he may very well be correct, but it is not the same assimilation suggested by Hooke.

2.2.3.1. Newton, "Borell's Hypothesis" and Hooke's Programme What we have seen so far should suffice to vindicate Hooke and secure his credit for the notion of planetary orbits as bent inertial (in the modem, rather than Galileo's or Kepler's, sense of the term) motion. One might even claim that it places Newton in bad light; he made. his plagiarism allegation in 1686, during the final stages of writing the Principia. Surely, by then he had a firm grasp on the difference between Hooke's concept of orbital motion caused by curving rectilinear motion and the Cartesian-

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Huygenian concept, employed by Borelli, of rectilinear tendency (centrifugal force) emerging from existing circular motion 14 • Yet as important as this credit was for its seekers and as luring as it is to adjudicate, the priority dispute is not the best perspective from which to consider the relations between Hooke's Programme, "BoreIl's Hypothesis" and Newton's understanding of both. Granting Hooke priority over Borelli suggests that the "assimilation of celestial mechanics to terrestrial mechanics" (see Koyre above) was a clearly defined goal towards which both were striving and which one attained earlier than the other. Condemning Newton for obscuring the differences between the proposals for approaching this assimilation implies that he was always aware of these differences, and that he had before him two self-explanatory hypotheses to compare and choose from. Both implications are, to put it mildly, problematic. To avoid these problematic implications one must approach Newton's role in the episode differently. Rather than portraying him as encountering two independent theoretical models-Hooke's and Borelli's-we should think of Newton as participating in their construction. Newton must interpret these models, endow each hypothesis with meaning when he first learns about it and when he later recalls it, and he is using whatever means he finds available and fitting at the time. Thus, while Borelli's familiar ideas direct Newton's early rendition of Hooke's suggestions (when he is introduced to them in their 1679/80 correspondence), it is his full commitment to Hooke's Programme that shapes his reconstruction of those ideas six yel;U's later (in the 1686 letter to Halley). Viewed this way allows us several insights into Newton's stance. First, we can see why Newton finds it reasonable to present Hooke's Programme as a version of "Borell's hypothesis." More importantly, it explains Newton's reply of December 13, 1679 to Hooke's criticism of his thought experiment (see Introduction): if its gravity be supposed unifonn it [the stone falling inside the earth-see Introductionl will not descend in a spiral to ye very center but circulate wth [sic.) an alternate ascent & descent made by its vis centrifuga & gravity overballancing one another (Correspondence II, 307).

As Whiteside ("Before the Principia," 13-14) points out, this paragraph is a leaf straight from Borelli: not, it is important to note, a polemic response. "I agree with you," are Newton's opening words. It is his genuine way of interpreting Hooke's ideas, and it was, one might add, Hooke who first introduced Borelli into the correspondence (in the letter of December 9, to which Newton is responding), if only to lament Borelli's "deserting

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philosophy" (Correspondence, 304-Borelli died three weeks later). It is a misinterpretation; Hooke does not suggest "two motions, the one, circular, the other, on the contrary, linear" and two forces "vis centrifuga & gravity overballancing one another," but one motion and one force: originary rectilinear motion curved by rectilinear gravity. Yet it is a legitimate and telling misunderstanding; Newton was to employ the model sketched in this last quotation for at least two more years, and would probably not relinquish it until he commenced work on De Motu Corporum in Gyrum (see Chapter 3)15.

2.3. Hooke Again Still, whether Newton could not, or would not recognize it, there was an important novelty in Hooke's formulation of the question of planetary motion. Sublunary rotation was ever a contentious point. A motion neither towards nor away from any natural place, it does not fall easily into Aristotelian categories and distinctions, and was a favorable point of assault for those seeking to replace these with a unified science of motion l6 . In fact, Hooke's 'sliced earth' fantasy of the correspondence carries a marked resemblance to the stone spinning at the center of the earth that Galileo presents in his juvenile De Motu l7 • However, the suggestion that orbital, and not just curved motion should be understood as a result of rectilinear motions, and in particular that this should also apply to the heavenly orbits, was not to be found by reading Kepler, Descartes, Borelli or any other source I am aware of. The concept of continuous curving of celestial motions was hard to grasp and hard to entertain even for Newton, and even with Hooke's own explicit presentation of it. Of course, Newton did not have the opportunity to witness Hooke's original attempt to try and "explicate from some experiments with a pendulous body ... the compounding of this [accelerating] motion with a direct or straight motion" (Birch II, 91), but then none of those who did witness it had much use for this novelty until Newton finally adopted by it, almost twenty years later. A quick look at those 1666 experiments confirms that the "compounding" which Hooke tries to "explicate" is indeed different from any previous attempt along the same lines. The experiments demonstrate the evolvement of a closed curve trajectory from rectilinear motion, which is bent by an external cause, itself operating rectilinearly. Unlike its seeming predecessor, the hand spinning the sling in Descartes' thought experiment, Hooke's hand, when it pushes the pendulum, applies "a direct or straight

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CHAPTER 1

motion," which is then clearly encurved by the operation of an independent. external force-gravity, represented by the tendency of the pendulum towards the plumb-line-again operating strictly along a straight line. The question, in Hooke's demonstration, is the construction of curved motion out of rectilinear motions and forces, rather than the analysis of curved motion into rectilinear tendencies as it is for Descartes (and Huygens-see Chapter 3). In fact, Hooke is so focused on the rectilinearity of motions and forces, that he carefully examines the imperfections of his pendulum model, due to the fact that the cord it hangs on limits the pendulum bob to a motion along an are, unlike, e.g., a body descending freely or along an inclined plane (Birch II, 91. Note that the pendulum in consideration is a conical one, orbiting around an imaginary line drawn vertically from its point of suspension.). To grant Hooke originality is not to claim that he was unaware or failed to use the texts discussed above, just that they should be treated as resources, rather than the sources, of his Programme. In the remainder of this chapter, I will attempt to trace some of the other resources employed by Hooke in producing this particular component of the Programme-the notion of continuous bending of (celestial) motion into a curve. Fortunately, Hooke himself conceived this notion as a great innovation; so unprecedented, that in his 1666 Address he found it advisable to coin a new term for it: "inflection." He does not offer an explicit definition of this term. but the context clarifies its meaning: "direct motion always deflected inward" (Birch II, 91). This tenn--"inflection"-is an invaluable clue. Albeit new in reference to planetary motions, it is not completely new in the context of Celestial mechanics. The Address to the Royal Society was not the first time Hooke used 'inflection' to express the idea of turning straightline motion into a curved one by gradual bending.

INFLECTION

Figure 4: A draft of a mite from the Micrographia (adjacent to page 206; original size). All drawings from the Micrographill, the Cutler Lectures, and the Diary are in Hooke's own hand.

33

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CHAPTER 1

Part B: Employing Inflection 3. INFLECTION One year before his Address before the Royal Society meeting reported by Birch, Hooke published his Micrographia l8 ; a "handsome book," originally "solicited" by the Royal Society as a gift for Charles II in exchange for the royal sponsorship desperately sought by the Society.19 It was well met by the general public: "a most excellent book," affirmed Samuel Pepys, after he had "sat up till 2 a-clock in [his] chamber, reading Mr. Hooke's Microscopical Observations." As Pepys attests and its name implies, "the most ingenious book" is mainly a collection of microscopic observations, but not exclusively so. Among other things, the Micrographia contains a theoretical discussion of colors (another bone of contention with Newton) and a number of astronomical observations with another theoretical discussion appended. 20 In this last discussion, Hooke purports to account for a series of phenomena related to astronomical observations close to the horizon. These include the appearance of "all the Luminous bodies ... above the Horizon, when they are below," the unsmooth image of these bodies, their twinkling, their special coloring and so forth (Micrographia, 217-219). His main explanatory tool in these accounts is the concept of 'multiple refraction,' and it is to convey this optical concept that Hooke first coins the term'inflection:,21 I find much reason to think, that the true cause of all these Phrenomena is from the inflection, or multiplicate refraction of those Rays of light within the body of the Atmosphere. and it does not proceed from. a refraction caused by any terminating superficies of the Air above. nor from any such exactly defined superficies within the . body of the Atmosphere. (Micrographia.219)

Attempting "to convince his readers that inflection offers a better account for these optical phenomena than simple refraction, Hooke presents a number of arguments. These arguments are worthy of some attention due to their complex and telling relations to his later considerations, when he employs the term in his discussion of planetary motion. Hooke's first argument (see quotation above) is that 'inflection' allows him to think about the light rays as changing direction in the absence of a surface between different media. Using it, Hooke can explain, for example, the red light of the setting sun and its dependence on weather conditions as a prismatic effect, albeit "no Experiment yet known to prove a saltus, or skipping from one degree of rarity [of the atmosphere] to another much differing from it" (Micrographia, 228). Secondly, the notion of inflection presents the

INFLECTION

35

possibility that the ray, traditionally perceived as a 'physical straight line,' can assume a curved trajectory. owing to the continuous 22 influence of some external cause: This inflection (if I may so call it) I imagine to be nothing else, but a mulliplicate refraction. caused by the unequal density of the constituent parts of the medium. wherehy the motion, action or progress of the Ray of light is hindered from proceeding in a streight line, and inflected or deflected by a curve. (Micrographia, 220)23

Inflection as curving enables Hooke to account, e.g.. for the 'wavy' appearance of planets near the horizon as a continuous change in their apparent size (Micrographia. 231). It also allows for the hypothesis that stars appear to change their color as they near the horizon, since their light is being differently "inflected" by different regions of the atmosphere, even though the angle of entering the spherical atmosphere, and therefore the refraction caused by it, does not change (Micrographia. 233). Presenting (closed) curve motion as a consequence of the continuous bending of a straight-line motion is exactly the breakthrough of Hooke's Programme. The use of the medium as a cause of that bending, however, did not last. But the role of 'inflection' in Hooke's account of astronomical observations is not my main interest here. I shall continue to concentrate on his development of the notion of inflection, from its coinage in the 1665 Micrographia to its use in the 1666 Address, in the Micrographia itself and in the work leading up to it. Apart from its historical import, this process poses an interesting challenge to the traditional depiction of Hooke and the epistemological. categorization that it implies (see Introduction). Not only does Hooke produce the concept and apply it while moving easily within and between the realms of theory, experiment and instrument building, but, within each of these realms, he seems to employ skills and techniques that are conventionally associated with the others.

4. ApPLICATION AS MANIPULATION One is struck by one thing on reading the 1666 Address to the Royal Society alongside the discussion in the 1665 Micrographia: although the issues are clearly general and theoretical. the line of reasoning, which leads from the first introduction of 'inflection' to its later use does not follow any textbook precepts for the theoretical transformati!Jn of ideasgeneralization. application. inference to the best explanation, analogical inference from models and so forth. Nor does it comply with any of the standards of theoretical adequacy commonly urged by philosophers. To be

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precise, when Hooke adjusted 'inflection' to its later use, he subjected it to such powerful manipulations, that the term lost the very aspects of its meaning that had justified its original use.

4.1. Medium In and Out When Hooke introduces inflection for the first time, as an optical phenomenon, he is particularly e"plicit about one aspect of it: This conclusion ["that the true cause of all these Phl1momenl1 is from the inflection"] is grounded upon two Propositions: First, that a medium, whose parts are unequally dense, and mov'd by various motions and transpositions as to one another, will produce all these various visible effects upon the Rays of light without any other coefficient cause. Secondly, that there Is in the Air or Atmosphere, such a variety in the constituent parts of it. both as to their density and' rarity, and as to their divers mutations and positions one to the other. (Micragraphia,219)

The use of 'inflection' "is grounded upon" the medium considerations on two levels. In general, the assumption that inflection is caused by the medium is what ties it (metonymically) to refraction and makes it a legitimate speculation concerning the behavior of light, especially since Hooke holds a quasi-wave conception of light (see below). In particular, it is this claim-that it is caused by the medium-that gives inflection its explanatory power as regards the phenomena in consideration, since the parts of the atmosphere are prone to present such irregularity "as to their density and rarity." This "difference of the upper and under parts of the Air" (Micrographia, 222) is the strongest argument in Hooke's case for inflection. It is not a mere speculation, but a phenomenon "clear enough evinc'd from the late improvement of the Torricellian Experiment, which has been tryed at the tops and feet of Mountains" (ibid.) and which Hooke simulates in the laboratory in two sets of e"periments which he describes in the Micrographia (pp. 222-227; see Section 6.1 for a short description of these experiments). Inflection is an effect caused by "a medium, whose parts are unequally dense:" this is the centerpiece of the meaning of the tenn in the optical context of its appearance in Micrographia. This line of reasoning, that an heterogeneous medium bends rectilinear motion to a curve, is still very much alive in the 1666 Address. In fact, Hooke dmws a clear analogy from air-the medium of light, to ether-the medium of planetary motion: ... if we suppose, that part of the medium, which is farthest from the center. or sun, to be more dense outward. than that which is more near, it will follow, that the direct

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motion will be always deflected inwards. by the easier yielding of the inward. and the greater resistance of the outward part of the medium. This hath some probahilities attending it; as. that if the rether be somewhat of the nature of air. 'tis rational. that that part which is nearer the sun, the fountain of the heal, should be most rarefied; and consequently that those, which are most remote. should be more dense. (Birch II. 91)

Hooke, so it seems, is careful to construct a proper context for the use of 'inflection' as it was coined in the Micrographia-a changing medium gradually bending rectilinear motion. It is natural to assume that the analogy between the ether and the atmosphere would be Hooke's leading argument for his idea-that planetary motion should be viewed as "direct motion ... always deflected." One would think that after establishing (already in the Micrographia) the idea of inflection-gradual bending of light rays by the heterogeneous air-and after suggesting reasons to believe that the "rether be somewhat of the nature of air," namely, a medium of varying density, Hooke would proceed to argue that that "all the celestial bodies ... [are] moved in circular or elliptical lines, and not straight" because they are inflected by the ether. Hooke, however, makes no effort to explain the curving of planetary motion by the medium. Owing to improbabilities. that attend this supposition. which being nothing to my present purpose I shall omit (ibid.),

he abandons all medium considerations without further ado. The reasons for this surprising move are "nothing to [Hooke's] present purpose;" Hooke, it seems, never intended to treat the gentlemen of the Royal Society to a serious consideration of the medium as the cause of the If he had ever entertained such encurvation of planetary orbits. speculations, he had rejected them before the Address; the only "cause of inflecting a direct motion into a curve" he fmds genuinely interesting by that stage is that of "an attractive property of a body placed in the center; whereby it continually endeavours to attract or draw it to itself." The experiments constituting the heart of the Address have nothing to do with the medium hypothesis; they are strictly intended to shew, that circular motion is compounded of an endeavour by a direct motion by the tangent, and of another endeavour tending to the center. (Ibid.)

The experiments consist, as mentioned in the last section, of a "pendulous body" with "an endeavour tending to the center," (Birch II, 92) representing "the attraction of the sun.,,24 By giving this pendulum an oblique "conatus" to represent "a direct or straight motion just crossing it" (ibid.), Hooke "endeavour[s] to explicate" the

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intlection of a direct motion into a curve by a supervening attractive principle. (Ibid.)

'Inflection', which in the Micrographia meant gradual encurvation by the medium, means in the Address gradual encurvation simpliciter, with its likely cause being "a supervening attractive principle." The medium has no role in Hooke's experimental representation of 1666, nor in any other allusion to inflection within the context of celestial mechanics. Hooke sheds that all-important aspect of the meaning of the term-the medium as the cause-without any explanation, let alone justificl\tion, but he does not shy away, as we have seen, from using that soon-to-be-discarded aspect to bolster his importation of 'inflection' from optics to celestial mechanics. Since Hooke does not intend inflection to be explained by the medium, the analogy between air and ether does not provide any foundation for the move. It does, however, offer a suggestive resemblance, which he uses, and then quickly abandons once it has fulfilled its function. Hooke's attitude towards 'inflection' is strictly practical: he uses it wherever and however he sees fit, and never allows the theoretical and logical conSiderations he employs in constructing it to confine him in its deployment.

4.2. The Context of Analogy Furthermore: if Hooke had a particle view of light, it might have been argued that in generalizing 'inflection' from optics to celestial mechanics, he was following a ready path; an existing analogical relation between the two realms. Within a corpuscularian framework, the motion of the very small objects (the light particles) could have served as a model for the motion of the very large ones (the planets). But as I rernatk above, Hooke's views concerning light do not allow such an analogy. This is made clear in the Micrographia itself: light, he proclaims, is "very short vibrative motion" (Micrographia, 56), an "orbicular pulse" (op. cit., 58)-not the rectilinear emission of particles. According to Hooke's OWP1 conception, there is no inherent resemblance between the motion to which he first ascribes 'inflection'-that of light-and the motion to which he later applies it-that of the planets. The planets are neither related to light in substance nor analogous to it in behavior: in importing 'inflectiofl' from the Micrographia to the Programme 25 Hooke does not follow any ready analogical path. The process described in Section 4.1 is not a natural eV~lution of the meaning of the term, but an act: appropriating the term from Ol:}e realm and deploying it to the other. It is indeed a bold and ingenious act, but not necessarily a mysterious

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one. To acknowledge Hooke's agency26 in redeploying 'inflection' for new use does not entail relinquishing the possibility of analyzing it. Its ingenuity notwithstanding, Hooke's move should not be seen as that of a genius, "a master of metaphor ... seeing similarities between the different,,,Z7 but rather as a well executed maneuver, in which old "similarities" are carefully manipulated to produce new and surprising ones. In fact, although not guided by any 'natural relations' between the two types of motion, Hooke did have some grounds on which to tread. In both Kepler and Descartes' work he would have found a close interdependence between the domains of optics and celestial mechanics. Kepler explicitly models the magnetic 'species' emanating from the sun (strapping the planets to the sun's revolution) after light (Astronomia Nova, Part III, Chapters 34-6). Descartes names Part III of his Principia PhilosophilE-the cosmological part-"Of the Visible Universe," and devotes a significant number of its articles to the phenomenology of light (e.g. 9-10) and its nature (55; 64). The sub-title of Descartes' unpublished Le Monde, one recalls, is A Treatise on Light. Kepler and Descartes' speculations about the cosmological import of light outline a context in which Hooke could legitimately discuss light alongside planetary motion. But then again, there is nothing in the existence of such a context to undermine the significance of his intervention. Quite the contrary. The challenge imposed by the use of 'inflection' in optics is diametrically opposed to that encountered in its application to celestial mechanics. Whereas in the former realm Hooke had to convince himself and his (Micrographia) readers that light, the epitome of rectilinear propagation, may be curved, in the latter he must demonstrate to his (Royal Society) listeners that the motion of planets, the paradigm of regular orbiting, is originally rectilinear. Thus, reading Kepler and Descartes, Hooke might have discovered an affinity between optics and celestial mechanics, but nevertheless, one which spelled as much hindrance as support for his move. The details as well as the justification for applying his notion of gradual encurvation of light to account for the planetary orbits were left for him to create. Kepler, especially, would have offered very little encouragement for ascribing rectilinear motion to the planets; as we saw in section 2.2.1, he held to a strict dichotomy "between everlasting and transitory bodies," from which follows that to the planets "will belong," by necessity, "circular motions (and hence revolutions)," whereas "rectilinear motions certainly [belong] to evanescent bodies" (see above). Moreover, the physical reasoning and stakes that for Kepler, Descartes and their immediate followers linked optics

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to celestial mechanics, were not acceptable to Hooke. He adopts neither Kepler's magnetism nor Descartes' vortices, and more important, he is not interested in the problem that occupied them both and shaped their cosmological discussions-what caused the planets' motion. His question relates to how this motion changes -from a "direct" to "circular or elliptical" path. Yet, again, these are not the kinds of consideration that obstruct Hooke. The relationship between optics and celestial mechanics, like the mediumistic explanations discussed in the previous section, are, to Hooke, a means to an end, the end being to depict planetary motion as continuously encurved. Hooke is not obliged by the reasoning which went into the construction of the relations, nor committed to these relations once they have served their purpose. Neither in the 1666 Address, nor in his letter of 1680 (nor, to my knowledge, anywhere else) does Hooke speculate about a possible affinity or analogy between light and planetary motion.

4.3. Make It Work Hooke never bothers to provide reasons for discontinuing the use of a theoretical element which exhausted its utility. He offers none conceming the relation between light and planetary motion and none with regards to the immediate and complete loss of interest in the mediumistic explanation of planetary inflection. The value of the term 'inflection,28 in the context of planetary !Dotion does not stem from Hooke's original motive for introducing it into the realm of optics (viz., considerations pertaining to the medium) or from the initial justification for its reassignment to from optics to celestial mechanics (viz., the cosmological import of light). The sole function of 'inflection' in constructing Hooke's Programme is to convey the image of continuous encurvation of celestial motion, and it is for this reason, and this reason alone, that Hooke retains the use of the term for this. In this sense, 'inflection' is literally a tool; in stark opposition to the relations we are taught to expect between elements of theoretical knowledge--continuity, coherence, consistency, etc.-the knowledge Hooke put into constructing his term does not actively constrain its further deployment. The same may be said about the concepts, perspectives, stand points, vocabularies and analogies employed in adapting 'inflection' for its new use; they are introduced when deemed useful, employed as long as they are efficacious and abandoned when they are no longer so. These are theoretical and linguistic tools, but Hooke treats them just as he would treat

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material ones; his reasons for adopting or discarding them are wholly pragmatic-his criteria not justification, but utility. Yet the instrumental nature of 'inflection' does not consist merely of Hooke's tool-like use of it. As the next and fmal part of this chapter demonstrates, the term is deeply embedded in Hooke's workshop practices, and the hands~on, local know-how he demonstrates in operating it evinces the same ingenuity that earned him fame as an instrument builder and designer. If 'inflection' is an example of Hooke's theoretical and linguistic tools, then, as I will show in the next section, these must be related to his material-mechanical, optical, pneumatic-tools and instruments, not by analogy, but by origin.

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Part C: Producing Inflection in the Workshop

Figure 5: «Scheme

XXXVII"

of the Micrographia (adjacent to page

220).

To recapitulate: in 1680 Hooke suggested to Newton that planetary motion should be accounted for as "a curve line ... made by a central attractive power which makes the [planet] descent from the tangent line ... motion" (Correspondence II, 313). Hooke introduced his first version of

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these ideas, which later became known as Hooke's Programme, in an Address to the Royal Society in 1666. The depiction of planetary motion as continuously curved, perhaps the most innovative features of the Programme, was presented in Hooke's Address with the aid of a new term-'inflection'-which was used to denote "direct motion always deflected inward" (Birch II, 91). Hooke coined this term for the Micrographia, which he published in 1665, and where he defines 'inflection' as "muItiplicate refraction of those rays of light within ... a medium, whose parts are unequally dense" (Micrographia, 219). The last part of this chapter is an attempt to unearth the origins of 'inflection', and the first clue is Hooke's thoroughly pragmatic administration of the term, which invariably reflects considerations of efficacy rather than justification. As we saw, Hooke imports 'inflection' from the Micrographia to the Programme to fulfill a particular function-to convey the gradual curving of rectilinear celestial motion-and in order to achieve this goal he powerfully manipulated the meaning of the term, stripping it of all redundant or disruptive connotation. This tool-like, instrumental use of the term suggests that its origins may have been instrumental as well. In other words, the term 'inflection', this use suggests, records Hooke's celebrated facility for constructing and utilizing (mainly scientific) instruments. It is one thing to proclaim Hooke "a mechanic of genius." It is quite another to look for "the conceptual role of Hooke's instruments." This is what J. A. Bennett does with Hooke's Programme. In Hooke's work, Bennett claims, the conceptualization of the problem and solution is intimately linked with a mechanical demonstration, and ... carrying· out quantitatively the Programme thus conceptualized is a matter-not for mathematical demonstration, as it was for Newton-but for experimentally applying the appropriate and specially designed instruments. (Bennett, "Robert Hooke as Mechanic and Natural Philosopher," 42)

Discussing the two definitive moments in Hooke's engagement with the problem of planetary motion, Bennett notes that as late as 1681, "after he had already set Newton on the path to a mathematical solution" in their 1679/80 correspondence, Hooke was still trying to determine the variation of gravity with distance experimentally. Alluding to the Address of May 1666, Bennett observes acutely that It is wholly typical of Hooke's mind that. less than a month after he had shown the Royal Society how the conical pendulum demonstrated the mechaniCal principles of planetary motion, he was showing them how it could be applied to a clock. (Op. cit., 42)

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Bennett's main conclusion is that for Hooke The mechanical demonstration had an explanatory power of its own; it could ... be a 'demonstration' in a stronger sense than merely as illustration, [it was] an account of the phenomenon, according to the common rules of mechanical motions. (Op. cit., 44)

Let us consider this understanding of Hooke further. One can hardly deny that it was Hooke's mechanical skills that enabled him to account for natural phenomena. However, generating mechanical demonstrations is only one aspect of the use he makes of this know-how. Hooke's theoretical discussions, I shall claim, and in particular the all-important Programme, are also products of his workshop and laboratory capabilities. The case of the development of 'inflection' for the explanation of planetary motion strongly substantiates this stronger variant of Bennett's insights, as do paragraphs like the following: we are certain, from the laws of refraction (which I have experimentally found /0 be so, by an Instrument I shall presently describe) that the lines of the angles of Incidence are proportionate to the lines of the angles of Refraction ... (Micrographia, "Preface," xxvi),

These clearly express, no doubt, Hooke's confidence in the explanatory power of his mechanical demonstrations. But they also recall, I would claim, the actual considerations culminating in his remarkable correspondence with Newton, in which he submitted his Programme to be finally carried out in the latter's Principia.

5.

CONSTRUCTION

5.1. First Stage: A Sphrerical Crystalline Viol If one reads the Mierographia as someone like Pepys would have read it, namely without Newton in mind, the theoretical discussion of multiple refraction, for which Hooke introduces the term 'inflection,' draws one'~ attention first by being seemingly out of place. It occupies the 58 observation in the Mierographia (217-240), and serves as a preface to two telescopic observations. These conclude the book. which is otherwise almost exclusively devoted to microscopic observations. It is Hooke's articulation of the meaning of 'inflection' that reveals the term's pertinence within the context of the book. Hooke endows his newly coined term with meaning through a series of mechanical demonstrations, so that 'inflection' becomes a legitimate part of the Micrographia as these demonstrations are

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an integral part of it. The following simulation of atmospheric refraction is an example of this: That it ["the redness of the Sun, Moon, and Stars"l proceeds from the refraction, or inflection, of the rays by the Atmosphere, this following Experiment will, I suppose, sufficiently manifest. Take a sph:erical Crystalline Viot, such as is described in the fifth Figure [in Scheme XXXVII of the Micrographia~Figure 2 above] ABCD, and, having fill'd it with pure clcar Water, expose it to the Sun beams; then taking a piece of very fine Venice Paper, apply it against that side of the Globe that is opposite to the Sun, as against the side BC, and you shall perceive a bright red Ring to appear, caus'd by the refraction of the Rays, AAAA, which is made by the Globe; in which Experiment, if the Glass and Watcr be very cleer, so that there be no Sands nor bubbles in the Glass, nor dirt in the Water, you shall not perceive any appearance of any other colour. To apply which Experiment, we may imagine the Atmosphere to be a great transparent Globe ... (Micrographia, 228-229)

The Micrographia provides more than the context for this paragraph. The optical contrivance used for what is certainly only a preliminary approximation of optical inflection is taken directly from the Preface of the tract: ... at about three or four foot distance from this [south] Window, on a Table, I place my Microscope, and then so place ... a round Globe of Water ... that there is a great quantity of Rays collected and thrown upon the Object: Or if the Sun shine, I place a small piece of oyly Paper very near the Object, between that and the light. (Micrographia, "Preface," xxiii. The "Globe of Water" is represented by Fig. 5 in Hooke's Scheme I (Figure 6))

It seems certain that the similarity between the elegant "sphrerical crystalline viol" with its "very fine Venice Paper" and the humble "globe of water" with its own "oyly paper," is too much to be coincidental, A careful observation of the figures may further suggest that the experimental version-the "viol"-is nothing but an invocation of the observation appliance-the "globe"-that need not have been, and, in fact, was probably not constructed independently: 'G' in Fig. 6, Scheme I (Figure 6) appears to be a depiction of an existing model, while Fig. 5 in Scheme XXXVII (Figure 5) is clearly an abstract sketch. 'Inflection', then, gained its preliminary form from an unpretentious laboratory device: the water globe, which Hooke used regularly in his microscopic observations, lacked any theoretical pretension; it represents no more than common laboratory know-how. Hooke endowed the notion with theoretical significance, however, through several rather simple steps (not necessarily taken in the following order). First, he envisioned an idealized version of the light-concentrating contraption, one with "no Sands nor bubbles in the Glass, nor dirt in the Water" (one wonders if such a

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Figure 6: ·Scheme [" ofthe Micrographia (adjacent to page 1).

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superlative device was ever available to Hooke). Secondly, he upgraded the "globe" to a "sphrerical crystalline viol" etc. Finally and most importantly, Hooke marshaled into a desirable experimental result what had most likely been a series of cumbersome artifacts, viz., the various chromatic effects of the globe, produced by the auxiliary equipment during his microscope observations. He achieved this by identifying the appearance of the "bright red Ring" as the 'real phenomenon', "caus'd by the refraction of the Rays, AAAA, which is made by the Globe" from the appearance of "any other colour," which was to· be attributed to impurities in the glass or water.Hooke, one should add, could not provide an independent theoretical justification to distinguish the "red Ring" from the "other colourls]." This distinction can only make sense to that reader of the Micrographia who is willing to follow Hooke and "imagine the Atmosphere to be a great transparent Globe." For that reader, indeed, the "red Ring" may resemble "the redness of the Sun, Moon, and Stars." But the only support Hooke can offer to the analogy between the water globe and the atmosphere is that red ring. Hooke is apparently aware of the limits of this 'bootstrapping', and at that early stage of the development of his concept writes hesitantly that he had therefore made it probable at least that the morning and evening redness may partly proceed from this inflection or refraction of the Rays. (Micrographia, 229-Italics added)

This theoretical reserve confirms, at least regarding this rudimentary aspect of its meaning, that 'inflection' is, as expected, a product of local technical knowledge. If Hooke were more confident regarding his speculations, one might argue that there is no reason to believe that the instrument preceded the theoretical hypothesis-either logically or chronologically-even if the order of presentation in the Micrographia would suggest as much. It might be argued that using the water globe to concentrate light was exactly the type of 'application of science to technology' which Westfall was seeking (see Introduction and 1$I Interlude), but as Westfall himself demonstrates, Hooke did not refrain from claiming theoretical background for his mechanical innovations even when such claims were shaky at best. In our case, Hooke did not bother to give the laboratory device any theoretical context, and does not refer to 'inflection' at all in the Preface to the Micrographia. This is hardly surprising since, for a start, water globes were in common use, and there was no need for Hooke to design one in order to acquire one, neither could he claim credit for doing so. More importantly, in the Micrographia, as will be shown shortly, technological innovations are those he calls upon to supply context and give

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credence to the theoretical considerations (as weIl as to each other). Westfall's "ideal of scientific technology" (see Section 1.2 in the 1st Interlude) admittedly remains unrealized. Rarely does Hooke provide theoretical support for technical practices or seeks to legitimize the construction and use of scientific instruments through theoretical hypotheses and arguments. 5.2. Second Stage: Microscopes and More I do not claim, to be sure, that 'inflection' is nothing but an elegant name for a simple laboratory device. On the contrary: 'inflection' is indeed a general theoretical term. Nevertheless, this does not mean that it has some entity 'out there; distinct from and independent of Hooke's local practices, by reference to which the term transcends its locality and achieves an overarching status, justifying its application in divergent contexts. The term is general and theoretical by virtue of the structuring role it fulfills within these practices: it is an organizing measure constituting and constituted by the assemblage of constructions, implementations and modifications of tools and instruments, along with the procedures of their use, which embody Hooke's workshop and laboratory skills. 29 Hooke uses the term to synthesize an array of relatively independent manipulations into what may be perceived as an integrated 'research and development' project, a concentrated effort to improve his competence in producing a set of desired effects and artifacts, which, in the Micrographia, are large scale drafts of minute creatures. The meaning of 'inflection' is exactly its role in this effort. Its uniqueness as a linguistic, rather than a mechanical contrivance, is not due to a unique relation it has to the world outside Hooke's workshop and laboratory, but rather to the particular place Hooke assigns the term within them. The manipulations of which 'inflection' is a linguistic counterpart make up a series of attempts to control the behavior of light as it passes through refracting instruments. 30 The water globes marked the first, modest step in this direction, and Hooke's use of them evokes Bennett's interpretation of the role of mechanical demonstrations in his conceptualization of existing theoretical queries. Hooke's next step was more ambitious and reveals that Hooke's development of his inflection theory had an even greater dependence on what he himself might have called, given hindsight, 'inflection technology.' The theoretical choice between surface refraction and continuous inflection, which Hooke offers his readers as alternative explanatory measures, emerges as a direct consequence of a technological

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choice. The choice was forced on Hooke by his dissatisfaction with his refracting instruments. His microscope observations suffered, among other things, from problems of (what would later be termed) chromatic aberration-"the colours which do much disturb the clear vision" (CL, 313), due to poorly ground lenses. The great difficulties in improving their accuracy prompted Hooke to try and minimize number of lenses in his microscopes. He thus remarks on various occasions in the Micrographia ("Preface," xxix; c.L., 313-314) that his favorite microscope was of a single lens and two refractions 3 '. This, in fact, was nothing but a piece of highquality glass held close to the eye; "a small round Globule, or drop" of "very clear ... Venice Glass" (ibid.)-virtually a simple magnifying glass. Trying to circumvent the numerous difficulties arising from the use of 'microscopes' like this, Hooke suggests a liquid-filled microscope; a highly translucent medium ("very clear water") connecting two plano-convex lenses: ... always the fewer the Refractions are, the more bright and clear the Object appears. And therefore 'tis not to be doubted, but could we make a microscope to have one only refraction, it would, ceteris paribus, far excel any other that had a greater number.... But because these [glass-drop microscopes), though exceedingly easily made, are yet very troublesome to be us'd, because of their smallness, and the nearness of the Object; therefore to prevent both these, and yet to have only two Refractions, I provided me a Tube of Brass [Fig. 4 in Scheme I (Figure 6)) into the smaller end of this I fixt with wax a good plano convex Object Glass, with the convex side towards the Object, and into the bigger end I fixt also with wax a pretty large plano convex Glass, with the convex side towards my eye, then by means of a small hole by the side, I fill'd the intermediate space between the Glasses with very clear water, and with a Serew stopp'd it in; then pUlling on a Cell for the Eye, I could perceive an Object more bright then I eould when the intermediate space was only fiU'd with Air. (Micrographia, "Preface," xxix_xxx)32

If the workings of the water globes offer a first glimpse into Hooke's development of 'inflection' as a technological and a theoretical device, his deliberations in the Preface as quoted above lead to the heart of the matter. The light, on its way through the water-filled microscope, does not yet undergo the inflection Hooke defines in Observation 58. That definition also relates to an "unequal density of the constituent parts of the medium" (see Section 3 above), while "the intermediate space between the Glasses" of the water microscope is homogenous (the heterogeneity would be added later-see Section 5.3 below). But this microscope is an important step towards 'inflection': the above quotation depicts the water microscope as

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having "only two refractions" which, in Hooke's terminology, is equivalent to presenting it as one elongated lens, refracting the ray at its extremities (see footnote 31 above). At that time, Hooke had not yet developed the idea of (or the instruments for) curving the ray; but he certainly tries to control it by manipulating the medium it passes through, rather than the surface between media. In order to appreciate fully the import of the water microscope on the route to 'inflection'. we need to reexamine its predecessor-the so-called 'single microscope.' While the development of both devices was motivated by practical, technical considerations, there is a major difference between the considerations concerning each one of them. When Hooke suggests replacing the double microscope with a magnifying glass, he is not merely making a 'practical' move, but virtually an anti-theoretical one. To the extent that whatsoever had been any optical theory whatsoever had been involved in developing refracting magnifying instruments in Hooke's time, it was related to the understanding of the complementary role fulfilled by two or more lenses of different shapes or sizes. In favoring the extremely simple 'single microscope', Hooke set aside precisely this piece of knowledge. He does so to solve a particular technical problem: "the colours which do much disturb the clear vision in double Microscopes is [sic.] clearly avoided and prevented in the single" eeL, 313). The single microscope goes some way toward eliminating the interference, but not as a result of any theoretical or even technical solution of the problem itself. It does so by simply reducing the number of refractions, .dismissing in the process the only available theoretical grounding for optical technology. Furthermore: in adopting the single microscope Hooke breaks with his own precepts regarding the application and advancement of technology, precepts which he had explicated most clearly in his Animadversions to the Machina CfElestis of the great Hevelius (C.L., 37-114). This review and critique of the opus magnum of that last major naked-eye astronomer developed into a debate concerning the advantages of state-of-the-art technology (in particular telescopic sights) versus those of time honored practices (of observation and in general). Hooke argues forcefully in favor of preferring the advancement of technology over perfecting existing practices, and his strongest argument rests on the notion of the essential imperfection of the human sense-organs. Technology, he argues, even if temporarily inferior, is always open to further improvement. The presentation of new instruments in the Preface to the Micrographia demonstrates this approach beautifully: every new invention gives rise to

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new technical difficulties, which in tum are solved by another invention and so forth. There is never an insurmountable obstacle, just yet-to-be-solved questions. On the other hand, Hooke explains, non-technological practices (of which naked-eye observation is a prime example) will always be finally confined by the bounds of human perception (C.L., 43-44). In reverting to the single-lens microscope Hooke is clearly working counter to this insight. He offers this 'microscope' as a solution for a technological difficulty-the inadequacy of lens-grinding-but it is not itself a technological solution, just a regression to a simpler practice, use of a less elaborate, less theoretically supported, less artificial tool: a glass drop. The type of difficulties that its use entails, which Hooke candidly acknowledges, marks the single microscope as a regressive step according to Hooke's own standards; these are difficulties caused by the shortcomings of the human eye: "I have found the use of them offensive to my eye, and to have strained and weakened the sight" (C.L., 312). Hooke's willingness to sacrifice the technological promise of progress for the immediate reward of convenience, limited "to those whose eyes can well endure it" (CL, 312-313), reflects the locality of the considerations that produced 'inflection.' But this regression is only temporary: the water microscope, the offspring of the single microscope, is not the technological dead end that its predecessor was. It does not reflect a neglect of a portion of technological know-how along with its opportunities for further development, but its replacement by another technological approach with its own credentials. The construction of the water microscope is a development, rather than regression, because it is justified-not by abstract considerations, but by the support of another set of instruments. It represents a token of what I pointed out earlier, namely, that the technology in the Micrographia functions as an integrated system whose constituents sustain both one another and more general theoretical claims mainly by virtue of their inter-relations. While the single microscope was nothing more than an accidentally usable piece of almost raw material, and therefore necessarily short lived as an instrument, the water microscope was a credible element of the technological network that Hooke was weaving. Itis tied to this network by one of the devices he most proudly presents in the Preface: an instrument "by which the refraction of all kinds of Liquors may be most exactly measur'd" (Micrographia, "Preface," xxvii, Scheme I, Fig. 2-see Figure 6). As Hooke's own description reveals, the 'refractometer' is by itself·· a technical achievement-"it consists of five Rulers ... AB denotes a straight piece of wood ... on the back side of which was hung a small plummet ... " and so on.

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Like his other inventions-the universal joint is perhaps the most famous of them-it testifies to Hooke's command of his workshop tools, rather than any theoretical knowledge he might have possessed. However, by providing control of the refracting medium- making it possible to use different 'liquors' with different refraction indices-the refractometer renders the water microscope a piece in a viable chain of technological research: enabling Hooke to manipulate the fluid between the two 'half lenses' (plano-convex, with their plain sides facing each other). This allows him to perceive it as a single microscope with a long lens and carries him another step towards inflection as continuous refraction.

5.3. Third Stage: Proof Sufficient Two further steps are needed for 'inflection' to be presented as a legitimate technological and theoretical rival to refraction. First, it must be related to the heterogeneity of the refracting medium. Secondly, the ray must be shown to be indeed inflected-i.e., as moving along a curved, rather than a broken trajectory. Hooke, as would befit him, establishes both these aspects of the meaning of his term through experimental demonstrations. The first experiment is a product of technologies already utilized: Take a small Glass-bubble, made in the form of that in the second Figure of the 37. Scheme [Figure 51, and by heating the Glass very hot, and thereby very much rarifying the included Air, or, which is better, by rarifying a small quantity of water, included in it, into vapours, which will expel the most part, if not all the Air, and then sealing up the small neck of it, and letting it cool, you may find, if you place it in a convenient instrument; that there will be a manifest difference. as to the refraction. (Micrographia, 221)

The eye situated at A (Fig. 2 of Figure 5) is able to follow the changing image of the object at C as the medium in B changes-first as a result of the gradual condensation due to cooling, and then, when the seal is broken, through the replacement of the vapors by the external air. The glass bubble is a combination of both the glass viol, and the "Venice Glass ... [melted into] very small hairs ... and run into a small round globe" used for the single microscope (Micrographia, "Preface," xxix). It simulates spatial heterogeneity by temporal heterogeneity; quite an ingenious contrivance, which offers another example of Hooke's way of endowing his theoretical concepts with meaning by constructing a device-a real working machine. The heterogeneity of the atmosphere and the effect of the medium on light provided the justification for applying 'inflection'. The motivation for

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its application, the explanatory advantage of inflection over refraction, was provided by the image of gradual encurvation. With hindsight, this was the aspect of the term's meaning, which proved to be most fertile-it was the possibility that an external force could transform the ray, the epitome of rectilinear progression, into a curve, which helped producing the Address of 1666 in particular and Hooke's Programme in general. In the Micrographia, however, this notion receives no special treatment; Hooke establishes the effect by yet another experiment. He fills a tank (Fig. 1 in Figure 5) with clear water and a strong solution of salt, which, he assumes, mix themselves together so as to be "continually more dense the neerer they were to the bottom." Then, exposing the side, which is opaque, to the sun, he observes its shadow, which represents the progress of the rays 'grazing' it from above, and declares: marking as exactly as I could, the points P, N, 0, M. by which the ray, KH, passed through the compound medium. I found them to be in a curve line. (Micrographia, 220; Fig. I in Scheme XXXVD (Figure 5))

By way of conclusion, and before moving on to the glass bubble demonstration, Hooke tellingly summarizes what he takes himself to have achieved: .../ have by this Example given proof sufficient (viz, ocular demonstration) to evince, that there is such a modulation, or bending of the rayes of light, as I have call'd inflection, differing from reflection, and refraction (since they are both made in the superficies, this only in the middle); and likewise, that this is able and sufficient to produce the effects I have ascribed to it. (Micrographia,221)

6. IMPLEMENTATION This experiment marked the final stage in the process of constructing 'inflection'. However, it is obviously not enough; to produce a tool, one also needs to demonstrate that it can perform the required tasks. In other words, Hooke could not suffice with establishing that a ray of light could be bent by any heterogeneous medium; since he intended to employ inflection in accounting for phenomena related to astronomical observation, he needed to demonstrate the ray could be bent by the atmosph~re. Hooke acknowledges this challenge in his two-tiered presentation of the hypothesis (see citation from Micrographia, 219, in Section 4.1 above), and sets out to discharge it.

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6.1. Experiments: Local Knowledge Turned General As may by now be expected, Hooke performs the demonstration through a series of mechanical simulations which allow him to celebrate some of the instruments he presented earlier, in the Preface to the Micrographia. ·'Now. that there is such a difference of the upper and lower parts of the air," he commences, is clear enough evinced from a late improvement of the Torrice/lian Experiment. which has been tryed at the tops and feet of mountains, (Micrographia, 222)

This is somewhat of an over-statement. Although the suggestion to "Try the quicksilver experiment at the top, and at several ascents of the mountain" was the first of the "questions, propounded by the lord viscount Brouncker and Mr. Boyle, according to an order of the [Royal] society of the 51b of December [166O--a year and a half before Hooke was retained by the society as curator of experiments], and agreed upon to be sent to Teneriffe" (Birch I, 8), the records of the Royal Society do not contain the unequivocally supporting resuJt Hooke alleges. The "late" experiment he refers to seem<; therefore to be the one he conducted himself in September 1664, and about which he "gave an account, that the mercury in the Torricellian experiment made at St. Paul's was on the top of the steeple fallen about half an inch beneath the station thereof at the bottom of the church (Birch I, 465). Be that as it may, in the Micrographia Hooke spends no further space on ascertaining that the atmosphere is indeed structured so as to allow inflection.' He offers no details of that experiment, and proceeds immediately to describe a means, which some whiles since I thought of and us'd, for the finding by what degrees the air passes from such a degree of density to such a degree of Rarity (Micrographia, 222; Fig. 3 in Scheme xxxvu (Figure 5)),

and then another experiment to find what degrees of force were requisite to compress, or condense, the Air into such or such a bulk. (Micrographia, 225; Fig. 4 in Scheme xxxvn (Figure 5))

The History of the Royal Society carries "Mr Hooke's account of the rarefaction of air" of November 26, 1662 (Birch I, 141-144), and according to his own report in the Micrographia, these experiments were first carried out back in 1661 (when he was still employed by Boyle-Micrographia, 225). The experiments can also be considered an "improvement of the Torricellian Experiment." The first, which demonstrates the rarefaction of air following a drop in pressure, consists of a glass tube DE and a wooden

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box attached to its top (Fig. 3 in Figure 5), which Hooke fills with mercury. This he dips into the fitting tube AB, and seals side A, allowing an inch of air above the mercury. He then draws tube AB up according to measured increments of the mercury column-2 inches; 4 inches etc., up to 27 inches of mercury-measuring the corresponding expansion of the air trapped above it- 1K6 inches; I Y7 inches-up to 15 ~ inches of air respectively. The other experiment, demonstrating compression, is simpler still; Hooke pours mercury into the longer, side AD of the siphon AB (Fig. 4 in Figure 5), and measures the height of the column of mercury required in order to compress the air in side CB by given amounts; 51<6 inches of mercury (in addition to the atmospheric pressure) compress the air from 24 inches to 20 inches and so forth. With these experiments Hooke achieves control of the actual mechanism that produces the heterogeneity of the atmosphere; the relationship between the force exerted on a volume of air and its density. In the atmosphere, the force is the very "pressure of the Air," which changes, naturally, with the height of the "Cylinder indefinitely extended upwards." The experiments also give Hooke a good estimation of the rate of change, since they "have somewhat confirm'd the hypothesis of the reciprocal proportion of the Elaters to the Extensions" or Boyle's pressure law (Micrographia, 227), and he concludes that There being such a difference of density, and no Experiment yet known to prove a saltus, or skipping from one degree of rarity to another much differing from it, that is, that the upper part of the Air should so much differ from that immediately subjacent to it, as to make a distinct superficies, such as we observe between Air and Water, & c. But it being more likely, that there is a continual increase of rarity in the parts of the Air, the further they are removed from the surface of the Earth: It will hence necessarily follow, that (as in the Experiment of the salt and fresh Water [Fig. I in Scheme XXXVII (Figure 5)1) the ray of Light passing obliquely through the Air also, which is of very different density, will be continually, and infinitely inflected, or bended, from the streight, or direct motion. (Micrographia, 228)

6.2.

Queries: General Knowledge Applied Locally

Having established this much, Hooke proceeds to suggest an account of each of the astronomical-observation phenomena referred to earlier, treating them as optical effects related to inflection, and using experimental simulations similar to the few examples described above. The "sphrerical Crystalline viol," we saw, was used to demonstrate that "The Redness of the sun, Moon, and Stars, [is] caused by the inflection of the rays within the

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Atmosphere" (Micrographia, 228). demonstration that the

To give just one more example, the

irregular, unequal an unconstant inflection of the Rays of light, is the reasone why the limb of the Sun, Moon, Jupiter, Saturn, Mars, and Venus, appear to wave or dace; and why the body of the Starrs appeat to tremulate or twinkle (Micrographia, 231)

is carried out, first by reference to the "tremulous motion you may observe to be caus'd by the ascending steams of Water." Still, if yet you doubt, let Experiment be made with that body that is accounted, by Chymists and others, the most ponderous and fix'd in the world; for by heating a piece of gold, and proceeding in the same manner, you may find the same effects (ibid.),

and so on. Hooke concludes with a series of more general hypotheses, relating inflection to parallax and thus procuring for it fundamental relevance for all astronomical measurements (Micrographia, 236-238). These moves are somewhat beyond the scope of this chapter, although an idea of the instruments involved can be obtained from the diagrams in Scheme XXXVII. I would still, however, like to cite one of the "queries" that constitute the main part of Hooke's concluding remark: This I should further proceed to hope, had anyone been so inquisitive as to have found out the way of making any transparent body, either more dense or more rare; for then it might be possible to compose a Globule that should he more dense in the middle of it, then in any other part, and to compose the whole bulk, so as that there should be a continual gradual transition from one degree of density to another; such as should be found requisite for the desired inflection of the transmigrating Rays; but on this enough at present, because I may say more of it when I set down my own Trials concerning the melioration of Dioptricks, where I shall enumerate with how many several substances I have made both Microscopes, and Telescopes, and by what and how many ways: Let such as have leisure and opportunity further consider it. (Micrographia, 234)

With this and similar 'queries' Hooke rounds off his development of 'inflection' for the Micrographia: building on his expertise as an artisan, acquired by systematically constructing and modifying instruments to serve the developing needs of his laboratory practices, he tries similarly to systematize a theoretical solution for difficulties arising in astronomical observations. Achieving what he deems a satisfactory theoretical structure, he returns and utilizes it to offer a "melioration" of the skills that allowed the enquiry to begin with, and in the process reveals considerable social skills in the presentation of his instruments and of himself. Hooke now shelves 'inflection' until there is occasion to use it again. That occasion, as we have seen, occurs about a year later, in his Address to the Royal Society,

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and demands certain careful modifications of the meaning of the term, modifications that Hooke willingly takes on.

7.

TENTATIVE CONCLUSION

We are now in a position to tell the story in its proper chronological order: in 1663-4, partly fulfilling a Royal Society assignmene3 and partly at his own initiative, Robert Hooke engages in developing his skills and his instruments for making microscopic observations. The fruits of these efforts saw light in his Micrographia of 1665. One of these was the term 'inflection,' which Hooke coined to mean the gradual bending of a ray of light into a curve by a heterogeneous medium. A year later, in an Address to the Royal Society, Hooke went on to use 'inflection' to ascribe gradual bending to another celestial motion; that of the planets. This was the first version of his Programme, and the first suggestion that the planetary orbits originate from the encurvation of rectilinear trajectories. The introduction, development and use of 'inflection' in the Micrographia reveals the function of the term as an integral part of the 'hands-on' manipulations by which Hooke's technological knowledge was produced and maintained. The term is coined with unmistakable reference to specific instruments and operations, endowed with meaning by mechanical demonstrations, and generalized and applied to nature by experimental simulations. Furthermore, the transfer of 'inflection' from optics to celestial mechanics, which enabled the major theoretical breakthrough of Hooke's Programme, was achieved by operating and utilizing the term in a pragmatic, result-oriented manner, befitting those instruments from which it was bred. Hooke's theory-construction appears, therefore, as a practice closely related to his instrument-construction, where what may seem as a revolutionary leap in the one is a product of careful tinkering in the other.

1ST INTERLUDE: PRACTICE 1. INTRODUCTION-METHODOLOGICAL LESSONS

1.1. The Scientist, the Mechanic and the Genius 'Inflection'-its production and use, its hybrid status between theory and instrumentation-reasserts and intensifies the question of suitable epistemological categories for analyzing Hooke's Programme. Those embodied by the scientist, the mechanic and the genius-the common heroes of traditional Hooke scholarship-need to be examined. One may find it easy to suspectthe 'genius'. An attempt to determine what exactly 'genius' means is beyond the scope of this interlude, but Drake, who uses it most conspicuously, provides some hints. Not only was Hooke "a pioneer geologist" (Restless Genius, 165), she tells us, "far advanced of his contemporaries" (51) but he also "hypothesized a number of extraordinary ideas, that in hindsight seem almost clairvoyant" (77). This seems to signify that the "genius," with his "clairvoyant" ability to foresee and "advance," turns his future (which is our present) into an explanation of his present (our past), and thus has no place in a historical account. However, the 'mechanic' and the 'scientist' are not beyond suspicion either. Hooke's easy transgressions of the boundaries between the theoretical, experimental and technological realms give us reasons to wonder whether the mechanic-scientist distinction itself is more than a fossil; whether these categories do not ossify into an epistemological relationship what was fundamentally a social hierarchy, namely, the hierarchy between Hooke's employers-the gentlemen-philosophers of the Royal Society, and his employees-the artisans-experimenters whom he trained or contracted. I

1.2. Westfall's Question The personification of the mechanic and the scientist- with Hooke representing "the makers and grinders" and Newton and Huygens as "the great Philosophers"- provides additional cause for suspicion. It suggests that the comparisons brought in the Introduction are nothing but reenactments of the personal struggles between the protagonists over priority, prestige and power; reenactments which usually sustain (but occasionally overturn) the winners and losers of the original struggles. The

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dissatisfaction with this categorization intensifies when the categories are applied to the actual interpretation of scientific work. This is the feeling of unease one encounters when reading Westfall's inquiry into Hooke's 'scientific technology': The ideal of scientific technology is, of course, only a restatement of Baconian utilitarianism. The problem I propose is to detennine not whether men of the seventeenth century subscribed to the ideal but whether the ideal was translated into fact; for this purpose Robert Hooke ... appears to be a perfect subject to examine. Among his works are three examples that supply the details of his scientific analysis of technical problems. By looking at his demonstrations we can arrive at a clearer understanding of the relations of science and technology in the late seventeenth century. (Westfall, "Robert Hooke," 94)

Yet 'Science', 'Technology' and how they relate are not only Baconian ideals. They are also epistemological concepts in the service of science historians, embodying presuppositions concerning knowledge and its production. In this respect, Westfall himself appears "a perfect subject to examine," and not because he uses these categories unwittingly. Quite the contrary, despite the uncomplimentary remark by him cited in the Introduction (which is also some fifteen years older than the last quotation), he appears not to accept 'science' and 'technology' as self-explanatory titles with self-evident laudatory or pejorative connotations. Instead, while discussing "scientific technology" Westfall attempts to investigate the actual relations between the skills and practices that these titles correspond to; the theoretical and speculative skills on the one hand, and the technical and experimental ones on the other. Consequently, he has no need to compare Hooke to anyone else and can refer to him as representing both a 'mechanic' and a 'scientist' of his period, thus stripping these categories of their protective personal affiliation with "the genius" and his "almost worthy rival." Laid bare, however, the categories lose their allure. As I will try to show, Westfall's use of them reveals, first, that the derogatory historical comparisons of Hooke to Newton and Huygens express not only residues of their erstwhile clashes, but also genuine epistemological prejudice. Secondly, that unless reinforced by this personification, the epithets of 'mechanic' and 'scientist' do not offer an adequate basis for understanding the episodes investigated. Of the three examples scrutinized by Westfall, one example partially relates to the areas of Hooke's work addressed in the next chapter, and thus is particularly suited for this discussion. It regards Hooke's theory of combustion, which alleges to be the theoretical grounds on which he designed the lamps he presents in his Cutlerian Lecture Lampas (reprinted

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in CL., 155-208). Hooke himself opens his lecture by referring to pages 103-105 of his Micrographia, where this theory is introduced, stating that he intends to employ it to "some pleasant and beneficial uses, and to hint some Mechanical contrivances for the supplying the Pabulum Oyl or spirit by the same Degrees which it is consumed in the flame of the Lamp" (CL., 155). Indeed, these two texts with their illustrations provide a case where both Hooke's ("genius") mechanical capabilities and his (perhaps less so) theoretical ones are present. Westfall's conclusion of his search for "scientific analysis of technical problems" is disappointing however: ... [W]hen we examine the scientific foundations of this invention [of steadily burning lamps] what do we find? [The hypothesis that combustion is] a dissolution of sui furious mailer by nitrous salts in the air, with concomitant generation of heal. It was less a hypothesis than an analogy to the dissolution of substances in acids; but he also forgot along the way that he had introduced it as a hypothesis and concluded by calling it a theory. He described as though it were empirical fact how particles of fuel, vaporized by heat, fly off the wick of a lamp and ascend in the air, where they are di ssolved ... The net result of this theory, nothing of which survived for long, was the conclusion that lamps need a steady supply of fuel to bum steadily. Surely any blacksmith could have told him as much. If this is the fruit of scientific technology, it is disappointingly meager. (Westfall, "Rohert Hooke," 95)

1.3. "Scientific Technology"

How exactly should one interpret this conclusion? What does the alleged 'meagerness' of "the fruit of scientific technology" refer to? If the 'fruits' in this case are the oil lamps designs, then they seem rather ingenious, and there is no reason to doubt Hooke that the lamps in fact work and perform as expected, namely "to supply the Pabulum to the flame equally and for a very long time till it be all consumed" (CL, 156), thus making the lamps useful for all kinds of "Chymical, Mechanical and Philosophical uses" (CL., 163). The theory, appreciated by Westfall or not, is there (partly in the Micrographia and partly in Lampas) to be examined. Hooke, for one, believes that his theory does carry some important consequences, for example, he sees the notion of a "perpetual Lamp" as "a Chimera which my hypothesis of flame doth seem to destroy" (C.L., 155). Thus Westfall's disappointment boils down to his failure to find an significant link between the theory and the lamps; either, as Westfall seems to conclude, Hooke's work is a testimony to seventeenth century's technology independence of science, or, as I am inclined to think, it suggests that we need to reassess

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Westfall's use of both notions-'science' and 'technology'-and more importantly, to reexamine the relations he presupposes between the two. If Westfall's frustration provides the final evidence that his search was misdirected, the phrase "scientific foundations of ... invention" suggests that the wrong tum was taken early. The search, the phrase indicates, was predestined to failure by the same divisions and hierarchies of knowledge responsible for obscuring Hooke's biographies. Together with the terms 'theory', 'hypothesis' and 'empirical fact', Westfall's phrase makes clear that in order for Hooke to demonstrate an example of "scientific technology" that would satisfy Westfall, he would have had to apply some abstract 'laws of nature', established theoretically, in manufacturing his lamps. Although there appears to be more to the theory than just "lamps need a steady supply of fuel"-for example, the theory explains why and how the surface of the oil should be kept warm (C.L., 162), we can still grant Westfall that Hooke does not use his theory in this way. The conclusion that Hooke does not demonstrate 'scientific technology', however, is simply self-defeating. The story of the development and use of 'inflection' suggests a possible reason for Westfall's exasperation: Hooke's repertoire of ways to relate theory to technology is much larger than what Westfall is willing to assume. Closer examination of Westfall's account confirms the suspicion that his disappointing conclusion should be ascribed to the epistemological presuppositions which structure his analysis, rather than to any specific want in Hooke's work. Westfall's epistemology is not merely a matter of philosophical niceties; it makes itself felt at the basic levels of historical interpretation. For example, contrary to the impression given by the above paragraph, Hooke never uses the term "empirical fact" with regards to the behavior of the fuel particles (insofar as I can attest, this term was simply not a part of his vocabulary). This fact should not be overlooked. The model of scientific knowledge with which Westfall approaches Hooke's text is one in which general theories explain particular 'empirical facts.' As the last chapter showed, this model is far from an adequate representation of Hooke's scientific practices: he is not bothered with 'facts'-those sentence-like entities lying 'out there,' as Richard Rorty calls them (see 200 Interlude)but phenomena. and phenomena, according to Hooke, are those occurrences, "excited and made vigorous by art" (Posthumous Works, 40) that he can steadily produce, "trying the experiment over and over again" (Posthumous Works, 28. See also 44f Furthermore, we find that Westfall disregards those very skills of Hooke

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that allowed him to produce the desired effects and phenomena he sought. Hooke, himself a 'blacksmith' of some repute, and indeed "a mechanic genius" (Hall, "Robert Hooke and Horology," 175-see Introduction)-the clever contrivance of the lamps providing one of the many proofs of thishardly needed other blacksmiths to instruct him on the necessity of a steady supply of fuel for combustion. Thus, although Westfall correctly senses that Hooke's work reflects an artisan's practical and creative knowledge, his concern with the application of what he terms 'scientific knowledge''hypothesis' and 'theory'-to technology leads him to criticize Hooke for failing to keep his promise 'to put the theory to use', and prevents him from accounting for Hooke's capacity to make the practical knowledge at his disposal transcend its locality by ascribing to it "nature and causes" (C.L. p. 163, also cited by Westfall, op. cit.). This was, perhaps, the most important lesson of the previous chapter; Hooke often relates theory to practice not by applying general laws to particular uses, but by producing general laws with local skills.

of

2. HACKING Hooke's work, then, presents an epistemological challenge. Westfall's terms-"scientific foundations of invention;" "hypothesis;" "theory;" "empirical fact"- while not appearing problematic, fail utterly to account for Hooke's achievements. Hooke's construction and use of 'inflection' intensify the challenge. Hooke's smooth movement through the realms of theory, observation, experimentation and technology hardly allows for the layered, orderly interconnections required by Westfall's approach and the comparisons between Hooke and Newton cited in the Introduction presuppose. Any adequate account of Hooke's Programme must have an epistemological framework such that the use of theory in producing instruments and the use of instruments in the construction of theory can be analyzed and described in similar terms: Hooke, for his part, was completely indifferent to the preeminence of one realm over the other. An important step towards the construction of such a framework was taken in a small book published by Ian Hacking in 1983-Representing and Intervening (henceforth: RI). Though not the only criticism leveled at the epistemological lore of science historians, Hacking's deserves special attention. It is, at least prima facie, both the most radical and the most directly applicable to the study of Hooke. Indeed, one of Hacking's favorite examples of what he regards as the predicament of contemporary history and

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philosophy of science is exactly the treatment of Hooke that 'Espinasse lamented: Hooke, the experimenter who also theorized, is almost forgotten. while Boyle, the theoretician who also experimented. is still mentioned in primary school textbooks. ... This man taught us much ahout the world in which we live. It is part of the bias for theory over experiment that he is by now unknown to all but a few specialists. It is also due to the fact that Boyle was a noble while Hooke was poor and self-taught. The theory/experiment status difference is modelled on social rank. (RI, 150-151)

It is towards this "theory/experiment status difference" that Hacking directs his assault: Indeed much recent philosophy of science paraUels seventeenth-century epistemology. By attending only to knowledge as representation of nature, we wonder how we can ever escape from representations and hook-up with the world. That way lies an idealism to which Berkeley is the spokesman. In our century John Dewey has spoken sardonicaUy of a spectator theory of knowledge' that has obsessed Western philosophy. Ifwe are mere spectators attbe theatre of life, how shall we ever know. on grounds internal to the passing show, what is mere representation by the actors, and what is the real thing? (RI, 130)

2.2. Back to Bacon 2.2.1. The Theoretical Bias Hacking does not aim his criticism of the "spectator approach" at the very notion of representation; his complaints are limited to philosophers' tendency to concentrate on representation, while neglecting all other modes and processes of knowledge production: .1 agree with Dewey. I follow him in rejecting the false dichotomy between acting and thinking from which such idealism arises. Perhaps all philosophies of science I have described are part of a larger spectator theory of knOWledge. Yet I do not think that the idea of knowledge as representation of the world is in itself the source of that evil. The harm comes from a single-minded obsession with representation and thinking and theory, at the expense of intervention and action and experiment. (RI,130-131)

Hacking characterizes his approach as "conservative" (RI, 215). Concerning the "theory/experiment" (as well as 'theory/technology' and 'theory/observation') issues crucial to the study of Hooke, however, his remarks are anything but mild. He expresses no instinctive solidarity with other p - . tiisciples, declaring that "Rorty's version of pragmatism is yet anot' ~rl ohiIosophy, which regards all our life as a matter of

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conversation" (RI, 63), and dismissing both advocates of the theoryladenness of experiments and of theory-independent observation language alike. Hacking crowds the followers of these two doctrines, antagonists in the most heated debate in the philosophy of science of the last century, under the same categorical roof. As he dryly remarks, in a somewhat different context, whenever we find two philosophers who line up exactly opposite of a series of half d07.en points. we know that in fact they agree about almost everything (RI, 5),

and just as Popper and Carnap (to whom the paragraph originally refers) "share a [particular] image of science" the unexpected doctrinal bed-fellows share "the vogue for what Quine calls semantic ascent (don't talk about things, talk about the way we talk about things)" (RI, 167) as a common grounds for their feud. As if on a mission to expose all celebrated radicals as counter-revolutionaries in disguise, his tolerance to representation notwithstanding, Hacking has no patience even for the late Paul Feyerabend, who for all his avowed rejection of linguistic discussions, ... still speaks as if the theory/observation distinction were a distinction between sentences. (RI, 173)

Thus Hacking's self-proclaimed 'conservatism' should be taken with a grain of salt. It is not uncommon to promote changes under the conservative banner, and it is not uncommon to aid such a cause with revivalist rhetoric, a strategy Hacking also adopts, calling "to initiate a Back-to-Bacon movement, in which we attend more seriously to experimental science" (RI, 150).

2.2.2.

In Praise of Practice

Sounding the "Back-to-Bacon" battIe cry Hacking counters 'the praise of talk' with a new emphasis on scientific practices-experimentation, observation, measurement. This reform begins with the realization that "experimentation has a life of its own" (RI, 150), It is not "the continuation of theory by other means" (RI, 238), as both positivists like van Fraassen and their critics, from Popper to Feyerabend, assume; "experimentation is not stating or reporting but doing-and not doing things with words" (RI, 173). That there is no point in attempting to look for "the scientific [viz.; theoretical] foundations of ... invention," that Westfall failed to find, does not mean that experimentation has no relation to theory, but that the two

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types of practices can have many different relations: Some profound experimental work is generated entirely by theory. Some great theories spring from pre-theoretical experiment. Some theories languish for lack of mesh with the real world, while some experimental phenomena sit idle for lack of theory. There are also happy families, in which theory and experiment coming from different directions meet. (RI, 159)

Sometimes "noteworthy observations" stimulate theory, as in the case of Bartholin's Iceland Spar observations and Fresnel's optics (RI, 155-156). Other times, theory may stimulate experiments and observations that outlast the theory's own life, as in the case of Brewster, who established Fresnel's (wave) laws while remaining a firm believer in the Newtonian (corpuscularian) theory of light (RI, 157-158). In addition, "plenty of phenomena attract great excitement but then have to lie fallow because no one can see what they mean" until the right theory comes by, as in the case of Brownian motion (RI, 158). Other relations are also possible-Haake's Programme alone could have offer Hacking several examples. Hacking makes a point of presenting a variety of actual historical and contemporary examples, which, besides supporting his own claims, also display the theoretically biased manner in which the story of science is usually told, especially by philosophers.

2,3.

Looking, Doing, Making

2,3.1. Seeing with a Microscope In proclaiming the independence of experiment and observation from theory, Hacking does not intend to advocate a return to the much-maligned empiricist foundationalism. He does advise, to be sure, that the word 'theory' should be used more cautiously. "Of course if you want to call every belief, proto-belief, and belief that could be invented, a theory, do so. But then the claim about theory-loaded [observation] is trifling" (RI, 176). It is again important to note that, as his unconventional mapping of the philosophical terrain has hinted, Hacking's alternative to theory-loaded observation is not theory-free observation. Not only has he no intention of re-instating the naIve trust in observation as an unbiased adjudicator, he is of the view that "Observation, as a prime source of data, ... is not at all that important" (RI, 167). The notion of observation that Hacking has so little respect for is the empiricist-phenomenalist one, what he calls the "philosophers' conception

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of observation: the notion that the life of the experimenter is spent in the making of observations which provide the data that test theory, or upon which theory is built" (RI, 167). This is very much the myth into which Hooke attempted to write himself when he offered "to serve" his "stock of natural Observations ... to the great Philosophers of this Age" to be used as "foundations whereon [they] may raise nobler Superstructures" (Micrographia, "Preface," xii-xiii), but a myth it is nonetheless. "It is hard to imagine a more wrong-headed approach to observation in natural science," continues Hacking, than Quine's proclamation that "observations are what witnesses will agree about, on the spot" (RI, 181i. Observation is not a neutral supplier of data because it is neither passive nor universal. "Often the experimental task ... is less to observe and report, than to get some bit of equipment to exhibit phenomena in a reliable way" (RI, 167); observation may not require theory, but it demands skills. The discussion of skills distinguishes Hacking's 'interventionism' from homespun Baconian empiricism6 • Hooke himself had already advocated "Attention and Diligence in making Observations and Experiments" (Posthumous Works, 62) and did not expect or encounter much controversy, but Hacking points out that these do not suffice. The laboratory is a complex and sophisticated workshop, and its successful operation requires talent, patience and training. Observation can hardly supply agreed-by-a11 data, since most people simply do not posses the skills required to perform even the simplest of its tasks: 7 a philosopher will certainly not see through a microscope until he learns to use several of them. Asked to draw what he sees he may, like James Thurber, draw his own eyeball, or, like Gustav Bergman, see only 'a patch of color which creeps through the field like a shadow over a wall'. (RI, 189)

The paucity of competent observers makes the notion of universal observation a useless philosophical fantasy, but more severe yet is the blow Hacking delivers to the notion of observation as a passive absorption of independent "empirical facts." Philosopher or not, he argues, you can actually regard yourself as seeing something through the microscope, say a part of a cell, only when you can manipulate it, e.g., when. using straightforward physical means, you microinject a fluid into just that part of the cell. (RI,190)

These considerations are not confined to complex experimentation or modem, high-tech, theory loaded microscopic practices. They are as applicable to Hooke's struggle with his microscopes, which, "though exceedingly easily made, are yet very troublesome to be us'd"

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(Micrographia, Preface, xxix). Hacking's arguments claim fundamental epistemological significance; his account of microscopy, he submits, is a genuine re-enactment of Berkeley's 'Theory of Vision': you learn to see through a microscope by doing, not just by looking. (RI, 189)

Seeing with a microscope is exactly the ability to tell 'a patch of color' from a cell wall, Hacking appears to be claiming, just like regular seeing involves the ability to tell a patch of color from a brick wall. In the macroscopic instance, he might have added, there are many other ways, beside from trying to drive through, of learning the difference between the two, and the great variety of practices actually and potentially involved may mask the fact that "We are convinced about structures we seem to see because we interfere with them in quite physical ways" (RI, 209). But the interdependence between seeing and doing in microscopy is nothing less than identity. The microscope is not just a tube with a light source of the one side and a lens on the other, but part of a cluster of tools and instruments of which we gain control as a whole, hence it would be much more accurate to say that we see with it, rather than through it (RI, 206-208); We see the tiny glass needle--a tool that we have ourselves crafted under the microscope-jerk through the cell wall. We see the lipid oozing out of the end of the needle as we gently tum the screw on a large. thoroughly macroscopic plunger '" John Dewey's jeers at the 'spectator theory of knowledge' are equally germane for the spectator theory of microscopy. (RI, 190)

2.3.2. Hooke Again With this bold application of the notion of 'doing', Hacking sketches a possible solution to epistemological riddle presented by Hooke: not only a new distribution of credit, in which "Hooke, the experimenter who also theorized," receives his due, but a genuine commitment "to destroy the conception of knowledge and reality as a matter of thought and representation" (RI, 63). The term 'observation' plays a double role in the "spectator theory of knowledge." Besides its function as a quasi-technical term for the most elementary, intimate, unmediated epistemic relation to the world, 'observation' also provides the main metaphor for this relation-that of, literally, observing-gazing attentively but passively. By demonstrating that the paradigm of scientific observation-actual looking through the microscope-is not, as he puts it, a matter of peering, but of interfering (RI, 189), Hacking points at what is false in "the false dichotomy between acting

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and thinking." Scientific knowledge, he establishes, is produced. It is generated through active choosing, manipulating and assembling. There is no 'primary' stage in which raw, unstructured data are acquired willy-nilly from the 'outside world', and consequently there is also no stage in which these data can be calmly inspected 'inside the mind'. All different phases of knowledge production-observing, experimenting, theorizing-involve active interference or 'doing'. Thinking is one type of acting. This is indeed an outline for a conception of knowledge that could make sense of Hooke's work and scientific persona. Applied to the case that Westfall brings, it reaps immediate insights. Hooke's lamps, according to this conception, may exemplify "scientific technology," without their "scientific foundations" imitating some textbook theory. As a stage in the production of the lamps, Hooke's combustion theory is of major importance, as it encompasses the procedures8 by which he avoids "vain attempts and blind trials" (CL., 163). It was Hooke's way to record and elaborate upon the actual physical manipulations employed in the construction and operation of the lamp, and through it to account for the resulting phenomenon, viz. combustion. The theory is the means by which the practices involved in producing and reproducing a phenomenon can be retained, referred to, related to similar ones, refined and used in other contexts-if indeed the particular 'phenomenon' merits such attention, as is the case with combustion or inflection. The prospect of better understanding of Hooke's Programme and, in particular, the construction of 'inflection', are even more exciting. When a hierarchy ceases to be imposed on "the scientific foundations of ... invention," it becomes possible to explore the actual relations between 'inflection' and the water microscope as well as those between Hooke's lamps and his combustion theory. Without the disparaging juxtaposition of 'the mechanic' vs. 'the scientist', Hooke's Programme can be regarded as an outcome of a collaboration (albeit short and tense) between Hooke and Newton.

3. THE REALISM SNARE

All the same, some degree of caution is advisable here. Replacing "the conception of knowledge and reality as a matter of thought and representation" with a concept of knowledge as actively shaping reality is a significant commitment. At the very least, it demands a re-interpretation of terms like Westfall's "hypothesis," "theory" and "empirical fact," that are

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so deeply embedded in traditional epistemology. Even if Hacking could not be expected to provide his readers with a system, we need to ask whether he is cognizant of the change and wiIling to adopt its ramifications.

3.1

Producing Phenomena

The answer indeed appears positive. Despite the probable offense to some deeply rooted epistemological intuitions, Hacking seems to take a radical stance: Tniditionally scientists are said to explain phenomena that they discover in nature. I say that often they create the phenomena that then become the centerpieces of theory. (Rl,220)

Indeed Hooke himself, with his first-hand expertise, recommends "To observe how much, and by what Degrees Nature is made to alter its Course by Art" and "To observe the Natural and Artificial ways of producing the same effect" (Posthumous Works, 44; c.! p. 58). However, the scientist's responsibility for her phenomena, according to Hacking, goes much deeper than recommended by Hooke. She is not only, "by Art," producing "the same effect" as "Nature," she "creates" through "Artificial ways" phenomena, which did not exist at all until and unless manufactured in the laboratory: the Hall effect does not exist outside of certain kind of apparatus. Its modem eqUivalent has become technology, reliable and routinely produced. The effect, at least in a pure state, can only be embodied in such devices. (RI, 225-226) The Josephson effect did not exist in nature until people created the apparatus. (RI, 229)

Cells, Hacking could have said, are natural objects. Cell-observations, on the other hand, and for that matter all other observational and experimental phenomena, are human-made, and therefore must be produced, just like any object of "Art."

3.2.

Entities Realism

We can thus conclude that Hacking is genuinely committed to doing away with the "spectator theory of knowledge", and sincerely determined to "free us from the notion of human knowledge as an assemblage of representations in a Mirror of Nature" (Rorty, Philosophy and the Mirror of Nature, 126--see 2nd Interlude). Instead of representing, replicating,

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copying or standing in 'a relation to propositions' (see 2nd Interlude) Hacking advocates creating, producing, manufacturing. His concept of knowledge seems almost modeled on Hooke; it makes clear philosophical sense of Bennett's observation that in Hooke's hands, "The mechanical demonstration had an explanatory power of its own" (Bennett, "Robert Hooke as Mechanic and Natural Philosopher," 44-see Chapter I). It presents the boundaries between the realms of theory, experiment and technology as contingent and tentative, and demystifies Hooke's transgressions of them as he produces 'inflection', endows it with meaning and proceeds to employ it in the Programme. Yet Hacking avows much humbler pretensions than an epistemological revolution, and his arguments, as far as he is concerned, offer support for nothing beyond a mild realist position. "The creation of phenomena," he argues, "more strongly favours hard-headed scientific realism" (RI, 220): Experimental work provides the strongest evidence for scientific realism. This is not because we test hypotheses about entities. It is because entities that in principle cannot be 'observed' are regularly manipulated to produce ncw phenomena and to investigate other aspects of nature. They are tools, instruments not for thinking but for doing. (RI, 262)

Hacking's adoption of this position is surprising, to say the least. Not because there is anything in his arguments which suggests anti-realism, but because one important lesson to be learned from the Deweyan analysis of epistemology is that the very apposition is moot; that we can only ask whether "we can ever escape from representations and hook-up with the world" (RI, 209-see above) if we buy into the spectator theory of knowledge. Furthermore, Hacking is fully aware of the claim that the whole family of issues about realism and anti-realism is mickey-mouse, founded upon a prototype that has dogged our civilization, a picture of knowledge 'representing' reality. When the idea of correspondence between thought and the world is cast into its rightful place-namely, the grave-will not, it is asked, realism and anti-realism quickly follow? (RI, 25)

Hacking leaves the question unanswered and remains within the realms of the realism debate. I do not think that this aporia can be maintained. Perhaps not the whole of "our civilization," but certainly the study of Hooke has been "dogged" by the "picture of knowledge 'representing' reality." Historians have always found it proper to judge Hooke's knowledge by criteria external to Hooke's own practices. Remarks such as "Hooke was face to face with the concept of universal gravity, but '" unable to grasp it" (Westfall, in Posthumous Works, xv) on the one hand, or "He was moving towards the discovery of oxygen" (Drake, 27) on the other, are the

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consequences of this "picture of knowledge 'representing' reality." They assume universal, a-temporal criteria, to which the historian has better access than Hooke himself, a unique "picture" of the world towards which Hooke should have been striving and against which he could be measured. The value of Hacking's philosophy for analyzing Hooke's work is its contribution to the development of a different "prototype" of knowledge, i.e., a perspective which allows Hooke's achievements to be recognized as the products of his labor and evaluated according to the standards which would have made sense to him and to his peers. If Hacking's own suspicions are founded, and the realism debate rests on "the idea of correspondence between thought and the world," then we should investigate his reasons for adhering to this framework, assess their adequacy, and most important-
3.3.

Notions of 'Real'

What, then, is the reality that Hacking wishes to defend? Is there a concept of reality that calls for philosophical concern and is not "founded on ... the idea of correspondence between thought and the world"? In fact, Hacking suggests at least three candidates for such concept. The first is predicated on representations: Once there is a practice of representing, a second concept follows in train. This is the concept of reality, a concept which has content only when there are first· order representations. (RI, 136)

The second is predicated on objects: Real leather is hide, not naugehide, real diamonds are not paste, real ducks are not decoys, and so forth. The force of 'real S' derives from 'not (a) real S'. (RI,33)

In Hacking's words, 'real', in the second sense, is a "noun-hungry" term (RI, 33); it is not "an attribute of representation" any more, but of 'things'. It is also not a simple attribute, but one connoting a contrast; the contrast between a likeness and the thing it presumes to imitate. 'Likeness', it should be noted here, is not a synonym for 'representation', as it is in Hacking's 'anthropology' (see below). Naugehide and decoys are not supposed to represent leather and ducks, but to replace them, carrying some of the original's genuine features and omitting less important ones, according to the dictates of the context in which the likeness is needed to replace (again-not represent) 'the real thing'. Hacking aptly discusses the

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contextual dependence of Ihis second concept of 'real' thus: To know who wears the trousers we have to know the noun, in order that we can tell what is being denied in a negative usage. Real telephones are, in a certain context, not toys, in another context, not imitations, or not purely decorative. This is not because the word is ambiguous, but because whether or not something is a real N depends upon the N in question. The word 'real' is regularly doing the same work, but you have to loolc at the N to see what work is being done. (RI, 33)

Hacking's third notion of the real is context dependent in a more subtle, but no-less acute way. It distinguishes neither between successful and unsuccessful representations nor between likenesses and originals but between "artifacts of the physical processes [and] real structures" (RI, 201). It is to satisfy this particular notion of reality that Hacking suggests arguments of the following sort: We are convinced of the structures that we observe using various kinds of microscopes. Our conviction arises partly from our success at systematically removing aberrations and artifacts. (RI, 208)

This notion is contextually dependent because, as we have seen, "most phenomena of modem physics are manufactured" (RI, 228). As Hacking says, following the last paragraph quoted: We are more convinced ... because of a large number of interlocking low level generalizations that enable us tu cuntrol and create phenomena in the microscopic world. (RI, 209)

Clearly, if we "create" the phenomena we observe, the difference between what counts as an artifact and what counts as a genuine phenomenon or structure depends on the desired effect, i.e., what we wanted our apparatus to create and what not.

3.4. "Realism no Problem" 3.4.1.

Local Realism?

The question emerging is whether this array of distinct concepts of 'real' can serve as grounds for a realism debate that is immune to the Deweyan dismissal. I think not. Certainly the variety of concepts itself is an argument against this possibility: if 'real' has different meanings in different contexts and as an attribute of different types of entities7""representations, likenesses. phenomena-then establishing a position regarding its attribution 'in general' appears rather pointless. Hacking's own indifference

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to the boundaries between the different senses encourages skepticism. He seems to offer the first notion as the basis for the realism debate, while taking the second to be the most common-sensical use of the term 'real', and while drawing arguments for his own position from his discussion of the third. Now, Hacking is quite aware of the different meanings that 'real' can take, and we cannot, therefore, be satisfied with the over-arching argument, but should grant that his decision to structure his claims as arguments for realism are motivated by concerns about reality in one of the concrete senses of the term that he presents. This notwithstanding, attempts to support a 'local' realism debate using any of the three notions do not lead to any dramatically different results.

3.4.1.2. Representations Hacking himself sees the origin of the concern with realism in 'real' as an attribute of representation. Still, he maintains, representation alone is not enough: If reality were just an attribute of representation, and we had not evolved alternative styles of representation, then realism would be a problem neither for philosophers nor for aesthetes. The problem arises because we have alternative systems or representation. (RI, 139)

Structur.ally, Hacking's argument here resembles Strawson's antiCartesian one of Individuals. According to this analysis, 'this is real' is meaningful only against the background of 'this is not real'; and in order for a question about what is indeed real to arise, here has to be competition between rival representations. I would like to argue that this is a very convincing analysis of skepticism, but not of anti-realism. Rivalry of representations, one may grant Hacking, is a necessary condition for the development of doubts regarding the adequacy of any of the rivals. However, this competition, or even the skepticism it may give rise to, are insufficient grounds for a realism debate. General skepticism (dubbed "Pyrrhonian" by Rorty-see 2Dd Interlude), which stresses human fallibility, or, as we might say here, the poverty of our criteria for telling real from imaginary, may indeed be nothing but an attitude taken towards conflicting representations. This skepticism does not, however, amounts to anti-realism, and, a{ortiori, does call for realistic counter-arguments. Antirealism is not just the ironic, non-comrnittal suspicion that our

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representations may be wrong. Rather, it is the concern that they might all be wrong at once. It assumes a gap between the knowing subject and the known object and assigns representations a fundamental role in bridging it. CartesianiHurnean anti-realist concerns and their contemporary versions are 'professional' and disciplinary. They rely on an elaborate, foundationalist theory of knowledge, precisely the kind of theory that the Pyrrhonian is skeptic about. To use Hacking's own favorite formulation again-both realism and anti-realism require a 'spectator theory of knowledge'. Since he clearly lacks sympathy for "the idea of correspondence between thought and the world," Hacking has no reason to trouble himself either with the antirealist claims that this picture of knowledge raises, or with possible rebuttals to these claims. 3.4.1.2. Things This point-that arguing (for or against) the reality of representations commits one to the spectator metaphor---does not completely escape Hacking's attention. He explicitly distances himself from the reality of theories debate, despite the fact that theories are his paradigm of representation by means of language. Nevertheless, the designated bearers of the attribute 'real' in Hacking's second use-'likenesses'-are even less prone to demanding a general, philosophical position regarding their reality. In a sense, the difficulties with grounding a realism debate in 'real' as an attribute of things are complementary to those concerning the previous, representation-related concept. Whereas reality as ascribed to representations appears not to be a trait at all, it can be one of many different traits when ascribed to objects. Hacking himself introduces the first hom of the dilemma. In his reluctance to meddle with realism as it relates to theories-those "complicated speculations which attempt to represent the world" (RI, 133)--he dismisses scientific realists' favorite argument-the so-called 'argument from the best explanation'. Referring to Kant, he points out that existence is a merely logical predicate that adds nothing to the explanation. To add 'and photons are real', after Einstein has finished. is to add nothing to understanding. (RI.54)

Thus reality is not an attribute that all representations of S aspire to possess and the successful ones do possess. The difficulty with attributing reality to likenesses is indeed the opposite: there are numy different ways in which it can be attributed to likenesses. There are many different ways in which likenesses can aspire, successfully or unsuccessfully, to approximate

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their model. These different relations between imitations and originals may hardly relate to each other; why should the way in which naugehide relates to real leather resemble in any particular and non-trivial manner the way in which decoys relate to real ducks? "Whether or not something is a real N depends upon the N in question;,,9 the former are expected to confuse 'real' ducks into the firing range of hunters, the latter to replace 'real' leather and allow for cheaper school bags; do ducks and leather have a common feature which decoys and naugehide lack? The problem we dismissed earlier, viz.; the multi-meaning of 'being real', appears to return with new vigor, notwithstanding the attempt to focus on one particular sense that 'real' can take. Although Hacking insists that, in this 'noun hungry' sense, "[t]he word 'real' is regularly doing the same work" (see above), he does not, and, one may dare say, cannot, specify wool this 'work' is, in a manner clear enough to define feuding lines for philosophical positions. By conceding that "the force of 'real S' derives from 'not (a) real S' ," Hacking eliminates the basis for the belief that being 'a real S' is a unique positive attribute, the possession of which distinguishes things from their likenesses. Furthermore, even the relation between a specific "real N' and its likenesses, so Hacking tells us, depends not only "upon the N in question," but also on the context, since "[rleal telephones are, in a certain context, not toys, in another context, not imitations, or not purely decorative" (see above). Consequently, there is no point left in arguing whether some sort of entities mayor may not pass some general test that would qualify them as real.

3.4.1.3. Structures There is yet another sense in which Hacking uses the term 'real'- to denote the difference between "structures that we observe" and "aberrations and artifacts," This is also the most important of the senses in which the term is used by Hacking, because it is this notion of 'real' that provides the motivation and the basis for his realist argument. Certainly, taken as suggested above, namely as the difference between favorable and unfavorable outcomes of experimental manipulations, this last notion of 'real' is the most contingent and contextually-dependent of the three, and thus the least suitable to support a realism debate. But this is not reason enough to dismiss Hacking's argument. First, because an off-hand dismissal might be interpreted as a bias towards anti-realism, whereas the suspicion we have been considering is "that the whole family of issues about realism

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and anti-realism is mickey-mouse," in other words, that this debate is the wrong framework for Hacking to set his arguments in, and that both realism and anti-realism should be avoided. Secondly and more importantlybecause Hacking's argument is a particularly spectacular one, and it beautifully demonstrates both the power and the limits of his epistemology, especially in its application to the study of Hooke's Programme.

3.4.2.

Arguments

3.4.2.1 The Grid Hacking presents, in essence, two different, though related, arguments for realism. The first concerns entities observable only with the aid of instruments. The second, entities which, at least for the time being and perhaps in principle, are completely unobservable. The two arguments also seem targeted against different opponents. Hacking calls the first "the argument of the grid;" It is impossible seriously to entertain the thought that the minute disc, which I am holding by a pair of tweezers, does not in fact have the structure of a labelled grid. I know what I see through the microscope is veridical because we made the grid to be just that way. I know the process of manufacture is reliable, because we can check the results through the microscope. Moreover we can check the results with any kind of microscope, using any of a dozen unrelated physical processes to produce the image ... To be an anti-realist about that grid you would have to invoke a Cartesian demon of the microscope. (RI, 203)

The grid argument is an expansion of the microinjecting argument discussed above, and is very effective in eroding the distinction between directly observable, macroscopic entities and instrument-observable, microscopic ones. It also makes a good case for the reliability of microscopic procedures by explicating once again the production aspect of knowledge. to Yet it is less clear what makes it an argument for realism, or what might be the position of the 'anti realist of the grid' against which it is directed. It does not seem likely that the opposition Hacking has in mind denies the very existence of the disc-Qne can hardly hold such a position without adopting the "idealism to which Berkeley is the spokesman" (see above)-a somewhat esoteric position, which is anyhow not so much of an epistemological doctrine as it is an ontological one. Rather, in claiming that "the microscope is veridical" Hacking suggests rather that he is arguing against the distrust in the "physical processes [that] produce the image,"

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against those traditional empiricists who, like van Fraassen II, assume that the intervention of the microscope makes what it brings to sight less reliable. If such skepticism is his intended target, then Hacking's argument is extremely convincing, since it establishes exactly the point of reliability. The microinjecting example underscores our ability to manipulate preexisting, natural structures under the microscope and-almost as definition of reliability-achieve the expected results. The grid example reinforces this demonstration by adding that most of what we 'observe' under microscopes are artifacts we put there ourselves, like the needle and the grid. The demonstration that "the microscope is veridical" does not make the "argument of the grid" an argument against anti-realism. Suspicion of scientific observations and instruments is a modem version of Pyrrhonianism, and this type of skepticism, as I argue above, has little to do with either sides of the realism debate. Anti-realists are usually willing to believe science (definitely van-Fraassen does), even in far less clear-cut cases than the grid. They just have certain claims about "the relation between a theory and the world" (van-Fraassen, 4). More specifically, antirealists deny that "the picture which science gives us of the world is a true one" (6-7) or that "Science aims to give us, in its theories, a literally true story of what the world is like" (8). If the grid argument is to be directed against claims in this vain, it must to be cast in similar terms; "the structure of a labeled grid" needs to be presented as part of a "story of what the world is like" that purports to be "literally true." Hacking partly complies with this requirement by introducing the "image" as the defendant in his argument, hinting that the structure revealed through the microscope is a representation of the microscopic disc-a pictorial representation albeit, rather than a "story." But this would be a particularly weak and uninspired interpretation of Hacking's argument. Construed as a defense of the accuracy of the gridrepresentation of the disk, it is deprived of its most important element, a description of the process by which the grid is produced: The tiny grids are made of metal; they are barely visible to the naked eye. They are made by drawing a very large grid with pen and ink. Letters are neatly inscribed at the corner of each square on the grid. Then the grid is reduced photographically. Using what are now standard techniques. metal is deposited on the resulting micrograph ... The procedures for making such grids are entirely well understood. and as reliable as any other high quality mass producing system.

The power of Hacking's argument stems from this insight. The gridimage, it clarifies, is not a 'veridical representation' of the miniature disc ....ore than the disc is a representation of the macroscopic grid, drawn

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"with pen and ink." All three-the drawing, the disc and the image-are temporary stations in a sequence of productions and reproductions. They are related to each other by specific, practical processes--drawing, diminution and magnification- which are not liable to be 'true' or 'false' but indeed 'reliable' or 'flawed'. It is not the trustworthiness of the microscope that discredits anti-realism. It is, rather, the hard-to-contest fact that the grid-image has been 'produced'-it is an artifact in its own right, just like the 'original' macroscopic grid. However, if the 'anti-realism of the grid' position is precluded by the realization that the disc and the image are products, realism does not become any more tenable. Quite the contrary: both sides of the debate require that "Science" and "the world" are treated as terminal points, connected to each other by some privileged relation, independent of the processes and practices used to create one from the other, a relation in whose regard the question of whether it is "literally true" or not can be debated. It is this type of relation, rather than any particular view concerning its validity, that "the argument of the grid" precludes. 3.4.2.2. The Electron Hacking's success, and the promise that his analysis carries for the study of Hooke, lies in bringing to light the practices and processes of material production and underscoring their indispensability. The grid argument cannot become an argument for realism without abnegating this achievement. Still, Hacking's realism is not limited to microscopy. His microinjecting example helped blur the boundaries between accurate observation and reliable manipulation, while the grid argument further eroded the distinction, partly by establishing a gradual transition from naked-eye observation to instrumentally aided observation. Thus Hacking has the stage set for an argument regarding the reality of entities farther removed from our reach than the microscopic grid, throwing down a gauntlet with his celebrated slogan: "So far as I'm concemed, if you can spray them then they are real" (RI, 23, italics original). It is the final development of the production theme: Experimenting on an entity does not commit you to believe that it exists. Only manipulating an entity, in order to experiment on something else, need do that. Moreover, it is not even that you use electrons to experiment on something else that makes it impossible to doubt electrons. Understanding some causal properties of electrons, you guess how to build a very ingenious complex device that enables you to line up the electrons the way you want, in order tu see what will happen to something else. Once yuu have the right experimental idea you know in advance roughly how to try to build the device, because you know that this is the way to get the electrons to

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behave in such and such a way. Electrons are no longer ways of organizing our thoughts or saving the phenomena that have been observed. They are ways of creating phenomena in some other domain of nature. Electrons are tools. (RI, 263)

Electrons are tools-they are not only objects to be manipulated, they can also be used to manipulate other things. Does this impressive ex.pansion of the notion of production necessitate, or even benefit from, being structured as an argument for realism? In contrast to the grid argument, Hacking is ex.plicit regarding the anti-realist position against which he directs the electrons argument. It is not against disbelief in their ex.istence, but against the belief that "Electrons are ... ways to organize our thoughts or saving the phenomena that have been observed." Attempting to counter this type of empiricist anti-realism, Hacking is drawn to frame his conclusion in similar terms. Electrons, he claims, "are tools, instruments not for thinking but for doing" (RI, 262). This last proposition best demonstrates why the study of Hooke's Programme can draw on Hacking's epistemological insights only if these are freed from "the whole family of issues about realism and anti-realism." The terminology of practices and skills, the powerful tie between observation and manipulation which Hacking labored to unearth, the reshaping of the possible relations between experiment and theory, all mark the possibility of accounting for both the lamps and •inflection' as "the fruit of scientific technology" and as legitimate phases in the production of theory. Why, one should ask, are electronic tools and theoretical tools considered to differ more than, say, mechanical and optical ones? Why does the fact that electrons can be used as tools both in constructing theories and in building microscopes make them anything other than ex.tremely efficient tools? The realist interpretation of the grid argument obscured this potential for an alternative to the "spectator theory of knowledge" when it re-introduced the representation juxtaposition of the grid and its "image." But whereas that flaw could be understood as merely rhetorical, the realist conclusion of the electrons argument is positively damaging. The phrase "not for thinking but for doing" reinstates what Hacking himself called earlier "the false dichotomy between acting and thinking." Bridging this dichotomy, reconciling the scientist and the mechanic, was, perhaps, Hacking's primary achievement in Representing and Intervening. In order to turn his electrons argument into a realist argument he has to eschew this achievement. Indeed, without the dichotomy between "thinking" and "acting" the question of whether the former can provide "a literally true story" about the latter just cannot arise, and a-fortiori cannot be answered. Hooke's 'inflection'

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showed how 'a tool for thinking' can be used for 'acting'-how a theoretical tool can be produced and manipulated as a mechanical or optical instrument. On the other hand, His theory of "power" demonstrates how a mechanical device-a spring in this case--can serve in the construction of theory.

CHAPTER 2: POWER Part A 1. INTRODUCfION

Inflection-the encurvation of celestial motion-was a great novelty and a major step towards meeting Galileo's challenge and establishing celestial mechanics. But it was not enough. For Hooke's speculations to become a Programme, i.e., an outline for research, he had to suggest a cause for this encurvation. To complicate mailers, the planetary trajectories are not only curved-they are cyclic. Unlike the effect on the light passing through them of the water in his microscope and the salt water in his tank, the gradual bending of the planetary motions results in continuous, repetitive orbits. Hooke's hypothesis of the cause of celestial inflection had to allow for that as well. Hooke was clearly aware of this aspect of his task, and the purpose of the conical pendulum of the 1666 Address was precisely to shew, that circular motion is compounded by a direct motion by the tangent, and another endeavour tending to the center. (Birch II, 92. Italics added)

He was also painfully aware of his inability at the time to explain this "endeavour." "I have often wondered," he cautiously begins his Address, "why the planets should move about the sun." Unable to support anyone answer to his query, he offers two hypothetical ones; the "cause of inflecting a direct motion into a curve may be" either "an unequal density of the medium," or "an attractive property of the body placed in the center" (ibid., 91. See Chapter I). However, the tone of his Attempt to Prove the Motion of the Earth in 1674 is markedly different. The original quavering presentation is replaced by the brazen title "a System of the World," and of the two "likely cause[s] for the performance of this effect," only one remains. Hooke has managed to dispense with the medium hypothesis altogether; the only candidate for explanation in this later version of the Programme is "That all Crelestial Bodies Whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts ... but ... also ... all the other Crelestial Bodies that are within the sphere of their activity" (see Chapter I). The last chapter showed that already in the Address, Hooke had decided that "attractive property" was the explanation of choice for inflection. In

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fact, he never gave any real consideration to any other hypothesis. His early attempts to endow the notion of "attraction or gravitating power" with meaning were, however, unsatisfactory. They were related to his attempts to capture and measure gravitation by means of pendulums, and by the time he gave his Address, these efforts had already produced some disappointment (although Hooke did not altogether abandon his pendulum experiments). Eight years later the situation was rather different. At the time he was writing the Motion of the Eanh, Hooke already had an alternative shaping up; a replacement for the pendulum in its technical as well as theoretical duties. The prospects of constructing "power" as a viable theoretical device were therefore much brighter, and it is this new self-confidence that the "System of the World" reflects. This was not an entirely new alternative. Hooke based it on the theoretical speculations he had allowed himself while operating his air pump at Boyle's service back in the late 1650s. Numerous diary entries from the 1670s, as well as his Cutler Lectures-the 1676 Helioscopes and 1677 Lampas--
POWER

Figure 7: Of Spring-the main diagram (C.L., 332).

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2. DE POTENTIA RESTHU'I'IVA, OR: OF SPRING

2.1.

A Theory of Matter and Power2

At the heart of Of Spring is an ambitious theory of matter. "The sensible world," Hooke submits, "consist[s] of body and motion" (De Potentia, 7; c.L., 339). These two are inter-translatable, if not outright "one and the same", as body is "somewhat receptive and communicative of motion" and motion is "power or tendency progressive of Body" (ibid.). It is their product-"body" times "motion"-which is the consequential magnitude, "for a little body with great motion is equivalent to a great body with little motion as to all its sensible effects in Nature." It is not clear whether Hooke is suggesting global conservation of this magnitude3, but he certainly thinks in terms of local conservation: "These two always counterbalance each other in all the effects, appearances, and operations of Nature" (ibid.). Hooke pursues the inter-dependence of matter and motion to an extreme, claiming that real 'substance' constitutes only a small part of the bulk of material bodies: "all bodies ... owe the greatest part of their sensible or potential Extension to a Vibrative motion" of their particles. This vibration, he argues, is the "power from within" which "defends" matter: thus according to Hooke, it is motion that causes impenetrability: To make this the more intelligible, Imagine a very thin plate of Iron. or the like, a foot square, to be moved with a Vibrative motion forwards and backwards ... the Length of a fnot with so swift a motion as not to permit any other body to enter into that space within which it Vibrates. this will compose ... a cubick foot of sensible Body (De Po/entia, 8; C.L. 340)

The idea that the solidity and spatiality of matter are effects of the motion of particles "differs from the common notion of Body" (ibid.), Hooke proudly declares. It is an idea Hooke has been most committed to; his earliest version of it had already been published in his unsigned contribution to Boyle's 1662 Defence of the Doctrine touching the Spring and Weight of the Air (Boyle, vol. I, 118-185)4. The precursory version involved "particles of the form of a piece of ribbon" with "innate circular motion" (Boyle, vol. I, 178-179), while the later version requires only "Vibrative motion forwards and backwards," and does not assign any particular form to the particles, although Hooke does find a theoretical role for their primary qualities: "Every particle of matter according to its determinate or present Magnitude is receptive to this or that peculiar motion and not other." Similarly to the way in which the length of the string will determine its oscillation, and thereby its tone, the magnitude of a particle

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will determine the amplitude of vibration to which the particle is receptive (De Potentia, 8-9; C.L., 340-341l Surprisingly, Hooke insists that the "Vibrative motion" is not "inherent or inseparable from the Particles of body" (De Potentia, 8; C.L., 340), which seems to contradict his note concerning the near identity between matter and motion. This could perhaps be interpreted as a gesture towards Boyle, who abhorred Epicureanism and its materialistic implications, and for that reason withdrew from his support of Hooke's early "vibrative" account of the "spring of air" as formulated in the Defence. 6 In the 1665 Micrographia, Hooke was still less restrained, denying "that there is any such thing in Nature, as a body whose particles are at rest" (16). The other factor determining the particle's vibration, besides its "Magnitude," is the balancing vibration of the surrounding particles. These belong, mostly, to the "Heterogeneous fluid medium incompassing the earth" (De Potentia, 15; c.L., 347). This "menstruum" is a central constituent of Hooke's theory: All bodies whatsoever would be fluid were not for the external Heterogeneous motion of the Ambient. And all fluid bodies whatsoever would be unbounded, and have their parts fly from each other were it not for some prevailing Heterogeneous molion from without them that drives them more powerfully together. (De Potentia, 12; CL., 344)

Nevertheless, the shape of bodies is not completely dependent on their environment. Reaching back to his very first publication, the Attempt for the Explication of the Phenomena Observable in an Experiment Published by the Honourable Robert Boyle (1661), Hooke imports into his theory that a concept he has hardly used since this early pamphlet. The harmonious motion of adjacent particles, he explains, creates 'congruity' among them, viz.: it "strengthen[s] the common Vibration of them all against the differing Vibrations of the ambient bodies" (De Potentia, 9; CL, 341). Bodies whose particles oscillate harmoniously have a relatively stable shape and volume. These are what are known as "solid bodies" (De Potentia, 10; c.L., 342). The particles of "Fluid bulks," on the other hand, are small and far apart, and are "consequently pervaded by the subtil incompassing Heterogeneous fluid menstruum" (ibid.). Thus, they are not congruoustheir vibrations are not in harmony, and their dimensions are determined solely by the dynamic equilibrium between the outwards and inwards pressures; between the vibrations of the aggregated partkles and those of the surrounding "fluid." Hooke's etudes on the theme of matter-in-motion are no mere flights of

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fancy. The two kindred, though distinct concepts inherent to these contemplations-namely, restrained motion and harmony--comprise a conception of force whose range and power was unparalleled within the mechanistic tradition. I will endeavor to elucidate the essential significance of this conception to Hooke's Programme in the next chapter. The rest of this chapter will be dedicated to exploring how Hooke constructs his unique concept of "power" within Of Spring.

2.2. Restrained Motion In Hooke's hands, the notion of "power" as restrained motion is particularly efficacious. It explains and justifies a series of bold experimental and theoretical moves, the chief of which being a theoretical principle of the widest applicability: Ut tensio sic vis; That is, The Power of any Spring is in the same proportion with the Tension thereof. (De Potentia, I; c.T.., 333)

2.2.1. Tension While Hooke first published "ut tensio sic vis" as an anagram in the 1676 Cutlerian Lecture Helioscopes, he had, In fact, been toying with a "Theory of Springs" all during the 167087 • Now, however, thanks, partly, to favorable comments from his colleagues at the Royal Society, he seems to have decided that his theory had reached sufficient maturity to offer adequate support for this "Rule or Law of Nature" (De Potentia, 4; C.L., 336). Such support was essential, since Tensio has no previous scientific connotations-its meaning was determined solely by and within Hooke's theory. As with the term "inflection" in 1666, in Of Spring of 1678 Hooke is coining a new term and a novel concept. Tension, Hooke's theory, is a measure of imbalance or dis-equilibrium. It is predicated on a world in which "all bodies ... owe the greatest part of their sensible or potential Extension to a Vibrative motion," whose amplitude is determined through dynamic relations with "subtil incompassing Heterogeneous fluid menstruum"(see above). It is to be understood as the tendency of a "bulk" to return to a state of balanced vibration-a slate of equilibrium between the outward pressure exerted by its vibrating particles and the inward pressure of the ambient particles. To illustrate his ideas Hooke provides his readers with a model. More than

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anything else, the model seems to reflect Hooke's enthusiasm, since it contains an obvious mistake which escaped his attention. This is a telling mistake, and I shall return to it later.

DAl}BFCG ,..·····•·..·..·1·..····,,·....··"1· ·

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Figure 8: Vibrating particles (A, B and C) in Of Spring IDe Potentia, 11; C.L. 343).

The model comprises a string of eight contiguous vibrating particles, exchanging their motions at the points of contact (Figure 8). Hooke assumes, for illustration purposes, that in a state of equilibrium between the spring and its environment, the particles oscillate 106 times per second. If, then, through the application of external force, the spring is extended by 50%, the number of collisions between the particles will drop, proportionally, to 2/3 the original number, with a commensurate reduction in the outward pressure of the spring (Figure 9-top). The balance with the inward pressure of the ambiance would then be proportionally altered, "and consequently the Spring inwards must be in proportion to the Extension beyond its natural length" (De Potentia, 14; C.L., 346). Hooke uses the model similarly to account for the application of force in the opposite (inward) direction, explaining bending as a combination of the two (Figure 9-botlom).

2.2.2.

Hooke's Law

Ut tensio sic VIS IS a primary demonstration of how the notion of restrained motion allows Hooke to treat power as an entity which can be transferred from one body to another, collected and spent, without departing from the mores of mechanical philosophy. In particular, tensio offers Hooke a mechanism by which a force deposited into a body to be translated into a force that can be extracted from it. Hooke's theory, we saw, stipulates that the shape and volume of a body is determined by the balance between the "Vibrative motion" of its constitutive particles and that of the "ambient Heterogeneous fluid" (De Potentia, 11; C.L., 343). Any distortion of this balance results in a proportional strive to return to the original dimensions. This strive, which represent a specific degree of dis-equilibrium between inwards and outwards "spring," is how a body records the "power" applied to it as a particular "Tension."

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With the license to move freely between the force exerted on the body and the force that can be obtained/rom the body, Hooke had acquired great flexibility for applying dynamic concepts to metaphysical and theoretical contexts. This flexibility is most conspicuous on the interface between theory and experiment. In good Royal Society fashion. Hooke does not embark upon 'fashioning hypotheses' before offering some empirical findings to serve as their basis. In fact; Hooke is so good at blurring the seams between the theory and the etnpirical generalizations he believes support it, that the importance. and sometimes even the existence of the former, have all but eluded most commentators. Indeed, his first presentation of his main insight, "Ut tensio sic vis," is followed so closely by a declaration of its experimental underpinning, that it is hard to distinguish between them: That is. The Power of any Spring is in the same proportion with the Tension thereof:

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91

That is, if one Power stretch or bend it one space, two will bend it two, and three will . bend it three, and so forwards. (De Potentia, I; C.L., 333)

A second reading of the paragraph reveals the status of each "That is" is different. Whereas the first precedes a literal explication of the law, the second is followed by its interpretation into the experimental finding which received the title Hooke's Law. This interpretation is far from trivial and called for some difficult and less than perfect adjustments to the notion of tension. But Hooke, who anyhow has yet to elaborate his theory, moves directly to a presentation of his experiments demonstrating that solid springs will alter in size along one dimension in proportion to the external power to which they are subject. Hooke describes a number of experiments, using different springs (sketched in Figure 7) and different ways of engaging them, and demonstrating his usual ingenuity, A casual glance at these experiments may suggest that they recount the discovery of the proportion between force and displacement. A closer look, however, reveals, that they are taught to the reader for him to carry out and thus convince himself-not that 'as the tension so is the power' is true, but that it is general: this is the Rule or Law of Nature, upon which all manner of Restituent or Springing motion doth proceed, whether it be of Rarefaction, or Extension, or Condensation and Compression. (De Potentia, 2; C.L, 334).

This conclusion is presented immediately after the first variance-a helix-shaped spring (Fig. I in Figure 7)-and is generalized to cover "all manner of ... Springing motion." Yet, to be precise, these experiments do not relate directly to Ut tensio sic vis. Each experiment involves a spring of different shape-straight, spiral, helical-and the instructions explain how to contrive these springs to pennit equal weights to be added and the consequent changes in length measured. "Observe exactly to what length each of the weights do extend it beyond the length that its own weight doth stretch it to," Hooke instructs his readers, "and you shall find that if one ... certain weight doth lengthen it one ... certain length, then two ... weights will extend it two" etc.; the changes in length should be directly proportional to the changes in weight (De Potentia; 2; C.L, 334). "The Power of any Spring," however, is not synonymous with the "Power [that] stretch or bend it." Hooke's experiments clearly demonstrate that "if one Power stretch or bend [a spring] one space, two will bend it two ... and so forwards," but in none of them does he attempt to measure the power of the spring---only the power operating on it. Hooke, we should recall, cannot use Newton's Third Law-in 1678, this was yet to be formulated. What he does provide is a narrative of how the change in the

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size of a spring is translated into a proportional tension, which can then be regarded as the spring's "power from within." It is this narrative that allows him to take experiments showing that the change in the length of a spring is proportional to the change in the weight that strains it, prescnt them as demonstrating "Ut pondus sic tensio" (as the weight so is the tension-De Potentia, 5; c.L., 334), and proceed as though he has demonstrated that the tension of a spring is proportional to its power.

2,3. Harmony Supported by the image of restrained motion, tensio relates pondus to vis and provides Hooke with the first justification of his use of the spring experiments. But this justification does not suffice. Whereas all the experiments described in Of Spring employ solids springs, Hooke's notion of tension is far better suited to account for the behavior of gasses.

2.3.1. Difficulties A quick review of Hooke's model will demonstrate the difficulty. As already noticed by Moyer ("Robert Hooke's Ambiguous Presentation of "Hooke's Law""). the vibrating particles model is not applicable at all to the empirical claim that "if one Power stretch or bend it one space, two will bend it two ... and so forwards." Instead of the direct ratio between displacement and force which Hooke's experiments demonstrate (and which came to be called Hooke's Law), the model depicts an inverse proportion between force and the total length of the spring (known under the title of Boyle's Law); 2/3 of the power translates to 1.5 the volume, etc. The same difficulty is raised by another set of experiments reported by Hooke as evidence for his theory, but which, in fact, do not form an integral part of Of Spring. The experiments recounted in details in Of Spring only illustrate the expansion of metal springs. For the details of "the manner of trying the same thing upon a body of Air, whether it be for rarefaction or for the compression thereof," the reader is referred back to experiments Hooke "did about fourteen years since published in [his] Micrographia" (De Potentia, 3; C.L.• 335). These early experiments, titled by Hooke "a late improvement of the Torricellian Experiment" (Micrographia, 222-Fig. 4 in Figure 5), consist of mercury-filled tubes of various shapes. with the heights of the mercury column collected as data attesting to pressure.

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Yet the hypothesis tested in the Micrographia is not the spring law, or the direct proportionality between change in volume and force, at all. It is, again, "Mr. Townly's Hypothesis" (Micrographia, 225) or Boyle's Law, i.e., the inverse proportion bctween total volume and force 8 . Hooke fills the left, longer side of his siphon with changing quantities of mercury, adds the height of the mercury column to the atmospheric pressure (equivalent to 29 inches of mercury), and measures the corresponding height of the air compressed on the right side. Boyle's law prescribes that the height of the mercury column plus 29 (representing the pressure of the mercury and the atmosphere combined) will be inversely proportional to the height of the compressed air column. As Hooke expects, the experiment establishes that if a combined height of 29 inches of mercury results in 24 inches of air, then double the pressure-to 58 inches of mercury---eompresses the air to half its volume-12 inches; one and a half times the pressure-43.5 inches of mercury-to two thirds-16 inches of air, etc. These calculations do nothing to support the claim that the Rule or Law of Nature in every springing body is, that the force or power thereof to restore itself to its natural position is always proportional to the Distance or space it is removed therefrom. (De Potelltia, 4; CL, 336)

If Hooke were after experimental support for this "Law of Nature," he should not have been comparing the volumes of mercury and air, but the changes in these volumes. This would have told him that on one occasion, the addition of 14.5 inches of mercury makes a difference of 8 inches in the height of the 24 inches air column-reducing it to 16 inches-while the next time, that amount of mercury gives a 4 inches difference-reducing the air column from 16 to 12 inches; quite different from a direct and simple proportion between force and displacement. In short, Hooke presents Vt tensio sic vis as a "Rule or Law of Nature, upon which all manner of Restituent or Springing motion doth proceed," but his own experiments demonstrate that the behavior of solid springs is quite different from that that of "fluid bodies." Whereas the statement "if one Power stretch or bend it one space, two will bend it two ... and so forwards" decrees a simple ratio between power and the change in the size of a spring, the statement "The Power of any Spring is in the same proportion with the Tension thereof' can, prima facie, be interpreted only as an inverse proportion between power and the total volume of a "bulk."

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2.3.2. Partial Solution Hooke tries to resolve this discrepancy using 'harmony'. The resolution should come by way of absorbing the distinction between solids and fluids into the theory. In the model and diagrams, the body's dimensions are determined strictly by the balance between the vibrations of the particles of a body and "the external Heterogeneous motion of the Ambient" (De Potentia, 12; c.L., 344), A disruption of this balance creates a proportional tension-the tensio of Ut tensio sic vis. This image, as hinted above, is well suited to Hooke's conception of gasses, those "Fluid bodies, amongst which the greatest instance we have is air" (De Potemia, 15; c.L. p. 347), "The particles of fluid bodies," it should be recalled, "do not immediately touch each other" and therefore "Heterogeneous motiuns from without are propagated" through them (De Potentia, 12; c.L., 344). Consequently, the vibrations of these particles are not in "congruity"-not "strengthened" by harmony-and are held together only by the pressure of vibrating particles of the ambient fluid: all fluid bodies whatsoever would be unbound and have their parts fly from each other were it not for some prevailing Heterogeneous motion from without them that drives them more powerfully together. (De POlelltia. 12; C.L.. 344)

As remarked above, it follows that "Fluid bulks" have no independent dimensions. Their extension is wholly determined by a precarious balance of motions and powers. And if the pressure of the "prevailing Heterogeneous motion" is understood as external power, it also follows that then fluids are always under tension; a tension which is inversely proportional to their volume, and which will be reduced to zero only when "their parts fly from each other." Solids, on the other hand, have a "natural state" or "natural position." Their particles, as we saw, "immediately touch each other" (De Potentia, 11; c.L., 343), and the harmony between the motions of those particles creates a particular, relatively well defined extension. This point is essential fot the understanding of their springiness: solid bodies. as Steel. glass, wood &c. ... have a Spring both inwards and outwards, according as they are either compressed or dilated beyo/ld Iheir /la/ural slale. (De Potenria, 13; c.L., 345, Italics added)

The notion of a "natural state" of solids departs from the framework concept of balance. The natural state of a solid is the result of harmony, which is a strictly internal property-a relationship between the vibrations of the solid's own particles. This concept ascribes to solids an additional

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resistance to displacement; in causing them to be "compressed or dilated" one not only disrupts the balance of internal and external vibrations, but also the internal harmony of the natural state. This already hints at the solution, suggesting a possible explanation for the fact that the 'spring of air' is predicated on total volume, while the spring of a solid is predicated on the "Distance or space it is removed" from its "natural position." When calculating the tension of solid springs, the idea is, one has to account for the additional power invested in the disruption of harmony. Thus Vt tellsio sic vis has to be applied differently to solids and gasses. Tensio measures a disturbance of the balance between internal and external vibrations. The dimensions of "fluid bulks" are fully explained by this balance, and the principle can be translated directly into the empirical Boyle's Law. This balance, however, only partially determines a solid's dimensions: only when the harmonious vibration of a solid's particles is disrupted, i.e., when the solid is forced out of its natural state, can Vt tensia sic vis be applied, and then only as regards that segment of the solid determined by the balance of vibrations, viz., "the Distance or space [the solid] is removed" from its natural state. This distance is proportional to the power applied, which becomes "the power of the spring," hence Hooke's Law. This, of course only sketches a solution: Hooke gives no reason to believe that he knows how to quantify "harmony" and use it to turn Hooke's Law into a phenomenal expression of Vt tensio sic vis. He might have been able, perhaps, to bridge Boyle's Law and Hooke's Law by treating the natural state of solids as one of zero tension, viz., a state completely dependent on internal vibrations. This would have explained why only the deviation from this state is subject to tension, whereas the dimensions of the solid in its natural state are not. However, for Hooke to take this step would have meant relinquishing the generality of his theory of matter, and render two virtually separate theories for solids and fluids-something he was unwilling to do. The difference between solids and fluids, he insists, is only relative, as "all solid bodies whatsoever would be fluid were it not for the external Heterogeneous motion of the Ambient" (De Potentia, 12; c.L., 344). This means that the "natural" dimensions of solids are also set by the balance of internal and external vibrations, and one cannot apply Vt tensio sic vis solely to their displacement. Moreover, Hooke is hardly careful in maintaining the distinction between states to which his principle can be applied. His vibrating particles model, we saw, can be directly applied only to fluids-it emulates Boyle's Law, or the inverse proportion between power and volume, and leaves no place for natural state or displacement. All the

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same, Hooke introduces it with the caption "First for solid bodies, as Steel, Glass, Wood etc." (De Potentia, 13; C.L., 345. Italics added).

2.4.

Uses

All inconsistencies notwithstanding, Hooke's explication of the structure of matter in terms of motions is a powerful tool, which he employs in a rather spectacular manner.

2.4.1.

"Aggregate of Powers"

Restrained motion-the theoretical mechanism embedded in the term tensio- offers Hooke a workable concept of power. "Power" not only changes motion; it is itself a modification of known, quantifiable parameters of oscillatory motion, namely frequency and amplitude. Admittedly, these are not directly measurable, since they pertain to the motions of "particles exceeding small" (De Potentia, 15-16; C.L., 457-458), but they are immediately indicated by the volume and the displacement of macroscopic "bulks," This 'substantive', quantifiable power can be captured in a body, and transformed from operating on the body into the power of the bodyand it can also be retained and accumulated in the body. With this for his base, Hooke constructs an original and highly practical concept of "aggregate of powers" (De Potentia, 17; C.L, 459). Establishing the 'aggregation' of powers requires just one step beyond the position that justifies Hooke's use of the spring experiments. The power of a body consists of the vibrations of its particles. harnessed in it as potential motion. This motion is a definite quantity, "proportionate to the degree of flexure" (De Potentia, 17; C.L, 459-Hooke is definitely thinking in terms of solid springs here). Each point of a 'flexed' spring represents a unique degree of tension; a particular strive to return to equilibrium; a particular level of internal vibration not balanced by external vibration in the case of contraction (or vice versa, in case of expansion). Hooke takes the necessary next step of pronouncing these tensions cumulative. The "aggregate of powers" stored in the spring is the accumulation of pulses. A releasing spring is continuously pushed back into its natural position by the pulses of the vibrating particles-a definite amount of pulses at every point of displacement, at every degree of tension. An external power displacing a spring is continuously investing or recording "powers" along the displacement by restraining vibrations, and thereby creating the imbalance.

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Thus, Tensio is not just a mechanistic whim. It also has another major advantage; the strict and direct relation between power and motion avails Hooke of a well-respected mathematical tool for calculating the "aggregate of powers," namely; the traditional Merton-style formula for the accumulation of 'degrees of motion' (De Potentia, 18-19; C.L, 350-351t Indeed, in an almost identical way to Galileo and O'resme before him, Hooke uses perpendicular lines to represent acceleration as a change in a quality of motion over time. What was 'intensity' for O'resme and 'degrees of speed' for Galileo, is mediated through the operation of 'power' for Hooke, but since power has been accounted for as nothing but a qualification of motion, this mediation does not jeopardize his use of the construction. The horizontal line AC in Hooke's diagram (Fig. 4 in Figure 7) represents displacement; "the way in which the end of the spring by additional powers is to be moved" (De Potentia, 19; C.L, 351). The vertical lines BE and CD "represent the power that is sufficient to bend or move the end of the spring" to those point (ibid.). Whereas for Galileo the area of the right angled triangles ABE and ACDexpressed distance lO, for Hooke it expresses the "aggregate of powers." The outcome follows necessarily from the geometrical treatment: the 'aggregate' is "in duplicate proportion to the space bended or degree of flexure" (De Potentia, 17; C.L, 349), just like Galileo's square proportion between distance and time. Or in modern terminology: the sum total of power restrained in a displaced spring is proportional to the square of displacement.

2.4.2.

Isochrony

Finally, Hooke puts the Merton proof to use once more, this time to produce a theorem that offers immediate technological implications: the comparative Velocities of any body moved are in subduplicate proportion to the aggregates or sums of the powers by which it is moved, therefore the Velocities of the whole spaces returned [by a displaced spring) are always in the same proportions with those spaces, they being both subduplicate to the powers, and consequently all the times shall be equal. (De Potentia, 18; c.L., 350)

"All the times shall be equal." This is Hooke's way of pronouncing that the oscillations of springs are isochronous; increasing the distance a spring is removed from its natural state does not increase the time it needs to return to its original state, since the increase in the velocity of receding will compensate for any increase in the distance traveled.

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The crux of the proof is the assumption that acceleration-the increase of the velocity of the oscillating body-is produced by the continuouslyoperating 'aggregate of powers' rather than by percussion-like force. This assumption allows Hooke to use his "General Rule of Mechanicks," according to which "Velocities [are] always in a subduplicate proportion of the powers, that is, as the Root of the powers impressed" (De Potentia, 1920; c.L., 351-352).11 This is a law of motion that Hooke uses on numerous other occasions, the most important being, of course, his Programme: "the Velocity will be in subduplicate proportion to the Attraction" (Correspondence II, 309-see Introduction). Since he has already shown that this quantity-the square root of "the aggregate or sums of the power by which it [the spring] is moved"-is "proportionate to the degree of flexure," Hooke can conclude that the (final and average) velocity of any solid spring returning from stress is proportional to its distance from its resting point. Hence the Vibrations of a Spring, or a body moved by a Spring, equally and uniformly shall be of equal duration whether they be greater or less. (De Polel1l;a, 16; c.L., 348)"

Reworking his diagram, Hooke plots approximating graphs for the velocity of the spring at each point, and the time required for each segment of its return. The trapezes DCBE represent the 'powers' operating on the spring returning from its displacement to C to its natural position at A, Thus, according to Hooke's "General Rule of Mechanicks," the velocities at points B will be proportional to the square roots of the trapezes DCBE or to ~(AC - AB )(cD + BE). The law of spring dictates that A( 0< CD and AB 0< BE, so the velocity is proportional to ~(AC -

AB )(AC + AB)

or: ~ AC 2

- AB

2

.

Hooke draws the circle ACF with A as its center and AC-its radius. The ordinates BG of this circle are equal to ~ AC 2 - AB 2 (by Pythagoras), thus they represent the velocities at points B. Another clever manipulation produces the "S-like Line of times" ClIIF. If BG represents velocity, CBdistance, and HI-time, then BG x HI 0< CB, or: BG: "CB ;; "CB : HI. Hooke then determines points H and I with the aid of CHF, which is a parabola whose ordinates HB are proportional to "CB, giving him BG; HB :: HB : HI (De Potelltia, 20; C.L, 352). Ingenious as these manipulations are, it is the previous paragraph that holds the key to Of Spring. This is not so much because the isochrony of springs is of obvious practical import. Rather, it is because the proof of isochrony introduces Hooke's reader into the realm of horology. It was his horological inquiries that first drew Hooke's attention towards springs.

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Springs were to fulfill a particular function in his watches, and as the above paragraph hints, they may have been only a means to an end in Of Spring as well. But first a short detour.

2.5.

Interpretations

A detour is required because the explication above differs from the way that Of Spring is commonly interpreted, and that difference merits attention owing to the unique place of the lecture in the Hooke legacy. A breeding ground for that all too rare species-a law of nature named after Hooke-Of Spring holds a special attraction for Hooke's admirers as well as his detractors. The common historical image of Hooke and his work is, to a large degree, a composite of the spoils of their respective explorations. And those spoils reported were usually meager. What most of these expeditions uncovered in their pursuit of Hooke's Law, they described as an "empirical law" (Open University Mechanics (in Hebrew); also Patterson, "Pendulums of Wren and Hooke," 307), "A relatively trivial principle of elasticity" (Westfall, Force, 206), or even a paradigm of "fortuitous approximation" (Teller, cited by Hughes, 297). Vt tensio sic vis being Of Spring's most coveted trophy, one would assume that these epithets would apply to it, yet the very difficulties that Hooke encountered in generalizing and applying the principle he advances as the centerpiece of Of Spring demonstrate that it can be hardly characterized as either "trivial" or "fortuitous." It could, perhaps, be claimed that what is preserved in modern textbooks under the tag Hooke's Law, namely, "strain is proportional to stress" (Hughes, 297), is rather well suited to these classifications. Whether or not this proportion deserves the title Hooke's Law, however, it is not what Hooke meant by Vt tensio sic vis. Indeed, the proportion between force and displacement in solid springs occurs often in Of Spring. Hooke does not shy away, one recalls, from declaring it a "Rule or law of Nature in every springing body," that the force or power thereof to restore itself to its natural position is always proportionate to the Distance or space it is removed therefrom. (De POlelltia, 4; C.L., 336)

But as we saw above, although Hooke does suppose this "law of Nature" to support Vt tensio sic vis, he by no means perceives the two as equivalent. There is an irony in the fact that the empirical generalization has come to be named after Hooke, while the theory it aims to support has attracted little interest. Certainly, Hooke's pretensions in Of Spring are far grander than a

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"fortuitous approximation" might support. While it is not impossible thaI Hooke promised more than he could deliver, nevertheless, identifying Hooke's "Theory of springs" with modern-textbook Hooke's Law is simply incoherent. If VI lensio sic vis is nothing but the proportion between power and displacement, then Hooke arrived at a correct empirical law by generalizing from experiments (the major part of which) follow another law. On the other hand, if the accomplishments Hooke presents in his Of Spring are considered from the modem-textbook point of view, one is liable to conclude, as does Luise Diehl Patterson ("Pendulums of Wren and Hooke,,)IJ, that the theory he develops in the lecture involved implicit knowledge of all three laws of motion, explicit use of the conservation of momentum, the conservation of vis viva. and the condition for isochronism, and even a suggestion of the equivalence of mass and energy. (Patterson,

op. cit., 319)

Contrary to what first impressions might suggest, they are very similar routes leading to both the complete dismissal of Hooke's argument as "confused" (Hesse. "Hooke's Vibration Theory." 435), and to the excited attribution to him of "the law of conservation of mechanical energy" (Patterson. op. cil. 307; 310). Both routes are embarked upon with the purpose of recovering specimens of known laws and procedures from Hooke's paper, and both are guided by the assumption that the success and failure of Hooke's theoretical maneuvers should be attributed to factors inherent to his concepts. The epistemological instincts embedded in this course of interpretation are easier to ridicule than to abandon, but by closely following. Hooke's own ways of manipulating his concepts, of producing and using his theory, one may avoid some of the traps into pitfalls to be met along the regular route and discover a few points of interest. For example, as mentioned earlier, we could note that Hooke demonstrates no knowledge of "all three laws of motion." In particular, he makes no allusions to Newton's Third Law, as Patterson wrongly exclaims. Yet to be formulated, this law simply was not available to Hooke to employ, either explicitly or implicitly. To convert the force exerted on a body (a spring) into a force extracted from it-where the law of action and reaction might have been useful-Hooke had to devise his own theoretical apparatus, which he does by constructing the vibrating particles model. On the other hand, not all of his theoretical tools are novel; part of the utility of the Cartesian, particles-in-motion concept of power for Hooke, was by making somewhat dated, pre-Cartesian, theoretical tools like Oresme's construction available for use. It is one thing to claim that we should understand Hooke's work on its

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own terms. It is a step farther to realize that his theory is not a simplified version of Newton's mechanics, that his notion of power is not Newton's notion of force, and that he constructs mechanical models to solve what Newton approached via definitions and axiomatic constraints l4 . It is, however, an altogether different task to bring these insights to bear upon unearthing the details of Hooke's production of his theory and the role of springs in that endeavor.

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PartB 3. HOROLOGY If some of Hooke's theoretical tools were dated, the effects of their implementation were far from it. The isochrony of the vibration of springs was a matter of extreme consequence and some urgency, related directly to the practice that generated Hooke's original interest in springs-the construction of timekeepers. A few introductory remarks are needed in order to appreciate Hooke's contributions to mechanical timekeeping, their theoretical significance, and the historiographic difficulties involved in analyzing them. It is perhaps best to start where this craft is commonly perceived to have originated-in China: The heavens move without ceasing but so does water flow. Thus if water is made to pour with perfect evenness, then the comparison of the rotary movements will show no discrepancy. (Landes. 8)

This 11 til century Chinese text is cited by Landes to support his claim that "one would have expected ... that time, which is itself continuous, even, and unidirectional, would be best measured by some other continuous, even, and unidirectional phenomenon". Yet, as he goes on to explain, "it has never been possible to keep anything moving at a continuous and even pace that even approaches the steadiness needed to track time l5 • Instead, the secret of keeping an accurate rate has lain in generating some kind of repeating beat and counting the beats-that is, in summing series of equal, discrete parts" (ibid.).

This captures the achievement of mechanical horology-from the Chinese clepsydra (water clock), through the turret clock to the spring watch- all involved the balancing of a driving force and a regulating motion. In traditional turret clock, gravity provided the force-through a weight tied to a train-and the task of regulation was assigned to inertiawith the verge and foliot escapement. The master clock-makers developed their craft, to and through Hooke's time, by tinkering with the two: replacing gravity as the driving force and gaining control over the regulating motion. Hooke's own achievements in the field lay in linking both the motor and the regulator, as well as the connection between them, to a single operative force: the spring.

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2

b

b

Figure 1U: Verge and foliot escapement. illustration by Uavid Penney ©. The verge (g) is attached directly under the foliot balance: note the movable weights (e) controlling the swing of the balance, and the teeth (a and b) connecting the verge to the crown wheel.

Hooke was not the first to employ springs in timekeeping technology. Some two hundreds years earlier (Macey, 25), the possibility of using springs to replace gravity as a prime mover had been explored. the successful result being the mainspring-a spiral, set in a barrel, moving the going train by unwinding. As the spring unwinds, the force with which it pulls the train decreases. To compensate for this, the mainspring is aided by afusee wheel (see Figure 11). This device. the earliest specimen of which dates from 1430 (White, Medieval Technology, 128), is a conical spiral barrel, which the mainspring pulls by a string (and later a chain)16.

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........-...,..,

Figure 11: Components of spring-motor mechanism. Top row: linking chain. Middle row, left to right: spring barrel and fusee linked by a chain; fusee wheel assembly; main spring. Bottom row; schematic representation ofcalculation of{usee profile. The diagram and the legend are from Landes (adjacent to page 236) who compiled them from Diderot and d'Alembert's Encycloplldie (1865, vol. 8, Pl. lo-top and middle rows) and Rees' The Cyclopredia (1819·20, 218, Pl. 36-bottom row). Reprinted with permission of Harvard University Press.

The increasing diameter of the fusee gives the mainspring an increasing mechanical advantage over the rest of the train mechanism-to which the pivot of the fusee is finnly connected-thus providing the required compensation for the spring's decreasing force 17 • The efficient use of the

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spring-cum-fusee as the driving mechanism enabled the introduction of the diminutive, portable clock-the watch. While these developments in clock motor mechanisms were taking place, the method of regulating them remained virtually unchanged. Though a few variations to the verge-and-foliot escapements had been attempted by such master-artisans as de Dondi, da Vinci and Borgi, it was Hooke's century that witnessed the first (successful) attempts at making the regulator an actual time-counter, viz.: a mechanism of an independent, equalized beat. The verge-and-foliot escapement, to which the task of regulating mechanical clocks had been delegated until the period under discussion, does not meet these demands (see Figure 10). It consists of a cross bar carrying a weight on either hand-the 'foliot'-which is mounted on a long axle-the verge. The verge has two teeth, set at right angle to each other, fitted, in diametrical opposition to each other, to the upper and lower points of a vertically-mounted crown wheel, so that when one of the teeth, on the one side, is engaged, the other, on the other side, is free, and vice versa. The wheel, connected to the train and continuously forced to rotate by the weight, beats against the teeth successively, thereby transferring its motion to the foliot's. When a tooth is struck by the crown wheel, the foliot rotates freely on its axis until the other tooth (attached at a right angle to the first) strikes the wheel in the opposite direction to its motion. The foliot's angular momentum arrests the wheel, pushing it back just sufficiently for the tooth to disengage allowing the cycle to resume. Watching the process continuously one sees the foliot rotating to and fro, intermittently pushing and being pushed by the crown wheel through the teeth, giving a stop-go pace to the moving train. The rate of the foliot's rotation is determined by the momentum of the cross bar (which is changeable by moving the weights away from and towards the center) combined with the pace of the train, to which the escapement is attached directly. Making the regulator a genuine time-counter meant that its own motion had to be controlled and measured independently, rather than being controlled by the moving train itself. This was the rationale behind having a pendulum, rather than a foliot, performing this task. Although the idea had first been first suggested by Galileo in the 1630s, the first pendulum clock ever built (by Coster-Robertson, 122) was designed in 1658-9 by Huygens. Seventeen years later, Huygens made another major contribution in the same direction, by geometrically proving the isochrony of cycloidal 18 pendulum, the consequence of which is the near-isochrony of spherical (regular) pendulums of small arcs. The originality of Huygens' geometric proof of isochrony was, to the

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best of my knowledge, never contested. The basic application of the pendulum to horology, however, was. A design for a pendulum clock by Galileo's son, Vincenzio, which was probably never realized, had survived and was known to Hooke and Huygens (Robertson, 75-115). Hooke used this fact to try and deny Huygens' claim to the mechanical implementation; the kudos for the geometrical demonstration should have been enough for the Dutchman, Hooke maintained (Robertson, 167; Hooke's Manuscript Concerning Huygens' Horologium Oscilatorium).

POWER

Figure 12: Galileo's design for a pendulum clock (Robertson, 112).

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108

4. THE SPRING WATCH

Prestige was only one aspect of the scuffle. Money was another. An accurate timekeeper bore the promise of a solution to the acute problem of oceanic navigation, namely, "the Invention of ye Longitude of places" (Hooke's Manuscript Concerning the Invention of a Longitude Timekeeper, Wright, 103. Henceforth: Longitude Timekeeper). With all other attempted methods failing, it became clear that the only reliable way to establish a longitude position on the open sea would be by comparing the local time, measured astronomically, to the time at the point of departure, supplied by a clock on board the ship. The benefits from the patent rights to such a marine chronometer were understandably expected to be enormous. No one could question the accuracy of Huygens' clocks on shore, but motion was obviously going to make pendulum regulation problematic (though Huygens continued trying to fit his pendulum clocks to the task until his death-see Figure 15). A new type of regulator was needed.

4.1.

Navigating in Troubled Waters

Which brings us to Hooke's own device. "Had Hooke carried out his design and built and perfected this timepiece," writes Landes "he might have changed the history of timekeeping and marine navigation" (Revolution in Time, 127). Regrettably, he did not. In 1660, Hooke presented what would probably have amounted to an outline of his invention to Boyle, Moray and Brouncker, and asked for their sponsorship. According to Hooke's account of the events in his Helioscopes, he demanded a £2,000 bond for his patent rights, and the "Treaty was broken off' when the honorable gentlemen were willing to offer only a limited guarantee. Hooke refused to accept a clause that would absolve the warrantors from their responsibility in the event of a third party introducing an improvement to his device "knowing 'twas easy to vary my principles an hundred wais." The incident left Hooke feeling betrayed even by his admired Boyle, and he did not return to the watch until the news of Huygens' spring balance in March 1675 sent him into a fury of work in an attempt to establish his priority over the invention l9 . "Because of pique," or so Hall explains it, "he renounced his claim for public recognition as the inventor of one of the most important mechanisms in horology, and retarded the developments of the art for a century" ("Robert Hooke and Horology," 177). An even more depressing outcome (from the historian's perspective) of this protracted strife, is that the remains of Hooke's actual

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ideas, designs and constructions of timekeepers are in much shorter supply than his and others' claims and counterclaims regarding dates, places and witnesses to such achievements. The relevant remains are, in fact, limited to two manuscripts, several scattered, short remarks, a description of "a fly moving Circularly instead of a ballance" in Lampas (eL, 197-198) with an attached diagram (preceding page 299), and a number of sketches of spring balances and 'flies' in his diary. These latter date from 1675, and relate to his fervent, last-minute efforts to construct a watch that would prove the priority and superiority of his design over Huygens'. The earlier text is a manuscript which Hall ("Horology and Criticism," 264-266) dates to 1664-5, with modifications and insertions added, most likely, during the 1675 campaign20• I shall refer to this manuscript as the Longitude Timekeeper after its main subject. The second manuscript dates from 1673, and contains an acidic but well-argued criticism of Huygens' Horologium Oscilatorium21 • To these can perhaps be added a number of clocks built by Hooke's collaborator, the celebrated clock and watch maker, Thomas Tompion. Of those that survived, some appear to implement contrivances of Hooke's design22. One other source is a description by Lorenzo Magalotti of "a pocket watch with a new pendulum invention" (cited in Robinson, 323) built by Hooke, which impressed him enormously at the Royal Society meeting of 21 February 1675 (and somehow-Hooke would probably not have been surprised-failed to be registered by Oldenburg).

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I Figure 13: HuygeTUJ' pendulum clock (Horologium Oscilatorium, 3). Notice the cycloidal 'cheeks' (Fig. II) forcing the pendulum into cycloidal, isochronous trajectory.

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111

The Poverty of Priority

The story of the spring regulator may seem to be putting Hooke, once again right where historians of science used to think he belongs, namely, on the losing side of a priority dispute. Indeed, if his altercation with Newton ended with him receiving neither the acknowledgement he thought he deserved nor the recognition of latter day historians (see Introduction), the consequences of his strife with Huygens and his Royal Society correspondent (or spy, if you were to ask Hooke) Oldenburg, over the invention of the spring watch were even worse: both his honor and his pocket suffered, as he had to give up his patent claims and was made to publish a humiliating apology. Posthumously, however, Hooke's complaints against Huygens have fared better than those he leveled against Newton. Thanks to that undisputed status of his as a 'mechanical genius' and the clear demarcation along national lines, "the general consensus of opinion has ... accepted the validity of Dr. Hooke's claim to the invention [of the anchor escapement)" (Robertson, 133) and "every English writer has attributed to Hooke the honor of inventing the spiral spring" (op. cit., 180). Given the role assigned to Hooke in the grand narratives of the history of science, this historiographic tum of events is hardly surprising. Thanks to the persistent rumor (bitterly belied by Hooke-Sloane, 172) about "the large rewards that have been promised both by the King of Spain And the States of ye Low Countries" (Longitude Timekeeper, 110)23, an air of uncomplicated greed wraps this episode, an atmosphere in which Hooke's pecuniary concerns appear less conspicuous than usual, so that granting him priority may appear less offensive to historiographic good manners. Furthermore, with Hooke's ready acknowledgment of what he terms Huygens' "invention that all the vibrations of a pendulum moved in a cycloeid are of /Equal Duration" (Sloane, 168), the priority dispute became neutered of its theoretical aspect and concentrated on a strictly mechanical invention, viz.: the application of a spring, instead of a pendulum, as a regulator for time-keepers. Since historians agree that "As an inventor of practical instruments, he was unrivaled in his age" (Westfall, Introduction to The Posthumous Works, xxvii), it is but natural that the honor of being the first to accomplish the nitty-gritty was awarded to Hooke. Yet the harmony of the variations on the theme of 'Hooke the (ingenious, but still only) mechanic' is deceptive. In fact, I shall try to demonstrate next that Hooke and Huygens' respective approaches to the problem of accuracy of timekeeping are so different, that the question of who did what first and the disagreement over the fair distribution of praise are not only moot, but

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positively misleading.

4.3. Theory vs. Technology As I claimed with regard to the priority dispute over the discovery of the Inverse Square Law (see introduction to previous chapter), the main reason that these debates are misleading is because they suggest that the disputants had a common goal they were competing to achieve. In fact, although Huygens and Hooke were seemingly committed to the same horological task, they differed fundamentally in their understanding of what the task entailed and what they would achieve by fulfilling it. Huygens leaves little room for doubt regarding what he perceives as the core of horology: this clock is not only a mechanical invention. but much more important it is constructed on geometrical principles. (The Pendulum Clock, 8)

For Huygens, the challenge of constructing accurate timekeepers is first and foremost one of geometrically construed isochrony: the simple pendulum does not naturally provide an accurate and equal measure of time since its wider motions are observed to be slower than its narrower motions. But by a geometrical method we have found a different and previously unknown way to suspend the pendulum; and we have discovered a line whose curvature is marvellously and quite rationally suited to give the required equality to the pendulum. (Op. cit., II)

Huygens' approach has very clear ramifications. Concentrating on isochrony, he introduced as few mechanical changes as possible in converting verge-and-foliot clocks to pendulum regulation. The trainspring or weight driven-remains untouched, and similarly the escapement; Huygens' pendulum replaced the foliot alone. The later introduction of cycloidal 'cheeks' to force the pendulum into an isochronous trajectory was, again, an addition to the old contrivance. This conservatism made his invention cheaper and immediately applicable, but the reasons for it are more deep-seated. The task of accurate timekeeping can be construed as a geometrical question of isochrony only once it is isolated from the mechanical challenges involved: the proof can only pertain to ideal pendulums, moving in ideal conditions. Moreover, the proof of the isochrony of a particular mechanical device-a pendulum, a spring--does not make it a regulator. A geometrical proof cannot contain instructions on how to make the device part of the workings of a clock-how to make its isochronous motion regulate the mechanism that produces and maintains the motion of the train, the regulator and the escapement connecting them.

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Huygens had to assume that that mechanism is reliable and essentially unvarying for his abstract solution to meet the practical challenge. Hooke had an equally firm belief in principles: the principle of clocks and watches is very good and if regulated after the manner I shall by & by shew, will afford and excellent measure of time. The Principle [isl A contri vance to make a determinate quantity of Strength to moue a determinate bulk of body such a determinate number of equall spaces in a Determinate time. (Longitude Timekeeper, 112- t 13)

Hooke's principle is clearly of an altogether different order from Huygens' "geometrical principles." It is, indeed, "a contrivance," and it is recruited to solve a wholly different problem: clocks and watches ... seem to be the most likely artificiall inuention for keeping time. But thes[e] being subject to many inequalitys and irregularities in their motion. from severall accidents make these [like other artificial timekeepersl vnfit to performe soe great a task as the exact keeping of time ...• for first such as are mooud w4I springs suffer an inequality from the vnequal strength of yo spring and secondly from the stretching or shrinking of the string. besides the inequality of the spirallingof yo fusy whereon the string is winded. those of them that are mou'd by dead weights suffer an irregularity from euery shake or jOping of yo ship. And both kinds suffer extremely in the motion of their ballance from the labouring of the Ship as they doe likewise from the inequality of the make of their wheels insoemuch that I never heard a clock or watch whose balance did not very sensibly beat vnequally. (Op. cit.• 105)

What was for Huygens a theoretical problem of isochrony was for Hooke a technological question of control. He had no intention of ignoring the "many inequalitys and irregularities" which beset any "artificial! inuention for keeping time," and would not reduce the "great task [of] exact keeping of time" to a single motion- even if it is, ideally, a motion of equal duration. He is not unaware of the importance of accurate, and if possibleisochronous-regulation, and like Huygens, he indeed hope to achieve it by "a simple & permanent principle:" if any kind of Instrument be soe made, that that mouing body (wd! is to regulate the motions of the whole engine) be w4I the most simple & permanent principle mou'd after the most simple and plaine manner soe as to be subject to the least kind of variation from extemall accidents and that the mouing power be always equally and in the same manner applyd that must certainly be the most exact & vsefull instrument for finding [timel. (Op. cit., 117)

Hooke is also far from ignorant of Huygens' successful application of the pendulum to "measure time ... exactly" Cop. cit., 116i4• But he refuses to view it as anything but another technological improvement: There is one way yet Remaining which was lately Invented by Monsr Zulichum which for a standing fixt instrument perfonnes very much but for transportation is

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altogether vnfit In regard that (besides that its motion whilst last is very irregular) it will very suddenly stand still and not move at all and [after?] a little time moue again and tis w~ut any certainty. (Op. cit., 105)

B

Figure 14: Cycloids from Huygens' Horologium Oseilatorium (l112).

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Indeed the Longitude Timekeeper-Hooke's most extensive horological manuscript---contains numerous references to "exact measure of time" (II 0; 116), "constancy" and "exactness" (111). Isochrony, however, is only mentioned once, and that indirectly, as part of the following remark, which further highlights the difference of his approach from Huygens'. Hooke's interest in "the equality of a pendulum" (116), this remark stresses, is not related to any geometrical principle, but to the fact that it proceeds only from this that there is always the same strength of gntity that does creatl?] its motion and that its motion is very little incumbredwlhchangable obstaldes ["atland"l. (Longitude Timekeeper. 116)

For Hooke, horology is the art of eliminating "changable obstakIes." It is less concerned with the "equality" of any particular part of the mechanism, and more with "equalling the motion of' all its various parts (Longitude Timekeeper, 116. Italics added). Huygens' later addition of the geometrical proof of isochrony along a cycloidal curve to support his pendulum invention does not affect Hooke's approach. He is not prepared to assign privileged status to the theoretical task-that of identifying a curve along which the period of oscillation is independent of the amplitude. Isochrony of the regulator, from Hooke's perspective, is just one of a host of difficulties and challenges encountered in horology-mechanical problems, problems of accuracy of design and production, problems of "variation from externall accidents." Furthermore, it is, in fact, the very proof of isochrony, that renders the cycloidal pendulum, when attached to the conventional clock's works, deficient in principle: if the motion of a Icycloidal] pendulum untoucht will make ,qual vibrations then certainly those vibrations must be unrequal if they are sometimes more and sometimes less promoted & sometimes less and sometimes more hindered by the impelling power ofthe clock work. (Sloane, 169)

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Ii

K.

Figure 15: Huygens' attempts to adjust his pendulum clocks "for transportation" (Ilorologium Oscilatorium, 19·20).

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The difference between Hooke and Huygens has already been noticed by Hall, who uses familiar tenninology to describe it: whereas Huygens had approached horological invention through his studies in pure mechanics. and left the work of construction to professional clock-makers, Hooke's attitude is that of a mechanic of genius, rather than a scientist. (Hall, "Robert Hooke and Horology." 175-----see Introduction)

But whatever Hall might mean by 'an attitude of a scientist' as opposed to that of a "mechanic" (if "of genius"), Hooke's thoroughly technological approach was more general, less bound to the local conditions of the problem at hand than Huygens' mathematical abstraction. As we have seen, Huygens needed to isolate the matter of isochronous osdilation of a pendulum from the whole task of accurate timekeeping. Thus the upper limit of accuracy for his clocks is set by the perfonnance of mechanisms with regard to which he has no new insights to offer. Settings in which the pendulum is impractical, such as a moving ship, neutralize his invention, as do other technological developments, such as miniaturization or the carry-on watch 25 • Hooke, on the other hand, sees no point in treating any aspect of mechanical timekeeping as separate from the rest. For him, the problem is that of the calibration of forces and the continual amendment of deviations: the pendulum is sensible of every inrequality of the motion [of the clock work] and though by reason of ye small proportion of the strength of ye watch work [the going train] to the strength of ye pendulum it is not sensible in any single vibration, yet in a Longer Duration of time it becomes most sensible ... the pendulum left free will ascend either a larger or a shorter arch of the cycloeid in the same time according to the degree of velocity it hath in the perpendicular. yet if that free motion be stoped by a stronger or weaker check of the clock work it shall much sooner or later make its retume and consequently all that Alquality demonstrated in the theory of the Cycloeid ... destroyed. (Sloane, 169-170)

This fonnulation of the problem (of accurate timekeeping, and thenceof marine navigation) transfonns the mechanical timekeeper into a configuration of mutually checking and balancing forces. Hooke's watch is to be A contrivance to make a determinate quantity of Strength to moue a determinate bulk of body such a determinate number of equall spaces in a Determinate time. (Longitude Timekeeper, I I3-see above)

Though essentially technological, it is a general and open ended challenge, just as required by Hooke's precept of technology, mentioned in the previous chapter. It is not defined by contemporary, state of the art horology, nor is it limited by the prevailing assumptions and practices of

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that art. In fact, Hooke's approach, as expressed in both the Longitude Timekeeper and Sloane, does not so much call for a solution to a particular technological problem, as it is a request for a heuristic. Hooke's response to his own request can be perceived as a proposal for a technological research project, a general strategy towards the challenge of accurate timekeeping. And Hooke's design indeed represents a principle of horological technology: it pertains to all the essential components of a timekeeper-the motor, the regulator and the escapement, and it makes use of only one force-the spring. It is this timekeeper (reconstructed by Wright in "Robert Hooke's Longitude Timekeeper") that captured the imagination of Hall and Landes.

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~" .

_.. : - - --~'.---'_.~ ~

;; Figure 16: Hooke's spring balances. Top three rows: Lampas (adjacent to page 209); bottom rows: Diary.

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c .8

Figure 17: Huygens' spring balances. Top row: Oeuvres 18, 506; bottom row: Robertson, 177.

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5. SPRINGS AND FORCES

5.1.

Artificial Gravity

As already discussed, one component of the all-spring watch-the mainspring-had already been invented, and its form determined as that of a spiral or flat coil. What remained for Hooke, therefore, was to design a spring regulator. The above quotation from Sloane clarifies that Hooke perceives regulation as comprising two inter-related processes, viz., ")Equal vibrations" and "check of the clock work," He expresses the same approach in the earlier text as well: the cause of the irregularity of motion ... I found two: first the Irregular or vneuen force of the crown wheel against the ballance. And secondly the swing or sweep of the Ballance itself which by mouing the whole frame might easily be a1ter'd. (Longitude Timekeeper, 106)

The problem of the regularity of "the swing or sweep of the Ballance" was supposed to be solved by the pendulum, but Hooke notices a very clear deficiency in this application, especially in the case of portable timekeepers, such as those on board ships: the center of the motion of the Swing is far remoued from its center of Grauity whereby any Shog ... does still alter its equal motion. (Longitude Timekeeper, 108)

What was needed, therefore, was a balance contrived so that "the center of its motion & that of its grauity were both the same" (ibid.). But such a balance, entailing a radial wheel, or rim, "poised ... soe exactly upon its two poles as sharp as needles," could clearly not be controlled by a pendulum. Thus, because natural grauity could take noe hold of it as to its motion about Its center; I contrived an artificial one which should perform the same effect. (Longitude Timekeeper, 108)

The 'artificial gravity' is the spring, and this technical comment is perhaps Hooke's most telling remark with regards to bis strategy for timekeeping technology and the theoretical significance of his achievements in horology. The spring replaces the pendulum, not just in performing a particular technical task; it inherits the post successfully occupied by the pendulum since Galilee's experiments, namely, that of a surrogate for gravity: as by weight there is a Naturall pendulum ... made... soe by Springs is a kind of artificiall pendulum made whose vibrating motion is determined by the spring towards a determinate point, or from one determinate point, in the same manner as a

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perpendicular or pendulum is by gruity determined towards the center of the earth. (Longitude Timekeeper. 117)

One may conceive the significance of the move still better by recalling that Hooke had a genuine interest in the pendulum as a representative of gravity, which he had pursued over the years in a variety of different experiments 26 , investigating both the numerical parameters of gravity on earth and, more interestingly for the issue at hand, the general behavior of gravitating bodies. To this latter context belong the 'inflection' experiments of 1666, which were the focus of last chapter. This point warrants further elaboration: at the top of his scale of priorities, so the paragraphs above reveal, Hooke does not place the establishment of isochrony, but of a constant and controllable force. Seen f rom this perspective, the substitution of the foliot by the pendulum, and subsequently of the pendulum by the spring are practical exercises in the manipulation of forces-vis insita, gravity, spring. For Hooke these forces are real in exactly the way Hacking prescribes; "they are ways of creating phenomena in some other domain of nature," (RI, 263-see I st Interlude), or in this case-ways of producing effects in a completely independent domain of technology, viz., horology. The forces embedded in springs are indeed "tools, instruments ... for doing" (RI, 262), but this by no means implies, as we shall see later, that either the forces or even the springs themselves are "not for thinking" (ibid.). Before we move on, however, it is worth noting that the presentation of horology as the art of equilibration of forces is not only an hindsight analysis.. It is also the way of the function of balances was understood by the practitioners of mechanical horology themselves, as testified the following technical textbook, published about a century after Hooke's invention: In the vibrating Pendulum; gravity is made by means of the vis insita, to counteract itself the Ballance Spring is also made to counteract itself in each Vibration. by means of the vis insita of the Ballance; and thus, by having the effect changed into the cause, in each Vibration; we have. in the vibrating Pendulum, and in the Ballance and Spring. the most perfect equillibrium of action and re-action, that nature can produce: what can be more equal than any power to itself? (Cumming, 130)

5.2. The Fly and the Anchor While the main horological priority dispute between Hooke and Huygens centered around the invention of the spring balance. the focus on this dispute tends to obscure the main issues at stake. Huygens' balance,

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designed in 1675, was controlled by a spiral spring attached to its center (see Figure 17). Such devices, as Defossez points out27 , had in any case already been envisioned and attempted by others in the early 166Os, and, although Hooke did consider similar designs, it is fairly uninteresting to know if he did so before or after Huygens. The spring regulator which was vested with most of Hooke's attention and hopes-both technological and pecuniaryand in which the dynamic concepts of the Programme were embedded and re-worked, was anyhow of an altogether different type-the flywheel. Hooke scattered numerous suggestions for different possible designs of flywheels through the Longitude Timekeeper (where, unfortunately the diagrams for "many ways as A, B, e" (108) are missing), his Diary and Lompas. It is not clear whether he was not completely satisfied with any of these designs (though on Tuesday, October 12th 1675, he happily proclaimed: "Invented the best way for a circular fly" (The Diary, 186», or was he perhaps amusing himself with his ability to "shew 100 distinct wayes" (Longitude Timekeeper, 115) to design a flywheel. Whatever is the case, the principle on which they all operate is the same: two springs rotating around a common center, so that any change in the rotating force is countered by a change in the stress of the springs, and any bias towards one is countered by additional stress to the other. So, as a simplified example, if the regularly vibrating flywheel experiences a sudden pulse in a particular direction, the springs' centrifugal force increases, they are stretched farther out, their path is elongated, their momentum on their return increases, and the bias is countered. Historians of technology note that Hooke's spring balances regularly had a much shorter motion than Huygens'. The reason for the idiosyncrasy is further testimony to Hooke's commitment to the principle of mutual compensation; even when he tried attaching the spring to the middle of the balance, similarly to Huygens, he preferred designs like that sketched in his diary on March 8, 1675 (Figure 16-middle bottom row), which employ two S-shaped springs instead of one spiral. Being the product of an interest in self-correction rather than in basic equality of oscillation, Hooke's regulators are genuine feedback mechanisms. Hooke's attempts to employ springs as "artificial grauity" did not end with the mainspring and the spring regulator. The vibrations of the flywheel are indeed self-adjusting and "if the wheel were removed out of yt situs, it would after many vibrations Retume to it And there Stay" (Longitude Timekeeper, 108), but this does not solve the problems caused by chronic irregularities in the rotating force. As Hooke poignantly explains, the isochrony of the regulator, be this a pendulum, a balance wheel or even a fly, can be maintained only in the ideal case, and its real pace will depend on

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the continual 'push' provided by the train's movement. To free the regulator from the irregularities of the motor, Hooke designs an escapement which supplies its own force, another ingenious application of a spring, this time a straight spring. Designed with the "the cock of a firelock" (Longitude Timekeeper, 106) as its model, Hooke's escapement uses the motor only to bend, or cock a spring, which "as soon as bent Stopt by a trigger wch trigger [by] the retume of the ballance is moued, wherby the Cock is let goe" (ibid.). The released cock provides the regulator with an equal pulse, independent of any changes in the force that bent and triggered it. A similar device needed to be re-invented a century later, and then it was named a 'd6tente' or 'constant force escapement', which indeed it is-an escapement operating by its own supply of force, a triggered spring.

5.3. The Meaning of Springs Hooke's impressive timekeeper, rightfully lamented by Hall and Landes, was not to be completed, and horology was to wait another century for a watch featuring all three elements-mainspring, flywheel regulator and constant force escapement. Hooke's 'take it or leave it' approach, however, his insistence on not exposing any component of his watch unless the watch received recognition and appreciation as a whole, was more than just a whim. What the last Section demonstrated is that Hooke was entitled to talk about "my principles" (see above)-his watch was not an haphazard assemblage of independent technological solutions to practical problems that happened to present themselves. It was, rather, a genuinely integral mechanism, the product of a consistent pursuit of a very specific direction in mechanical horology. For Hooke, the challenge of accurate timekeeping was to make different forces check, balance and correct one another, as "the force of the crown wheel against the ballance," "the strength of ye watch work to the strength of ye pendulum" (see above) and so forth. Not only was the problem formulated around a single principle. so was the solution: Hooke reduced the challenge into a manageable project by implementing one single "principle by which action is produced, inspired, or instigated,,28-the spring. This was an accomplishment of great consequence. By constructing the watch as a system of springs, Hooke transforms the spring into 'artificial gravity', while the traditional role of gravity, as a synecdoche for all forces of nature, bestows this transformation distinctive significance. Hooke's spring was not only a surrogate for gravity itself, but for 'power' in its

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various manifestations. Hooke's spring is not only a surrogate for gravity itself, but for 'power' in its various manifestations. When operating as a mainspring, the spiral spring is harnessed to supply constant, equal drive, capturing power in its gradual, continuous action-the same aspect of power which gravity expresses through the weight moving the train. As a regulator, the S-shaped or jack-in-the-box flywheel springs embody power in its manifestation as self-maintaining, inertial motion: an expression, as Cumming puts it, "of the vis insita," by whose means, "in the vibrating Pendulum; gravity is made ... to counteract itself' (Cumming, l3o-see above). Finally, the leaf springs of the cock escapement manifest a third aspect of power: an immediate, violent "strong pulse," which, Hooke teaches us in the Mierographia (see below), is the operation of heat. The knowledge produced while working on the mainspring, the anchor, the flywheel and the firelock escapement was therefore not entirely lost. The appointment of the spring to represent all different forms of causing, changing and regulating motion provided Hooke with the wherewithal to structure his mechanical investigations. By gaining control over the various motions of his springs-pulse, oscillation, or continuous rotation-and developing the techniques for translating those motions one into the other, he has made 'power' into a concrete entity to be brought forth, manipulated and experimented on. This achievement had obvious empirical implications, yet the decision to use the spring watch to give distinct shape to the relations between power and motion had even further-reaching theoretical ones. They are recorded in Of Spring.

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Figure 18: Wright's reconstruction of Hooke's trigger escapement (Hunter and Schaffer, 84. Reprinted with permission ofBoydell & Brewer).

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Parte 6. TilE ORIGINS OF THE VIBRATION THEORY

6.1. The Attempt for the Explication ofthe Phenomena Of Spring is the obvious source to consult when investigating the relations between Hooke's spring theory of matter and his spring horology. But before returning to it, let us briefly consider his earlier attempts at developing a theory in which vibration accounts for the essential characteristics of matter. As mentioned above (Section 2.1), these are recorded in three related texts compiled in early 1660s: An Attempt for the Explication of the Phenomena Observable in an Experiment Published by the Honourable Robert Boyle of 1661 (henceforth: Attempt), which was the very first paper Hooke published under his own name; the "Explication of Rarefaction" (henceforth: Explication), published by Boyle, without acknowledging Hooke, as a chapter of his 1662 Defence; and "Observation VI" of the Micrographia of 1665, in which the Attempt is recapitulated almost verbatim, but with a few additional paragraphs (and some telling omissions). The primary phenomenon under consideration in the Attempt is the rising of water in thin pipes. Hooke hoped, however, that the hypothesis he presents would also account for a variety of fluid behaviors, such as the differences in chemical affinity between fluids and other materials (water and oil as opposed to water and salt); the different curve of the surfaces of different fluids (water, oil, mercury); the spherical shape of drops and bubbles; etc. His terminology in the Attempt has, on first reading, a strong naturalist-alchemical resonance, with its main explanatory device being "inconformity or incongruity (call it as you will)" (Attempt, 7). His explanation for these terms tends to reinforce this impression: What 1 mean hereby, I shall in short explain, by defining confonnity or congruity to be a property of a fluid body, whereby any part of it is readily united or intermingled with any other part, either of it self, or of any other Homogeneal or Similar, fluid, or firm and solid body: And unconfonnity or incongruity to be a property of a fluid, by which it is kept off and hindered from uniting or mingling with any heterogeneous or dissimilar, fluid or solid body. (Attempt, 7-8)

Moreover, the implied alchemical tendency cannot be immediately dismissed, since Hooke explicitly shies away from elaborating on the notion of congruity:

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from what cause this congruity or incongruity of bodies one to another ... 1 shall not here determine. (Attempt, 9-10)

Hooke discharges this aporia in the Micrographia. In two added paragraphs he injects a clear mechanistic sense into the alchemical-sounding terminology, turning the modest speculation of the Attempt into a blueprint for a full-fledged theory of matter. As in Of Spring, where this theory is to reach its final formulation, the main image that Hooke mobilizes in the Micrographia is that of vibrating particles, but instead of the generality he claims for this idea in the Cutlerian Lecture, the earlier version relates entirely to fluids, using an auxiliary image: the cause of fluidness ... I conceive, to be nothing else but a certain pulse or shake of heat; for Heat being nothing else but a very brisk and vehement agitation of the parts of the body ... the parts of the body are thereby made so loose from one another that they easily move any way, and become fluid. (Micrographia, 12)

6.2.

Heat and Vibration

It is Significant that Hooke chose to introduce a mechanistic interpretation to 'congruity' by claiming that "Heat [is] nothing else but a very brisk and vehement agitation," since heat was also an important theme in his Explication of Rarefaction, which was published by Boyle in 1662midway between the 1661 (Attempt) and the 1665 (Micrographia) versions of Hooke's theory. One would expect to find a discussion of heat in a text "explicatiQg the rarefaction and spring of air" (Explication, 178), but the heat of the Explication is very different from that of the Micrographia: "rarefaction by heat," explains Hooke in 1662, is caused by "the atoms of fire flowing in," exciting the particles of the heated body (Explication, 179). ''There is no such thing as the Element of Fire," he proclaims in 1665 (Micrographia, 105). This unequivocal rejection of his previously held concept of heat highlights the curious fact that in the Micrographia Hooke does not as much as mention the hypotheses for "explicating ... spring" of his Explication, which Boyle found attractive enough to feign authorship of (see Section 2.1). As discussed in Section 2.1, Hooke's Explication of the spring of air relied on an image of "very long, slender, thin and flexible laminae"ribbon-like particles, "coyled or wound up together as a cable, piece of ribbon, spring of watch, hoop, or the like" (Explication, 178), rotating around their coiling plane (the axis of rotation orthogonal to the axis of coiling). With this rotation, the laminae describe "a sphere equal in

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diameter to their own, after the manner that a meridian turned about the poles of a globe will describe by its revolution a sphere of the same diameter with its own," and "acquire a springiness outward like that of a watch spring" according to the speed of their revolution (Explication, 179). This was not an altogether bad idea. It was thoroughly mechanical, and nicely related to the suggestion of "the most acute modem philosopher Monsieur Des Cartes ... That the air is a body consisting of long, slender, flexible particles, agitated and whirled around by the rapid motion of the globuli crelestis" (Explication, 180). It employed the relatively well understood centrifugal force to explain the relatively mysterious force of spring, and, after some convincing, it also won the approval of Huygens 29 • Yet Hooke never refers to his laminae again. Thus Hooke commences work on a theory he would finally dub "a theory of springs," by disengaging himself from his work on "the spring of air." It may be that the only the explanation needed for Hooke's abandonment of his concept of swirling laminae is that he realized that it relied on a deficient understanding of Descartes, or that he came to appreciate the dangerous implications of his Epicurean leanings. However, the important and surprising fact is that Hooke's vibration theory is not founded upon his early work on springs, nor is it developed in critical engagement with his previous thoughts. Moyer's attractive and commonsensical hypothesis ("Robert Hooke's Ambiguous Presentation," 274), that the purpose of the vibration theory was to bring spring phenomena, solid as well as fluid, under a single explanatory roof, cannot be true, and Hooke's partial success (at least in his own eyes) in doing so has to be seen as a byproduct. Not only does Hooke abandon his spring speculations when he began his work on vibration theory, he also introduces the most characteristic feature of this theory-the very notion of vibrating particles-as an account of heat rather than of springs. This introduction demands, as we have seen, a clear rejection of the substantive concept of heat used in the Explication: it seems reasonable to think that there is no such thing as the Element of Fire that should attract or draw up the flame, or towards which the flame should endeavour to ascend out of a desire or appetite of uniting with that as its Homogeneal primitive and generating Element; but that that shining transient body which we call Flame, is nothing else but a mixture of Air, and volatil sulphureous parts of dissoluble or combustible bodies, which are acting upon each other whilst they ascend, that is, flame seems to be a mixture of Air, and the combustible volatil parts of any body, which parts the encompassing Air does dissol ve or work upon, which action, as it does intend the heat of the aerial parts of the dissolvent, so does it thereby further rarifie thouse parts that are acting, or that are very neer them, whereby they growing much lighter then the heavie parts of that Menstruum that are more remote, are thereby protruded and driven upwards; and this may be easily observ'd also in

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dissolutions made by any other menstruum, especially such as either create heat or bubbles. Now, this action of the Menstruum, or Air, on the dissoluble parts, is made with such violence, or is such, that it imparts such a motion or pulse to the diaphanous parts of the Air, as I have elsewhere shewn is rcquisite to produce light. (Micrographia, 105)

6.3.

"A Gross Similitude"

The original core of Hooke's 'kinetic' conceptions, then, is the conception of heat as a form of pulse, and not the nolion of a spring-like vibration; it is with pondering heat and fluidity, rather than springs, thaI he begins his quest for a Cartesian theory of matter. In the Attempt and the Micrographia, long before he expands it into "a theory of springs," Hooke uses of the image of "heat and agitation" (Micrographia, 103-104) to tie in an explanation of how substances tum liquid when heated with explanations of the changes in weight and solubility due to .temperature change; explanations for respiration and body temperature, for the fact that flames rise, for the shape of flames and for the fact that fire emanates light. The theoretical maneuvers that will transform this "Hypothesis of Fire and Flame" (C.L., 155: the first sentence of Lampas) into a general theory of matter also stem from those early texts. Again, they do not revolve around springs, but rather around what Hooke calls, with undue humility, "a gross Similitude:" let us suppose a dish of sand set upon some body that is very much agitated, and shaken with some quick and strong vibrating motion, as ... on a very stiff Drum-head which is vehemently or very nimbly beaten with the Drumsticks. By this means, the sand in the dish, which before lay like a dull and unactive body, becomes a perfect fluid; and ye can no sooner make a hole in it with your finger, but it is immediately filled up again, and the upper surface of it levell'd. Nor can you bury a light body, as a piece of Cork under it, but it presently emerges or swims as 'twere of the top ... (Micrographia, 12).

Besides demonstrating Hooke's considerable feel for rhythm3o, this engaging "similitude" constitutes a fundamental relationship; the affinity between heat and fluidity. Fluidity is the motion of particles, claims Hooke, a motion set by heat; heat is pulse, fluidity is vibration. Hooke, as we know, will make this affinity the centerpiece of Of Spring. The theoretical moves by which Hooke transforms the drum similitude into the "vibrative motion" of Of Spring are still more telling than the obvious ancestral relationship between the two versions. In the Micrographia, vibration is what differentiates between particles of fluids

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and particles of solids; the former vibrate, the latter do not. In Of Spring, this distinction is relativized and generalized: all particles are in motion (though Hooke shies away from the implied Epicureanism). Fluids and solids are distinguished not by the whether or ~ot their particles move, but by how they move: according to Hooke, the motion of that of solids is harmonious. If Of :-'pring is read as a theory of springs, it seems as though Hooke developed the notion of harmony especially to account for the difference between solid springs and "the spring of air" and to allow the application of Vt tensio sic vis to both. In fact, Hooke introduces harmony already in the Micrographia: if we mix in the dish several kindf of sands, some of bigger, other of less and finer bulks. we shall find that by the agitation the fine sand will eject and throw out of it sel f all those bigger bulks ... and those will be gathered together all into one place ... for particles that are all similar. will. like so many equal musical strings equally strecht. vibrate together in a kind of harmony or unison. (Micrographia. \5)

Moreover: just as he would later do in Of Spring, Hooke uses this musical metaphor to explain "what congruity is" (Micrographia, 15). Harmony, already in the 1665 Micrographia, is Hooke's way to "Mechanically produce" (Micrographia. 13) "congruity"-that alchemical sounding term which he uses to explains why "Liquor will ascend to some height in ... long and slender pipes" (Attempt, 1). In a similar vein, a reader of Of Spring could suspect that Hooke suggests that particles come in different sizes for the sole purpose of distinguishing solids from fluids so that his law may be generalized to both types of springs (solid springs and the spring of air). This is clearly that this is not the case either. Hooke already used the different sizes of particles in the Micrographia, to distinguish the "relative properties of fluids" (Micrographia. 16), and its application to the distinction between solids and fluids is a natural step for him, especially since he remarks in the Micrographia that the parts of all bodie,f. though never so solid. do yet vibrate [sincel all bodies have some degrees of heat in them, (Micrograph/a. 16)

7. OF SPRING AGAIN

The inevitable conclusion is that springs are neither the primary target of Hooke's theory, nor his main source for analogies and metaphors. All the mechanisms he applies in Of Spring-"vibrative motion," congruity, harmony, the relative distinction between solids and fluids-were developed

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in the Attempt and the Micrographia, over a decade before the publication of Of Spring. Not that Hooke was ignorant of or disinterested in springs in the early I660s. In fact, he had carried out the bulk of his work on the spring watch precisely during those years (as early as 1658, according to his later, 'improved' records, and certainly by 1664). However, the early version of his hypothesis does not assign to them any special theoretical status. In the Attempt and the Micrographia, springs are just one of the many phenomena that Hooke accounts for: A Fifth thing which I thought worth examination was, Whether the motion of all kind of Springs, might not be reduced to the Principle whereby the included heterogeneous fluid seems to be moved; or to that whereby two Solids, as Marbles, or the like, are thrust and kept together by the Ambient fluid. (Attempt, 31; Micrographia, 25)

This being said, it is important to note that, already in those early texts, Hooke was considering the idea of assigning springs a more dominant role in his theoretical apparatus. What this role would be was still undecided: ... there is an extraordinary and adventitious force, by which the globular Figure of the contain'd heterogeneous fluid [like a bubble or a drop] is altered; neither can it be imagined. how it should be otherwise be of any other Figure then Globular: For being by the heterogeneous fluid equally protruded every way, whatsoever part is protuberant, will be thereby depresl. From this cause it is that in its effects it does very much resemble a round Spring (such as a Hoop). (Attempt, 20; Micrographia, 19)

What role then did Hooke finally assign to springs in his theory? The time has come to finally lay aside the critique and suggest a positive interpretation of the way that Hooke uses springs in OfSpring. As remarked earlier, I mean to argue that although this tract is not about springs, and although they offer no empirical support for the theory elaborated in it, nevertheless, springs still fulfill an essential theoretical function in Of Spring.

7.1. The Problem of Structure If the Attempt was a first attempt at a theory of matter and power, and "Observation Vf' of the Micrographia represents a further development of the same theme, then in Of Spring, this undertaking assumes its most complete and ambitious form; a scheme that should allow Hooke to come to grips with any apparent natural force-from impenetrability to gravity. This requires a wide variety of metaphors, analogies, mathematical constructions, experimental techniques and metaphysical precepts, to some of which, e.g.,

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the vibrating particles model, the O'resme-style diagram and the Toricellian experiments, have already been discussed in Section 2. OfSpring, however, does not disintegrate under the pressure of this diversity; it has, as I attempted to demonstrate in that Section, a rather neatly woven argument. It is to enable this orderly argumentation, I shall try to demonstrate next, that Hooke employs springs in the tract named after them. The effort required of Hooke to consolidate Of Spring into a coherent whole is better appreciated when one notes that the conception of power he develops in the tract is comprised of three independent notions. First, there is the notion of restrained motion, embodied the image of vibrating particles. Secondly, there is the 'aggregability' of power, and thirdly there is the quasi-infinitesimal treatment of its aggregation and release. It is not difficult to observe that these three components of the main idea, though not incompatible with one another, are quite independent. It is a legitimate interpretation of the vibrating particles model, that power, continually applied to a body, should be somehow gathered and maintained in that body. The notion of accumulation of power, however, is not an integral feature of the model; the concept of harnessed vibration does not preclude, but also does not necessarily generate the idea of aggregation. The O'resrneian construction, on its part, may be implied in the reference to 'degrees of motion', as discussed in Section 2, but it is by no means dictated by any of the other two aspects.

7.2.

The Structure of Harmony

Hooke's theory, in other words, presents him with a structural problem, namely the need to compose a coherent whole from his collection of dispersed elements. This problem becomes all the more acute when he deposes of the obvious candidate for providing the required structure, namely harmony. Hooke's main reason for introducing harmony was to inject respectable mechanistic significance into the dubious term "congruity." In the Attempt Hooke is still non-committal concerning the question from what cause this congruity or incongruity of bodies one to another, does proceed, whether from the Figure of their constituent particles, or interspersed pores, or from the differing motions of the parts of the one and the other, as whether circular, undulating, progressive, etc., I say from one, or more, or none of these enumerated causes, I shall not here determine. (Attempt, 9-10)

But as we saw above, in the Micrographia Hooke abandons his

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indeterminate posture, and explicitly attributes congruity among particles to the "harmony or unison" of their motions. This is a crucial theoretical move. Hooke's choice of 'harmony' to fill this important explanatory gap---without it, 'congruity' remains unacceptably obscure--establishes this concept as his central theoretical concept. Beyond the causal explanation, from the Micrographia on, 'harmony' establishes, for Hooke, the routes that his arguments regarding congruity can take. Above all, it is 'harmony' that determines the leading metaphor of the discussion-the oscillating string. It is this metaphor that finally resolves the aporia of the Attempt: the motion of the particle that causes congruity is clearly "undulating", rather than "circular" or "progressive." It also rules out some explanations; "interspersed pores", for example, lose their relevance. Moreover, since the motion of strings is a well-theorized phenomenon, Hooke can use it as an elaborate model for the motion of particles: consider that a unison may be made by two slrings of the same bigness, length and lension, or by two strings of the same bigness, but of differing length. and a contrary differing tension ... and several other such varieties, (Micrographia, 15)

However, the use of 'harmony' in this manner also mandates certain directions that Hooke is apparently less comfortable with. Explicating the model, Hooke finds himself obliged to introduce 'positive analogies' (a term developed by Hesse in her Models and Analogies in Science) for each of the three determinants of oscillation that the model prescribes, and the outcome is somewhat awkward: To which 'three properties in strings, will correspond three properties also in sand, or the particles of bodies, their Matter or Substance, their Figure or Shape, and their Body or Bulk, (Ibid.)

This three-fold specification of the properties of particles is definitely not a deliberate theoretical move-it is dictated to Hooke by the choice of the oscillating string as his leading metaphor. The three properties accountable for this oscillation-Ubigness, length and tension", require three "corresponding properties", and Hooke fulfills the requirement by "Matter or Substance, ... Figure or Shape, and ... Body or Bulk." The very terminology he uses clarifies that he does so reluctantly; there is no way to distinguish, in the context of a Cartesian theory of matter, between "Body or Bulk" and "Matter or Substance." In fact, 'substance' has a suspiciously Aristotelian, not to say obscurantist resonance, and its use it but obliterates the mechanistic respectability that the explanation using harmony conferred upon 'congruity'. Judging from the final version of his theory (see below),

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it seems more than plausible to assume that, if not for the need to present three analogues-a structural constraint imposed by the string modelHooke would have avoided "Matter or Substance" altogether. As it is, Hooke uses this combination of terms as a placeholder for the third property needed to complete the analogy. The. significance of choosing the term 'harmony' thus stretches well beyond providing an explanation for 'congruity'. 'Harmony' has a particular structural force in Hooke's early texts. It is "force" in the sense of providing a desired congruence among the arguments concerning "heat and agitation," as well as in the stronger sense of compelling Hooke, after he has introduced it, into making what he sees as undesirable moves. It is to achieve this type of congruence, and because of those undesirable effects, that Hooke replaces harmony with springs once his early speculations mature into a theory of matter.

7.3.

Detour: Tropes and Topics

In another context (my "Tropes and Topics") I purported to elucidate what I have called here 'structural force', with the aid of terminology borrowed from the traditional study of rhetoric. I would like to shortly present this terminology here, with no particular theoretical commitment, in the hope that it might assist in understanding the way Hooke uses 'harmony' in the Micrographia, and the reason and manner in which he replaces it with springs in Of Spring. The basis of this line of analysis is a distinction between two levels on which a theoretical term can function linguistically within a given text. The first level consists of the relations the term can have to other terms through the use of tropes-the metaphors, metonyms, synecdoches etc. 31-which refer to the term, as well as those tropes which employ the term to explicate other terms. These 'tropic relations' between terms may be thought of as the semantic network wherein the terms are placed, and which infuses them with 'meaning' in the ordinary sense. The second level, which is more pertinent to us here, could be called 'topic relations' to evoke the rhetorical notion of tapas, (topic; commonplace). Within a local and limited range, usually set by a limited number of key terms, the topos provides a structural framework that functions in much the same way as a logical structure. Primarily, it dictates an obligatory ordering of textual elements, in other words it determines the order in which terms should appear, and their order of superiority, adjacency, etc. 32 As with the structures of formal logic, this

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context-dependent ordering makes it possible for the reader to identify and follow arguments and to distinguish proper modes of argumentation from inadequate ones. Albeit not as restrictive as the structures required by logical validity, those imposed by topic relations insure the communicability and authority of arguments. Deviations from them, unless carefully justified or disguised, render argumentation inadequate, if not outright unintelligible. Hooke's use of 'harmony' displays exactly these topical characteristics; it provides, but also mandates a structure. 'Harmony' provides the tropes through which 'congruity' can be imagined and discussed-metaphors, analogies, the models built upon them etc.-and it provides them as an ordered cluster. In this sense it operates as a topos. Integral to the meaning of 'harmony' and projected through it is a structure which allows Hooke and his readers to develop and follow consistent lines of argumentation and presentation. Let us then follow Hooke's use of 'harmony' as topos a little further. By adding a third property to his particles, to complete the analogy to strings, Hooke is being consistent with the mandates of the topos of harmony. However, the dictates of topical structuring are not absolutely rigid, and because he is particularly uncomfortable with the reference to 'substance', Hooke can and does omit it in the Of Spring version of his theory: This only I suppose, that the Magnitude or bulle of the body doth malce it receptive of this or that peculiar motion and no other ... (De Potentia, 8; c.L., 340).

Gone are the "Matter or Substance", and "Figure or Shape" seem to be assimilated into "Magnitude or bulk". The notion of congruity remains illustrated by the "similitude or example ... of musical strings ... tuned to the same sounds" (ibid.) and, as we found that musical strings will be moved by Unisons and Eights, and other harmonious chords ... so do I suppose that the particles of matter will be moved principally by such motions as are Unisons. (De Potentia. 9; C.L.. 341)

But the use of the metaphor is limited to illustration, and Hooke has to drop the elaboration of the model of oscillating strings and explicate the notion of harmony of vibrating particles in its own terms; the topical role of 'harmony' has been terminated.

7.4. Changing Structures The presentation of a new and original theoretical speculation calls for creative operation of topoi. 'Harmony' served Hooke successfully in the

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early workings of his theory of matter owing to its rich ('tropic') meaningespecially the fertile strings model. Once this model became too restrictive, however, Hooke stripped it down and maintained it only as a rather marginal metaphor for illustration purposes. Terms with a long and powerful tradition to their side may continue to fulfill their role as topoi even after their meaning is impoverished or radically changed 33 • However, 'harmony', though well entrenched in musical theory and mentioned in astronomical speculations, could not claim such a status; as a theoretical term in the service of matter theory, it was a novelty, which Hooke had introduced for the first in the Micrographia. After discarding its central metaphor and eliminating most of its complexity, Hooke can still use 'harmony' as an important theoretical tool-it can still explain "congruity" (De Potentia, 9; c.L., 341) and the difference between solids and fJuids-but it cannot bear the burden of formatting Of Spring as a whole, and Hooke must find another structuring element, another topos for this task.

8.

SPRINGS AS A

Topos

This, I shall demonstrate presently, is the role of springs in Of Spring. They are the topos used by Hooke to crystallize the three different aspects of his notion of power discussed above into one argumentatively solid theory. As a topos by which he can structure his theory of matter, springs present Hooke with some clear advantages over 'harmony'. Not the least of these is Hooke's direct unmediated and intimate acquaintance with springs, the acquisition of which we followed earlier. With this acquaintance comes better control, which indeed allows Hooke to configure the theory without the difficulties entailed in working with 'harmony', and allows for the theoretical consistency in Of Spring that impressed Patterson. Nevertheless, the most striking difference between springs and 'harmony' is, of course, that the latter is a theoretical-linguistic element to begin with, while the former are material and practical. The claim that Hooke uses springs to fulfill the same linguistic assignment for which he used 'harmony' needs therefore to be carefully refined and supported.

8.1.

Oscillation

The most conspicuous decision taken by Hooke in replacing 'harmony' with springs, is that of changing his main metaphor: the vibrating particles

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take the place of the oscillating strings. Hooke opens Of Spring with a presentation of "the Phenomena of Springs and springy bodies" (De Potentia, 6; c.L., 338), continues with reference to the "Congruity and Incongruity of bodies" (ibid.), and then unfolds the hypothesis of vibrating particles. At this stage he returns to springs: These principles thus hinted, I shall in the next place come to the particular explication of the manner how they serve to explain the Phrenomena of springing bodies whether solid or fluid. (De Potentia, 13; c.L., 345)

The "particular explication," we saw earlier (Section 2.3.1), cannot be taken as a mere application of Hooke's "principles" to the "the Phenomena of Springs" with which Of Spring commences. Hooke used 'harmony' to differentiate fluids from solid springs in order to explain both by the same principles. Yet he did not complete the maneuver. If he had simply wanted to develop a theoretical explanation for empirical phenomena, then his attempts were less than successful, and it is surprising, as Moyer notes, that the failure was never put at his doorstep. Hooke's diagrams (Figure 9: De Potentia, 13, 15; C.L., 345, 347) offer a solution to this conundrum. These diagrams do not pertain only to springs; they portray the dynamic equilibrium between the vibrating particles of any body and its ambiance. In fact, even from Hooke's own theoretical perspective, the diagrams provide a much better representation of fluids than of solid springs, since (as he himself interprets them-see Sections 2.2.1 and 2.3.1) they relate only to displacement, and ignore the dimensions stabilized by harmony in the "natural state." As an image, however, the diagrams are schematic representations of solid springs. The top trio (from De Potentia, 13; C.L., 345), showing compression and dilation, are sketches of the coil or helix type (the type used in the various flywheels drafted in Lampas-see Figure 16). The bottom duo (from De Potentia, 15; C.L., 347), which illustrate bending, provide outlines of leaf springs (the type used in the cock escapement). They do not refer to real springs; the theory's predictions simply do not correspond to real springs, at least not straightforwardly. These diagrams merely evoke springs, present them before us and establish them as the basic leitmotif for the discussion. With regard to that function, the empirical discrepancy is only marginally relevant. The role of real springs here is not to support the theory with confirming data but to ensure continuity of argument and presentation. In other words, springs do not provide the content, about which the hypotheses are advanced, but the form, or structure, by which they are. This 'form', it is worth reiterating, is not completely independent of

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'content'; the structure provided by a tapas relies on its meaning. Hooke's ability to use 'harmony' in a structuring role was contingent upon-and finally failed because of-the strings metaphor. Correspondingly, the tropes . that constitute the meaning of springs are material and practicalcontraptions, skills, phenomena. Thus Hooke's ability to use springs in the same structuring role that he used harmony for relies upon his ability to make his practical manipulations of them relevant to his theoretical speculations. Since, as I wish to argue, Hooke does not expect springs to provide an empirical basis for his theory, 'relevance' here does not imply strict quantitative confirmation, although obvious refutation would not help Hooke's cause either. Rather, to employ springs as a tapas, Hooke needs to induce from springs behavior suggestive of his speculations. Hence the claims made through the diagrams are general and theoretical, even though the diagrams themselves are of a wholly local and practical orientation. They are meaningful in that they pertain to devices Hooke has direct and thorough acquaintance with, by virtue of a concrete skill; material devices which enable him to think and work through the theory.

8.2. Aggregation If the leaf spring can function as a synecdoche for vibrating particles, the spiral and the coil springs are natural metonymies for the aggregation and release of power. This is their role when Hooke designs watches and when he conducts experiment, and he incorporates them into Of Spring for this selfsame purpose. Hooke refers to the flat metal bar simply as a "Watch Spring"(De Potentia, 2; c.L., 334) and inserts a draft of a very practicable arrangement of it among the figures prefacing the tract (Fig. 2 in Figure 7). Bent into a spiral, it may serve as a mainspring, providing-in a real watch-and embodying-in Of Spring-'power aggregated' which is then released gradually. A similar spiral can be made into a spring balance, epitomizing power aggregated and released intermittently, as does the coil spring (Fig. 3 in Figure 7) in its flywheel manifestation. Contrived as they are in these figures. Hooke notes, each one of the springs can also be used as a "Philosophical Scale"-a materialization of Ut pondus sic tensio-the reciprocal formulation of Hooke's Law (De Potentia, 5; C.L., 337). Again, the purpose of encapsulating abstract hypotheses in workable machines was not to confirm them, but to relate each hypothesis to the main 'narrative' of Of Spring-springs.

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8.3. Geometrization Yet the most intriguing example of springs in their function as a topos concerns the incorporation of the O'resme/Galileo construction into the argument as the basis for the diagram supporting the proof for isochrony. On first inspection, the diagram appears to be a simple system of coordinates on which displacement is represented on the horizontal axis, and power-<m the vertical. This, however, is not exactly the way Hooke perceives it: let A in the fourth figure represent the end of a Spring not bent ... draw the line ABC. and let it represent the way in which the end of the Spring by additional powers is to be moved. draw to the end of it C at right Angles the line CaDdo and let CD represent the power sufficient to bend or move the end of the spring A to C. (De Porentia. 1819; C.L, 350-351)

Only the vertical axis is an abstract representation, of power, to be exact. The abscissa takes the form of an actual spring; there is no x-coordinate representing displacement, but a point, A, which stand for the end of an actual spring. Fig. 4 is a hybrid between an analytic-geometrical diagram and the naturalistic drafts drawings of springs that share its page. As such, the figure can perform a mediating role: linking the geometrical proofwhich relates acceleration and distance-to Hooke's theory-which relates power and displacement-through the medium of the practical manipulation of springs.

9. A CLOCKWORK THEORY OF MATTER AND POWER This, then, is Hooke's notion of power. This is the concept from which he derives the "attraction or gravitating power" he employs in the Programme (Motion of the Earth, 27-28-see Section 1.1) and the "attractive motion towards a central body" he brings to his correspondence with Newton (Correspondence II, 297-see Introduction). It is an extremely rich concept. Its effects are not limited to changes in velocity: they include the creation of cyclical. repetitive motion, of regular oscillation, of internal structure of matter. It is an "endeavour" capable of producing "circular motion" when "compounded by a direct motion by the tangent" (Birch II, 92-see Introduction). For Hooke, power generates order. Not the calm stability of a revolving celestial sphere or the static perfection of the harmony of solids, but the dynamic, self-correcting, yet precarious order of his watch.

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And like that watch, Hooke's concept of power is constructed through springs. The construction of 'power' is what one witnesses while reading Of Spring. From its title onwards, Of Spring uses springs in a whole manner of ways: naturalistic drafts, schematic diagrams, operating instructions, metaphorical connotations and suggested experiments. Contrary to expectations, these lend little empirical support for Hooke's speculations (see section 2). To the degree that empirical data are presented in Of Spring, they are only obliquely relevant to the matters discussed, and hardly provide for inductive generalizations, confirmation procedures etc. The search for these overvalued relations between the practical manipulations of springs and the theoretical manipulations concerning matter and power is the main reason why Of Spring appears confused and ambiguous to some (Hesse and Moyer) and superbly coherent, by virtue of 'tacit knowledge' injected in hindsight, to others (Patterson). Both appearances are deceptive. Springs are not the subject matter of Of Spring-power is. Springs are not intended to provide the empirical content of the tract, but the common core, by which the various elements constituting 'power' are tied together in a coherent whole. They function as a tapas, structuring Of Spring and Hooke's theory by extending a different trope to every one of those disparate elements, allowing Hooke to weave a stable network out of the technological devices, mathematical constructions and theoretical speculations he assembles. Springs metonymically represent power both as aggregated and released over time (the spiral "spring watch") and as a "strong pulse" (the leaf spring of the "cock" escapement). They replace strings as a metaphor for oscillation (the spring balance and the flywheel), and offer a synecdoche of all natural powers and of gravity in particular (the "artificial grauity" of Longitude Timekeeper). Finally, springs actualize the O'resmean construction, reifying the abscissa as displacement. Hooke embodies each of his theoretical moves in Of Spring in a particular mode, feature or operation of a spring, so that each move 'makes sense'; at will, he can bring it to life through a practice he is a master of. The moves are thereby related to each other, they are presented in a comprehensible (first to Hooke, and hopefully to his readers) order, comparable the one they might have had if presented as a narrative or a deductive argument. Hooke can securely use springs in all these different ways, since he can actually make them perform the various tasks. Thus, Of Spring, as an attempt at an encompassing theory of matter and power, is indeed a pretentious scheme, but not a reckless one; in a sense, Hooke is not attempting this grand scheme for the first time in Of Spring, but is recounting his success in doing so in the past. It is the success of his

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horological technology. Finally, there is also a slightly different way to perceive Of Spring. Just as we have termed the way in which the ~~pring serves the text 'linguistic', we can say that the text is 'mechanical'. Hooke uses the spring to structure his horological research, and he uses it in a virtually identical way to structure his theoretical investigation. This is, therefore, the real root of the tract's title; OfSpring, one might say, is constructed like a watch.

2ND INTERLUDE: REPRESENTATION 'Innection' was a theoretical term produced by Hooke in his workshop. Springs are material objects used by Hooke for theoretical purposes.. It appears that Hooke was moving between the theoretical, experimental and technological domains with the same ease with which he was moving in and out of the circles occupied by gentlemen-philosophers, university mathematicians, instrument makers, technicians and servants. It is this ease, if nothing else, which calls for a more radical critique of "the false dichotomy between acting and thinking" than Hac'king is ultimately willing to offer, It suggests that the very distinction between Representing and Intervening concedes too much to the epistemological picture in which Hooke is "a mechanic of genius, rather than a scientist" (Hall, "Robert Hooke and Horology," 175-see Introduction). It further indicates that the depiction of Hooke as "not a Newton unrecognized" (Westfall, "Introduction" to Posthumous Works, xxvii-see Introduction) imposes more than just false hierarchies "modelled on social rank" (RI, 150-151see 1" Interlude).

1. RORTY In other words, the defiance that can be identified in Hooke's Programme toward the epistemological categories dominating the historiography of science compels a direct and fundamental challenge to the "spectator theory of knowledge." Such a challenge is offered by Richard Rorty in his 1979 Philosophy and the Mirror of Nature (henceforth: PMN). In that book, which has already gained something of a classic status, Rorty takes on the whole epistemological tradition in modern Western philosophy, from Descartes to Putnam.·

1.1. The General Structure of the Argument Rorty assaults epistemology in a pincer movement. One arm of his argument is aimed at its self-conception as an a-temporal. general, universal discipline, whose claims are prior to and independent of any specific knowledge. He undermines these pretenses by exposing the very particular concepts of 'accurate knowledge' and 'man as a knowing subject', which needed to emerge before such a discipline could be conceived. Rather than

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being self-evident and universal, Rorty demonstrates, these concepts are heavily dependent on a unique historical and cultural context, and their seemingly intuitive appeal is an artifact of their entrenchment in modern philosophical discourse. The target of the main arm of his argument is the integrity of the epistemological function of these now-contextualized concepts. The ontology of the mind by itself, he maintains, is rather harmless, but with the injection of the 'ocular metaphors of knowledge' and the endemic confusion between the acquisition of knowledge and its justification, it created the craving for •structural' , founding, pre-empirical knowledge, and the belief in the attainability of such knowledge. Together, these constitute the essence of the epistemological project in its contemporary, as well as its classical guise. Together, they breed the phantasms of "truth as correspondence" and "knowledge as the accuracy of representations" (PMN, 166), which makes historians search for, and bemoan the lack of, "the scientific foundations of [Hooke's] invention" (Westfall, "Robert Hooke," 95-see I st Interlude), rather than pursuing the actual maneuvers and manipulations by which Hooke produces his material and theoretical inventions.

1.2. The Historical Narrative If Hacking finds an example for "the theory/experiment status difference" (RI, 151-see 1st Interlude) in Hooke, Rorty discovers the origins of the epistemology in which this difference is grounded within the very same vicinity. It is the seventeenth century's '''idea' idea" (PMN, 60), he argues, which created both the need to secure firm foundations for science and the conviction that this need could be satisfied. 'Ideas' are still the core of the common philosophical conception of knowledge, but epistemology would not have developed if not for the introduction of the image of an 'inner eye' which observes and examines these quasi-objects in the privacy of its enclosed terrain. A combination of two elements created a place and a call for this fiction, Rorty explains; the visual metaphors of knowing, inherited from antiquity2, and Descartes' brainchild-the mind as a self-contained substance, an inner space in which sensations, emotions and thoughts reside together as representations of the outer world (PMN, 38-45). As opposed to the Aristotelian-Thomistic hyolomorphic conceptionknowledge as the assimilation of forms-the representation picture of knowledge raised the question of accuracy; what warrants the identification of the internallrepresenter and the external/represented? How can we be

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certain that our internal 'mirror of nature' is not clouded? And an additional problem of communication emerged; how can we know whether we are all using words---outer representations of inner representations-in the same way? As can be seen in Descartes' Meditations, the image that created the problem also provided the basic tools for contemplating an answer; a correlate of the difficulty in crossing the boundaries of the inner space is the privileged access to whatever is inside. Initiated by Descartes, the epistemological project was then shaped by the great philosophers of enlightenment. Locke is responsible for the careful elaboration of the 'idea' idea. It is his 'physiology of human understanding' that enabled Hume to elaborate Descartes' general doubt into a set of clear skeptic theses. These had fairly little to do with the traditional "practical" (or "Pyrrhonian"- PMN, 46; 94 n. 8) remarks about the fallibility of all human knowledge. They were, rather, substantive, theoretical arguments concerning the quandaries of matching the visions on the inner mirror with their counterparts 'out there'-the problematics of the "veil of ideas" (PMN, 113; 140 n.14). Locke is also responsible for epistemology's genetic fallacy-the equivalent of the naturalistic fallacy in ethics-the implicit assumption that an account of the acquisition of beliefs would supply justification for holding them (PMN, 139 ff.), but it was Kant who finally turned epistemology into a profession. He achieved this by crystallizing the division of external and internal space into two independent faculties-the passive intuition and the active transcendental ego---and by equating the investigation of the constitutive, structural faculties with geometrical analysis, thereby claiming Cartesian certainty for its outcome (PMN,137-139).

1.3. The Argument Against the Mental One might question the details of Rorty's historical accoune, but the main thrust of his argument lies in his reading of twentieth century linguistic philosophy, and especially its attempts to naturalize epistemology, as "a return to Kant and the notion of transcendental argumentation" (Rorty, "Epistemological Behaviorism," 97) rather than a reaction to the Kantian tradition. Still more important to our own interests here are his arguments against that feature of the image of 'the knowing subject' that gave rise to the epistemological project, viz., the notion of knowledge as accuracy of representation in the "mirror of nature." If a philosophical revolution was lurking in Rorty's writings, one that would have enabled, and would have

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been supported by a new Hooke, it lies in these claims. I shall therefore attend to them carefully.

1.3.1.

What is the Mind?

The capacity to represent-to mirror nature-presents an epistemological difficulty only when perceived as unique to the mind and its products. Thus Rorty begins his attack on epistemology with a careful demolition of the philosophical notion of "The MentaL" Whether defined as "the phenomenal" or "the intentional" (or both, disjunctively) the mental is first and foremost not physical. But why, asks Rorty (PMN, 31), "do we think of the phenomenal [hence the intentional] as immaterial?" True, Understanding about the physiology of pain does not help us feel pain ... , but why should we expect it to be, any more than understanding aerodynamics will help us fly? (PMN,29)

Rorty's answer, after Ryle, is that the immateriality of the mental emerges only because "we insist on thinking of having a pain in ocular metaphors-as having a funny sort of particular before the eye of the mind" (PMN, 31). If not for the mind's eye, he argues, we would have had no problem to accept that sensations are simply properties of bodies, no less contextually dependent, and "no more mysterious than the relation between a functional state of a person, such as his beauty or his health, and the parts of his body" (PMN, 26). However, once we do have this have this "funny sort of particular," it turns out to have only one essential property-its "esse is percipi:" its appearance is its reality (PMN, 30). But it is hardly surprising that the mental particular has none of the properties of material particulars-above all, no "spatio-temporal habitation" (PMN, 31). This is exactly what should be expected when a quality-a universal-is converted into a particular. This philosophical conflation is almost as old as philosophy itself: in construing both the Lockean Idea and the Platonic Form we ... simply lift a single property from something (the property of being red, or painful, or good) and then treat it as if it is itself a subject of predication, and perhaps a locus of causal efficacy. (PMN,32)

The division between the mental and the physical turns out to be nothing but the old universal-particular division; the modem epistemological project is grounded in an ancient ontological confusion.

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Antipodeans and Incorrigibility

Rorty does not leave the matter at that. "The dualistic intuition" (PMN. 18) is too well entrenched to be rooted out simply by unearthing its shaky origins. So well entrenched. that even Hacking cannot .escape the juxtaposition of "the experimenter who also theorized" to "the theoretician who also experimented" (RI, 150-see 1st Interlude)-and Rorty wisely elects to approach it indirectly. Imagine, he suggests, a culture virtually like ours, but for the fact that they "did not know that they had minds" (PMN,70). Assuming that these "Antipodeans" have an advanced enough command of neurology to allow them to refer to the operations of neurons whenever we would be inclined to talk of 'mental states', how are we to explain to them what it is that they are missing? What would we lose, Rorty asks in effect, if we were to completely eschew the vocabulary of the mental'! At first glance, Rorty may appear to be committing a petitio principii. The possibility that each well-formed sentence in the language ... could easily be correlated with identifiable neural state (PMN, 71)

seems to be exactly what should be in question. This might not be a fair objection: the indispensability of the mental should rest on firmer foundations than our perhaps-accidental ignorance of the bodily substratum of our sensations. Rorty, for his part, circumvents this qualm by turning it upon itself: "do [the Antipodeans] in fact have minds?" (PMN, 74) he asks. Formulated either way, Rorty's query is but one: what is it that we ascribe to "pains, moods, images ... dreams, hallucinations, beliefs, attitudes, desires and intentions" (PMN, 17) when we designate them "mental"? Formulated either way, the answer to the query is the same: incorrigibility. The unique quality of 'the mental', that which distinguishes it from 'the physical' is "the fact that pains, like thoughts and most beliefs, are such that the subject cannot doubt that he has them, whereas doubt is possible about everything physical" (PMN, 54). Incorrigibility, or "indubitability" (PMN, 54), is the attribute we would have to deny the Antipodeans if we were to decide that they did not possess 'minds'; the authority we claim for ourselves when we insist that our sensations (as the paradigm of "mental states") are not merely states of our bodies: "the person who has the pain cannot be mistaken about how the pain feels" (PMN, 29). Incorrigibility, explains Rorty, was extremely important for Descartes. It was his "criterion for the mental" (PMN, 54; 58-9); the only feature he could find common to sensations, emotions, judgments, moods etc. But if we do

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not commit ourselves to Cartesianism in advance, why should we believe that "the epistemic privilege we have of being incorrigible about how things seem to us reflect a distinction between two realms of being?" (PMN, 29). The answer is the same as above: the only reason to conflate incorrigible knowledge with knowledge of incorrigible entities is the "initial image of the Mirror of Nature---{)f knowledge as a set of immaterial representations" (PMN,93).

1.4. The Quest for Authority, Then and Now The real measure for the success of Rorty's critical project, as far as it relates to our concern here, is the liberation of Hooke from the persona imposed on him by a historiography permeated and enlivened by the epistemology "of immaterial representations." The suggestion that we should "think of incorrigible knowledge simply as a matter of social practice---{)f the absence of a normal rejoinder in normal conversation to a certain knowledge-claim" (PMN, 96) is a step in that direction. Stripping incorrigible knowledge-claims from their status as foundations may create an epistemic space where Hooke's laboriously constructed knowledge would appear less suspicious-a space where no one will chastise Hooke for lacking "scientific foundations" (see Westfall above). Rorty, of course, does not have Hooke but traditional philosophical questions in mind-and these are indeed similar to those that engage Hacking. But Hacking only wondered whether "the whole family of issues about realism and anti-realism is Mickey-mouse, founded upon a prototype that has dogged our civilization, a picture of knowledge 'representing' reality," and suspected that "when the idea of correspondence between thought and the world is cast into its grave ... realism and anti-realism [may] quickly follow" (RI, 25-see 1st Interlude). For Rorty, the issue is c1earcuring philosophy of the 'mirror of nature' image would dissolve a whole realm of conundrums created by the notion of incorrigible representations. Not the least of these are the problems related to the skepticism about other minds. We would not even have to give up the idea that "(1) We know our minds better that anything else". This is quite an innocent notion, as long as we do not buy into "the principle of the Naturally Given and the metaphor of the Inner Eye." These have tempted philosophers to infer from (1) that "(2) We could know all about our minds even if we knew nothing else," or worse yet, to render "the whole complex of social institutions and behavioral manifestations which surround reports of ... raw feels" irrelevant, thereby

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slipping into "(3) Knowing something has a mind is a matter of knowing it as it knows itself," which is the birth bed of solipsism (PMN, 107-108),

1.4.1.

Mirrorless Mind

But the cure for solipsism is only a fringe benefit that we areto rip from eschewing "the metaphor of the Inner Eye:" other minds ,.. are not more susceptible to skepticism than anything else that is outside one's own mind. The seventeenth century gave skepticism a new lease on life because of its epistemology, not its philosophy of mind. Any theory which views knowledge as accuracy of representations, and which holds that certainty can only be rationally had about representations, will make skepticism inevitable. (PMN, l13)

This distinction between epistemology and philosophy of mind reveals a surprising and important feature of Rorty's critique. In spite of the dependence of the epistemological project on the specific picture of the mind developed in the seventeenth century-a dependence he went into some pains to establish-and in spite of his plea to abandon this project altogether, Rorty does not wish to forsake "the Mind." He indeed rejects "the image of the mind as mirroring nature" (PMN, 97), and, following Sellars, eschews "the Myth of the Given" (PMN, 95), but there are certain elements of that image, which he would very much like to retain. In particular, he is unwilling to give up the sentimental intellectual conviction that there is a private inner realm into which publicity, "scientific method," and society could not penetrate. (PMN,122-l23)

Rorty, then, is not a member of the 'death of the subject' movement. He is also no reductionist, since this would entail taking a stand in a debate he does not believe should take place at all (e] his "Epistemological Behaviorism," 100-10 I) and he may be dubbed materialistic only by default. Furthermore, even the ill-fated invention of the Mind's Eye would have remained a harmless component of the Cartesian ontological fantasy, he tells us, if not for the hope that it would discharge the epistemological urge to ground judgments. The impasse in classical epistemology has not been created by the adoption of this metaphor, but, on the contrary, by the inability to come to terms with it: Whereas Aristotle had not had to worry about an Eye of the Mind. believing knowledge to be the identity of the mind with the object known, Locke did not have this alternative available. Since for him impressions were representations, he needed a faculty which was aware of the representations, a faculty which judged the representations rather than merely had them-judged that they existed, or that they

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were reliable, or that they had such-and-such relations to other representations. But he had no room for one, for to postulate such a faculty would have introduced a ghost into the quasi-machine whose operation he hoped to describe. He kept just enough of Aristotle to retain the idea of knowledge as consisting of something object-like entering the soul, but not enough to avoid either [Humean] skeptical problems about the accuracy of representations or Kantian qoestions about the difference betwecn intuitions with and without tbe "I think." (PMN, 144)

And while the philosophical jargon has changed significantly since the enlightenment, Rorty contends, the basic set of ocular metaphors, and more important, the confusion between explanation and justification, have remained virtually the same, and with them that same epistemological hope: The common motive of Quine's 'Epistemology Naturalised', Daniel Dennett's hints at 'evolutionary epistemology', the revivification by Kripke and Fisk of the Aristotelian notions of essence and natural necessity... has been to detrancendcntali7£ epistemology while nevertheless making it do what we had always hoped it might: tell us why our criteria of successful inquiry are not just our criteria but also the right criteria, nature's criteria, the criteria that will lead us to the truth. (PMN, 299)

lA.2. Psychology In short, Rorty has few misgivings about the ontology of the mind, as long as it does not entail the pseudo-explanation of epistemic authority through the notion of "direct acquaintance" by the "Eye of the Mind" with mental entities such as sense-data and meanings. (PMN, 209)

It is this pursuit of authority, rather than the concept of the mind, which is the core of the epistemological project and of which philosophy has to rid itself if it is to be relieved of that set of misguided problems relating foundationalism to skepticism. And clearly, if there is any theme that captures Hooke's plight. both during his life and posthumously; it is his failed quest for "epistemic authority." The quest can be traced from his tense positioning of himself between "the great Philosophers of this Age [and] the makers and grinders of my Glasses" (Hooke, Micrographia, "Preface"-see Introduction) early in his life to his delicate allusion to himself as "a Literatus in the Language and Sense of Nature" (Hooke, Posthumous Works, 338-Discourse of Earthquakes) in the waning years of his career. The failure is attested for in remarks such as Westfall's "he was not a Newton unrecognized" (Introduction to Posthumous Works, xxvii), and documented in observations such as Shapin's "Hooke's masters and colleagues in the Royal Society

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reserved the right publicly to withhold trust from his experimental testimony" (Hunter and Schaffer, 283, f. n. 2). It would far exceed the scope of this interlude to attempt a full philosophical account of why an "Eye of the Mind" epistemology should endow the likes of Huygens and Newton with epistemic authority that Hooke could not hope to command. But even without such account, there is no doubt concerning the significance of deciphering the leading metaphor of the "spectator theory of knowledge" (see I sl Interlude). Portraying the "epistemological project" as an attempt to understand the matters which Descartes wanted to understand-the superiority of the new Science to Aristotle. the relations between this science and mathematics. common sense. theology and morality (PMN, 210).

Rorty traces its origins to Hooke's own contemporaries. Hacking suggested that Hooke's inferior epistemic status "is modeled on social rank" (RI, 151-see 1'1 Interlude), and Shapin forcefully demonstrated that it stemmed from the fact "that Hooke's entitlement to the standing of Christian Gentleman was problematic" (Shapin, op. cit.). Rorty offers the philosophical underpinning to these observations by "pursuing the analogy between goodness and truth." Relating the craving for foundations for the "good" to that concerning ""true" and "real" and "correct representation of reality"" (PMN, 308), Rorty captures the philosophical reflection of the cultural relations between epistemology, morality and religion emerging from Hooke's cultural environment and still shaping his place in the history of science. But note: although there is no epistemology without representations, Rorty does not wish to do away with the former by eliminating the use of the latter. In accord with his general lenience towards the ontology of the mind, he is perfectly happy to allow representations as legitimate theoretical entities in linguistics and psychology. And although he fully agrees with Quine that "there are, for the holistic reasons given in "Two Dogmas" no privileged representations" (PMN, 208), Rorty does not join ranks with him in his debate with Chomsky over hypothesizing internal mental structures for the explanation of linguistic phenomena. Like Chomsky, Rorty does not see any unique indeterminacy of the linguistic theory by the linguistic facts-anything beyond the indeterminacy that Quine himself taught us is endemic to the relations between any scientific theory and the facts within its range (PMN. 197-199). It is only the function of representations in epistemology-representations as foundations of knowledge-that Rorty would like to eradicate, and in this campaign he is only too happy to call to his side linguists and cognitive psychologists. Scientists should, in general, be encouraged to help themselves to any ontology they find useful, as "the

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only way one can do ontological damage is to block the road of inquiry" (PMN, 209). The worry about "rehabilitation of the traditional seventeenth century philosophical problematic" notwithstanding, once explanation and justification are held apart, there is no reason to object to explanation of acquisition of knowledge in terms of representations. (PMN, 210)

Moreover, scientists' use of 'representations' would in fact help the cause, as it is naturalistic, empirical and non-pretentious, and the more we accustom ourselves to 'representations' in this sense, the less prone we would be to think that there might be some other, pre-empirical way of knowing about them, knowledge that would guaranty all that is known through them. This is definitely in line with the anti-epistemological therapy Rorty suggests for philosophy: putting to final rest 'The Very Idea of Conceptual Scheme'-the notion of "an organizing scheme and something waiting to be organized" (PMN, 259). It may also be in line with a different notion of knowledge. This should be a notion which allows for the term "Conceptual" to be employed as a verb, as in the following: "the conceptualization of the problem and solution is intimately linked with a mechanical demonstration." This, we may recall, is the way which Bennett chooses to describe Hooke's Programme: carrying out quantitatively the Programme thus conceptualized is a maller-not for mathematical demonstration, as it was for Newton-but for eKperirnentaJly applying the appropriate and specially designed instruments" (Bennell, "Robert Hooke as Mechanic and Natural Philosopher," 42-see Chapter I)

2. 'KNOWLEDGE OF' AND 'KNOWLEDGE THAT'

2.1. The Need for Replacement At this point, it is true; the reader would probably feel disinclined to ask Rorty for an affirmative conception of knowledge. After all, not only has he made clear his Wittgensteinian aversion to philosophical theorizing, he has also declared that if we have psychophysiology to cover causal mechanisms, and the sociology and history of science to note the occasions on which observation sentences are invoked or dodged in constructing and dismantling theories, then epistemology has nothing to do. (PMN, 225)

But the request is not out of place. Rorty cannot discharge his therapeuticcritical promises to "free us from the notion of human knowledge as an

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assemblage of representations in a Mirror of Nature" (PMN, 126) without at least a sketch of an alternative notion of knowledge, and he is definitely aware of this requirement. The last sections of his book are dedicated to proposing hermeneutics as a candidate for the vacancy to be created by the abolition of epistemology, and as any student of the hermeneutic tradition will quickly point out, every "sociology and history of science" is necessarily epistemological. One does not have to help oneself to the rather blatant examples from Hooke's historiography to note that since 'knowledge' itself is a laudatory term, even the very decision whose story is going to be told by the historian or sociologist is judgmental and evaluative. And since decisions have to be made, failing to put forth a new conception of knowledge simply means that the old one is left in charge, and the sociology and history of science will continue to produce the 'epistemological' stories for which especially the latter is noted; stories that "tell us why our criteria of successful inquiry are not just our criteria but also the right criteria" (see above), or worst still-take these criteria for granted. Again, this point is made painfully clear by the all-too-uniform depictions of Hooke and Newton cited in the Introduction.

2.2.

Knowledge without Representations

Rorty does not consider this line of thought explicitly, and does not submit, to be sure, a 'theory of knowledge', but in the process of delineating the pit of conflating explanation and justification, carefully avoiding slipping into epistemology, he does gesture towards an 'ontology of knowledge'. He suggests, that is, a few insights into what knowledge is, without presuming to know what it should be-a few remarks concerning the categories in which knowledge may be studied, without adorning these categories with primacy or certainty: we understand knowledge when we understand the social justification of belief, and thus have no need to view it as accuracy of representation. (PMN, 170)

This, admittedly brief and preliminary, 'positive' characterization of knowledge crystallizes one aspect of Rorty's historical-critical analysis. One could interpret his conciliatory attitude towards representations in their scientific, epistemologically-neutral use as willingness to tolerate them as long as "explanation and justification are held apart" (see above), and hence to allow them, given the proper provision, to be used philosophically. This last paragraph clarifies that this is not the case. In whatever way philosophers discuss knowledge, "accuracy of representation" should not

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form part of the vocabulary. The last paragraph is still misleadingly mild in suggesting that Rorty takes representations to be simply 'not needed', when in fact he urgently advocates their complete dismissal: We must get the visual, and in particular the mirroring, metaphors out of our speech altogether ... we have to understand speech not only as not the externalizing of inner representations but not as representations at all. We have to drop the notion of correspondence for sentences as well as for thoughts. (PMN,372-373)

This is a daring and difficult move, but the risk may be worthwhile. It serves Rorty's purposes well, because without "mirroring" and "correspondence" there is no epistemology. Without the concern over whether "inner representations" manage to capture the external world (and whether an external language properly represents those internal representations), there is no need for a philosophical discipline explaining how they do. More important still, a "sociology and history of science" without representations is exactly what is required for a convincing account of the construction of 'inflection', of 'power', of the Inverse Square Law, as I shall demonstrate in the next chapter, and of Hooke's Programme in general. The elimination of "the visual, and in particular the mirroring, metaphors" from our conception of knowledge is, however. a formidable task. It is not even clear what 'knowledge without representations' might mean. Even Hacking, who boldly vows "to destroy the conception of knowledge and reality as a matter of thought and representation" (RI, 63) is careful later to attenuate his belligerence, declaring "I do not think that the idea of knowledge as representation of the world is in itself the source of that evil" (RI, 130-131), and proceeding to proclaim: Human being are represenlers. Not homo faber, I say, but homo depictor. make representations. (RI, 132. Italics original)

People

Regardless of Hacking's surprising metaphysical about-face, the difficulty is painfully obvious in Rorty's own metaphysical musings. The phrase 'social justification of belief, his draft of a concept of knowledge unstained by representations, still contains at least two components-justification and belief-which do not only naturally (that is-habitually) relate to representations. but are also closely linked to the whole set of images from which we were supposed to be freed once we removed representations "out of our speech altogether." Nothing has been gained unless 'justification' is understood in terms other than correspondence. and 'belief-in terms other than internal impressions. Aware of the predicament, Rorty attempts to circumvent the danger of

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sliding back towards "the visual ... metaphors" by avoiding the problematic 'belief' altogether and purging 'justification' of its harmful connotations: [WJe can think of knowledge as a relation to propositions. and thus of justification as a relation between the propositions in question and other propositions from which the former may be inferred. Or we may think of both knowledge and justification as privileged relations to the objects those propositions are about. If we think in the first way, we will see no need to end the potential infinite regress of propositions-broughtforward-in-defense-of-other-propositions. It would be foolish to keep conversation on the subject going once everyone. or the majority. or the wise. are satisfied. but of course we can. If we think of knowledge in the second way. we will want to get behind reasons to causes. beyond argument to compulsion from the object known. to a situation in which argument would be not just silly, but impossible. (PMN. 159)

Propositions, therefore, are to carry the load of a representation-free concept of knowledge. If we are to reject the notion of knowledge as a "privileged relation" between the eye of the mind and representations in an inner space, then belief, as a knowledge claim. should be understood as a relation to propositions, and justification--as a relation between them. Definitely, the difficulties are not yet solved. To support knowledgewithout-representations with propositions. Rorty must offer a way to understand these in terms that do not connote representations. Common philosophical parlance, with its 'facts', 'states of affairs', 'possible worlds' and 'association of ideas', does not provide him with such a terminology, ready-made.

2.3. Ties Undone 2.3.1.

Relations

What then is Rorty's conception of propositions? 'Propositions' are well entrenched in the old complex of mirroring metaphors, and it is less than clear that Rorty can employ them to discard these very metaphors. The tension inhered in the move is indicated by Rorty's use of the term 'relation' to pave his way from the discarded view to the favorable one; 'privileged relations to objects', he suggests, should be replaced by "a relation to propositions" and "a relation between the propositions in question and other propositions." But what are 'relations between propositions'? As long as we were accustomed to think in terms of representation and correspondence, these could be understood as some reflection of the relations between "the objects those propositions are about," but since "we have to drop the notion of correspondence for sentences as well as for thoughts," this route is no

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longer open to us. Rorty's expression "social justification of belief' may suggest that he understands relations between propositions as standing for relations between the people holding these propositions, but this is a problematic line of interpretation. First, as Bernstein points out, if in Rorty's mind "social practices are the sort of thing that are given, and that all we need to do is to look and see what they are," then he "himself is guilty of a version of the 'Myth of the Given'" (Bernstein, "Philosophy in the Conversation of Mankind," 83). Secondly, it is not clear how relations between people can be transformed or translated into relations between propositions. 'Standing for' is nothing but a cumbersome way of saying 'representation' and no better candidate comes to mind. Social relations should no doubt enter the picture if 'social justification' is to mean anything, but they should not be allowed to re-instate givenness or representations en route. The flaw in Rorty's ontology of knowledge is, however, more fundamental still. As he stresses time and again, the ocular images of knowledge are faulty not because of some immanent ontological deficiency, but because of those of their features which give rise to epistemology: the strict separation between the knower and the object of knowledge and the passivity of the former with respect to the latter. But the knowing subjects in Rorty's picture are far from immune to the epistemological ailment; they are as detached and passive as the most platonic of all cave dwellers. For them to know is to 'stand in relation' to propositions over which they have no power or control, as these propositions themselves stand, independently, 'in relation to each other', and it is the latter relation that determines their significance. True: Rorty's knowers are not the lonely and autarchic subjects of Locke's 'physiology'-their knowledge is "social;" they do converse. Their conversation, however, social and 'external' as it is, is suspiciously reminiscence of what used to be the internal march of ideas carrying their meaning on their sleeves: a "regress of propositions-broughtforward-in-defense-of-other-propositions." Not only does Rorty tend to take social practices as given, his image of the social is conspicuously independent, not to say utterly devoid, of human practitioners; it is not a relation between agents but between propositions. His 'social justification' is therefore 'social' only in the sense of 'not internal'; although his knower is no longer the internal mind's eye, it is still just an observer. This is not to say that the 'externalization' is completely inconsequential. Rorty's poignant criticism of epistemology leaves one with little sympathy for the Eye of the Mind, and by delegating the responsibility over knowledge and justification to propositions, 'outside' the private domain of

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the mind, he makes this particular image untenable. Yet, as he also makes clear, the mind's eye has not been the problem, only a problematic solution to the difficulties created by the separation of knower from known by the 'veil of ideas'. It is hardly clear why Locke required a "faculty which was aware of the representations, a faculty which judged the representations rather than merely had them" (PMN, l44-see above), whereas knowledge as 'relation to propositions' is exempt from the need for an observing-andadjudicating faculty. In fact, the opposite seems much more likely, as propositions, unlike 'simple idcas', also demand interpretation. Seventeenth-century style skeptical questions about the certainty of knowledge, should anyone still insists on raising them, 'are therefore not blocked by Rorty's move from objects to propositions, only a particular style of answering them is. Rorty's efforts to restrain the very desire for this type of skepticism are misdirected. Characterized as 'she who relates to propositions', the new, social human knower is just not different enough from the old human mind, characterized as 'that which perceives universals' (PMN, 31-32), even if what has been presumed to take place in the privacy of an inner realm is now understood as a public affair. If what we are seeking is a new understanding of Hooke, with his "pleasant and beneficial ... Mechanical contrivances" (c. L., 155), then, definitely, propositions are not likely to be our saviors. On the other hand, the important antiepistemological point Rorty is making in the last paragraph quoted, namely that one should not hope to get "beyond argument to compulsion," carries considerable force, although it gains little from setting propositions against objects.

2.3.2.

Propositions vs. Objects

It is, in fact, the very dichotomy between 'propositions' and 'objects', which, like Hacking's sharp distinction between 'tools for thinking' and 'tools for doing', reveals Rorty's inability to shake off the old picture. And Rortts distinction, just like Hacking's, is central to his argument. It constitutes his defense against the confusion between explanation and justification of belief-the original sin, from which epistemology was begotten. "Why," he asks, should he have thought that a causal account of how one comes to have a belief should be an indication ofthe justification one has for that belief! (PMN, 141)

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Rorty's answer to his own question provides the reason for insisting on propositions. It points its finger, once again, at seventeenth century philosophy: Locke did not think of "knowledge that" as the primary form of knowledge. He thought, as had Aristotle, of "knowledge of' as prior to "knowledge that," and thus of knowledge as a relation between persons and objects rather than persons and propositions. (pMN, 142)

If our paradigm of knowledge is acquaintance, Rorty maintains, then we would be inclined to think of the circumstances of its acquisition as the justification for holding it, as when we "justify a belief by saying, for example, 'I have good eyes'," (PMN, 141). On the other hand, We find it natural to think of "what S knows" as the collection of propositions completing true statements by S which begin "I know thaL .." When we realize that the blank may be filled by such various material as "this is red." "e = mc 2," "my Redeemer liveth," and "I shall marry Jane," we are rightly skeptical of the notion of "the nature, origin, and limits of human knOWledge," and of a "department of thought" devoted to that topic. (PMN, 142)

It is therefore essential for Rorty that there are two distinct types of knowledge-"knowledge of' people and objects, and "knowledge that"knowledge as "justified true belief' (PMN, 141) in propositions. Thinking of the former as the primary type, we are prone to confuse acquisition with justification. Thinking in terms of propositions, we risk, as we saw, meddling with the ocular metaphors, although we should be relatively safe from treading into the genetic fallacy. Rorty chooses the latter. Is Rorty's choice wise? This, of course, depends on the value one assigns to the respective sides of the trade-off. Rorty's goal is "to drop the notion of the philosopher as knowing something about knowing that nobody else knows" (PMN, 392), and for that purpose, he seems to assume, it is crucial to avoid Locke's mistake. This measure is not a foolproof, however. As he himself stressed (see Section 1.4.1 above), the linguistic turn, with its terminology of propositions, has done little to curb either the urge to unearth the foundations of knowledge, or the Lockean hope that this might be achieved 'naturalistically'. Our goal, in any case, is more modest than Rorty's, namely-to sketch a suitable framework for the interpretation of Hooke's Programme. For that purpose, the very distinction between "knowledge of' and "knowledge that" is the problem-it is, after all, the selfsame distinction impersonated by the unflattering comparisons of Hooke and Newton. The next and final chapter considers Hooke's Programme in its concluding phases, as it is passed from Hooke's hands to Newton's, where

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it receives its final theoretical-'propositional'-and mathematical shape. The crafty manipulations Newton employs in the process and the close dependence of the intellectual exchange between the two on their complex personal acquaintance demonstrate that Hooke is not the only one whose knowledge producing practices defy Rorty's distinction. They raise grave doubts concerning the assumption that propositional knowledge is radically different from knowledge of objects and people.

3.

HACKING AND RORTY

3.1

Acquaintance

Doubts concerning the notion of knowledge as "sentences ... connected to other sentences rather than with the world" (PMN, 372) also appear to be the cause of Hacking's somewhat surprising hostility towards "Rorty's version of pragmatism." True, when he titles the hard-won conclusions of his fellow Dewey disciple "yet another language-based philosophy," it is not exactly Rorty's allusion to propositions that he sneers at, but his notion of "conversation:" Dewey rightly despised the spectator theory of knowledge. What might he have thought of science as conversation? In my opinion, the right track in Dewey is the attempt to destroy the cunoeption of knowledge and reality as a matter of thought and representation. He should have turned the minds of philosophers to experimental science, but instead his new followers praise talk. (RI, 63)

But Hacking's own analysis constitutes a powerful call for a return to the exact concept of knowledge as acquaintance that Rorty shuns. Consider one of his favorite examples: Caroline Herschel (sister of William) discovered more comets than any other person in History ... several things helped her do this. She was indefatigable ... She also had a clever astronomer for a brother. She used a device ... that enabled her, every night, to scan the entire sky ... When she did find something curious 'with the naked eye' , she had good telescopes to look more closely. But most important of all, she could recognize a comet at once. (RI. 180)

Hacking is keen to point out the independence of Herschel's discoveries of any theory-the abstract hypotheses concerning comets and their. nature appear to have had a rather marginal import in her work. But it is not so much theory, in the sense of a system of hypotheses, ,whose absence is conspicuous here, as the fact that, pace Rorty, there were fairly little propositions involved in Herschel's work, and very little 'justification', in

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the sense of "propositions-brought-forward-in-defense-of-otherpropositions" (PMN, 159-see section 2.2 above). Instead, it was Herschel's "knowledge of' her instruments, her brother and the behavior of comets that enabled her to produce that extensive body of new knowledge. There is no other way to capture Herschel's work but as an acquaintance with objects-<:omets-achieved by skillfully operating other, already wellacquainted objects-instruments. Moreover, the unique, personal aspect implied by the notion of 'acquaintance' powerfully captures the 'relationship' between Herschel and her objects that Hacking highlights. Without her, he stresses, these observations would simply have not existed, and even after she has produced them, no-one in Caroline Herschel's speech community would in general agree or disagree with her about a newly spotted comet, on the basis of one night observation. Only she ... had the requisite skill. (RI,181)

This, Hacking is quick to acknowledge, does not rule out the need to "understand the social justification" (PMN, 170-see section 2.2 above) of Herschel's claims. Indeed, Herschel's authority is a perfect example of what Rorty refers to as "incorrigible knowledge [which is] a matter of social practice ... the absence of a nonnal rejoinder in nonnal conversation to a certain knowledge-claim" (PMN, 96-see section 1.4 above). But the fact, that it took that particular person with her particular skills and instruments to create those observations using those instruments\ provides a strong argument for why this justification could not be understood as "a relation between the propositions in question and other propositions from which the fonner may be inferred" (PMN, 159-see section 2.2 above). Without Herschel's active and continuous 'intervention', Hacking indicates, no 'proposition' would have stood in any 'relation' to any other proposition or person. Rorty is wary of a "doctrine of "knowledge by acquaintance," which will give us a foundation" (Rorty, "Epistemological Behaviorism," 102), because he has in view a clear route leading from perceiving knowledge as relation to objects, to perceiving it as relation to "some sorts of objects," and from there to the perception that knowledge means "lwving" these objects. This is how one gets to think "of "having an impression" as in itself a knowing rather than a causal antecedent of knowing," and the genetic fallacy is born (PMN, 142). The lesson learned from Hacking's example is that no one is compelled to progress along this TOute. There is especially no compulsion to allow the ocular metaphors sneak back in-acquaintance can signify many other things apart from 'what is initiated by visual encounter', such as the ability to recognize upon encounter, to put into use, to manipulate.

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161

The Conflict

Thus Hacking and Rorty suggest seemingly opposing ways to dismiss the "spectator theory of knowledge." Whereas Rorty believes that we should understand ''''what S knows" as [a] collection of propositions," Hacking insists that we should tum "to experimental science" and away from "talk;" where Rorty stresses "knowledge of," Hacking clings to "knowledge that." The conflict is surprising, to be sure; not so much because of the very fact of the opposition, but because of the line along which it is drawn. The sharp distinction between propositional knowledge and knowledge of objects and people is none other than the division between the scientist and the mechanic, i.e., between Newton and Hooke. By setting their camps on their respective sides of this line, Hacking and Rorty reinforce the alleged boundary. This is disappointing. Hooke's Programme is an outcome of an easy and willful transgression of this boundary---on Hooke's part, to be sure, but no less so on Newton's, as the next chapter will demonstrate. A philosophically infonned interpretation of the Programme cannot suffice, therefore, with paying closer attention to "the social justification of belief' (PMN, l7O-see above), or showing better respect for "the experimenter who also theorized" (RI, l50-151-see 1" Interlude). It requires a philosophical framework in which the demarcation between the two types of knowledge does not play a larger role than it played for Hooke-a framework which now seems even less close at hand. Beyond the irony and criticism, the distinction is apparently founded on a powerful intuition-the difference between knowledge as a representation of an external reality, independent of the representer, and knowledge as a construction of new artifacts from a reality in which the knower is not only fully involved, but, ipso facto, capable of changing. Hacking and Rorty's final inability to truly abandon this intuition is the best testimony for its power, but still, they are the ones to provide the best arguments why it should be abandoned. Hacking, by demonstrating how much 'doing' is involved in getting acquainted with the allegedly independent reality; Rorty, by demonstrating the incoherence of the concept of a passive 'internal representer'. More important yet, Hooke's himself defies this distinction by using his artifacts to represent and his representations-as mere artifacts; by employing his springs, pendulums and "Sphrerical Crystalline Viol" in his theorizing, and treating his "inflection," "power" and "tensio" as malleable artifacts. I think that despite Hacking's unfortunate phrase about "tools, instruments not for thinking but for doing" (RI, 262-see lSI Interlude), and

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despite Rorty's genuine commitment to the "Wittgensteinian notion of language as tool rather than a mirror" (PMN, 9), it is still Hacking who offers the most promising overture towards a merger between the two conceptions of knowledge, albeit in the form of a playful 'philosophical anthropology'. I will therefore dedicate the last part of this interlude to a short exploration of this segment of Hacking's Representing and Intervening.

3.3. Practices of Representation (Representation and Likeness) 3.3.1.

Homo Depictor

It is in this lighthearted discussion that Hacking finally takes the bull by its horns. Instead of devising ways to bypass representations, he coins the surprising term "homo depictor" (RI, 132-see section 2.2 above) to proclaim that "Human beings are representers" (ibid.). This announcement seems to repudiate all Hacking and Rorty's hard-earned insights; especially since Hacking endows 'representing' with the very visuaUmirroring connotations they were wrestling against: People make likenesses. They paint pictures, imitate the clucking of hens, mould clay, carve statues, and hammer brass. (RI, 132)

Prima facie, representations and likenesses cannot and should not survive the criticism leveled against "the idea of correspondence between thought and the world." True, Hacking insists that Locke's notion of 'impression', which developed into Kant's 'Vorstellung' is "exactly what I do not mean. Everything I call representation is public" (ibid.), but this is not enough to remove the suspicion that he is falling back into the "spectator theory of knowledge." The presumption that representations are private, that they reside within some inner mental space-to which the individual, and only the individual, has immediate and reliable access-is an important feature of that conception of knowledge. However, as we have learned from Rorty, privacy is only one feature of the 'spectator' image. The visual metaphors, which Hacking skillfully undermines through his analysis of microscopy, and which he reinstates by heralding representations are not eliminated by transferring those representations from the private to the public realm.

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Making Likeness

Yet Hacking's likenesses do not re-establish the spectator-spectacle relations in the public arena. They are not the foundations of knowledge, they are not guarantors of accuracy and they are not mirror images created within the passive knower by independent objects outside it. Hacking does not expect representations to be an unexplained explanation, to stand in relation to one another or to the world independently of human intervention, or to be simple. He evades the trap of the "spectator theory of knowledge," not by making his likenesses public (though that, of course, does no harm), but by insisting that they are produced: "people make likenesses" (ibid.). What, then, makes an artifact a "likeness?" What is "a human-made representation," according to Hacking, 'like'? This, he appears to suggest, is a misconceived question. "Likeness stands alone," he explains, " It is not a relation" (RI, 139). It is not likeness that adjudicates human attempts to represent, but the other way around. Things "must be like or unlike in this or that respect," but "a particular type of thing, namely a human-made representation, can unqualifiedly be like what it is intended to represent" (RI, 137). It is a Kantian-Copemican reversal that makes Hacking's reflections qualify as 'anthropological' (in the Kantian sense of the term): Should the ethnographer tell me of a race that makes no image (not because that is taboo but because no one has ever thought of representing anything) then I would have to say that those are not people, not homo depiclor. (RI,134)

The making of representations is so universally and exclusively human that "[w]e know likeness and representation even when we cannot answer, likeness to what?" (RI, 138). In recognizing some human artifact as a representation, Hacking suggests, we do not recognize a common 'objective world' that we share with other representation-makers-"very foreign and very ancient people," for example. Nor do we help ourselves to a shared phenomenological infrastructure, nor even to common practices or common doings, since even if "I do not know what [the likenesses] are for, I do know that [they] are likenesses" (ibid.).

3.3.3. Tools for Thinking and for Doing Hacking's flirtation with homo depictor is thus unspoiled by his unhappy engagement with realism. He does not expect likenesses to be the way by which the world warrants or secures our terms, propositions or theories. Always a product of human labor, they are neither objective nor subjective.

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Likeness is simply not predicated on the dichotomy between inside and out, between knowledge and the world knowledge is 'about'. Hacking does not assign representations the task of impartial mediation between the human mind and the world because, as noted above, he does not believe such thing as primitive representation exists. 'Simple sentences'-Tractatus-stylc Satze-are not representations at all, he maintains. Theories, complexes of many sentences and other linguistic elements, represent; 'the cat is on the mat' does not. This is Hacking's way to reconcile between "the creation of phenomena" and the seemingly contradictory "homo depictor." Representations are essential, but not fundamental. They are not the building blocks of human knowledge-there are no such blocks-but the quintessential buildings. Hacking's notion of complex, purposefully produced representation is a promising step towards bridging the gap between 'knowledge of and 'knowledge that'. The bridge may be constructed on the humdrum but easy-to-forget fact that 'theory' covers lots of productions (RI, 212),

which the anthropology of representations endows with new import. If representation is the most prominent human practice and theories are its paradigmatic products, then there really is no philosophically interesting difference between 'electrons' as 'tools for thinking' and electrons as 'tools for doing' (see l't Interlude). "When I speak of representations, I first of all mean physical objects: figurines, statues, pictures, engravings," says Hacking (RI, 133), and he may have been referring directly to Hooke, whose objects-micrometers and barometers, lamps and microscopes-are particular types of representations, and his theoretical solutions and speculative terminology are artifacts, produced and used like all his other artifacts. Those are all "physical objects;" mechanical devices, phenomena, and stories intended "to represent the world, to say how it is like" (RI, 134). To the last category belongs Hooke's Programme.

CHAPTER 3: NEWTON'S SYNTHESIS 1. INTRODUCTION 1.1. The Happy Ending The end of the story, almost invariably told with Newton as the lone hero!, is very well known. In the summer of 1684, Edmund Halley paid a visit to Newton in Cambridge, and questioned him about his views concerning the latest speculation in London cafes, namely, that the planetary trajectories could be calculated based on the assumption that the sun attracts the planets by a force which diminishes by the square of the distance between the planet and the sun. To Halley's surprise and delight, Newton replied that he had already done just that. Moreover, his calculations showed that if the "force of attraction" between the sun and each planet is taken to be inversely proportional to the square of the distance between them, the resulting planetary orbit is elliptical, just as Kepler had suggested some seventy years earlier. Unable to reproduce the calculations on the spot, Newton promised Halley he would send them to him. He kept his promise several months later, by sending Halley a short tract- De Motu Corporum in Gyrumwhich while not exactly answering Halley's question, offered much more in exchange. It was, it turned out, an initial draft of the Philosophiae Naturalis Principia Mathematica, which Newton completed in less than two years and the Royal Society published in 1687.

1.2. The Question There is hardly any doubt that the correspondence with Hooke in 167980 dramatically changed the way that Newton pursued Galileo's project; i.e. that one cannot understand Newton's work in De Motu unless what he learned in this communication is taken into account. With regard to the important question for our purpose here, namely, what precisely did he learn, there is much less of a consensus. Several answers suggest themselves. The first, stemming directly from the original priority dispute between Newton and Hooke, is that Hooke taught Newton the inverse square ratio between gravity and distance, and that Newton slighted Hooke by not attributing to him the discovery of this

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law. This dispute was picked up by historians, and for more than a century (since Rouse Ball, and especially since Lohne's rebuttal in "Hooke versus Newton"), the investigation of Hooke's contribution to celestial mechanics has revolved almost exclusively around the question of his eligibility to the title of the discoverer of the Inverse Square Law (henceforth: ISL). More recently2, it has been forcefully argued that the change that occurred in Newton's work, which enabled him to compose De Motu, and which should most probably be attributed to his encounter with Hooke, is the move from concentration on centrifugal tendencies to a consideration of centripetal forces. In a very preliminary way, which will be qualified later, I shall say that it has been shown that while Newton's early gestures towards understanding planetary motion consisted of attempts to find the forces needed to keep bodies in circular orbits by calculating the force by which they strive to break away, in the years following his exchange with Hooke, his concentration shifted to calculating the relations between hypothetical centripetal forces and the curves into which they would force the planets. The most general possible answer emanates from the way in which Newton's achievement has come to be perceived following the seminal works by Wilson ("From Kepler's Laws, So-called, to Universal Gravitation") and Westfall (Force in Newton's Physics), i.e., as being first and foremost the universalization of gravity. My presentation of it here, as the culmination of 'Galileo's Project,' is firmly within this tradition. And since Newton's success came on the heels of his encounter with Hooke, both Westfall and Wilson have asked whether in fact Newton acquired the concept of universal gravity from Hooke, and if indeed Hooke ever possessed such a concepe

1.3. Difficulties None of these answers is generally accepted as conclusive. Rather, each serves as a focus of debate concerning Hooke's role in the tum that took place in Newton's work in the 1680s. For the most part, the debates revolve around priority, and are characterized by questions such as "What elements in [Newton's] new Synthesis did he borrow from his contemporaries and what were the products of his own insight" (Whiteside, "Newton's Early Thoughts," 129), or did Hooke or "did [Hooke] not hold a conception of universal gravitation" (Westfall, "Hooke and the Law of Universal Gravitation," 245). While these discussions highlight various important aspects of the Hooke-Newton encounter, this chapter does not come to

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summarize them. Instead, it will attempt to determine what part of the achievements credited to Newton was developed within and in response to his correspondence with Hooke. Epistemologically, this is a completely different challenge. Attempting to determine whether it was Newton who learned the inverse square law (or the notion of centripetal force, or universal gravity) from Hooke, or vice versa, leads to the question of which protagonist was first to arrive at any of these pieces of knowledge. The following discussion, on the other hand, will concern the question of the skills and theoretical tools employed by Newton and Hooke in forging and fusing these pieces. This inquiry may be conducted without accepting two fundamental presuppositions that underlie the priority debate. Although these assumptions are mentioned briefly in the previous chapters, they are nevertheless significant enough to consider from yet another perspective. First, the question 'who taught whom' or 'who got there first' assumes that the knowledge in question-ISL or any of the other candidates-has an existence prior to, and independent of, its discovery by the one who taught it to the other. In asking about the skills and tools used to bring about this knowledge, on the other hand, one stipulates that the outcome of the correspondence might have all been new; not only new for one of the interlocutors, but novel a product of the exchange itself. To accept a similar claim about Newton's mature work on celestial mechanics in general is to admit that, as and indisputable as any of it may seem with hindsight, it was all completely contingent upon the historical vicissitudes of its production. Secondly and connected to this point, the question of priority assumes that either Newton or Hooke deserves the credit for prior discovery (of the inverse square law, or the notion of centripetal law, or universal gravity). This entails that the alleged discovery is fundamentally an act of an individual. In contrast,. in attempting to determine Hooke's contribution toward composing the texts leading to the Principia, we allow the possibility that both Hooke and Newton deserve the credit together. We thus assign primacy to the process of producing knowledge over the end product, and imply that this may be a cooperative process-taking place within the correspondence, between the two men.

1.4. Different Approach This epistemological tum has some immediate historiographic ramifications, the most obvious being that it makes it all the more desirable

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to avoid "read[ing] the future into the past, with a sense of elation" (Sabra, 224). The priority question calls for careful dating and authorizing of previous appearances, in different contexts, of ISL, centripetal attraction and universal gravitation. But this antiquarian pursuit is of little value if these elements of Newton's work in the 1680s have no standing of their own, if their meaning and their significance are completely dependent on the historical contingencies of their production and employment. If, as this chapter will suggest, the way Newton uses ISL, centripetal attraction and universal gravitation in De Motu and the Principia have been established through, and in response to the encounter with Hooke, then the interpretation of these texts gains little from the knowledge of when, before the correspondence, they were first declared, and by whom. My strategy will therefore be somewhat different. I will attempt to determine the constitution of the new knowledge transmitted and created in the correspondence between Hooke and Newton by comparing Newton's work immediately following the exchange with his work on similar issues before it. Looking back at Hooke's knowledge, I will not attempt to adjudicate his priority claims, but rather to account for his contribution to this cooperative effort. Since Hooke is the main hero of this work, the preliminary comparison will have to be restricted to a relatively small sample of Newton's relevant work. To investigate the immediate outcome of Newton's correspondence with Hooke, I will explore the De Motu of 1684 and a manuscript entitled by Herivel "The Kepler-Motion Paper (The Newton Copy)" (henceforth: KMP), whose dating is more problematic. If Newton had written anything directly relevant to the question of planetary motion in"the 1670s, none of it has survived, so the outcome of the exchange with Hooke will have to be traced by comparing Newton's work of the 1680s to two of his manuscripts from the late 1660s which Herivel entitles "On Circular Motion" (Herivel, 192-198, henceforth OeM) and "The Laws of Motion" (Herivel, 208-218, henceforth LaM).

2.

NEWTON BEFORE AND AFTER

2.1. The Inverse Square Law The oldest and most heated of the debates mentioned above is the one concerning the credit Newton owed Hooke for first proclaiming the inverse square ratio between gravity and distance (ISL). It is debated today in virtually the same terms used by the two practitioners, yet, like many other

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hindsight priority disputes and specifically the ones mentioned in previous chapters, it is seriously misguided. The question whether Hooke deserved Newton's recognition for the discovery is misleading-not because the ISL appears in Newton's writing previous to the correspondence with Hooke (as indeed it does)-but because ISL was never 'discovered'. It had been suggested, speculated and hypothesized by different people, for different reasons, in different contexts, to fulfill different goals. Hooke had applied the ISL already in 1665-much earlier than is usually noted. He certainly did not foresee the priority dispute looming, for he did not even bother to explicitly formulate it. The allusion to ISL comes in the Micrographia, in reference to the "Toricellian" experiments discussed in the previous chapters. Using the outcomes to calculate the size of the atmosphere, he explains why, in calculating atmospheric pressure, he resorts to counterfactual assumption that the column of air, weighing on his mercury tube, is "a Cylinder indefinitely extended upwards:" [I say Cylinder. not a piece of a cone. because, as I may elsewhere shew in the Explication of Gravity. that triplicate proportion of the shels of a Sphere. to their respective diameters. I suppose to be removed by the decrease of the power of Gravity] (Micrographia. 221. Square parenthesis in the original)

Hooke's succinct remark is an abridgment of the following argument: the atmosphere is a sphere of air enveloping the earth. Each point on earth can be taken as the apex of a cone of air, "indefinitely extended upwards."4 The volume of a sphere (or a cone) is in "triplicate [cubic] proportion" to its "respective diameters," and the same proportion holds true between the volume of the cone and its height. If the air's density is equal at all heights, then the volume of the air is proportional to the cube of the height of the atmosphere. The volume of a cylinder, on the other hand, varies only in simple ratio to its height. However, if gravity decreases in proportion to the square of distance, then "that triplicate proportion ... [is] removed," namely, the weight of the air varies with the height of the atmosphere. The atmospheric pressure can therefore be calculated, for convenience sake, as if it were a cylinder of air, rather than a cone supported by each point, and as if gravity were constant, rather than decreasing according to the ISL. Hooke was so cavalier with this ingenious argument and with the use of ISL for the simple reason that neither was original. Early suggestions that the sun's influence on the planets diminishes by the square of the distance are to be found in medieval optics, and were supported by arguments of the same structure as Hooke's: light is distributed in concentric spheres around its source (the sun, in the case of the heavens). Since there is a set 'quantity' of light, the larger the sphere, the smaller the 'density' of light

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will be falling on each point in it. And since the surface of a sphere is proportional to the square of its radius, the amount of light received hy any given area is diminished proportionately to the square of its distance from the light source. Or in other words: the amount of light falling on the planets is inversely proportional to the square of their distance from the sun. Kepler, who developed his notion of "virtus motrix" in a close and explicit analogy to light (and magnetic force), was fully aware of this idea, which he put forward as a part of an argument pertaining to the limits of the analogy: It is demonstrated in Chapter 32 [of his ASlronomia Noval that the intension and remission of the motion of the planets is in a simple proportion to their distance [from the sun]. But the virtue emanating from the sun seems to increase and decrease in double or triple proportion to their distance or [to the virtue's] lines of flow. It follows thaI the intension and remission of the motion of the planels will nol be lcaused] by the attenuation of the virtue emanating from the sun. (Astronomia Nova, Part Ill, Chapter 36)5

Kepler's fascination with the inverse proportion between each planet's velocity and its distance from the sun (his commitment to developing a unifying 'celestial physics' is reflected in his insistence that the proportion holds for different planets, or different orbits, as well as for different locations along the orbit), was picked by Ismael Boulliau in his 1645 Astronomia .Philolaica. Boulliau, however, was not affected by the difficulty expressed in the paragraph cited above. He prefers the analogy between the sun's 'motive virtue' and light to both the magnet analogy and Kepler's reservations, and adopts an inverse square ratio between distance and "virtue,,6. Both Newton and Hooke were familiar with BoulJiau's version of the medieval quasi-quantitative argument. In his Lectures of Light, delivered between 1680 and 1681, Hooke submits an unabridged version of the Micrographia argument, and adds: This is the proportion that the ingenious Kepler allows to the Decrease of Light, supposing it to be only in Duplicate Proportion of the Distance reciprocal; and according to thi s, he found the Proportion of the Power of the Sun in moving the Planetary Bodies at several Distances (Posthumous Works, 114).

Similarly, in a manuscript inscribed "Sept. 1, 1685" Hooke deduces the inverse square law from the notion "that gravity is a continuall impulse expanded from Ihe center of the earth indefmitely by a conicall Expansion" (Trinity College MS 0.11.a.1 16c). Newton, for his part, in that angry letter of June 20, 1686 to Halley (Correspondence n, 438-see Chapter 1, Section 2.2.3), insinuates that "this general proposition in Bullialdus" was Hooke's only recourse to "this proportion here." Clearly, then, the very notion of an inverse square ratio between a

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planet's distance from the sun, and sun's influence on the planet (whatever that influence might be) was not a new idea. This has led Johanes Lohne to proclaim: "Did Newton get the idea of the inverse square law... from Hooke? Very unlikely! Not that it matters much. Kepler had already discussed this law... and rejected it ... Boulliau criticized Kepler for rejecting it. And no doubt also others had noted how light decreases, and from that analogy had thought of an inverse square law of attraction also. So why quarrel about priority?" (Lohne, "Hooke versus Newton," 19). Lohne would have constituted an invaluable ally for my cause here, if he could be understood as claiming that, in general, the question of 'who got there first', while sometimes extremely important for the credit-seeking practitioner, may be rather misleading for the historian. Disappointingly, however, Lohne immediately re-instates the priority question on a different level: "the essential thing was to use this law in a consistent theory of planetary motions. Until 1680 only Hooke had such a theory" (ibid.). Yet there are much more fundamental reasons why the "quarrel about priority" is misleading, which are just as devastating to the attempt to determine who was the frrst to have "a consistent theory of planetary motions." As the following will demonstrate, the very meaning of ISL cannot be treated as self-evident. Not only was the significance and applicability of the ISL altered by different people at different times to conform with the practices in which they embedded it, but, more important still, it was produced and used by Newton himself several times, in different ways and for different purposes.

2.1.1.

On Circular Motion

Newton first introduced ISL as a derivation from Kepler's harmonic ('third') law already in the OeM paper from the late 1660s. Helping himself to a simple geometric construction Figure 19 and a number of bold mathematical moves, he proved that for a body revolving in a uniform motion, the 'conatus from the center' (already labeled by Huygens 'vis centrifuga') is proportional to the radius of the circle divided by the square of its period of revolution. I will address the diagram and proofs in some detail in the next section, but here I would like to concentrate on Newton's uses of the proportion fcc Rlr, the first use being to calculate the centrifugal force (and the corresponding gravity) on the earth's equator and along the moon's orbit (the famous "moon test"-see f. n. 29). After accomplishing this Newton applies his findings to regular and conic pendulum. But before

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doing this, he adds this rather marginal remark at the end of his corollary: Finally since in the primary pla!,ets the cubes of their distances from the sun are as the squares of the numbers of revolutions in a given time: the endeavours of receding from the sun will be reciprocally as the squares of the distances from the sun.' (Herivel. 197: OeM)

This is not a difficult derivation: iff oe RIY- and Y- oc RJ , then foe RIR1 or foe IIR z, namely: the "conatus a sole recedendi" is inversely proportional to the square of the distance from the sun.

Pigure 19: Centrifugal force in "On Circular Motion"

Unless mesmerized by the very proclamation of an inverse square ratio between distance and force, one cannot fail to notice the provisional, conditioned status of ISL in OeM; the ratio, as far as Newton is concerned in this tract, to is only as true as Kepler's third law. Just like Boulliau's adoption of ISL with regards to Kepler's "virtue," Newton's application of the ratio to the planets' "endeavours of receding from the sun" is a remark about the consequences of Kepler's novel astronomical endeavors. It is of significance only if one is willing to adopt this difficult combination of Copernican convictions, Tychonian observations, approximation techniques, and theoretical speculations. But as Wilson has demonstrated more than once8, Newton's faith in any of these was never unqualified. Thus, this corollary is not presented as a major-and certainly not the majorachievement of the paper. It is neither the first nor the last theorem, it is limited to the primary planets (Kepler's Astronomia Nova concentrated on Mars), the derivation, simple as it is, is only hinted at, and the effort at precision is minimal. In particular, Newton makes no effort to accommodate this corollary with

NEWTON'S SYNTHESIS

173

the two other Kepler laws, He does not explain how one could move from uniform circular motion to non-uniform elliptical motion, neither does he attempt to clarify what he means by the "distantia" of the planets, if their orbits are indeed, as Hooke will later paraphrase Kepler, "not circular nor concentricall." More significant still: this presentation of ISL is the law's final appearance. Newton has no further use for it, and it serves no obvious theoretical purpose. It has neither an explanatory value nor a theoretical explication-Newton does not even bother to clarify whether it is the centrifugal tendency that interests him, or the countering force holding the planets to their orbits. This marginal status of ISL will change completely in Newton's later writing.

2.1.2. De Motu The first introduction of ISL in De Motu, over fifteen years later, is rather similar to its presentation in OCM. Newton begins with definitions of "vis centripeta," "vis insita" and "resistentia," then adds hypotheses for resistance, uniform motion under 'vis insita', the parallelogram of forces and a version of Galileo's theorem whereby "the space described by a body at the beginning of its motion under the action of centripetal force is proportional to the square of time,,9. He proves, (Theorema l) the area law (which we will return to in Section 2.3.3). Next, as Theorema II, and without making use of the area law, Newton presents a geometrical construction (Figure 20) resembling that in OCM, by which he proves that The centripetal forces of bodies revolving unifonnly in the circumferences of circles are as the squares of the arcs described in the same time divided by the radii of the circles. 1O (Herivel, 278: De Molu, Version !)

Figure 20: Centripetal force in De Motu

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There are a number of telling differences between the OCM formulation and proof of the theorem, and this one, differences to which I will return in the next section. However, one thing has clearly not changed, viz., the noncommittal attitude towards claims and arguments based on astronomical observation: once again Newton presents this theorem, which concerns uniform circular concentric motion, as having relevance to the elliptical nonuniform motion that Kepler assigns to the planets. Here, however, Newton puts an end to the apparent similarity between De Motu and OCM by adding five corollaries. These corollaries are all simple derivations from f = AD 2IR, where AD is an infinitesimal arc. Since the motion is uniform, AD is proportional to the body's velocity. Thus, combining AD oc V withf= AD 2IR, it follows that: I. f= y21R. Since the velocity of rotation is inversely proportional to the period of revolution, i.e., Yoc liT, this is equivalent to: 2. f= Rrf-. This provides basis enough for a force law-a ratio between force and distance-for any given ratio between the radius of the orbit and the period of revolution, and Newton indeed offers three different force laws: 3. if T oc R, then f is distance-independent, 4. if T oc R2, thenfoc lIR, and 5. ifT oc R3, thenfocllK. Of course, as the scholium has it, "the case of the fifth corollary holds for the celestial bodies ... astronomers are now agreed"l1 (De Gandt, 29). But the new and exciting skill Newton demonstrates is not that of accounting for the particular empirical generalizations upon which "astronomers are now [jam] agreed," but rather his ability to construct a force law for any set of time-distance proportions; what astronomers agree upon is here no more than a reference point. This baroque presentation of a variety of force laws sheds light on the more rigorous introduction of ISL later in De Motu. Aided by the area law, for which he provides a most general proof-for any law of force and any center of force-Newton establishes (Theorema 1If), an entirely general geometrical expression of centripetal force-for any center of force and any curve about it. He proudly presents the' exceptional power of these tools in a corollary: if any particular figure is given and a point in it to which the centripetal force is directed, it can be found what law of centripetal force makes the body revolve in the perimeter of that figure. 12 (Herivel, 280: De Motu, Version I)

NEWTON'S SYNTHESIS

175

Employing these two powerful tools-the area law and the geometrical expression for force-Newton embarks upon a series of 'Problemata', based on the conditions set in the corollary. Much more than an attempt at a geometrical account of what "astronomers are now agreed," this is a tour-deforce of geometrical control over the relations between force and orbital motion. As if to highlight this, Newton commences with a clearly fictive Prohlem: to find a force law for a circular orbit with a center on the perimeter, which is found to be inversely proportional to the fifth power of the distance (Herivel, 261: De Motu, Version I). This serves as pretext to a scholium on paths that are not, strictly speaking, orbits, such as a spiral, for which Newton claims (without offering a proof) that the force would be inversely proportional to the third power of the distance. The second Problem (262) deals with an elliptical orbit with the force tending towards the center, which turns out to be inversely proportional to the distance. Only in the 3rd Problem, after the unparalleled scope and power of the new approach-'give me an orbit and a center and I shall produce a force law' -is fully established, does ISL make a new appearance, and with it the Keplerian picture: A body orbits in an ellipse. It is required to find the law of centripetal force tending towards the focus of the ellipse. 13 (De Gandt, 38)

The force is indeed found to be inversely proportional to the square of the distance, and from here on Newton continuously enriches the ISL-Kepler Laws relation. First, he explicates this relation in a scholium, presenting the first and second laws, for the first time, as an integrated whole, following from the solution to Problem 3: Therefore the major planets orbit in ellipses baving a focus at the center of the Sun; and by radii drawn to tbe Sun describe areas proportional to the times, just [better: all] as Kepler supposed. 14 (De Gaud!, 38)

And in the following Theorema (IV) this particular force law, endowed with its new significance, is used to derive Kepler's third law: Supposing that the centripetal force is inversely proportional to the square of the distance from the center, the squares of the periodic times are as the cubes of the transverse axes. 15 (De Gandt, 41)

The direction of this last theorem is opposite to that of Theorema 1I16; Newton now assumes the ISL, and uses it to prove the harmonic proportion between distances and periods. The conditions, as in Problem 3, are planetary-like: uniform circular ",,,tion has irrevocably given way to nonuniform motion along an ell' ~enter of force in one of the foci. In

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the next exercise, Problem 4, Newton "comes closest to responding to Halley's question: if the force varies inversely as the square of the distancc, what will be the trajectory?" Assuming ISL and an elliptical orbit, he demonstrates how the particular parameters of the ellipse-the latus rectum and the focus of force-can be calculated. The journey amid Kepler laws has been completed. Still, this is not Newton's final word: "Matters are thus when the figure is an ellipse" he carefully qualifies, "For it can happen that the body moves in a parabola or hyperbola."17 If the initial velocity of the body has a different proportion to the latus rectum, "the figure will be a parabola having its focus at the point S... But if the body is projected in yet greater velocity, it will move in a hyperbola"18 (De Gandt, 46-48). Kepler's ellipse, Newton is demonstrating, is one particular conic section, which an orbiting body might assume as its trajectory, contingent upon the proportions between its initial velocity and distance from the source of force. This, as De Gandt rightly insists, is an "astronomy reformulated in dynamical terms" (49), in which the parameters of force, motion, distance and the proportions among them determine the particular-real, possible or imaginary-orbits and periods. In this newly formulated astronomy, the inverse square ratio between force and distance is assigned a role it never previously had. It provides mathematical context for the ellipse in the realm of conic sections, it is the instrument by which Kepler's first 'law' is deduced from the third, and the third-from the second; in general, it is Newton's means of framing Kepler's laws into a coherent theoretical whole.

2.1.3.

A Force Law to Work With

"The question itself is misleading," said N. R. Hanson 40 years ago regarding "the celebrated question 'What is the logical status of the laws of classical particle physics?''' The preceding account demonstrates that Hanson's pronouncement is as applicable to the question 'who was the first to discover ISL', and for similar reasons: "It is like asking 'What is the use of a rope?' The replies to this are no fewer than the uses for rope. There are as many uses for the sentences which e"xpress dynamical law statements as there are types of contexts in which they can be employed" (Hanson, Patterns of Discovery, 93)19. There were as many inventions of ISL as there were reasons leading to it, significations attached to it and applications of it. Newton's ISL changed dramatically between OeM to De Motu, and had very little to do with the form in which it had been introduced and applied

NEWTON'S SYNTHESIS

177

by others, decades and centuries before him. The exact moment of the first ever declaration of an ISL is thus neither unequivocal, nor of major consequence, and any attempt to adjudicate the "quarrel about priority," which necessitates assuming at least a close similarity between the earlier and later uses of inverse square relations, is not only pointless, but a hindrance to the quest for understanding its import and development. Definitely, the notion of an inverse square ratio between distance and force was not first introduced to Newton by Hooke. Nor was the deduction of such a ratio From Kepler's Laws initiated in their correspondence. Nor did Newton regard the Kepler laws as an unquestionable empirical criterion against which to judge his abstract constructions, either before or after that exchange. Still, in his writing following the correspondence with Hooke, Newton assigns ISL an altogether different role than that it occupies in his early tracts. A rather marginal curiosity in OCM, ISL is Newton's main theoretical tool in De Motu. Employing it, he can link Kepler laws theoretically to one another, and embed them in a well-charted mathematical realm. Newton, we saw, assnmes Kepler's so-called third law, proves the ISL, and then uses it to deduce the first law. Conversely, he assumes Kepler's second law, deduces the ISL and uses it to prove the third law. Moreover; Kepler, Newton suspects, merely "knew l Orb to be not circular but oval & guest it to be Elliptical" (Correspondence II, 437). With the aid of ISL Newton can place ascribe clear mathematical meaning to the 'oval'; it is a conic section, as would be described by any body "projected from a given point with a given velocity along a given straight line" (Herivel, 284: De Motu, Version I, Problem 4). The particular parameters of distance and velocity make 'y [planetary] Orb ... Elliptical," and different parameters would produce parabolic or hyperbolic trajectories. In this integrating function lies the real and new importance that Newton assigns to ISL following his correspondence with Hooke. Kepler laws, Newton would have learned from the likes of Mercator (whose Institutionum Astronomicum he had in his Iibrary20), are not independent empirical generalizations, but intrinsically related hypotheses, which cannot be empirically verified separatell 1• It was a tremendous achievement to link them through a single theoretically motivated law, especially since the parameters of the law-the particular ratio between distance and attraction-were also entrenched in Kepler's own speculations, as Newton knew from Boulliau. And indeed, having integrated Kepler laws through ISL, Newton declares them a substantiated whole. Newton, one may agree with Wilson ("From Kepler Laws" 90), sees himself as confirming Kepler's

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laws, rather than relying on them to provide empirical support for his theory, and to do so he uses ISL as his agent. Using ISL to transform this inter-dependence of Kepler's laws from an empirical worry to a theoretical achievement epitomizes the novelty in Newton's writing following (and I shall claim later-accountable by) his correspondence with Hooke. 22 Moreover, making a force law-any force law-the main explanatory vehicle in an astronomical theory represents a far more radical and consequential move on Newton's part than resolving which of the possible force laws corresponds to what "astronomers are now agreed" upon. This is the point that Newton forcefully establishes with De Motu's five corollaries (see above, section 2.1.2), viz., that ISL is only one possible ratio between force and distance, producing particular outcomes when incorporated into the newly constructed formulas linking centripetal forces, tangential motions and planetary trajectories. The mathematical tools for calculating the proportions between distance, period and centripetal force for any set of empirical generalizations-any orbit and any periodare the real achievement of De Motu, and they testify to a new conception of the challenge posed by planetary motion. This new conception holds the key to Newton's most basic moves in De Motu. De Gandt, for example, shows that Newton could not develop and prove De Motu's geometrical expressions without first proving Kepler Area Law. Newton could not prove his own theorems, De Gandt convincingly argues, before he transformed the claim that "All bodies circulating about a center [of force] sweep out areas proportional to the times [of description]"23 (Herivel, 278: De Motu, Version I, Theorem l) from the approximation device it was for Kepler to a universally proven theorem. What De Gandt does not stress enough, is that this. series of theorems-as I tried to demonstrate above-and this way of proving them-as I will try to demonstrate in Section 2.3.3-represent a novel astronomical project. De Motu is a preliminary effort at something neither astronomy nor natural philosophy had known before: a mathematically-adequate account of planetary orbits as a product of a combination of centripetal force and tangential motion, an account in which the particular parameters of this force and this motion-the force law, the distance between the orbiting body and the center of force, the initial inertial velocity-are the factors that determine the shape of the orbit. It is this new project, this new conception of the astronomer's task, which Newton develops in response to the correspondence. This conception is founded on the introduction of new relations between force and motion, in which centripetal force causes a body with an initial rectilinear motion to

NEWTON'S SYNTHESIS

179

orbit around the center of that force. To fully understand the significance of this novelty, we should consider more generally the relations Newton assumes between force and trajectory. and indeed, according to one school of thought, it is exactly Newton's conception of these relations that changed following his exchange with Hooke.

2.2.

Centrifugal vs. Centripetal Force

Thanks, mainly, to the work of D. T. Whiteside 24, it is widely recognized that the correspondence with Hooke led Newton to replace the centrifugal perspective from which he had been considering the question of planetary motion with a centripetal one. To wit: whereas in his early manuscripts, Newton sought to calculate the (centrifugal) forces by which the planets strive to escape their orbits, in the years following the exchange, his focus moved to calculating the (centripetal) forces constraining the planets into these orbits. There is hardly any doubt that Newton's treatment of the relation between force and orbit changed dramatically after his exchange with Hooke2s • and as I discussed in detail in Chapter I. Hooke's Programme is unique in being thoroughly 'centripetal' (a term which Hooke later acknowledges, but never adopts). It is less clear, however, whether the labels 'centrifugal' and 'centripetal' alone suffice to distinguish Newton's early approach from his mature one. First, because, even as late as April 1681, months after his correspondence with Hooke, Newton was still using centrifugal terminology when discussing comets with Flamsteed (Correspondence II. 361: Newton to Crompton). Secondly, because mathematically the two perspectives are easily inter-translatable. and thirdly. because Newton was fully aware of that inter-translatability, an awareness he demonstrated by freely moving between the two perspectives already in his early manuscripts. Understanding the results of the correspondence requires, therefore, a more thorough account of the change in Newton's use of force from OCM to De Motu, which I shall try to provide by comparing the two constructions he uses to produce ISL. These were touched on only briefly in the last section, and merit a closer examination. Comparing the constructions brings to light the intricacies and actual significance of Newton's move from a 'centrifugal' to a 'centripetal' approach. It appears not to be simply a change in the direction in which force is conceived to operate on revolving bodies.

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2.2.1.

Centrifugal Force in On Circular Motion

The earlier proof of the proportion f oc Rff is the hallmark of the OCM paper, and it is couched in strictly centrifugal terminology, as follows z6 , A body uniformly circulates counter-clockwise on the circumference of the circle ADEA, whose center is point C (Figure 19). Since the velocity is uniform, the length of the arc traversed is proportional to the time of traversal, and in all the following proportions arcs will represent times; e.g.: tAD will be replaced by AD. In a given, infinitely small time, the body moves from A to D. If whatever constrains its motion to ADEA is removed when the body reaches A, the body would continue to move in uniform velocity along tangent AB, traversing, in the same time, a distance equal to AD. When tAD is infinitely small, namely; when the discussion is limited to infinitesimal times and infinitesimal arcs, AD can be approximated by AB, B being the point where the extension of the diameter ECD cuts the tangent AB. BD is therefore the distance that the body would have acquired due to its conatus from the center ("conatus a centro") in time AD. If this conatus operates like gravity ("ad modum gravitatis"), then the distances through which it impels the body will be proportional to the squares of the times, as taught by Galileo (though Newton does not refer to him). It is important to note that BD, not AB, is proportional to the square of time; not the distance the body will have traversed in its tangential motion-a motion which, according to the first Cartesian law of motion, should be rectilinear and uniform-but its distance from the original circular orbit. In other words, BD is the distance between the point reached by uniform circular motion and the point reached by uniform rectilinear motion, and it is proporti<1llal to the square of time. Based on these assumptions, Newton constructs an expression for the total "conatus a centro" in one complete revolution-the distance S-which the imagined body, carried by the unhindered operation of that conatus, would traverse in time ADEA. As claimed, BD oc ADZ. Similarly, the distance S will be proportional to the square of the perimeter ADEA. To find this distance S, therefore, we can use 2 S : BD :: ADEA 2 : AD or, using notation more agreeable to the modem eye: ADEA

Z

So< 8 D - -Z

AD

Now, as assumed above, since we are dealing with infinitely small AD, it can be replaced by AB. According to Euclid, AB 2 =BD x BE, and since BD is infinitely small, BE can be replaced by DE. Thus, ADz is replaced by BD x

NEWTON'S SYNTHESIS

181

BE, giving: ADM 2 S

~

RDx--BDx DE

or: s

ADM 2

~

--; DE

If we call the circumference C and the diameter 2R, we amve at S <X CI2R, and since the circumference is obviously proportional to the radius, namely; C R, and C J?l (in our notation, C==27tR and C == 4r(R2), the distance which the body would have traveled under a constant operation of the centrifugal force in one complete period-the time of one complete evolution-is proportional to the radius of the circle; S is simply proportional to R. The significance of this finding is twofold. First, using it Newton can provide an explanation for the fact that bodies do not fly off the face of the earth. Assuming particular parameters for the constant of gravity on the face of earth and for the earth's size, Newton calculates that "the force of gravity is many times greater than what would prevent the rotation of the earth from causing bodies to recede from it and rise into the air,,27 (Herivel, 196: OCM). Secondly, since the hypothetical S would be the result of a continuously operating force (the conatus from the center) it should be proportional to fx 'fl (Galileo once again), so S R can be translated to foe RIfI-. With the aid of this formula, which incorporates periodic times, Newton can compare the centrifugal force suffered by the moon due to its monthly rotation to that at the earth's equator due to its own diurnal rotation. Applying the previous result, he then calculates a numerical ratio between the earth gravity (near its surface) and the moon centrifugal force, which he finds to be about 4,000 : 12B. <X

<X

<X

Figure 21: Left: OeM, right: De Motu

182

2.2.2.

CHAPTER 3

Centripetal Attraction in De Motu

Now compare these early, centrifugal considerations with the unambiguously centripetal approach taken in Theorema1l of De Motu discussed in the last section. In both cases, Newton presents a uniformly revolving body, and considers the tangential path AB it would take if, at point A, it were released from the centripetal force binding it to orbit ADEA. The geometrical model in both cases is all but identical; the only difference related to the change of perspective is the addition in De Motu of line AC (see Figure 21 righe9), which now signals the direction of the centripetal force. According to the parallelogram rule (Hypothesis 3 in De Motu) and its application in the proof of the area law, BD should be parallel to AC, and that is the way the diagram is reproduced in Herivel, but in the diagrams drawn in Newton's own hand, E seems to lie on the extension of AC, as it does in OCM. Of course, as AD diminishes, AC and BE converge, whether they are parallel or not. Again, the distance BD between the tangent and the circle is the measure of force-which in De Motu is indeed centripetal. Were the body to continue along its inertial path AB, it would reach point B, and it is the centripetal force that restrain it to point D of the orbit. In contrast to OCM, however, in De Motu Newton does not bother with the long detour of calculating the would-be effect of this force during a complete revolution and then applying Galileo's theorem twice. Rather, he directly addresses BD, which represents the effect of centripetal force f in an infinitesimally small time period AD. Using the same Euclidean theorem he uses in OCM, he concludes that BD is proportional to BA 2IBE. Assuming, as in OCM, that for very small distances, BA can be replaced by AD and BE by the diameter DE, he arrives at f 0<: AdIR, from whence he continues in the manner discussed in section 2.1 .2 to reach the same f 0<: Rff he arrived at in OCM, and from there the resulting force laws. The comparison between Newton's earlier and later handling of the problem of orbiting, and especially the comparison of his uses of the geometrical construction, substantiates the hypothesis that, without any additional qualification, the labels 'centrifugal' and 'centripetal' carry little explanatory value. The first reason for the poverty of this distinction is the fact that a significant feature of Newton's early, centrifugal considerations is their essential reference to gravity. Even though the initial setting of the question is in centrifugal terms (in those early, Cartesian days of his Newton seems to consider the "endeavour" to continue in a straight line the more fundamental effect), his presentation implies that centrifugal force can only acquire

NEWTON'S SYNTIlESIS

183

meaning in a context involving gravity. This is not really surprising; one can hardly discuss the centrifugal tendencies of a planet orbiting the sun or a body participating in the earth's diurnal rotation without addressing the force that keeps the one in orbit and secures the other from flying away.30 What it implies, however, is that both the centrifugal and centripetal perspectives were already available to Newton in those early stages. The second reason is that the mathematical skills and techniques employed in OCM and in De Motu are essentially the same. The use of infinitesimally small lines and curves, the assumption that converging magnitudes are interchangeable in proportions, and the assumption that Galileo's theorem (implying uniform force) can be applied, for small enough distances, to context in which the force is distance-dependent-all these are as much part of OCM as they are of De Motu, and Newton indeed arrives at the same basic expression in the later text as in the early one; foe RJf.31 Even the geometrical diagrams attached to both texts are, as shown above, virtually the same. In short: just like the centripetal perspective, the mathematical tools Newton uses in De Motu were already available to him when he was composing OCM. Newton's adherence to the centrifugal perspective in OCM is thus a matter of preference, and the change to the centripetal one in De Motu represent a change of preference; it does not signify the acquisition of a new capacity, but of new ways of using existing ones. 32 Yet there is one significant difference between Newton's application of the same mathematical procedures in OCM and De Motu, a difference which sheds light on these choices and the tum Newton's work took in response to Hooke's Programme. . In his early text-OCM-Newton takes the complete period-the time T for a complete revolution, represented by the circumference ADEA-as the unit, and thence calculates a line for any unit of time with the help of an imaginary straight line (which I called S in the previous section) representing the operation of the force during this T. His comparison of centrifugal forces to gravity is a comparison of these straight lines. In the later text Newton does not bother with either straight lines or complete periods. Instead, he compares infinitesimal arcs directly and immediately arrives at a geometrical expression for the instantaneous operation of force if oe AD2/R). He does derive the very useful expression for the whole period if DC RJf) by generalizing the whole period from the infinitesimal arc through the assumption of uniform velocity, but this latter proportion is an end product constructed especially in order to take advantage of Kepler's third law. In De Motu, neither the whole period nor the circumference as a

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whole are taken as measures, and Newton does not bother, as he was careful to do in OCM, to eliminate the partial arcs and remain with regular closed curve or straight lines. Mathematically, the difference may seem minor. However, the boundary between the closed curve and the straight line, which· Newton imposes in OCM, is not a whim. The work carried out by Christiaan Huygens at the very same years Newton was writing this text reveals that this imposed boundary is far from being idiosyncratic of Newton or peculiar to OCM. Representing force-driven motion by straight lines or open curves, while reserving the closed orbit to represent force-free motion, expressed a common understanding of the relations between force and motion as represented through the mathematical practices and procedures.

2.2,3.

Changing Frames of Reference in Huygens' De Vi Centrifuga

In his De Vi Centrifuga (Oeuvres 16, 254-328i 3, which he began writing in late 165934, Huygens sets out to investigate gravity, centrifugal force (a term he coins for the occasion) and the relation between them. One reason for the relevance of De Vi Centrifuga for our interests here, is that in order to determine that relation, Huygens suggests a geometrical construction similar to Newton's OCM construction. Even more important is that Huygens' text testifies to the same combination of metaphysical and mathematical instincts that guided Newton in OCM. Like Newton, Huygens considers a body revolving uniformly in a given circle ADE (Figure 22)35, which, at a certain point A, is allowed to continue uniformly along the tangent AB. Like Newton, Huygens regards the growing distance BD between the body's location B along the (virtual) tangential path, and the corresponding point D, its location if it had maintained its original orbit, as capturing the continuous operation of the centrifugal force. Like Newton, he claims this distance to be proportional to the square of time, and concludes that the distance, which the body would travel under a constant operation of the centrifugal force in the time of one complete revolution, is proportional to the radius of revolution CEo Huygens does not go on to combine this finding with Kepler's third law, but otherwise his paper is far more ambitious than Newton's. It attempts to detennine, among other things, the distance a body traverses in its first second of fallon earth (which amounts to establishing the particular intensity of earth's gravity)36, the length of a pendulum beating seconds (namely, a pendulum completing one full swing in one second) and of a

NEWTON'S SYNTHESIS

185

comc pendulum (see Chapter 1, Section 2.3) whose revolution is one second. Furthermore, Huygcns is more careful in his combination of dynamical assumptions with geometrical constructions. He does not, in fact, restrict himself to 'a distance' between the tangent and the circle at the beginning of their separation and his proof does not rely on the Galilean assumption that this distance is proportional to the square of time. Instead, he seeks to establish a 'virtual path' caused by centrifugal force-a series of distances between the moving point of departure and the circular orbit. To prove that these distances grow in proportion to the square of time Huygens constructs a parabola AG whose latus rectum 37 is equal to the diameter of the circle. For small distances, such a parabola closely approximates the circle. Huygens also allows himself to assume that for such small distances, the secants BD may be taken for the perpendiculars to the tangent AB; in other words, that the angles ABC are all right angles. H all this is granted, then the distances BD are proportional to the squares of segments AB of the tangential path, simply by virtue of the definition of parabola. In contrast to Newton, Huygens leaves little doubt as to what he considers primary: his investigations of gravity are merely a prop on the way to investigating centrifugal force, which Huygens with staunch Cartesianism holds to be the only 'force' in a nature devoid of any distance actions and influences. Hence, when, for example, he compares a weight revolving in a sling to the same weight hanging from a chord, he considers the centrifugal tension of the sling to be the real effect and the gravity-produced tension of the chord to be only an experimentally accessible phenomenon through which to explore that effect.

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--)L--~4---------1c

Figure 22: Huygen's approximation of circle by parabola in De Vi Centirfuga (Oeuvres 16, 302; lettering added).

Yet Huygens is even more skillful than Newton in moving back-and-forth between different perspectives and frames of reference. Concentrating on the sling and its centrifugal tendencies, Huygens encounters a discrepancy, which is in fact endemic to Cartesian treatments of circular motion (see Chapter 1; Section 2.2.2). The analogy to the chord ascribes to the revolving body a radial tendency from C along OV. However, when analyzed according to both Descartes' first law of nature, which Huygens adopts, the body, if released from its circular orbit at A, would not follow a radial and accelerated path, but instead the tangential, uniform path AB. Huygens attends to the discrepancy by moving on from the approximation described above to considering the path of the body as viewed from the point of view of an observer situated at point O-the point where the body was released. Revolving counter-clockwise, this observer perceives himself as stationary, and the original point of release as moving in the opposite, i.e. clockwise direction. From the vantage point of 0, the body, moving tangentially, rectilinearly and uniformly along AB, appears to be accelerating along the curve BBBB. 38 BBBB is tangent to the radial

NEWTON'S SYNTHESIS

187

direction COY, which is the cause of the experience of radial centrifugal force. And Huygens is perfectly willing to acknowledge the ramifications of this free-floating between frames of reference:

Figure 23: Huygens' analysis of radial centrifugal force as the evolute of circular motion in De Vi

Centrifuga.

quc Ie mouvment d'un corps puet estre en mesme temps veritab1ement ega! et veritablement accler? scion qu'on raporte son mouvement a d'autres differents COrpS.39 (Huygens, Oeuvers 16, 197)

With such clear evidence of his ability to move freely between perspectives, Huygens' adherence to the centrifugal perspective should, just like Newton's, be viewed as a choice. We can discover the reason for this choice by looking back at Figure 22, particularly at parabola AG and its relation to the line ABBB on the one hand and the circle ADE on the other. As Yoder puts it "the approximating parabola is more than a mere mathematical equivalent to the circle, conveniently introduced to reduce a relationship involving centrifugal force to an easily stated equivalence; the parabola also represents the distance traveled by a freely falling body" (Yoder, 22). In one diagram, Huygens inserts a straight line representing uniform rectilinear motion, a circle representing uniform circular motion, and a parabola representing accelerated motion. Although masterfully operating his mathematical representations, Huygens omits to consider one direction. He is willing to represent accelerated motion by a series of straight lines; the DB's of both figures, or by an open curve; the parabola AG of Figure 22 or the evolute BBBB of Figure 23. However, just like

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Newton in OCM, Huygens invariably reserves the closed curve-the circle-for representing force-free motion.

2.2.4.

The Primacy of Force over Orbit

The novelty of De Motu is thus encapsulated in the willingness to represent forced motions by closed curves. It is this willingness that allows and embodies the re-shaping of the astronomical project, indicating that the change from the centrifugal approach of OCM and De Vi Centrifuga to the centripetal approach Newton that adopts in De Motu is not primarily a change in the direction of force. It is, rather, a change in the direction of explanation.

2.2.4.1. The New And this change consists of coming to treat the planetary trajectory as a contingent effect afforce and motion. To wit: in OCM Newton assigns a unique status to the circular trajectory, its dimensions and its period. He postulates the circular orbit ADEA (Section 2.2.1) to set up the problem, and then treats it as a given whole; as though the question and any answer to it would be meaningless unless formulated in terms of the complete circle. In contrast, the circle in Theoremall of De Motu-like the curves in the succeeding theorems and problems-represents one possible trajectory produced by the impact of a rectilinearly operating force on a rectilinearly striving body, which continually curves the body's motion. To be precise, from the perspective employed in De Motu, the immediate result of this "compounding" (see Introduction) of force and motion is not a complete circular orbit, but an infinitesimal arc. Far from being a testimony to some unique and allimportant heavenly harmony, the complete circle, in De Motu, is nothing but a consequence of these arcs having a particular (and uniform) curvature, due to the particular proportions between the parameters of motion, force and distance from the center of force-f oc V2/R. These proportions, Newton clarifies in Problem 4 (Herivel, 267), are the only essential difference between open paths and closed orbits; higher relative velocity would result in a parabola, higher still-hyperbola. But, given the right proportion, the circle or ellipse would be completed. The way young Newton deployed his mathematical procedures in OCM

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reflects a genuine commitment, a specific conception of the relations hetween force and motion. Huygens' treatment of orbital motion in De Vi Centrifuga confirms that at least he, among Newton's contemporaries, shared this conception. The break with this conception in De Motu signified, therefore, a major change in approaching the mathematical task at hand and the physical processes it represents. Some of the most exciting chapters of Newtonian research have dealt with the sources and resources of his ontology of force 40, and the mathematical niceties of Newton's progression from the centrifugal to the centripetal approach indeed betray a crucial ontological shift in conceiving force, trajectory and especially the relations between them. In a nutshell, the new centripetal approach is the belief that compounding rectilinear motion and centripetal force produces an orbit around the source of force, and that only the parameters of force and motion separate open trajectories from close and continuous orbits.41

2.2.4.2. The Old

One way to illustrate the radical novelty of Newton's approach in De Motu is by applying it to examine the previous approach-the one adopted by Huygens in De Vi Centrifuga and by Newton himself in OCM. Both Huygens and Newton of the 1660s appear occasionally to be willing to analyze stable trajectories-closed, continuous, repetitive curves of which the circle is a paradigm-as maintained by a balance between centrifugal and centripetal tendencies. But as we saw in the last two sections, neither conceives of the possibility of a force creating such trajectories around its source, and neither ventures to construct the closed curve representing such a trajectory42. Considered from the new vantage point offered by Newton in De Motu, this 'centrifugal approach' seems to reflect a basic, almost instinctive conception: forces cause acceleration, and accelerating bodies approach the source of the force, if the force is attractive, or recede from the source, if the force is repulsive. This assumption is never explicated, let alone defended, by either of them, but once forced orbital motion is introduced, the insistence that forces create open trajectories, straight lines or parabolas, whose direction is either towards or away from their source, becomes the most conspicuous feature of Huygens' approach in De Vi Centrifuga, which is shared by Newton in OeM. Thus, by shifting from assuming (closed) trajectories to be the cause of (centrifugal) forces to considering (centripetal) forces as the cause of such trajectories Newton exposes two convictions embedded in the centrifugal

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approach, two presuppositions whose rejection defines his new centripetal approach. One conviction relates to the 'directionality' of the effect of forcc on motion-towards or away from the centcr of forcc. This presupposition is vividly reflected in the following speculation concerning the motion of comets that Flamsteed sent to Newton via Halley in 1681: I conceave therefore that the Sun attracts all the planets and all like bodies that come within our Vortex. more or lesse according to the different substance of tbcirc bodycs and neamesse or remotencssc from him. ... When [tbe comet] came within [its I Compasse ... this attraction ofye Sun would have drawn it near him in a streight line. had not the laterall resistance of ye Matter of ye Vortex moved against it bent it into a Curve.... [Wjhen .it ... crosse ye motion of ye Vortex till haeving ye contrary End opposite the Sun hee repells it as the North pole of ye loadstone attracts ye one end of ye Magnetic needle but repells the other. This act of repulsion would carry ye Comet from the Sun in a streight line, were it not that the crosse motion of ye Vortex bends it back. (Correspondence 11.337-8: Flamsteed to Halley. 17 February 1680/1. Italics added.)

The spiral trajectory. which Newton contemplated for the falling stone in his reply to Hooke's first letter (November 28, 1679-scc Introduction), attested to a similar presupposition; the forced motion, although not rectilinear, was presented there as ending, as a matter of course, in the center of gravity-the center of the earth. Newton's reply to F1amsteed on February 29 1680/1 echoes Hooke's comment in his second letter (December 9, 1679) about that spiral, and clearly reflects the new approach Newton adopted in response to this comment. His sardonic tone does not disclose that this conversion is only 13 months old: I can easily allow that the attractive power of ye Sun as ye Comet approaches ye Sun ... will make ye Comet verge more & more from its former line of direction towards ye Sun ... but I do not understand how it can make ye Comet ever move directly towards ye (1) •• , much less can it make ye line of direction verge to ye other side of ye Sun. (Correspondence. II, 341: Newton to Crompton to Flamsteed.)43

The other, related 'centrifugal conviction' eschewed by De Motu is the intuitive distinction between open and closed orbits. This distinction, for a seventeenth century mathematician such as Newton or Huygens, could not be grounded in a mathematical difficulty; circles and ellipses, parabolas and hyperbolas are all conic sections, with which they were proficient. What De Vi Centrifuga reveals, however, is that the application of these mathematical skills for dealing with curves, to the analysis of physical orbits was far from automatic. Even the nex.us he himself introduces between the parabola and the circle does not lead Huygens to consider the possibility that the closed curve can be produced by the same combination of rectilinear motion and encurving force that produces the parabola. With the introduction of forced orbital motion, and the rejection of those

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convictions Newton distinguishes De Motu from De Vi Centrifuga, OCM and the views F1amsteed stiIl held in 1681, and gives new meaning to the title Physica CrE[estis.

2,2.5.

Closing the Curve

It should perhaps be stressed, that the novelty of De Motu, as far as the shift from the centrifugal to the centripetal approach is concerned, does not lie in the conception that attracting forces cause motions to curve, but rather in the notion that the curving should result in a trajectory around the source of force, and in the insight that that trajectory may be a closed orbit. The mastery of the Galilean treatment of acceleration which Newton displays in OCM c demonstrates that at the time of composing tliis text Newton was already fully aware that forces may produce curved trajectories; parabolasGalileo's favorite curve-in particular 44 . But in this early tract Newton, just like Huygens, does not proceed from the open parabola, which collapses towards the source of attraction, to the closed and continuous curve-the circle-around this source. In OCM, the effect of force is always represented by a straight line, just as F1amsteed would have it; Newton does not envision that the same cause may produce both acceleration and a stable, or at least continuous and repetitive trajectory such as a circle. And it should perhaps be stressed again, that the novelty is also not in the mathematical tools at Newton's disposal, but in their application and interpretation. It is questionable whether Newton possessed, in the early 1680s or even later, the mathematical wherewithal to compose45 the complete curve from the partial force-produced infinitesimal arcs, required if one is to mathematicaIly mimic the physical composition of a trajectory by synthesizing a curve from straight lines representing inertial motion and rectilinearly-operating force. The question put to him by Halley in the summer of 1684 demanded as much: it could be formulated as 'given a force law, find the curve'. Yet Newton does not show himself anymore capable of answering it in De Motu than he does his in OCM.46 Instead, De Motu's problems, as well as the proof for Theorema II, are structured as 'given a trajectory, find a force'. But although he still does not actually 'create' the c1osed-eurve orbit out of the force and the tangential motion, Newton dares in this later text to treat the circular, as well as the elliptical orbit, in a way that neither he nor Huygens had ventured before; as trajectories of accelerated, force-dependent motion, just like the straight line or the parabola. Treating open and closed curves on a par means allowing that a

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curved orbit can be successfully 'closed' by a continuous rectilinear attraction. Newton's mathematical tools only allow him to solve problems in which the curve is given, and he composes numerous such problems, assuming numerous different open and closed curves (and numerous different centers of force)-some imaginary, some provided by astronomical observation. But in De Motu, it is always the force that is sought after. The closed curve, representing the planetary trajectory, its period and circumference, is only the effect of force on motion. Newton's introduction of the closed-eurved orbit as an outcome of the curving of motion by an acceleration-causing force, just like any rectilinear or open curve trajectory, constitutes his conversion from a centrifugal to a centripetal approach to planetary motion. It is, as claimed above, far more dramatic a transformation than the labels 'centrifugal' and 'centripetal' suggest. Indeed, after De Motu, Newton will almost always consider force as directed towards, rather than away from, the center of the orbit. But the change of direction is a relatively minor modification in the manner in which force functions within Newton's formulas. The significant change is in the new status of these formulas and in the explanatory role of force they reflect; rectilinear force, from De Motu on, is the cause of curved, orbital, planetary orbits.

2.3. Universal Gravity The assignment of a curving role to rectilinear centripetal force in the analysis of planetary motion leads us naturally to the last and most general question that Newton scholarship has set itself regarding Newton's indebtedness to Hooke: "from the very day in 1686 when Edmund Halley placed Book I of the Principia before the Royal Society, Robert Hooke's claim to prior discovery has been associated with the law of universal gravitation" (Westfall, "Hooke and the Law of Universal Gravitation," 245). Westfall's paper is dedicated to demonstrating that Hooke, in fact, did not have in his grasp the concept in the title-"Universal Gravitation"-and this view (which Westfall himself argues against what he perceives as a pervasive sentiment) seems to have prevailed. Wilson, for example, holds a similar position, which under closer scrutiny seems to combine at least two different claims, namely, that "the search for indications of Newton's belief in universal gravitation before 1684 is doomed to failure; and the attempt to argue that all of Newton's ideas are due to Hooke is wrong" ("From Kepler's Laws," 167).

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t93

The arguments given by Westfall and Wilson are convincing and extensive enough to preclude an attempt to recount, let alone debate them here. Moreover, in his Force in Newton's Physics47, Westfall demonstrates no less convincingly that before 1686 Newton himself had but entertained the notion of universal gravity only sporadically and inconsistently. If "Newton had not arrived at the concept of universal gravitation when he began to compose De Motu" (Force, 460), then the adoption of this concept could not be tied to his assimilation of Hooke's Programme. Nevertheless, a brief discussion is necessary. If "the decisive discovery was that of the argument for universal gravitation" (Wilson, op. cit.), if "universal gravitation" indeed captures the essence of Newton's mature cosmological approach and the breakthrough that distinguishes it from his and others' earlier approaches, then interpreting the Hooke-Newton exchange requires at least a basic understanding of the meaning of the phrase "universal gravitation" and an account of its role (or lack thereof) in De Motu.

2.3.1. In the Eye ofthe Historian Surprisingly enough, the former presents some difficulties. As useful as this phrase has been to historians of seventeenth century science, one is hard pressed to find a clear formulation of its meaning, and we are forced to try and understand it by implication. Westfall, in the paper arguing Hooke's want of the concept ("Hooke and the Law of Universal Gravitation"), seems to contrast universal gravity to particular gravities (247) on the one hand, and to universal power (250, f. n. 15) on the other. Herivel concludes that in Newton's letter to Halley of June 20, 1686 "there is apparently no indication whatsoever of the notion of universal gravitation" on the basis of the fact that Newton "makes no mention of the forces on the planets towards the sun, or of the force on the moon towards the Earth" (Herivel, 72, italics in original). Whiteside, concentrating on Newton's evolving mathematical apparatus, seems to have little use for this notion, while Wilson concludes that Newton's 1675 Hypothesis Explaining ye Properties of Light "is incompatible with universal gravitation," first, since "Newton does not assume that the parts of solid or fluid bodies act upon one another in the same manner that the earth and or the sun attracts bodies," and secondly, because "the particles of aether used to account for gravitational action do not themselves gravitate towards one another" (op. cit., 144-145). Westfall comes closest to providing a summary of all the elements present in the allusions cited above to universal gravitation, albeit still in a negative mode:

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"before he achieved the demonstration that an homogeneous sphere, composed of particles that attract with inverse square forces, itself attracts any body external to it with a force inversely proportional to the square of the distance from its centre, Newton had no reason to carefully recompute the correlation of the centripetal acceleration of the moon with the measured acceleration of gravity on the surface of the earth. And until that correlation was demonstrated, he cannot be said to have discovered the law of universal gravitation" (Westfall, Force, 461). Each of the above citations appears to imply a somewhat different use of 'universal gravitation', but even if the overlap is not perfect, historians seem to agree that the concept is presented in Newton's proclamation in the Principia that there is a power of gravity pertaining to all bodies, proportional to the several quantities of mailer which they contain. (Principia. 414, and cited in this context by Westfall, Force, 464)

In other word, universal gravitation implies that all particles of matter attract each other in proportion to their mass, and this attraction is the cause of the mutual attraction of all macroscopic bodies. Hence, the gravity of earthly bodies towards the center of the earth is the very same and obeys the same rules as the gravity of heavenly bodies towards the sun. This means, of course, that the sun attracts the planets, but also that the planets attract the sun as well as each other. Not all writers are clear on whether or not adopting universal gravity entail adopting ISL, but it definitely a entails conceiving it as an attraction, a centripetal force, whether or not Newton envisioned some "ad hoc mechanism to account for" it in line with his Cartesian commitments (Westfall, Force, 465). If we limit our understanding of 'universal gravitation' to this set of notions, then the concept seems to be suggested, almost fully, already in the version of the Programme that Hooke sketches on the last page of his 1674 Attempt to Prove the Motion ofthe World (to which I shall return later): all Crelestial Bodies whatsoever, have an allraction or gravitating power towards their own center, wherby they attract not only ther own parts, and k.eep them from flying from them, as we may see the Earth to do, but they also allract all the other Crelestial Bodies that are within the sphere of their activity ... these allractive powers are so much more powerful in operating, by how much the nearer the body wrought upon is to their Centers. (Attempt, 26-27)

The only element missing here is the law governing the diminishment of the powers of attraction, concerning which Hooke admits "what these several degrees I have not yet experimentally verified," and, perhaps, also a clear concept of mass or 'quantity of matter'. Thus, Westfall's contention that

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Hooke "did not hold a conception of universal gravitation" ("Hooke and the Law of Universal Gravitation," 245) and that "Newton had not yet arrived at the concept of universal gravitation when he began to compose De Motu late in 1684" (Force, 460) stems from Westfall's requirement that we understand "[u]niversal gravitation, as a demonstrated conclusion rather than a mere idea, rested on '" the demonstration that elliptical orbits entail an inverse square force, and the demonstration of the attraction of homogeneous sphere" (Force, 461).

2.3.2.

Constant Motion

Westfall's use of the term 'universal gravitation' is of course legitimate, especially since it is an historians' category rather than a term used by Hooke or Newton. Yet there is an important aspect to the set of notions discussed above which is obscured by the opposition between "demonstrated conclusion" and "mere idea." In adopting the notion that "all Crelestial Bodies whatsoever ... attract all the other Crelestial Bodies" (as Hooke had it in his 1674 Attempt) Newton not only chose a particular way of addressing planetary orbits, but let himself into a whole new heavenly landscape: the whole space of the planetary heavens either rests (as is commonly believed), or moves uniformly in a straight line, and hence the communal center of gravity of the planets ... either rests or moves along with it. In both cases ... the relative motions of the planets are the same, and their common centre of gravity rests in relation to the whole of space, and so can certainly be taken for the still centre of the whole planetary system. Hence truly the Copernican system is proved a priori. For if the common centre of gravity is calculated for any position of the planets it either falls in the body of the Sun or will always be very close to it. By reason of this deviation of the Sun from the centre of gravity the centripetal force does not always tend to that immobile centre, and hence the planets neither move exactly in ellipse nor revolve twice in the same orbit. So that there are as many orbits to a planet as it has revolutions, as in the motion of the Moon, and the orbit of anyone planet depends on the combined motion of all the planets, not to mention the action of all these on each other. But to consider simultaneously all these causes of motion and to define these motions by exact laws allowing of convenient calculation exceeds, unless I am mistaken, the force of the entire human intellect. Ignoring those minutiae, the simple orbit and the mean among all errors will be the ellipse of which I have already treated. (Herivel, 301: De Motu, Version III)48

The slight sense of vertigo imparted by these lines, I submit, is the scholium's most telling feature. Newton paints here an overwhelmingly mobile cosmological picture. Nothing in it is at rest' neither the earth, as is "proved a priori," nor the planets, nor even the sun and "the whole space of

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the planetary heavens." All move together and with respect to each other with such complexity as to defy "the force of the entire human intellect." Nothing is left of the old stable, rational motions of the heavens, eternal and as akin to rest as any motion can be; "Astronomy's aim" cannot be anymore, as Kepler had it, "considered to show why the stars' motions appear to be irregular on earth, despite their being exceedingly well ordered in heaven" (Astronomia Nova, Part I, Chapter I, 115)-they are not so well ordered. Yet the real unprecedented aspect of this presentation is that it leaves Newton undeterred; "all these causes of motion and [all] these motions" are but "minutiae," which he is "ignoring." There is no Cusanus-Iike skepticism or Bruno-style enthusiasm in Newton's words-even if "there are as many orbits to a planet as it has revolutions." The new world, pervaded and held together by gravity, does not need to be "exceedingly well ordered" in order not to fall apart, and the new astronomy of forces is not expected to provide anything more than a "simple orbit and the mean among all errors."

2.3.3.

Appropriating the Law of Areas

The scenario Newton adopts with universal gravitation. the cosmological picture he paints by basing his inquiry of heavenly motions on "a power of gravity pertaining to all bodies," is one of "planetary heavens" in a state of constant motion and infinite fluctuation. In order to handle this, he turns to a rather obscure mathematical tool: Kepler's "second law"-the law of areas.

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t:.~

.

l}:";:;'~'~:,;l'~:~'~f ,

./<:.~~~~·).··'·~:1:;;~·:···;· . ..'..', •.~';~~ .

Figure 24 - proof of the area law in De Motu (Herivel, adjacent to page 292).

. ...., · ..,r,. ·t.····

}i~~;;;:·~·~:<~.·.· ·7-~-'-·<·

Section 2.1.2 touched upon the importance of the area law in De Motu, both as a geometrical lemma and in its relation to the two other "Kepler laws, so called" (Wilson, op. cit.). Still, the area law deserves a closer look, if only for the fact that De Gandt chose to conclude his excellent book with it:

s"f-._.c.~~._.--'-.-.~

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Placed at the head of the theorems of the Principia. the law of areas is a presentation of force; it specifies the essential features of centripetal force and indicates at the start that this force is henceforth a mathematical entity. (De Gandt, 272)

"The law of areas was the key to the dynamics of the De Motu and the Principia," explains De Gandt (155), because it "made possible the appearance of time in the diagrams-the translation of interval of time into the sizes of segments, whatever the velocity of the body on its trajectory" (272). The ability to represent time is of course crucial to any mathematization of motion. Bodies moving in uniform velocity surpass distances proportional to the time of motion, so that, if their trajectory is represented by a line, the time of motion can be expressed by the length of that line. But this convenient method is not open in the case of the planets, whose apparent motion is nothing but uniform. Indeed, this was the point of the 'equating' exercises of traditional astronomy; to reduce the planetary apparent motion to motions of uniform velocity, where equal times are expressible by equal segments (since traditional astronomy did not deal with actual distances, these were segments of a circle-viz., angles; and the velocity considered was angular velocity). When attempting a physical description of the heavens-an account of the true motions of the heavenly bodies--one cannot employ fictive equant points and mean motions. Thus, the law of areas supplies a solution to this predicament: All orbiting bodies describe, by radii drawn to the center, areas proportional to the times49 (De Gandt, 22),

so these areas (Figure 24) can be used to represent times, even if the orbiting velocity and the distance from the center (of force-the orbit does not have to be circular and the reference point does not have to be in its geometric center) are not uniform. And as we saw in Section 2.1.2, Newton indeed makes extensive use of this important tool. Kepler never proved the law of areas. He introduced it as an approximation device-a means for equating planetary motion-and it was usually too cumbersome for astronomers to prefer it to the traditional equating methods. By providing a geometrical proof for it, Newton transformed the law of areas into a universally applicable theorem (Theorema I in both De Motu, the Principia and the Kepler Motion Paper, which 1 shall discuss below). This was undoubtedly a brilliant achievement, and the proof is so simple and elegant that it is worth sketching here (I will use the De Motu version, but the differences between versions are negligible): A body moves in uniform velocity from A to B in time t (Figure 24). "If nothing were to impede it," it will, given the next "equal time" t, continue

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along a straight line to e, where AB == Be. With S as the center (of force), we draw the radii SA, SB and Se. The areas of triangles SAB and SBe are equal, since they are both half the product of the base (AB or Be) and the height, which is the perpendicular from S to ABc. Suppose that the attraction from S forces the body to C instead of B. According to the parallelogram rule, Ce will be parallel to AB, which means that the perpendiculars from C to AB and from e to AB will be equal--eall them h. The areas of triangles SBC and SBe are equal, being half the product of h and SB. Thus, the area of SBC is also equal to the area of SAB; "in equal times, therefore, equal areas are described" (De Gandt, 22). The simplest of geometries-the only problematic move involves applying this rectilinear triangles and instantaneous force to curvilinear orbit and continuously operating force, and Newton nonchalantly solves the problem by assuming "these triangles ,.. infinite in number and infinitely small" (ibid.). Yet exactly the importance of the area law, and exactly this simplicity and elegance of the proof, makes one wonder what prompted Newton to adopt the area law, use it, and attempt to prove it. Clearly, appropriating the law was not completely straightforward for Newton; as De Gandt acutely points out (153-155), he does not use it in his December 13, 1679, letter to Hooke. The analysis of the motion of the stone falling into and around the center of the sliced earth, which he offers in the letter, provides an excellent opportunity for applying the area law; it is an argument concerning precisely non-uniform motion around an arbitrary center of force. Yet Newton suffices, instead, with a loose concept of enumeration, referring to the "innumerable and infinitely little motions ... continually generated by gravity in its passage" (Correspondence II, 308). The relevance of the area law to that particular turn in the correspondence is so clear in hindsight, that De Gandt takes the fact that Newton refrains from using it as evidence "that Newton at this date had not yet demonstrated, nor even definitely accepted, the proposition that Kepler had advanced but which was not universally accepted among the astronomers" (De Gandt, 154). It is difficult to contest De Gandt's general conclusion, but his implication, that Newton did not use the law because he could not yet prove it, is clearly wrong. To avail himself of the law of areas, Newton did not have to prove it. He could have presented it as an empirical finding, just as he accepted Kepler's harmonic (third) law, and used it just as he used Galileo's law of free fall-as a simple truth about nature. His bold generalization of the proof to a continuous curve reminds us that rigor of proof was not Newton's most cherished criterion when it came to efficient

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mathematical tools. The primary importance of the proof, I would like to claim instead, does not lie in justifying Newton's use of the area law, but in expressing the change in his conceptualization of the problem of planetary motion-the change that attracted his attention to this law. We find one important aspect of this change reflected in the most conspicuous feature of the diagrams providing the various versions of the proof, namely, that no real orbit is shown-just a series of contiguous triangles approximating an open curve. This is no trivial matter: the idea that the complete orbit can be constructed from infinitesimal triangles, each having a different shape (though an equal area!), embodies two of the main insights of Newton's new approach to celestial mechanics. The first insight, dealt with extensively in Chapter 1 and ascribed to Hooke, is that one need not assume any rotation among the causes for orbital planetary motion: the latter can, and should be explained in terms of rectilinear motions and forces alone. The other insight, which we addressed in the last section and is captured by its title 'Closing the Curve', is that the trajectories of "orbiting bodies" are not essentially different from any other curved trajectories, and that they can be described using the same mathematical tools-just as Hooke argued in his letter to Newton of January 6, 1680 (see Introduction). The other aspect of this change in Newton's celestial mechanics is disclosed by the very universality of the proof. This, I submit, is the universality of 'universal gravitation'. By committing himself to a cosmology of force, i.e., to analyzing heavenly motions according to relations of attraction between the heavenly bodies, it is not only the notion that all bodies attract each other that Newton adopts. and definitely not the idea that this attraction should follow the same laws everywhere. Rather, the commitment he takes upon himself is, first and foremost, to the forceruled cosmological landscape laid down in the Scholium from De Motu (see last section), and, specifically, to the unceasing, seemingly order-less motion it entails. One can accept that "the planets neither move exactly in ellipse nor revolve twice in the same orbit" (Herivel, 301-see previous section) Newton seems confident. without fearing complete chaos. Newton's proof of the area law is universal. since it does not set any limitations on the operation of force. besides that of a constant center (all lines of force converge in the same point) and rectilinear operation; and assumes nothing about the motion of the orbiting body except that "under the sole action of its innate force it moves uniformly in straight line"50 (De Motu, 2nd Hypothesis). The law of areas is. indeed, "the emblem of a new concept of force, disembarrassed of phantasms and indifferent to physical

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causes" (De Gandt, 272), but no less important, it conveys a new conception of orderliness in nature; a precarious stability which emerges from processes of compensation and mutual balancing. The point where Newton "arrived at the concept of universal gravitation" (Westfall, Force, 460) is not marked by a mathematical proof, but by a new conviction in the possibility that even if "there are as many orbits to a planet as it has revolutions" (Herivel, 301see previous section), there may still be a law which governs that orbiting and can be adequately captured by simple mathematical manipulations.

3. HOOKE'S PROGRAMME REVISITED We can now attempt a comprehensive account of the significance of Hooke's Programme; of the difference between Newton's work on celestial mechanics in his early writings of the 1660s, and his work in the 1680s manuscripts following his correspondence with Hooke-his workbench for the Principia. Beforehand, however, it may be a appropriate to seek more direct evidence for the claim that in the 1680s, Newton was realizing Hooke's Programme; that he not only adopted an approach similar to Hooke's, but actually followed the path laid down in those six letters between November 24,1679 and January 17,1680. Such evidence exists, though it cannot be found in De Motu. As may be recalled from the Introduction, Hooke's suggestion that Newton's stone, falling through the earth, would travel in an "Elleptueid," met with Newton's objection (in the December 13 letter) that there is no reason to suppose that the curve should be a neat ellipse; that a rectilinear motion, curved by force, would orbit the source of force in a closed curve with a constant line of apsides. Accelerating towards the center, Newton contended, the orbiting body should change its apogee and perigee with every cycle. In answering, Hooke outlined a possible solution with a few heuristic remarks:

3.1.

Hooke's Hints

my supposition is that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocal, and ... 5\ that the Velocity will be in subduplicate proportion to the Attraction and consequently as Kepler Supposes Reciprocall to the Distance. And that with Such an attraction the auges will unite in the same part of the Circle and that the neerest point of accesse to the center will be opposite to the furthest Distant. (Correspondence II, 309)

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201

For those lured into the dispute over priority rights, this is an important document: Hooke's first pronouncement of the Inverse Square Law. For our purposes, it is much more important to notice the terms on which ISL is being proposed. I have dealt with this letter in the Introduction, so suffice it here to stress the clear theoretical-mathematical framing of the question. Hooke, who in h the last rendition of his Programme (in the Appendix to the 1674 Attempt to Prove the Motion of the Earth) declares that he had "not yet experimentally verified" the law by which the "attractive powers" decline with distance (27, italics mine), presents this law here, in this letter, as a theoretical assumption. As such, the law represents one element of a particular solution to a clearly formulated question. The question concerned the stability of the orbit, and was framed, in response to Newton's query, as a question of the permanence of the apsides (or "auges"). Another element of the solution is a (faulty-see Introduction, Section 2) version of Kepler's second law: the inverse ratio between the velocity of an orbiting body lind its distance from the center of attraction. Assuming all three-ISL, the inverse ratio and the "General Rule" of square proportion between force and velocity (see Introduction, Section 2.5)-it is possible, Hooke surmises, to calculate an orbit around a center of attraction in which the apsides "unite in the same part." This letter was sent to Newton on January 6, 1680, and was not honored with a reply. However, the Portsmouth Collection of Newton's papers contains a manuscript, which clearly demonstrates that the reason was not any lapse of interest. Herivel, who was the first to describe it (in his "Newtonian Studies Ill" and in Herivel pp. 246-256), titled it "The KeplerMotion Paper (The Newton Copy)" (henceforth: KMP), and suggested that this manuscript constitutes no less than the calculations Newton promised, but could not recover for Halley in 1684. He dated it, accordingly, as earlier than the first version of De Motu, and Westfall enthusiastically agrees 52 • Hall & Hall, Whiteside and De Gandt contested this dating53 , and while nothing in my argument depends on the exact ordering of these texts I cannot but side with Herivel and Westfall. KMP follows so strictly the line of progress sketched by Hooke in the paragraph cited above, that it is tempting to speculate that its original version was written immediately following Hooke's January 6 letter and before Newton received the January 17 letter, which, like the previous one, he did not honor with a reply.

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3.2. The "Kepler-Motion Paper"

KMP is a short paper. It comprises three hypotheses, three lemmas and three propositions, all in English. The hypotheses cover (I) the continuity of uniform, undisturbed, rectilinear motion (2) the proportionality of force and "alteration" of motion, and (3) the parallelogram of motions. The propositions are proofs of (I) the area law (2) of ISL for the apsides of a body revolving in an ellipse with the center of "attraction" at one of the foci, and (3) proof of ISL for the entire perimeter, which Newton produced with the aid of the lemmas, but without reference to (2). The problem of 'closing the curve', as it emerges from Newton's December 13 letter and Hooke's January 6 reply, is that of ensuring a stable line of apsides. Hooke suggested that this should be done by setting the attraction according to ISL and applying Kepler's second law, and this is exactly how Newton proceeds inKMP. Newton begins by proving for the first time (Prop. J) that (the radius vector of) a body revolving around a center of force sweeps equal areas in equal times, which is the correct formulation of the inverse proportion between distance and velocity suggested by Hooke. The proof is essentially the same as the De Motu proof described above (see Section 2.3.3), and offers no clue as to which of the texts was written earlier. It is in the second Proposition that Newton turns to Hooke's challenge. Employing the area law, he proves ISL for the "auges" of the ellipse (Prop. 2):

AI--~=------~

Figure 25: Proof of ISL for thR. apsides of elliptical orbit in thR. "Kepler Motion Papers" (Herivel, 248).

If a body is attracted towards either focus of an Ellipsis and the quantity of the attraction be such as suffices to make the body revolve in the circumference of the Ellipsis; the attraction at the two ends of the Ellipsis shall be reciprocally as the square of the body in those ends from the focus. (Herivel, 248: KMP, Prop. 2)

As would be the case throughout De Motu, Newton cannot compose the desired curve from the parameters of force and motion, and suffices with

NEWTON'S SYNTHESIS

203

assuming the ellipse and proving that the required relations hold. Thus, he does not actually show that the ISL and the area law imply a neatly closed ellipse with "the neerest point of accesse to the center ... opposite to the furthest Distant." Rather, he proves that for a body revolving in a properly closed elliptical orbit with a center of force given at one of the foci, the force at the apogee and perigee is inversely proportional to the distances from that focus. The proof is telling. Let AECD [Figure 25]. be the ellipsis, A. C its two ends or vertices [or apsides or auges] F the focus towards which the body is attracted and AFE, CFD areas which the body with a ray drawn from that focus to its (the body's] center, describes at both ends in equal times. (Herivel, 248: KMP, Prop. 2)

By Kepler's second law, just proved as Prop. 1, the areas of AFE and CFD are equal. But from this point on Newton's proof takes several bold turns. First, he assumes that "supposing the arches AE and DC very short," he can treat these figures as right-angle triangles whose areas are (FAx AE)/2 =(FC x DC)I2. This allows him to assume that AE: DC:: FC: FA. He then draws tangents AM and CN at the apsides A and C, respectively, and also secants EM and DN perpendicular to these tangents, claiming that "because the ellipsis is alike crooked at both ends" (Herivel, 249: KMP, Prop. 2), he can apply the geometry of circles. In a circle 54 2 2 EM: DN :: AE : CD , and from 2 EM:DN::AF: CD and AE: CD:: FC: FA follows easily that EM:DN:: Fd: FA 2 , or: EMIDN = CFz I AF2

This is a complete, though 'inverse' (see De Gandt, 8) solution to the question discussed in those final stages of the correspondence; FC and FA are the distances from the center of attraction F at the apsides A and C. EM and DN are the perpendiculars to the tangents at those points. As was Newton's custom since the 1660s (see Section 2.2.1), the distance from the tangent is taken as the measure of force, and EM and DN are indeed inversely proportional to the square of their distances from that center. Two moves in this proof are, mildly put, unconventional: the treatment of AFE and CFD as triangles, and the application of the geometry of the circle. While the former~rafty use of limits and infinitesimals-is rather common in the work of Newton we have encountered, the latter is less so. It is tailored specifically to suit the question as formull}ted, namely, as pertaining to the apsides. The willingness to compromise the rigor of his proof, though not rare with Newton, indicates his special interest in its

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particular setting. Moreover: as Westfall pointed out, Newton makes no use of Prop. 2 when he sets out to prove Prop. 3, which is the general claim that an elliptical orbit around a center of force in one of the foci implies ISL: "[this] proposition [Prop. 2] did not contribute to the general proposition on the ellipse and was pointless once the general one had been arrived. It did not appear in De Motu or in the Principia" (Westfall, "A Note on Newton's Demonstration," 53). The theorem concerning the apsides is completely autarchic. It serves only one purpose: to "resolve the problem the correspondence defined" (op. cit., 54). Newton's answer to the challenge presented by Hooke was not only general-it prompted Newton's meticulous response to the questions as formulated in the correspondence.

3.3.

Conclusion

What, then, was the project, which started for Newton where it culminated for Hooke 55-in the correspondence between November 24, 1679 and January 17, I680? Newton's approach to the question of planetary motion changed dramatically following those six letters, and at the core of this change is a crystallized conunitment to celestial mechanics: Newton takes upon himself to account for celestial motions employing the very same tools used in analyzing the motion of terrestrial bodies. Such a conunitment entailed that only rectilinear motions and rectilinear attractions would be incorporated into the explanation, which meant abandoning the conception of the orbit as a given curve whose evident stability implied equilibrium between inward and outward tendencies. It was this conception of equilibrium which allowed both Huygens and the young Newton to investigate gravity by calculating centrifugal forces, but in Newton's later work it is replaced by a conception of the orbit as an effect-a contingent outcome of a continuous dynamic-active process of reciprocal balancing. According to this new approach the closed planetary orbit, like all curved trajectories, is determined exclusively and entirely by (a) the velocity of the planet's 'original'-rectilinear, uniform and unhindered motion, before being captured by (or abstracted from) the attraction of the sun-(b) the distance between the planet and the sun; and (c) the law governing the rectilinear attraction between them. The new task for the natural philosopher, emerging from Newton's later texts, is to construct the formulae into which these parameters are incorporated so as to create curves that model possible trajectories, and then compute the unknown parameters

NEWTON'S SYNTHESIS

205

based on those gained through observation... Different force law; different initial distance; different initial velocity-and the curve would be different. The planetary orbits are contingent phenomena, capable of a complete causal and mathematical account in terms of force and motion. The novelty of the approach, the change that took place in Newton's celestial mechanics, encompasses all the themes discussed above: the progression from calculating centrifugal tendencies caused by curvilinear motion to explaining encurvation by centripetal force; adopting gravity as the paradigm for such a force and transforming it into a universal force by which all heavenly bodies attract each other; the construction of a specific force law-an inverse square ratio between distance and intensity-to account for the astronomical regularities and harmonies made known by Kepler. None of these changes and developments, however, constitutes the breakthrough; Newton's new mechanical picture of the heavens was motivated and enabled, rather by the intricate relations between these new ideas. The newness of Newton's work in the 1680s lies not in the discovery or invention of any singular concept, but in the altogether new conception of what can and should be achieved by a theory the heavenly motions. Could the road to the Principia, then, be properly described as a realization of Hooke's Programme? I would like to claim that it should. By this I do not "attempt to argue that all of Newton's ideas are due to Hooke" (Wilson, op. cit., 167-See Section 2.3). The complex of skills, attitudes, metaphysical assumptions and mathematical tools, some newly developed, some newly recruited, constituting Newton's conversion is so poorly captured by labels like 'ideas' or 'concepts', that the question of whether Hooke himself did or "did not hold a concept of universal gravitation" (Westfall, "Hooke and the Law of Universal Gravitation," 245), is utterly besides the point. As we have seen, even in the case of universal gravitation, Newton did not adopt one particular 'concept', but at least two hardly-compatible, if not outright contradictory doctrines. On the one hand, the belief that the operation of centripetal force on body in inertial motion results in a 'neat'---closed and stable---curved orbit around the center of force. On the other hand, the belief that that stability is of no major consequence-that deviation from a neat orbit, caused by the presence of many other gravitating bodies, does not result in its collapse. Thus, the question about Hooke's Programme is not regarding Hooke's Programme is not who thought of which idea first, but which part of the tool kit unveiled in Newton's later work has been adopted, produced or perfected in, and as a direct response to, his correspondence with Hooke. Hooke did not need to acquaint Newton with the inverse square law, with centripetal

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CHAPTER 3

(rather than centrifugal) force, with the universality of gravitation or with Kepler's area law-these were all available to Newton before the correspondence. It was, however, Hooke's reformulation of the question of planetary motion that deemed all these elements essential to the solution, ascribing to them the roles and relations analyzed above. In summary, though, what I would like to claim is that the correspondence between Hooke and Newton has initiated the following undertaking: the calculation the orbits of the planets as rectilinear trajectories encurved by an attraction, itself operating along straight lines and diminishing as the square of the distance from the sun; this calculation applying Kepler's second law to provide that the gradual encurvation results in a relatively-stable ellipse. This was the project Newton pursued in the manuscripts leading to his Principia, and as the final version of the question formulated by Hooke in the 1666 Address and the 1674 Attempt to Prove the Motion of the World, it definitely deserves the title "Hooke's Programme."

NOTES INTRODUCTION

5

c.t Schaffer, "Glassworks;" Shapiro, "The Gradual acceptance" for two different versions about this dispute. c.t Bennett, Hooke and Wren, 37; De Gandt, 6-7. The correspondence has been presented and interpreted in various levels of details by Westfall, "Hooke;" Force, 424-431; and Never at Rest, 382-388; Nauenberg, "Hooke;" Lohne, "Hooke versus Newton;" Whiteside, "Before the Principia," 9-15; "Prehistory," 20-24; and "Newton's early Thoughts," 129-137; Erlichson, "Newton's 1679/80 Solution," 728-729 and "Newton and Hooke," 56-62; Pugliese, "Robert Hooke:" 182-186. Kepler adopted this proportion citing Aristotle (Copernicus took it on the authority of Euclid's Optics), and reasoned from it to his second law, viz.; that the (vector radii to the) planets sweep equal areas in equal times. He then realized that the two 'laws' are not equivalent, and abandoned the Aristotelian one for his own. There is no indication in Hooke's letter that he is aware of the relation or the difference between the proportions. See Barker and Goldstein; Wilson, "Prom Kepler Laws;" 96-98 for details. Westfall, Force, Chapter 5. Unless otherwise stated, all italics, capital letters and other stresses used in citations, especially from primary sources, arc original. I have also kept the original spelling, and avoided 'sic.' as much as possible. The pages of the Mierographia's Preface are not numbered, and I have assigned Roman numerals to them starting with Brouncker's acknowledgment on the fIrst page.

CHAPTER 1: INFLECTION

c.t Herivel, 192-198; MS IVa; and Hall, "Newton on the Calculation of Central Forces," 63-64. An extensive analysis of theses two issues and the relations between them see Pugliese, "Robert Hooke," 181-205. For a discussion of Wren's claims to priority of this idea, see Bennett, "Hooke and Wren," esp. 3339. Hall, "Two Unpublished lectures," 226; Address to the Royal Society, February 19, 1690. A notable exception is Whiteside's, "Newton's Early Thoughts," and especially "Before the Principia." See my reference to the latter bellow. There are other mentions of the Address, but there are usually cursory, such as Puglisese's "Robert Hooke," 194-198. . Por careful discussion of this issue see Aiton, 10-65 and 91-98. Aiton does not seem to recognize the importance of the difference between Hooke's and

208

NOTES

Descartes' accounts. Astronomia Nova, Part III, Chapters 33-37 and Part IV, Chapter 57. Principia Philosophire, Part III, Article 57. "Species ergo mota in gyrum, ut eo motu Planetis inferat, corpus Solis, seu fontem, una moveri necesse est; non quidem de spacio in spacium mundi: dixi enim me id corpus Solis cum COPERNICO in centro mundi relinquere: sed super suo centro, seu axe, immobilibus; partibus ejus de loco in locum (in codcm tamen spacio, toto corpore manente) trancentibus." (Kepler, Werke, 3,d vol., 243) "Et cum differentia perenium temporariorumque corporum sequatur in eorundem etiam motus; circulares vtique revolutiones erunt perenium corporum; seu Sol moueatur, seu eius loco Tellus; rectiIinei verll vanescentium: habent enim vtrique conditionis suae causam in forma quisque sua: aetemitatis in circulo, motilitatis in linea recta, quae infinita vtique nequit esse." (Kepler, De Cometis, 93-94. Cited by Ruffner, 192) c.f. Miller and Miller's footnotes to their translation of these Articles. In Chapter 3 (section 2.2.3) I touch summarily upon Huygens' grappling with the notion of radial centrifugal forces. 10 I am thankful to the anonymous Kluwer referee who directed my attention to these Articles in the Principia Philosophire. 11 McGuire and Tarnny, 167-175. 12 Herivel, 192-198: MS IV, Hall, "Newton on the Calculation of Central Forces," 63-64 and Whiteside, "Before the Principia," 11. 13 Concerning the former see McGuire & Tamny. In the debate concerning the latter Whiteside ("Newton's Early Thoughts") maintains that this knowledge was limited, while Russell ("Kepler's Laws") holds a more favorable opinion. 14 Whiteside ("Newton's Early Thoughts" and "Before the Principia") makes the clearest -case concerning Newton's difficulties to abandon centrifugal for centripetal force, even after the correspondence with Hooke. 15 In her Janus Faces of Genius the late Betty 10 Dobbs has convincingly shown just how difficult it was for Newton to finally assimilate Hooke's challenge in its own terms and abandon his alchemically motivated vortical notions (cJ 117132). Dobbs, however, concentrates more on the notion of gravitation than on that of encurvation or bending. Whiteside ("Before the Principia," 14) makes a similar point. 16 c.f. Koyre, Galileo Studies, esp. Part I. 17 See my "Tropes and Topics." 18 "MICROGRAPHIA or some Physiological Descriptions of MINUTE BODIES made by Magnifying Glasses with Observations and Inquires thereupon. By R. Hooke Fellow of the Royal Society. LONDON, Printed by 10. Martin and Ia. Allestry, Printers for the Royal Society, and are to be sold at their Shop at the Bell in S. Paul's Church-Yard. M DC LX V."

5

NOTES

19

20

209

Birch 11,272: July 6, 1663. C.f Harwood in Hunter and Schaffer, 119-147; 'Espinasse, 42-59; Drake, 23-32.

I have tried to consistently follow the philosophical convention by writing 'inflection' in single quotes when referring to the linguistic object-the term as it appears in Hooke's texts, and inflection without quotes when using it the way Hooke himself does. The decision whether to use quotes or not was often more difficult than expectcd. 22 Or perhaps intermittent-I am not sure whether Hooke is settled on this issue. n This depiction of the behavior of light in the atmosphere seems to have been more readily incorporated by Hooke's contemporaries than either his term or the further uses he has made of it. This is suggested by the following lines, taken from Lowthrop's introduction to some observations on refraction: ''The Air being no uniform Fluid, the Rays of Light are not refracted in anyone terminated Superficies, but continually into a Curve" (Hooke, Philosophical Experiments and Observations, 338). 24 In the version of this Chapter in my "Producing Knowledge in the Workshop" I wrongly claimed that the 'attractive principle' in this experiment is represented by the chord. The exact representation of this 'endeavour' does not affect the argument here, but it will have some bearing on the discussion in Chapter 2 and I will attain to it in detail there. 25 In his Cometographia of 1668 HeveIius used the Latin form of the verb in a similar manner: "...Cometa: neutiquam in exquisia linea recta, ut quidern Keplerus, alliq; arbitrati sunt, sed in linea ex parte inflexll, & incurvata, cujus concavita pepetuQ Soli prona est ..." (658, cited by Ruffner, 194, f. n. 43). Though published two years after the Address, most of Hevelius work on the Cometographia was simulaneous with Hooke's Micrographia. The delay was caused by the debate (and scandal) over the comet of 1664, during which Hevelius turned to the Ruyal Society to argue his case. Whether the term 'inflection', in the sense discussed here, came up in that correspondence and, if it did, by whom, I simply do not know. Note, however, that Hevelius uses 'inflection' in a manner closer to Hooke's use in the Micrographia then in the Address, namely; as bending rectilinear motion into an open curve. He employs it to account for slight variation of the ephemeral comets from rectilinear projection, which he explicitly opposed to the perpetual revolutions of perfect, eternal planets. 26 Concerning agency in science c.f Gooding, Experiment and Latour, We Have Never been Modem. 27 Rorty is somewhat prone to this approach, c.f Hesse and Rorty, "Unfamiliar Noises," 296 and 2nd Interlude bellow. 28 In my "Tropes and Topics" I called this function of language 'tropical meaning.' 29 Somewhat similar to what I termed the ''topical force" of central theoretical terms in structuring scientific texts ("Tropes and Topics").

21

210 30

3l

32

33

NOTES In his Culterian Lecture Helioscopes (Gunther, vol. 8., 119-152. Henceforth: C.L) Hooke presents a somewhat similar line of technological inquiry: various ways of compounding retlecting mirrors in order to control the amount of light reaching the eye and enable observation of the sun. Hooke notes that 'single microscope,' one of a single lens, has, in fact, 'double refraction,' and a double microscope has four refractions, as the ray is refracted once upon entering the lens and once upon exiting it (CL, 312). Hooke adds: "but this, for other inconveniences, I made but little use of' but does not specify what were these "other inconveniences." C.! Birch I, 268; 272.

1ST INTERLUDE: PRACTICE This was a hierarchy that Hooke himself acutely experienced. See Shapin, "Who Was Robert Hooke?" and Pumfrey. For analysis of its epistemological significance see Shapin, Social History of Truth. These citations are from Hooke's "General Scheme ... of the Present State of Natural Philosophy and How its Defects may be Remedied .. ." published in Waller's posthumous edition of Hooke's works (Hooke, Posthumous Works, 170). 1 bring them here by way of suggestion-my main arguments are going to be drawn from Hooke's actual scientific work, rather than his didactic presentations. However, this particular work does read as a real methodological treatise by a highly experienced practitioner, and not merely a collection of Baconian commonplaces, and is therefore worth more attention than Jean dedicate to it here. 'Of poor origins' would have been more accurate; his legacy included, among other things, close to £10,000 left in his money chest. See Appendix to Hunter and Schaffer. Rorty, the focus of the 200 Interlude, also uses Dewey's phrase "spectator theory of knowledge," e.g. in his "Epistemological Behaviorism," 119, f. n. 18. Quine's position is not that naIve after all, and he does allow that "ones man's observation is another man's closed book or flight of fancy" ("Epistemology Naturalized," in his Ontological Relativity, 88) An earlier philosophical discussion of skills that comes immediately to mind is Polanyi's. His account resembles Hacking's in the stress on the non-theoretical nature of skills, but his notion of tacit knowledge, as some additional information hidden in the achievements of one genius to be discovered by a later one, is in direct opposition to Hacking's strongest point-the notion of knowledge production. An interesting scrutiny of skills as an essential element of human reason is Dreyfus, What Computers Can't Do. Hacking does not pay much attention to the positive secretive tendencies of experimenters, as pointed out, e.g. by Collins, but this addition of course only

NOTES

10

11

strengthen his point. For a discussion of procedures in knowledge producing practices c.f Gooding, Experiment, especially Chapters I and 2. In his "Empiricism, Semantics and Ontology," Rudolph Carnap, from very different presuppositions and on his way to almost opposite conclusion, arrives at a very similar claim about "the reality of entities." It also reveals the original context of Hacking's monograph-a reply to the empiricist, anti-realist position developed by Bas van-Fraassen in The Scientific Image. c.t van Frassen, 15-19. Van Frassen himself, an avowed empiricist and antirealist, presents these two philosophical positions as an indivisible pair. This pairing, however, is not self-evident. One need not commit to any attitude towards realism in order to count as an empiricist.

CHAPTER 2:

10

II

12

211

CLOCKS, PENDULUMS AND SPRINGS

My references will be both the edition of published of De Potentia published independently by John Martin in 1678 and to the edition published in Gunther (vol. 8: C.L) which is more available. Reconstructions of the theory were offered by Hesse ("Hooke's Vibration Theory") and Patterson ("Pendulums of Wren and Hooke"). Patterson ("Robert Hooke and the Conservation of Energy," 151) thinks he does. The part authored by Hooke is titled "An Explication of Rarefaction" (178-182). C.f Hesse, ("Hooke's Vibration Theory," 436-437); Clericuzio. I will attend to this analogy in details later. C.f Clericuzio, 74-75. On January 23rd, 1675/6, Hooke fIrst remarked in his Diary: "wrote a theory of springs." See Clericuzio for Hooke's part in formulating Boyle's Law and the 'spring of air' hypothesis. Hooke's acquaintance with it was probably via Galileo's writing, in which he was clearly versed. One reason to believe that he has learned of O'resme's diagram from Galileo is the fact that, like the latter, he treats the areas as sums of the ordinates (De Potentia, 19; CL, 351). See Discorsi, Third Day, Theorem I, Propositions I and II and Corollary I; Figs. 47-49. For an earlier, somewhat different diagram see Dialogo, Second Day, Fig. 15. c.t Westfall (Force, 206-208) and Pugliese, in Hunter and Schaffer, for other occasions in which Hooke makes use of this assumption. Pugliese remarks that this assumption is 'an axiom of motion' for Hooke, but does not elaborate on the particularities of Hooke's notion of 'powers'. In the Introduction, I presented Hooke's "General Rule of Mechanicks" as

212

NOTES

derived from interpretation of Galileo's theorem. One may understand Hooke's proof here as proceeding along the same lines; if (translating Galileo into "Mechanicks") constant power along distance produces velocity proportional to the root of the distance, then power which varies as the distance (as, according to Hooke, is the case with displaced springs) produces velocity proportional to the distance. 13 Patterson's is still the most extensive analysis of Of Spring. 14 "The distended rope, by the same endeavor to relax or unbend itself, will draw the horse as much towards the stone as it does the stone towards the horse" (Newton, Mathematical Principles, 14. Henceforth: Principia). It is tempting to wonder whether Newton did not have Hooke in mind when he formulated his third law in the Principia. Otherwise, the rope illustration seems somewhat out ofplace. IS The problem, as Peter Machamer has pointed out to me, is principal: parallel processes cannot measure each other. 16 White notes that the origins of the fusee mechanism are probably in military technology-a device for spanning heavy cross-bows called in typical medieval chivalry 'the virgin'. 17 Another mechanism for this purpose is the staclcfreed, which operates on similar principles but to a somewhat less satisfactory results, and was therefore less popular. 18 Cycloid is the curve described by a point on the circumference of a circle rolling on a plain (see Figure 14-top). A cycloidal pendulum can be visualized as a ball rolling up and down in a bowl whose cross-section is a cycloid. A cycloid, Huygens proved in his Horologium Oscilatorium, is it own "evolute" (see Figure l4-bottom). Therefore the pendulum can be made to describe a cycloid by two cycloidal 'cheeks' limiting the motion of its chord (see Figure 13). 19 Cf 'Espinasse, 1956,62 ff. 20 This tellt survived as Trinity College Ms. O.lIa.IIS, without the diagrams referred to in the text, and was transcribed by Wright (102-11 S), who also beautifully reconstructed the devices described. The 1675 dating is hindered by the absence of any reference to Huygens' all-important Horologium Osci/atorium of 1673. 21 Hooke, A Manuscript Concerning Huygens' Har%cium Osci/atarium. British Museum MSS, Sloane 1039, folio 129. Transcribed by Robertson (167-173). Henceforth: Sloane. 22 Most notably the clock given by Charles 11 to his mistress Countess of Castelmaine-cf Symonds, 21. 23 A prize of £20,000 was finally offered by the British Government in 1714, and won by John Harrison in 1761 (but was only half-paid in 1765). Cf Gou,ld. 24 Writing the Longitude Timekeeper, however, Hooke is not yet famiHar with

NOlES

25

26 27

28 29

30 31

32

33

213

Huygens' proof of isochrony, which was published only in the Horologium Oscilatorium of 1673. If he learned about the proof before amending the text, he did not add anything to indicate that (see Section 4.1). Huygens did try to develop methods of suspending pendulum clocks that would make them immune to "the heaving of the ship" (The Pendulum Clock, 30-32). See Figure 15. C.! Patterson, "Pendulums of Wren and Hooke." Cited by Wright, "Robert Hooke's Longitude Timekeeper,"66-67. This is Oxford English Dictionary's definition of 'force'. C.! Hesse, "Hooke's Vibration Theory," 437; Clericuzio, 73-74. Concerning his musical interests see Gouk. For a modern theory of tropes and the difference between metaphors, metonyms and synecdoches see Vickers. A more philosophical approach to these particular 'master tropes' is Burke's Grammar ofMotives. The examples in my "Tropes and Topics" are terms like gravity, levity, proper places and natural form, the never-questioned relations between which structured texts in the tradition of Aristotelian cosmology. I show there how Galileo, ·carefully observing these relations, is able to introduce radical changes into the ('tropic') meaning of these terms without rendering his text unintelligible. In ''Tropes and Topics" J explored Galileo's use of terms like 'natural motion' and 'proper places' in discussing falling bodies after depriving these terms of their traditional Aristotelian (tropic) meaning.

2ND INTERLUDE: REPRESENTATION For another account of Rorty's argument see Bernstein (J 985). My interpretation is similar to Bernstein's on a number of points, but my motivation is concerned with Rorty's criticism of the theory of knowledge, and Bernstein's in his reflections in the role left for philosophy. As Ong (Ramus, Method, and the Decay of Dialogue) forcefully argues, these metaphors gained new vigor with the invention of the movable type, which encouraged the use of diagrams, tables and emblems for pedagogical and rhetorical purposes. Foucault, for one, offers in The Order of Things a very different interpretation of enlightenment concept of representation. According to his interpretation language "does not stand in opposition to thought as the exterior does to the interior" (82). A most potent argument in favor of personal knowledge is provided by Collins in his Changing Order.

214

NOTES

CHAPTER 3: NEWTON'S SYNTHESIS "On the tercentenary of the first publication of his master work on 'The mathematical principles of science' my final words are simple: 1 give yuu its onlie begetter: Isaac Newton I" (Whiteside, "The Prehistory of the Principia," 35). And Whiteside is one of the more sophisticated readers of this 'prehistory', giving much attention to the roles of others in its shaping. Especially by Whiteside, "Prehistory" and "Before the Principia," and also by Westfall, "Hooke and the Law of Universal Gravitation" and Pugliese, "Robert Hooke." Westfall, "Hooke and the Law of Universal Gravitation;" Wilson, "From Kepler's Laws," especially 143 ff. Nauenberg ("Hooke," 335) argues that Hooke's 1666 Address "shows Hooke's understanding of the universal character of gravitational force." To be exact, the apex of all the cones lies in the center of earth. "Demonstratum est cap. XXXII. Planetarum motus intensionem et remissionem sequi proportionem distantiarum simplicem. At videtur virtus ex Sole emanans intendi et remitti debere in proportione duplicata vel triplicata distantiarum seu Iinearum effiuxus. Ergo intensio et remissio motus Planetarum non erit ex attenuatione virtutis ex Sole emanantis." (Kepler, Werke 3, 248) Kepler investigates the analogy and its boundaries again in his Epitome AstronomilE Copernicance, explicitly rejecting an inverse square law for the solar force moving the planets (Kepler, Werke 7,304-305). C.f Wilson, ''From Kepler's Laws," 107; De Gandt, 4-5. "Denique in Planetis primarijs cum cubi distantiarum a sole reciproce sunt ut quadrati numeri periodorum in dato tempore: conatus a sole recedendi reciproce erunt ut quadrata distatniarum a sole." (Herivel, 195) 8 Wilson, "From Kepler Laws," especially 89-92, 133-135: "Newton and Some Philosophers," 233-240. Whiteside ("Newton's Early Thoughts," 121-129), agrees with Wilson about the first two laws, but is wavering about Newton's acceptance of the third law from "degree of confidence" (125) to "unequivocally" (129). Russel's demonstration that Kepler's laws were widely known in the seventeenth century strengthens the impression that Newton positively chose not to accept them. "Spatium quod corpus urgente quacunque vi centripeta ipso motus initio describit esse in dupllicat ratione temporis." (Herivel, 258) 10 "Corporibus in circurnferentijs circulorum uniformiter gyrantibus vires centripetas esse ut arcuum simul descriptorum quadrata applicata ad radios cireulorum." (Herivel, 259) 11 "Casus corolarij quinti obtinet in corporibus erelestibus ... jam statuunt Astronomi" (Herivel, 260. Herivel's translation is on page 279). 12 "Hinc si datur figura qrevis et in ea punctum ad quod vis centripeta dirigitur,

NOTES

13

14

15

16

17

18

19 20

21 22 23

24

25

26

27 28

29

215

inveniri potest lex vis eentripetae quae corpus in figuras iIIius perimetro gyrare faciet" (Herivel, 261). De Gandt's (33) translates "gyrare faciet" as "will cause ... to orbit." 1 think Herivel's use of the present tense better captures the impression of saving a given astronomical phenomenon that Newton is working to create, but the difference is of eourse minor. "Gyrat corpus in ellipsi: requiritur lex vis centripetae tendentis ad umbilicum Ellipseos." (Herivel,263) "Gyrant ergo Planetae majores in ellipsibus habentibus 'umbilicum in centro solis, et radijs ad solem ductis describunt area temporibus proportionales, omnino ut supposuit Keplerus" (Herivel,263) "Posito quod vis centripeta sit reciproce proportionalis quadrato distantiae a centro, quadrata tenporum periodicorum in Ellipsibus sunt ut cubi transversorum axium." (Herivel, 263) The proofs are extremely interesting, but accounting for them in any detail will carry us too far away from our main inquiry. They were excellently interpreted in De Gandt, 31-42. "Haec ita se habent ubi figura Ellipsis est. ffieri enim potest ut corpus moveat in Parabola vel Hyperbola." (Herivel,267) " ... figura erit parabola umbilicum habens in puncto S ... Sin corpus rnajori adhuc celeritate emittitur movebitur id in Hyperbola ..." (Herivel, 267) lowe this citation to Sophie Roux. Trinity College Library, Newton Library, NQ.10.52. CJ Wilson, op. cit.. 92; 132-133. Cf Wilson, op. cit., 136. "Gyrantia omnia radijs ad centrum ductis areas temporibus proportionales describere." (Herivel, 258) Cf his "Newton's Early Thoughts on Planetary Motion," 119-120; "Before the Principia," 10-15. Wilson presents somewhat of an exception. Op. cit., 140-141. Cf Wilson, op. cit., 140-144. "[V]is gravitatis est toties major, ut ne terra conventendo faciat corpora recedere et in aere prosilire." (Herivel, 196) According to Whiston and De Moivre (Whiteside, "Before the Principia," esp. f. n. 30), this was an early test-the "moon test" (see Section 2.1.1)---Qf the theory of universal gravity and ISL. The theory failed the test because, following the common assumption that the distance between the moon and the earth is 60 times the Earth's radius, Newton expected the result to be was 3,600: 1. Thus, according to this almost legendary story, the world was deprived of the Principia for another 20 years. As can be understood, I follow Whiteside in rejecting this account In order to facilitate understanding, I replaced Newton's original lettering in the De Motu diagram to match the lettering he uses in OCM. The original letters are

2t6

30

31 32

3l 34

35 36

37

38

39

40

41

42 43

NOTES S; B; C; D; F which I exchanged with C; A; B; D; E respectably. This is somewhat dangerous. For example, the letter S is consistently used by Newton in his later writing for the center of motion, designating Sol, and is therefore rather important for manuscript dating. However, my interest here is in the comparison, which is rather cumbersome otherwise. Newton also produces two diagrams, as opposed to only one in OCM, and his procedure is that of proportions; F:/:: CD: cd which I abbreviated as ratios. See also Wilson, op. cit., 141. See also De Gandt, 55-57. In Yehuda Elkana's terminology, this would be a change in the image, rather than the body of knowledge (c.j "Two-Tier-Thinking" and "A Programmatic Attempt," esp. 15-21). C.f De Gandt, 124-139; Yoder, esp. Chapter 3, Erlichson, "Huygens and Newton." Though slightly earlier than OCM, De Vi Centrifuga was published only posthumously and was not known to Newton when working on his text. Huygens published most of its theorems, but without proof, in the Horolgium Oscilatorium of 1673. I have, again, installed a comparable lettering to that used by Newton in OCM. It is a problem Huygens adopted from Mersenne, and constitutes an important departure from physics of proportions towards physics of constants. C.f Yoder, esp. Chapter 2. In modern notation: Latus Rectum =x'ly or tla in y = ax'. The segments DB, which are the path AB viewed as receding from the point 0, are equal to-not just approximating-the arcs DO. The curve BBBB will be titled the 'evolute' of the circle when investigated in the Horologium Oscilatorium. De Gandt (134-137) provides an excellent interpretation of the Huygens'- reasoning here. ''The motion of a body can be at the same time truly uniform and truly accelerated, according as one relate its motion to different other bodies." (De Gandt, 137) C. f. Dobbs; McGuire and Rattansi. Of course, because of "the progression of the auges" (Birch, 92) the planetary orbits are not properly closed. Hooke clarified that point in his 1666 address, and the Programme in the letter to Newton on 6 January 1679180 also requires only that "the auges are almost opposite" (Correspondence II, 309. Italics mine). I shall return to this theme in the next section. See also Whiteside, "Newton's Early Thoughts," 119. In the 168I correspondence with F1arnsteed Newton reverts to Borelli's model. Whiteside ("Before the Principia," 15) takes it as evidence to his claim that until 1684 Newton did not complete the transition from the centrifugal to the centripetal approach. My analysis of this transition is very much informed by

NOTES

44

45

46

47 4R

49

50

51

52

53

54

217

Whiteside's, but here I think he overlooks an important phase of it. On the role of the parabola in Galileo's mathematical mechanics see Renn et aI., "Hunting the White Elephant." I purposefully shy away from the anachronistic 'integrate'. It is questionable if Newton was able to solve this 'inverse problem', as it has come to be called in the 18th century, even in the Principia. C. f. De Gandt, 8-9 and 244-250. Esp. 456-466. "Creterum totum cedi Planctarij Spatium vel quiescit (ut vulgo creditur) vel uniformiter movetur in directum et perinde Planetarum commune centrum gravitatis ... vel quiescit vel una movetur. Utroque in casu motus gravitatis inter se ... eodem modo se habent, et eorum commune centrum gravitatis respectu spatij totius quiescit, atque adeo pro centro immobili Systematis totius Planetarij haberi debet. Inde veru systema Copemicreum probatur a priori. Nam si in quovis Planetarum situ computetur commune centrum gravitatis hoc vel incidet in corpus Solis vel ei semper proximum erit. Eo Solis a centro gravitatis errore fit ut vis centripeta non semper tendat ad centrum iIIud immobile, et inde ut planetre nec moveantur in Ellipsibus exacte neque bis revolvant in eadem orbita. Tot sunt orbitre Planetre cujusque quot revolutiones, ut fit in motu Lun? et pendet orbita unaquareque ab omnium Planetarum motibus conjunctis, ut taceam corum omnium actiones in se invicem. Tot autem motuum causas simul considerare et legibus exactis calculum commodum admitentibus motus ipsos definire superat ni fallor vim omnium humani ingenii. Omitte rninutias iIIas et orbita simplex et inter omnes errores mediocris erit Ellipsis de qua jam egi." (Herivel, 297) "Gyrantia omnia radijs ad centrum ductis areas temporibus proportionales describere." (Herivel, 258) "Hypoth 2 Corpus omne sola vi insita uniforrniter secundum rectam Iineam in infinitum progredi nisi aliquid extrinsecus impediat." (Herivel, 258) Hooke writes "consequently" here, which seems to me as a lapse, since it is followed by another "consequently" which signals a perfectly good argument. On the other hand the assumption that "Velocity will be in subduplicate proportion to the Attraction" (namely f oc ...JV) is a ratio between motion and force that Hooke used regularly and for many years, completely independently ofISL. Herivel, 108-17; Westfall, Force, 513-514, f. n. 6. Hall and Hall; Whiteside, "The Prehistory," 53-54, f. n. 87; De Gandt, 283, f. n. 62. In the case of a circle, this is a straightforward consequence of the fact that the angle between a tangent and a chord equals half the central angIe on that chord. Here is the proof in short:

218

NOTES Given a circle with center 0, radius R, AC tangent at point A, BC 1- AC and OD 1- AB, then: sinot!2 '" ADIR '" ABI2R and sinp", CBIAB. Now p", aI2, therefore: CBIAB '" ABI2R, or: CB '" AB'12R, which means that CB ~AB' (because R is a constant). And since the arc AB is proportional to the chord AB, the ratio holds for the arc as well. I thank E. Gal for helping me with this proof.

55

This is, admittedly, a little overstated-see Nauenberg, "Hooke."

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INDEX

Aiton, E. J., 207 Animadversions to the Machina Crelestis, 50 area law, 22, 173,174, 175, 182,196,198,199,202, 203,206 Aristotle, 24, 31, 134, 144, 149,150,151, 158,207 Astronomia Nova, 25, 39, 170,172,196,207 astronomy, 25, 176, 178, 196, 197 Astronomy, 22, 34, 35, 53, 55, 56, 137, 172, 174, 178, 188,192,205 authority, 148 Bacon, Francis, 60, 64, 65, 67 Bennett, J. A., 43, 44, 48, 71, 152,207 Bernstein, R. J., 156 Birch, Thomas, 19,23,31, 32,34,37,43,54,83,140 Borelli, Giovanni Alfonso, 2, 28,29,30,31 Bourdieu, P., 17 Boyle, Robert, 14,54,55,64, 84,86,87,92,93,95,108, 127, 128 Carnap, R., 65 clocks, 14,34,43,98, 102, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117, 121, 124, 125,

128, 132, 139, 140, 141, 142 congruity, 87, 94, 127, 128, 131, 133, 134, 135, 136, 137 Copernicanism, 25 Copernicus, Nicolaus, 23, 25, 207 cosmology, 22, 25, 39, 40, 193,195,196,199 credit, 3, 14, 17, 18,29,47, 68, 167, 168, 171 cycloid, 105, 110; 111, 112, 115, 117 De Gandt, F., 174, 175, 176, 178,196,197,198,200, 201,203,207 De Motu Corporum in Gyrum, 31,165,166,168, 173,174, 175,176,177, 178,179, 181,182,183, 188, 189, 190, 191, 192, 193, 195, 196, 197, 199, 200,201,202,204 De Potentia Restitutiva or Of Spring, 10,84,85,86,87, 88,89,90,91,92,93,94, 95,96,97,98,99,125, . 127, 128, 130, 131, 132, 133, 135, 136, 137, 138, 139, 140, 141, 142 De Vi Centrifuga, 184, 187, 188,189,190, 191

234 Descartes, Rene, 2, 21, 24, 26,27,28,29,31,39, 129, 143,144,145,147,151. 186,207 Dewey, J.,64, 68, 159 Drake, E. T., 15,59,71 ellipse, 6, 7, 19,23,29,37, 40, 165, 173, 174, 175, 176,177,188,191,195, 199,200,202,203,204, 206 epistemology, 13,26,62,64, 70,71. 77, 143, 144, 145, 146,148, 149, 150, 151, 152,153, 154, 156, 157 Epistemology, 35, 59, 60, 62, 63,68,70,71,77,80,100, 143, 144, 145, 146, 149, 150, 151, 152, 153, 156, 157,167 Erlichson, H., 207 escapement, 102, 103, 105, Ill, 112, ll8, 124, 125, 126,138, 141 Euclid,180,207 evolutes, 187 facts, 7, 20, 29, 31, 32, 36, 39,45,49,60,61,62,63, 64,65,67,68,69,72,75, 77,79,80,84,88,90,92, 95,99, 106, 109, Ill, 112, 115,118,128,129,130, 131, 132, 134, 138, 147, 151,152, 154,155,157, 159, 160, 161, 164, 166, 181, 182, 185, 186, 192, 193,196, 198

INDEX

Flamstead, 20 Flamsteed, John, 20, 179, 190,191 force, 11,21,24,29,31,32, 117,122,124,166,173, 178,179,183,189,191, 193,196,198,199,204 attraction (see also force gravity), 2, 5, 7,8,9, 10, II, 19,20,21,22,23, 24,37,83,84,98,99, 140, 165, 168, 171, 177,182,190,191, 192, 194, 198, 199, 200,201,202,203, 204,206 center of, 9, 174, 175, 178, 188,190,198,201,202, 203,204,205 centrifugal, 18, 21, 22, 27, 28,30,31,123, 129, 166,171,173,179,180, 181,182,183, 184, 185, 186, 187, 188, 189, 190, 191,192,204,205,206 centripetal, 18,22,23, 166, 167, 168, 173, 174, 175, 178,179,182,183,188, 189,191,192,194,195, 197,205 gravity, 121 gravity (see also force attraction), 1,7, 10, II, 17,18,21,23,30,31, 32,43,71,84,86,91, 92, 102, 103, 105, 112,121,122,124,

INDEX

130,132,141,165, 166, 167, 168, 169, 170,171,180,181, 182,183,184,185, 190, 192, 193, 194, 195, 196, 198, 199, 200,204,205,206 Force, 11,21,24,29,31,32, 117, 122, 124, 166, 173, 178,179,183,189,191, 193,196,198,199,204 force (see also power), 3,18,21,22,23, 24,26,27,28,30,31, 32,53,54,55,72,76, 88,89,90,91.92,93. 97,99, 100, 102, 103, 104, 112,118,121,122, 123, 124, 129, 132, 135, 157,165,166.167,170, 171,172,173,174,175, 176,177,178,179,180, 181,182, 183,184,185, 187,188,189,190,191, 192,193, 194, 195, 196, 197,198, 199,200,201, 202,203,204,205,206, 207 Galilei. Galileo, 1,2,4, 10, 11,24,25,29,31.83,97, 105,106,107,121, 140, 165, 166, 173, 180, 181. 18'2,183,191,198 Galileo, Galilei, 1,2,4, 10, 11 Gassendi, P., 2 genius, 2, 14, 15,39,43,59,

235

60,61,63, Ill, 117, 143 God, 21, 26 Hacking, I., 63, 64, 65, 66, 67,68,70,71,72,73,74, 75,76,77,78,79,80,122, 143, 144, 147, 148, 151, 154,157,159,160,161, 162, 163,164 Hall, A. R, 14, 15, 17,63,70, 108, 109, 117, 118, 124, 143,201,207 Halley, Edmund, 17, 18,28, 30, 165, 170, 176, 190, 191,192,193,201 Hanson, N. R, 176 harmony, 87,88,94,95, Ill, 131, 133, 134, 135, 136, 137, 138, 139, 140, 188 Helioscopes, 84, 88, 108 Herivel, J. W., 168, 172, 173, 174,175,177,178,181, 182,188,193,195,196, 199,200,201,202,203, 207 hermeneutics, 13, 153 Hesse, M. B., 100, 134, 141 historiography, 13. 14,23. 102, 111, 143, 148, 153, 167 Hooke's law, 14,93 Horologium Oscilatorium, 106, 109, 110, 114, 116 Horrox, J., 2 Hunter, M., 126, 151 Huygens, Christiaan, 2, 10, 14,18,21,27,32,59,60, 105, 108, 109, 110, Ill,

236 112, 113, 114, 115, 116, 117,120, 122, 123, 129, 151, 171, 184, 185, 186, 187, 189, 190, 191,204 incorrigibility, 147, 148, 160 Inflection, 20, 32, 34, 35, 36, 37,38,39,40,41,43,44, 45,47,48,49,50,51,52, 53,54,55,56,57,62,63, 69,71,80,83,88,122, 154, 161 invention, 14,50,61,62,63, 65,69, 108, 109, III, 112, 115,117,122,144,149, 205 inverse square law, 18,22, 166,167,168, 169, 170, 171,172,173, 174, 175, 176,177, 178, 179, 194, 201,202,203,204,205 isochrony, 97, 115 Kant, Imanuel, 75, 145, 162 Kepler, Johannes, 1,2,9,22, 24,25,28,29,31,39,165, 166,168,170,171,172, 173, 174, 175, 176, 177, 178, 183; 184, 192, 196, 197,198,200,201,202, 203,205,206,207 Knorr-eetina, Ko Do, 3 Koyre, A., 29, 30 laboratory, 22, 36,44,45,47, 48,56,67,70 La~as,60,61,84,109, 119, 123, 130, 138 Landes, Do So, 102, 103, 104, 108, 118, 124

INDEX

language, 26,64, 75,147, 150, 154, 159, 162 likeness, 72, 73, 75, 76, 162, 163 Locke, John, 145, 149, 156, 157, 158, 162 Lohne, J., 1,5,8,166, 171, 207 McGuire, J. E., 28 mechanic, 14, 15,43,59,60, 63,69,80, Ill, 117, 143, 161 mechanics, I, II, 14,21,22, 24,27,29,30,32,38,39, 40,57,83,100, 117, 166, 167,199,200,204,205 celestial, 11, 19,21,22,29, 30,32,38,39,40,57, 83,166,167, 194, 195, 199,200,204,205 medium, 36 Mersenne, Mo, 2 MicrQgraphia, 15,33, 34, 35, 36,37,38,39,42,43,44, 45,46,47,48,49,50,51, 52,53,54,55,56,57,61, 67,68,87,92,93,125, 127,128,130,131, 132, 133, 134, 135, 137, 150, 169, 170 microscopes, 47, 49, 50, 51, 52,67,68,69,73,77,78, 79,80,83,164 moon test, 171 motion accelerated, 8, 9, 21, 97, 140, 189, 191, 192, 194

INDEX

circular, 25, 27, 28, 29, 30,

37,39,83,86,140,173, 175, 180, 186, 187 curved, II, 19,20,24,25, 27,29,31,32,35,39, 43,52,53,83,124,140, 190,191,192,199.200, 204,205 free fall, 10, 198 inertial, 11, 18,20,26,29, 125, 178, 182, 191,205 oscilation, 86, 87,88,95, 96, 102, 117, 127, 129, 130, 131, 133 planetary, 2, 3, 6, 10, 11,

18, 19,20,21,22,23, 24,25,26,28,29,31, 32,34,35,36,37,38, 39,40,42,43,44,57, 83, 165, 166, 168, 169, 170,171,172,173,174, 175,178,179,190,192, 193,194,195,197,199, 204,206,207 projection, 11 rectilinear, 2, 9, 11,20,21, 22,24,25,26,27,28, 29,31,32,35,36,37, 38,39,43,53,57,178, 180,187,189, 190, 192, 198,199,200,202,204, 206 rotation, 2, 4, 24, 25, 27, 29,31,105,125,128, 174,181,183,199 tangential, 7, 22, 27,178, 180, 182, 184, 185, 186,

237 191

velocity, 10, 98, 200 natural philosophy, 178 nature, 28, 37, 39,41,57,62,

63,64,70,71,80,99,122, 124, 145, 146, 148, 149, 150, 158, 159, 185, 186, 198,200 Nauenberg, M., 1,207 Newton, Isaac, 1,2,3,4,5,7, 8,9, II, 13, 14, 15, 17, i8, 19,20,21,22,23,28,29, 30,31,34,42,43,44,59, 60,63,69,84,91,100, Ill, 140, 143, 150, 152, 153, 158, 161, 165, 166, 167,168,170,171,172, 173,174,175,176,177, 178,179,180,181,182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198,199,200,201,202, 203,204,205,207 observation, 19,20,22,34, 35,44,45,49,50,53,55, 56,57,63,64,65,66,67, 68,70,71,78,79,80, ISO, 151, 152,160, 172, 174, 192,205 Oldenburg, Henry, 1,3,109, 111 On Circular Motion, 168, 171,172,173,174,176, 177,179,180,181,182, 183, 184, 188, 189, 191 ontology, 26, 77, 144, 146,

238 149,150,151,153,156, 189 Oresme, Nichol, 100 parabola, 98,176, 185, 186, 187,188, 190, 191 Parallax, 20, 56 Patterson, L. D., 99,100, 137, 141 pendulum, 31, 37, 43, 83,84, 105, 106, 107, 108, 109, 110,111,112,113,115, 116, 117, 121, 122, 123, 124, 125, 171, 184 Pepys, Samuel, 34, 44 Petty, William, 10 phenomena, 22,34,36,44, 53,55,62,63,66,67,70, 71,73,80, 122, 129, 132, 138, 139, 151, 164,205 planetary orbits, 2, 6, 7, 8, 9, 11,21,24,26,29,31,37, 39,57,83,165,166,170, 171,173,174,175,176, 178,179,180,182, 183, 184, 185, 186, 188, 189, 190,191, 192, 195, 196, 197,198,199,200,201, 202,203,204,205,206 power (see also force), 10, 11, 19,20,21, 22,23,25,28,36,42, 44,59,71,77,78,81, 83,84,86,88,89,90, 91,92,93,94,95,96, 97,98,99, 100, 113, 115, 122, 124, 125, 132, 133,137,139, 140,141,

INDEX

154,156,161,169,170, 174,175,190,193,194, 196 pragmatism, 64, 159 Principia PhilosophilE, 21 , 24,26,28,39,207 priority, 17, 18,20,23,28, 30,59,108, 109, 111, 112, \22,165,166, 167, 168, 169,171,177,201,207 propositions, 71,80, 155, 156,157,158, 159, 160, 161, 163, 170, 198,202, 204 Pugliese, P. J., 207 Putnam, H., 143 Quine, W. v. 0., 65, 67, 150, 151 realism, 71, 73, 74, 75, 76, 77,78,79,80,148,163 local,73 representation, 38, 62, 64, 65, 68,69,70,71,72,73,74, 75,78,80,104,138,140, 144,145,148,149,151, 152, 153, 154, 155, 157, 159,161,162,163,164, 187 Robertson, J. D., 105, 106, 107, Ill, 120 Robinson, H. W., 109 Rorty, R., 62,64,70,74, 143, 144, 145, 146, 147, 148, 149,150,151,152,153, 154, 155, 156, 157, 158, 159,160,161,162 Rouse Ball, W. W., 166

INDEX

Royal Society of London, 1, 3,5, 10, 13, 14, 17, 19,20, 23,24,32,34,35,37,39, 43,54,56,57,59,88,90, 109,111, 150, 165, 192, 207 Ruffner, Jo A., 25 Sabra, A. I., 168 Schaffer, S., 126, 151, 207 scientific technology, 48, 60, 61,62,69,80 scientist, 14, 15,59,60,69, 70,80,117,143,161 Sellars, W., 149 Shapin, So, 150, 151 Shapiro, A. Eo, 207 skepticism, 74, 78, 148, 149, 150,157,196 Pyrrhonian,74, 145 skills, 3, 12, 35, 44, 48, 56, 57,60,62,67,80,139, 160,167,183, 190,205 Skills, 15, 139, 160, 174 springs, 10, 14,66,81,84, 85,86,88,89,90,91,92, 93,94,95,96,97,98,99, 100, 102, 103, 104, 108, 109,111,112,113,118, 119,120,121,122, 123, 124,125, 127, 128, 129, 130,131, 132, 133, 135, 136, 137, 138, 139, 140,

239

141, 142 Strawson, P. E, 74 technology, 47, 48, 50, 51, 60,61,62,63,64,69,70, 71,80,103,117,118,121, 122, 123, 142 Technology, 50, 60, 61,103, 112 tools, 2, 12, 21, 24, 26, 34, 40,41,43,48,51,52,53, 68,71,80,81,96,100, 102, 122, 137, 145, 157. 161, 163,164,167,174, 175, 177, 178, 183, 191. 196,197,199,204,205 van Fraassen, Bas, 65, 78 verge and foliot. 102, 103, 105,112.122,190 Westfall, R. S., 13,47.59, 60,61,62.63,65.69,71, 99, 111, 143, 144. 148, 150, 166, 192. 193, 194, 195,200,201,204,205, 207 Westman, R. So, 14 Whiteside, D. T.• 30, 166, 179,193,201,207 Wren, Christopher, 99. 100, 207 Wright, M., 108, 118, 126 Yoder, G., 187 Yoder, Go, 187