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