Iliffe Newton

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Stud. Hist. Phil. Sci. 35 (2004) 427–454www.elsevier.com/locate/shpsa

Abstract considerations: disciplines and theincoherence of Newton’s natural philosophy

Rob Iliffe

Centre for the History of Science, Technology and Medicine, Sherfield Building 452, Imperial College,London SW7 2AZ, UK

Abstract

Historians have long sought putative connections between different areas of Newton’sscientific work, while recently scholars have argued that there were causal links between evenmore disparate fields of his intellectual activity. In this paper I take an opposite approach,and attempt to account for certain tensions in Newton’s ‘scientific’ work by examining his

great sensitivity to the disciplinary divisions that both conditioned and facilitated his earlyinvestigations in science and mathematics. These momentous undertakings, exemplified byresearch that he wrote up in two separate notebooks, obey strict distinctions betweenapproaches appropriate to both new and old ‘natural philosophy’ and those appropriate tothe mixed mathematical sciences. He retained a fairly rigid demarcation between them untilthe early eighteenth century. At the same time as Newton presented the ‘mathematical prin-ciples’ of natural philosophy in his magnum opus of 1687, he remained equally committed toa separate and more private world or ontology that he publicly denigrated as hypothetical orconjectural. This is to say nothing of the worlds implicit in his work on mathematics andalchemy. He did not lurch from one overarching ontological commitment to the next (forexample, moving tout court from radical aetherial explanations to strictly vacuist accounts)

but instead simultaneously—and often radically—developed generically distinct conceptsand ontologies that were appropriate to specific settings and locations (for example, private,qualitative, causal natural philosophy versus public quantitative mixed mathematics) as wellas to relevant styles of argument. Accordingly I argue that the concepts used by Newtonthroughout his career were intimately bound up with these appropriate generic or quasi-disciplinary ‘structures’. His later efforts to bring together active principles, aethers andvoids in various works were not failures that resulted from his ‘confusion’ but were boldattempts to meld together concepts or ontologies that belonged to distinct enquiries. His

E-mail address: [email protected] (R. Iliffe).

0039-3681/$ - see front matter # 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.shpsa.2004.06.004



analysis could not be ‘coherent’ because the structures in which they appeared werefundamentally incompatible.# 2004 Elsevier Ltd. All rights reserved.

Keywords: Connectionism; Incoherence; Appropriateness; Setting; Discipline; Genre; Structure

1. Introduction

Early research into Newton’s archival bequest was naturally dominated by atten-tion to his seminal achievements in mathematics, physics and chemistry.1 When his‘alchemical’ and theological writings were investigated in more detail in the 1960sand 1970s, they were not seen initially as relevant to Newton’s scientific pursuits.Consequently, a deep fissure emerged between historians working on the scien-tific and non-scientific areas of his research. Partly as a response to this situation— and as a corrective to the implication that it rendered Newton a divided self—anumber of scholars argued that there were conceptual links between Newton’s the-ology or alchemy, and his natural philosophy or mathematical physics. Mostnotably, perhaps, Betty Jo Teeter Dobbs and Richard S. Westfall argued thatNewton’s alchemical research possessed a degree of quantitative precision that wasunmatched by contemporary adepts. More boldly, they claimed that with noapparent antecedent in standard mechanical philosophy, Newton’s notion of Uni-versal Gravitation owed a great deal to alchemical categories such as ‘sympathy’.2

The idea that apparently disparate parts of his writings are somehow connectedwas to some extent a response to the positivist emphasis of earlier Newton scholar-ship, but more generally, it was based on the metaphysical presumption that theindividual ‘Isaac Newton’ was the undifferentiated author of a group of writingsthat were all coherent or unified at some level . In his Religion of Isaac Newton of 1974, for example, Frank Manuel rehearsed pertinent connections betweenNewton’s theological conception of God as pantokrator and his notion of absolutespace, and pointed to virtually identical passages in both the 1713 GeneralScholium and Newton’s contemporaneous ‘History of the Church’. Manuel added,quite plausibly, that Newton’s condemnation of metaphysical corruptions of early

Christianity bore some relation to his early eighteenth-century attack on Leibniz’sphilosophy. Beyond this, he remarked that whatever Newton scrutinised he was‘searching for a unifying structure’; all his studies ‘bespeak the same mentality andstyle of thought. If nature was consonant with itself, so was Isaac Newton’s mind’.More recently, Dobbs and Jim Force have extended this approach to argue thatother fields of Newton’s research were linked or unified in some manner. Accord-ing to Dobbs, ‘The Janus-like faces of Newton were after all the production of asingle mind [that] was equipped with a certain fundamental assumption, common

1 See inter alia Newton (1959–1977, 1967–1981, 1962); Herivel (1965); Westfall (1971); Cohen (1971,1980).

2 See Westfall (1984), pp 388–390, and Dobbs (1975), p. 11.

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to his age, from which his various lines of investigation flowed naturally: theassumption of the unity of Truth’.3

However plausible a priori an integrated identity of author and the oeuvre

appears, this assumption has not gone without major criticism. Attacks on author-ial unity and textual coherence, and the celebration of the death of the author,have all been staples of recent literary criticism. While not embracing the moreextreme implications of deconstructionist approaches, Brian Vickers suggested twodecades ago in his Occult and scientific mentalities in the Renaissance that a unifiedNewtonian ‘mind’ was no longer tenable. Vickers’s distinction between ‘occult’ and‘scientific’ is rather anachronistic, and his use of the notion of ‘mentalities’ detractssomewhat from the force of his anti-mentalist argument. While I concur with thegeneral anti-connectionist thrust to his approach, I develop a different view in thisessay. I suggest that from the very beginning of his researches, Newton shaped his

own work according to distinctions between what was appropriate to the distinctdisciplinary traditions of natural philosophy and mixed mathematics. The way heviewed his own roles as a practitioner within these fields, and what these produc-tions were, can only be understood by grasping where they stood vis-a-vis otherexemplary writings within given disciplines or traditions, and not through theirputative connection to other parts of his research. In short, what I propose is therecognition of metaphysical heterogeneity—at both the textual and authoriallevels—rather than the unity presupposed by many other historians.4

Of course, there is a danger of merely rehearsing the older view—licensedby Newton in his own writings in mixed mathematics—that mixed mathematicswas a superior form of enquiry to more ‘hypothetical’ research, and that themathematisation of nature was the only proper fate of such material. Against theview that there was a strong causal link between Newton’s alchemical conceptsand those of his mathematical physics, Bernard Cohen argued in 1980 thatthe route to the enunciation of Universal Gravitation was the result of Newton’sscientific ‘style’. According to Cohen, Newton’s approach—exemplified by thelogical structure of the Principia —separated the study of the exact sciences intoa number of stages and the development of Newton’s master-concept could beexplained perfectly adequately without recourse to his other pursuits. Cohen

pointed to the significant distinctions that Newton maintained in the Principiabetween the abstract categories deployed therein, and the more privately conductedprogrammes or projects concerning the physical causes of natural phenomena.These last activities Newton denigrated publicly as ‘hypotheses’ or ‘conjectures’,and he often professed his unwillingness to release his own theories to the public,

3 Manuel (1974), p. 103; see also Dobbs (1991), pp. 5–15 (esp. p. 6), and Force (2000), esp. p. 254. Seein particular McGuire & Rattansi (1966) and Kubrin (1967). As a further variant of the holistic perspec-tive, it has been implied that a particular area of study, particularly Newton’s theological studies, con-

stitutes a conceptual or methodological fons et origo for all of his other researches. See in particular

Castillejo (1981), esp. p.15.4 Vickers (1984), pp. 6, 15–16. For comments relating to the existence of the author and authorial

unity see Eakin (1985); Soderqvist (1996), esp. pp. 55–58; Burke (1998).

429R. Iliffe / Stud. Hist. Phil. Sci. 35 (2004) 427–454



for fear (as he put it) of causing unnecessary disputes. In the Principia and else-where Newton remarked on the incomplete nature of these studies, as if they couldonly be fully legitimated by their later incorporation into a mathematical natural

philosophy.5

I have sympathy both with Cohen’s argument, and with his sensitivity tothe disciplinary compartmentalisation that Newton introduced into his work.However, in this paper I claim that throughout his career he performed philosophi-cal and ‘chymical’ research at the same time and with the same commitment ashe developed mixed mathematical approaches to geometrical optics and rationalmechanics. Although his writing in these fields ostensibly concerned identicalphenomena (such as gravitation), for the most part they were fundamentallyincompatible and there was little if any interaction or connection between them.I do not deal here with putative relations between Newton’s natural philosophy

and theology (or alchemy). However, it should be apparent that the recognitionof disciplinary compartmentalisation within his analyses of the natural worldhas ramifications for larger claims about the unity of his entire oeuvre, or forsorts of connection between different areas of his research. Attention to discipline-specific discourses and epistemological demands detracts from explanations thatmake use of Newton’s much vaunted ‘caution’, or of his later ‘confusion’ or moregenerally of a schizoid ‘mind’ whose various parts worked in ignorance of eachother. Rather, those actions of Newton that have traditionally been attributed tomentalist or psychologistic categories, I view as being shaped by sophisticated con-cerns with settings that were appropriate to the disciplines or genres in which he

wrote.

2. The power of discipline

The importance of disciplinary divisions is the overriding theme in the histori-ography of early modern science in the last two and a half decades. At the heart of this recent research has been an awareness of how contemporaries were partly con-strained by, but also manipulated the features pertaining to the basic division

between mixed mathematics and conventional natural philosophy.6

In his pioneer-ing article on sixteenth-century astronomy, Robert Westman first drew attention tothe socio-epistemological significance of this disciplinary distinction for Copernicus(and by extension for Osiander) in his De revolutionibus, while Nick Jardine and

5 Cohen (1980), pp. xii–xiii, 64–67, 71, 52, 82–83, 92–93, 106, 109–111, 130–131, and esp. pp. 10–11(where Cohen rejects Westfall’s attempt to ‘give a unity to Newton’s intellectual endeavour’ on the basisof seeing Universal Gravitation as primarily the offspring of ‘alchemical active principles’). Note therefined version of Cohen’s model, describing Newton’s approach as using ‘if-then’ models, in Harper &

Smith (1995) and Smith (2001). Ernan McMullin pointed to a similar process (McMullin, 1978, esp.

p.2).6 For distinctions between natural philosophy and mixed mathematics see Weisheipl (1965);

McKirahan (1978); Livesey (1985), esp. pp. 127–128.




others have shown how in the field of astronomy, Kepler was interested in elidingthis division and in creating a new discipline of ‘celestial physics’.7

Mario Biagioli has shown in detail how Galileo manipulated disciplinary con-

ventions in his successful bid to become the prestigious Philosopher-in-Chief at thecourt of the Grand Duke of Tuscany, and Galileo’s greatest intellectual triumphwas arguably to transform the discipline of natural philosophy by creating a math-ematical science of motion. The exorbitant price for this was that some conceptswere ruthlessly shorn of their traditional physicalist associations. For example, inhis Discourses and mathematical demonstrations concerning two new sciences of 1638, his spokesman Salviati called previous philosophical explanations of accel-erations fantasies, noting only that it sufficed if the odd-number rule obtained innature. Contemporaries recognised that Galileo’s mathematisation of the naturalworld could scarcely be accommodated within conventional natural philosophy,and asked quite reasonably whether what applied in the abstract was relevant tothe concrete.8 In the second half of the century the distinctions in the approach tonature embodied in these basic disciplinary divisions were the source of substantialdisagreements across Europe between empiricist experimentalists, mechanisticsystem-builders, mathematicians, and those who still professed allegiance toAristotelian systems.9

Newton himself explicitly compartmentalised his work according to these divi-sions and he recognised that different subjects required discipline-specific discursiveforms. Following in the path of the Italian maestro, he would have similar pro-

blems in trying to convince fellow natural philosophers that some parts of theworld could be mathematised, and that natural philosophy should not concernitself with less-than-certain conjectures about the causes of things. Nevertheless, hisdeployment of disciplinary distinctions is much more subtle than this general state-ment suggests. Even within the Principia itself he made use of a distinction betweena mathematical, idealised world analysed in terms of both infinitesimal-impulse andcontinuous force ‘attractions’, and the physical ‘system of the world’ of BookThree that is accounted for in terms of ‘real’ entities such as Universal Gravitationand short-range attractive or repulsive forces. In turn, the analysis in the Principiawas itself contrasted with private and more orthodox research in natural philo-sophy. Although they were conducted according to very different rules, Newton’sexperience in publishing his mixed mathematical researches did have an effect on

7 See Westman (1980); Westman (1990), esp. pp. 178–185; on textual incoherence see Jardine (1992).For Kepler see Jardine (1987), pp. 138–139, 144–145, 230–254; Westman (1980), pp. 117–129; Rose(1975).

8 Galileo (1974), pp. 152–153, 159, 223–225. For commentary on different aspects of the Galilean pro-gramme, see Koyre (1968); Clavelin (1974), pp. 384–391 (for the critique of Aristotelian accounts of essences); Shea (1978); Biagioli (1993); McMullin (1985), esp. pp. 255–262; Feldhay (1998), esp. p. 132.

9 Dear (1995), pp. 180–207 (esp. pp. 180–187, 197–201), and Jones (2001), esp. pp. 141–145. For Boyle

see Shapin (1988), esp. pp. 42–54; Shapin (1994), pp. 181, 316–317, 310–353, and Dear (1995), p. 226.For the early Royal Society’s views on mathematics see Shapiro (1993), pp. 227–231, and Feingold(2001), esp. pp. 81–83.




the presentation of his more private work. Even non-mathematised physical con-cepts such as ‘aether’ would be ‘neutralised’ (that is, Newton stated that he was notconcerned with its physical cause) when moved to what he took to be a more pre-

carious public forum for presenting his work.10

3. The Barrovian programme

As part of the Quadrivium, mathematics was an intrinsic part of the early mod-ern undergraduate curriculum at Cambridge University and in the 1650s IsaacBarrow developed a series of treatises on, or epitomes of, central texts in Greekmathematics, mainly directed at beginners. He delivered his first Lucasian lecturesin March 1664, six weeks before Newton was elected a scholar at Trinity. Although

he rarely acknowledged it, Newton almost certainly attended the bulk of Barrow’slectures, which concerned limit sums and infinite series, and his confidant of the1720s, William Stukeley, understood Barrow to have been Newton’s tutor. In amemorandum from 1699 Newton recorded that shortly before Christmas 1664‘I bought Schooten’s Miscellanies & Cartes’s Geometry (having read this Geometry& Oughtred’s Clavis above half a year before) & borrowed Wallis’s works & byconsequence made these Annotations out of Schooten & Wallis in winter betweenthe years 1664 & 1665’. In another recollection from the end of his life, Newtonfamously reported that he was elected to the scholarship only after an examinationon Euclid at the hands of Barrow. This had gone badly because although Newtonwas already a ‘master’ of Descartes’s Ge ome trie, he failed to impress Barrow withhis knowledge of Euclid. He passed nevertheless and was to show Barrow many of his mathematical productions over the following years.11

In his Lucasian lectures, which are saturated with discussion about disciplinarydivisions, Barrow claimed that all branches of natural science could be made a partof mixed mathematics and that all of the latter could be subordinated to geometry.As for ‘Physics’ he remarked that ‘there is no Part of this which does not implyQuantity, or to which geometrical Theorems may not be applied, and conse-quently, which is not in some Way dependant on Geometry’. The distinction

between mathematics and the mixed sciences was artificial since once the mixedmathematical sciences were ‘disrobed of particular Circumstances, and their ownfundamental and principal Hypotheses come to be admitted (whether sustained bya probable Reason, or assumed gratis) they become purely Geometrical’. Further-more, he strove to show that mathematical reasoning was causally demonstrativein the Aristotelian sense, since mathematical axioms were universally and necessar-ily true, ‘Primary and Immediate’ and ‘More Known and More Evident than the

10 Cohen (1980), p. 61. For recent discussions concerning Newton’s mathematical techniques for ana-

lysing force, see Gandt (1995) and Blay (2001). For the exclusionary effects of Newton’s work, and the

Continental reception of the Principia, see Gingras (2001), esp. pp. 386–396, and Iliffe (2003).11 Feingold (1990), pp. 40–45; Feingold (1993), esp. pp. 314–318; Stukeley (1936), pp. 53–54;

Cambridge University Library (CUL) Add. Ms. 4000, fol. 14v; Westfall (1984), pp. 98, 99 n. 91, 102.




Conclusions inferred’, while propositions arising from these axioms and definitions

‘must needs flow from the intimate Essences and Causes of the Things’. According

to Barrow, the truth of philosophical principles did not depend only on induction

by simple enumeration, or on the ‘perpetual observation of Particulars’, but ‘con-stant Experience’ and ‘frequent Experiments’ could provide a ‘ready Assent’ to a

proposition. However, one experiment, if it were ‘sufficiently clear and indubitable’

could corroborate a true hypothesis. Philosophers could achieve something more

than probabilistic statements, and he argued that in certain circumstances, given

the ‘Constancy of Nature, we may prudently infer an universal proposition even by

one Experiment alone’.12

Barrow’s strong presumption in favour of a mathematical approach to natural

philosophy, coupled with the mathematical content of his lectures as Lucasian

Professor, had a strong effect on Newton, and the latter quickly learned to innovatein the subject. Even before he took notes from Wallis and Schooten, he had com-

posed his first mathematical essay (in the summer of 1664), and he stormed into

the front rank of European mathematicians following the researches of 1665–1666

that gave rise to discoveries such as the Binomial Theorem and the fundamental

theorems of the calculus. Conceptually, his geometry was already becoming physi-

calised. By the summer of 1665 he had broken away from Wallis’s technique of

considering quadratures as summations of infinitesimals, and had begun to develop

techniques for thinking of areas as swept out by lines, and solids as swept out by

areas. In November 1665 he began to develop a more general kinematical

approach to mathematics based on the idea that curves or ‘crooked lines’ were

traced out by a point in a ‘space’ over a given portion of ‘time’ and hence pos-

sessed a ‘velocity’. This method of solving problems by motion was not simply the

preserve of Barrow, although Newton later recalled that Barrow’s lectures were

probably pivotal in inspiring him to develop this sort of analysis. Possibly the first

sets of curves subjected by Newton to this kind of approach were the so-called

‘Mechanicall Lines’, or curves that could in principle be constructed with a special

instrument such as the Mesolabum. As early as November 1665 he invented

the term ‘fluxion’ to capture the kinematic aspect of his new approach, and he gen-

eralised his discoveries in a seminal paper on mathematical motion in October

1666.13

12 Barrow (1970), pp. 22, 27, 80–100 (esp. p. 83), 73–74, Shapiro (1993), pp. 30–37, Dear (1995),pp. 222–227, Malet (1997), and especially Mancosu (1996), pp. 19–24.13 Newton (1967–1981), Vol. 1, pp. 4–5, 25–121 (for notes on Oughtred, Descartes, Schooten, Huygens,

Viete and Wallis); pp. 377–381 (‘How to draw tangents to Mechanicall Lines’, 8 November, 1665); pp.382–389 (‘To find ye velocitys of bodys by ye lines they describe’, 13 November, 1665); pp. 392–398(‘To resolve Problems by motion ye 6 following prop: are necessary & sufficient’, 16 May, 1666); pp. 400–448(‘To resolve problems by motion these following Propositions are sufficient’, October, 1666); pp. 146–147.

See also Westfall (1984), pp. 123–127, 131–134. Due to the plague, Newton left Trinity at the end of July orstart of August 1665 and returned in March of the following year; a recurrence of the pestilence forced himto vacate his rooms once more in June 1666 and he only returned in April 1667.




Notably, many of the so-called ‘Problems’ he laid out as part of a potentialmathematical programme in November 1665, were concerned with areas, volumes,points of maximum and minimum curvature, collisions and centres of gravity etc.

In dealing with the resolution and composition of vector speeds, and invoking theinertial or uniform motion of points moving in virtual space, many entries in the‘Waste Book’ (originally his stepfather’s religious commonplace book) from late1664/early 1665 blurred the distinction between mechanics and mathematics. Asearly as 1665, for example, Newton was attempting to construct a parallelogramrule of vector motions in which the diagonal of the parallelogram was understoodas being composed of both ‘motions’ from one end of the diagonal to its neigh-bouring points. The fluxional form of the calculus that he developed soon after-wards was based on the velocity, acceleration and retardation of a point in motionwith respect to invariant moments of ‘time’. Occasionally, it is unclear whether

problems in the ‘Waste Book’ concern mathematics or mechanics, or even whetherthe distinction is valid. Aside from this tension, a more pervasive division betweenmixed mathematical topics and philosophical questions was already integral to theway Newton composed and presented his work.14

At the same time as he mastered contemporary mathematical texts, he criticallyscrutinised the latest journals and books in natural philosophy, and from his mus-ings on these works he swiftly and almost seamlessly concocted new notions andprojects. From early 1664 he began to make notes on metaphysical and philosophi-cal questions in a notebook (the Trinity Notebook) in which he had previouslymade annotations on works from the traditional Cambridge curriculum. For most

of the notebook, Newton subjected contemporary natural philosophy to a pen-etrating critique. Many of the conceptions he formulated in these passages, as ayoung student of twenty-three or twenty-four, formed the basis of his later work inoptics and natural philosophy. The earliest entries in the section, aptly entitled‘Questiones quædam Philosophiæ’ concern more traditional topics, such as theexistence of ‘first matter’, the nature of quantity, and aspects of time and eternity,but scholastic metaphysical arguments of this kind were soon to hold little interestfor him. Although the topics varied widely, the treatment of natural philosophy inthe Trinity Notebook completely distinguished the relevant subjects from those

treated in the ‘Waste Book’.

15

4. The mathematical theory of colours

Newton’s interest in the implications of the heterogeneity of white light evolvedrapidly in the mid-1660s. A section of his Trinity Notebook entitled ‘Of col-

14 For the ‘Waste Book’ researches see Herivel (1965), pp. 128–182; Newton (1967–1981), Vol. 1,

pp. 452–465 (esp. p. 456 n. 2), and Cohen (1980), pp. 27, 56–62. Other early researches in mechanics are

to be found in CUL Add. Ms. 3958.15 Newton (1983), pp. 15–25, 26–126 (esp. pp. 26–43, 112–113); Newton (1967–1981), Vol. 1, pp. 89–91.

For the quaestiones tradition see Thijssen (1986).




ours’ was transformed by 1666 into an extended essay of the same name thatappeared in a separate notebook largely devoted to notes and researches in whatcan loosely be termed chemistry and alchemy. In the earliest researches recorded in

the Trinity Notebook, Newton mixed a basic description of simple prismaticphenomena with accounts of the role of the aether, the ‘elastick power of ye subtilmatter whereby ye motions of ye rays are conserved’, the speed of various rays,self-experimentation and the way the perception of colours depended upon the dis-position of the sensorium. By the time of the 1666 essay, he was describing a runof experiments in which aspects of the experimental set up were described in min-utes of a degree and ten thousandth parts of an inch. When he analysed thephenomenon of periodicity, comments on the nature of the vibrating mediathrough which light travelled clearly constituted a different feature of the subjectand they were apparently added later.16

Separately, and following his reading of Descartes’s Ge ome trie and Dioptrique, heinserted notes on reflection and refraction in the ‘Waste Book’ in September 1664and performed experiments on the same topics in late 1665 and early 1666. As foraysinto geometrical optics he entered the results of this programme—largely concerningrefracting surfaces caused by the revolution of conics and notes on hyperbolic andparabolic lens-grinding machines—into yet another notebook. In this case, of course, his acknowledgement of the chromatic aberration inherent in ordinary lenseswas intimately bound up with his research into differential refrangibility of primarycoloured rays. He attended Barrow’s lectures on geometrical optics in 1667 and1668, and Barrow allowed him to proofread the published version of his optical lec-tures that appeared in 1669. Before he began delivering his Lucasian lectures inJanuary of the following year, Newton added some notes to the essay on refractions,exploring the possibility of a compound achromatic lens and writing down a table of refractions and reflections for glass, crystal and water.17

The content of his Lucasian lectures shows that well before he experienced nega-tive criticism as a result of publishing his theory in the Philosophical Transactions(in 1672), Newton believed that only a mathematical approach to nature coulddeliver an indisputable level of certainty. There are two versions of the optical lec-tures given by Newton when he assumed the Lucasian Chair. Neither the first, the

‘Lectiones opticae’, nor the second, the ‘Optica’, can be conclusively proved to cor-respond exactly to the actual lectures that he gave, and the ‘Optica’ was at leastpartly rewritten after he received criticisms of his paper on light and colours. Atvarious points in the ‘Lectiones’, there appears to be a positive attitude to the cor-roboratory role of experiments that is lacking from the main part of the laterTransactions paper. For example, after describing experiments designed to show

16 The notebook is now CUL Add. Ms. 3975; the essay ‘Of colours’ from it appears on fols. 1–22 andis reproduced in Newton (1983), pp. 466–489; cf. esp. pp. 476–477, 481. For the earlier notes from the

Trinity Notebook itself, see ibid., pp. 430–441 (esp. p. 434).17 The earliest notes are from CUL Add. Ms. 4004 fols. 1v–4r; cf. ‘Of refractions’ in CUL Add. Ms.

4000 fols. 26r–33v; see Newton (1967–1981), Vol. 1, pp. 551–555, 559–576; Newton (1984), pp. 7–8,13–15, 18–20.




that different primary rays have different degrees of refrangibility, Newtonremarked that since

the agreement of several [‘plurimorum’] things imparts an intellectual pleasureand a generally more assured acceptance than the evidence of a single, thoughhighly scientific argument [‘quam unici licet maxime scientifici argumenti testi-monium’], it will not be without benefit if I briefly introduce investigators toanother kind of experiment related to the preceding ones.

This experiment merely involved looking through a prism at the rays emergingfrom it, and noticing that the image seen thereby was oblong. This was not pre-sented in a historical narrative style, but rather as a set of precise directionsaccompanied by a diagram.18

In the ‘Lectiones’ Newton considered the efforts of previous scholars in consider-ing the nature of colours. The Peripatetics neither considered how colours weregenerated, nor the means by which they became differentiated, thereby dismissing‘those things the explanation of which seems the highest function of philosophyand indeed, [which] alone can satisfy the mind eager for natural science’. Othersreferred the generation of colours to the mixture of light and shadow ‘or from aspinning of little balls or their various pressures, or, finally, from the various waysin which a certain aetherial medium is vibrated’. However, all previous theoriesrested on the modification theory of light that Newton had conclusively refuted,and so all were ultimately unsatisfying. At this point he stated that the generation

of colours included so much geometry that the science of colours properly had tobe considered a branch of the mixed mathematical sciences, along with astronomy,geography, navigation, optics and mechanics. So despite the fact that coloursbelonged to physics, ‘the science of them must nevertheless be considered math-ematical insofar as they are treated by mathematical reasoning’. With great confi-dence he pronounced that

Since an exact science of [colours] seems to be one of the most difficult thatphilosophy is in need of, I hope to show—as it were, by my example—howvaluable mathematics is in natural philosophy. I therefore urge geometers to

investigate nature more rigorously and those devoted to natural science (‘avidosscientiae naturalis’) to learn geometry first. Hence the former shall not entirelyspend their time in speculations of no value to human life, nor shall the latter,while working assiduously with an absurd method, perpetually fail to reach theirgoal. But truly with the help of philosophical geometers and geometrical philo-sophers, instead of the conjectures and probabilities that are being blazonedabout everywhere, we shall finally achieve a natural science supported by thegreatest evidence.19

18 Newton (1984), Vol. 1, pp. 75–77, 309.19 Ibid., pp. 87–89 (and p. 439), and pp. 161–162 (and p. 533). ‘Optica’ was deposited in the University

Library as his Lucasian lectures in 1674.




This mathematicist approach clashed with the dominant probabilistic approachof the Royal Society. Yet following the transmission of his reflecting telescope tothe Society at the end of 1671, Newton published an account of his novel views on

light and colours in the Philosophical Transactions. He began by relating his‘surprising’ observation of the elongated image made by light passing througha prism. After carefully measuring the shape of the image, the distance between theprism and the image, the diameter of a hole made in his ‘window-shuts’, andthe angle of incidence of light both before and after meeting the prism, he invokedthe sine law of refraction to show that the angle subtended by the emerging rayscould not be accounted for by the angle of the incident rays. Having consideredthe possible physical causes of this, he attempted to show, by means of a new,‘crucial’ experiment, that each individual ‘colour-making’ ray had its own degree of refrangibility. This was constant after successive refractions, and thus could

not have been caused by modification of the incident ray. Hence white light washeterogeneously composed of all such primary colour-making rays. The crucialexperiment (which did not appear in the ‘Lectiones’) seems to have been anidealised amalgamation of Experiments 7 and 44 of the 1666 essay on colours and,perhaps as a result of this, many contemporaries had difficulty reproducing theexperiment.20

At this point in the narrative Newton remarked that although ‘naturalists’ wouldnot expect to see the treatment of colours become part of mixed mathematics,there was as much certainty in it as any other part of optics. This was not merely

an ‘Hypothesis’ but was based on incontrovertible conclusions based on manyexperiments carried out in private. He now remarked that continuing in the histori-cal narrative mode would ‘make a discourse too tedious & confused’ and statedthat he would now lay down the ‘doctrine’, afterwards supplying one or two fur-ther experiments for its ‘examination’. Accordingly, he laid down a set of ‘proposi-tions’ in which the doctrine was ‘comprehended and illustrated’. It is significantthat he withheld his private thoughts about the physical causes of light, remarkingonly that it could ‘perhaps’ no longer be doubted whether light was a body: ‘todetermine more absolutely, what Light is, after what manner refracted, and bywhat modes or actions it produceth in our minds the Phantasms of Colours, is not

so easie.’ He would not, he said, ‘mingle conjectures with certainties’.21

This abstract account, drawn from the tradition of mixed mathematics, was castin a discursive style with which Newton had long been familiar, and his publicationrepresented a deliberate and ambitious attempt to transform contemporary naturalphilosophy, and closer to home, the nature of enquiry at the Royal Society. Forcing

20 Newton (1959–1977), Vol. I, pp. 92–107, 92–95; Newton (1983), pp. 468, 478; Feingold (2001),pp. 81–85; Schaffer (1989), esp. pp. 76–78; Shapiro (1996). See also Laymon (1978) and especiallyMcMullin (1985).21 Newton (1959–1977), Vol. I, pp. 97–100. Interestingly, when Barrow cited Aristotle’s injunction that

mathematical exactness should not be expected from a natural philosopher, he included colour (as partof physics) and the ‘Law of Nations’ as pursuits not susceptible to mathematical treatments; see ‘Math-ematical lectures’ in Barrow (1970), pp. 53–54.




the Society to recognise that a mathematical natural philosophy was not justpossible but was preferable to what they routinely endorsed would have been everybit as momentous as the content of the discovery itself. He himself noted in a letter

to Henry Oldenburg (who as editor of the journal had removed the more extrememathematicist statements) that the style of his presentation was perhaps inappro-priate for the Philosophical Transactions, being ‘too straight & narrow’, anddesigned ‘onely to those that know how to improve upon hints of things’. Indeed,in July 1672, he suggested that the apparent obscurity of his exposition was due toits ‘brevity’. Such a format, describing an experimental set-up shorn of the sorts of corroborative procedures more apt for an empiricist, probabilist setting, was par-tially responsible for the mixed response to his work, even if senior philosopherslike Robert Hooke agreed with the basic phenomenon of differential refrangibility.Hooke denied that Newton’s explanation for his observations need be saved byNewton’s ‘hypothesis’ alone, and he affirmed that his own hypothesis was based onhundreds of experiments. Newton’s main experiment was neither crucial, nor washis theory as certain as a mathematical demonstration. While Newton took theheterogeneity of white light and the constant index of refraction of specific colour-making rays to be necessarily implied by his crucial experiment, Hooke took theformer to be a ‘hypothesis’ epistemologically on a par with whatever Newton tookto be the physical cause of light—which, Hooke claimed (with some justice),Newton had as good as affirmed to be corporeal.22

As the year wore on, Newton’s theory was described on a number of occasions

by critics as an ‘hypothesis’ and the combination of their criticisms and requestsfrom others for more information forced him to reconsider the advisability of pub-lishing at all. However, gripped by the conviction that his approach was the onlyone that would deliver absolutely certain truths about nature, he composed alengthy response to Hooke. He denied that he had made the corporeity of light afundamental presupposition of his theory and had propounded it ‘without anyabsolute positivenesse, as the word perhaps intimates’:

I knew that the Properties wch I declared of light were in some measure capableof being explicated not onely by that, but by many other Mechanicall Hypoth-

eses. And therefore I chose to decline them all, & speake of light in generalltermes, considering it abstractedly as something or other propagated every wayin streight lines from luminous bodies, without determining what that thing is. . . and for the same reason I chose to speake of colours according to the infor-mation of our senses, as if they were qualities of light without us.

Here Newton combined a mixed mathematical approach with a standard anti-essentialist feature of the ‘mechanical philosophy’ as it was conventionally under-

22 Newton to Oldenburg, 10 February 1671/1672, Newton to Oldenburg, 8 July 1672, and Hooke to

Oldenburg, 15 February 1671/1672, in Newton (1959–1977), Vol. I, pp. 108–109, 212, 110–111.Newton’s comment about the inadvisability of merely trying to save the phenomena had been excisedfrom the printed version.




stood. He immediately followed this with the claim that rays of light were actuallysmall bodies ‘emitted every way from shining substances’ that could excite vibra-tions in the aether, though this was presented as an hypothesis that was being

‘assumed’. His response to Hooke was a public statement that he could producedifferent sorts of aether-based accounts as well as anybody, although most of theletter was taken up with criticisms of hypothetical explanations in general andHooke’s own views in particular.23

When this reply was printed in the Transactions, Oldenburg again removed asection in which Newton reaffirmed his belief that the science of colours ‘was math-ematicall & as certain as any other part of Optiques’. Everyone knows, Newtonhad continued, ‘that Optiques & many other Mathematicall Sciences depend aswell on Physicall Principles as on Mathematicall Demonstrations: And the absolutecertainty of a science cannot exceed the certainty of its Principles’. Although theprinciples of the propositions in his original letters had been ‘physical’, he wrote, if a mathematician could determine every feature of refractions ‘by computing ordemonstrating after what manner & how much those refractions doe separate ormingle the rays in wch severall colours are originally inherent’, then the science of colours could be considered mathematical and as certain as any other part of optics. Far from being cowed by his critics, this was a still more strident presen-tation of his mathematical approach although it was a somewhat toned down ver-sion of an earlier draft. Alan Shapiro has pointed out that in an earlier version of this letter, Newton had called ‘Properties’ ‘Theorems’ and after referring to light

‘in generall termes’ had added the qualifier ‘after the mode of the Mathemati-cians’.24

Newton’s unwillingness to deal with the physical cause or nature of light was dee-ply and genuinely perplexing to contemporaries—just as later, his phenomenalisttreatment of Universal Gravitation and other forces would be puzzling to readersof the Principia. In an account of his own theory given to a Society grandee in thewake of Newton’s retort, Hooke apologised for the fact that his own explanationsseemed unintelligible to Newton and sarcastically remarked that he was sureNewton ‘understood’ how it was that individual primary rays always had a constantdegree of refrangibility when they entered a new refracting medium, and how ittranspired that these rays could be brought together again ‘and keep on their wayDirect & undisturbed as if they had never mett’. In a draft of a reply to Newton’scritique, Hooke remarked that Newton seemed ‘to be very shy of supposing bywhat means’ these motions were performed but in the last version as it stands hemade the related but different point—using Newton’s own words—that Newtonseemed now to be ‘afraid of saying What a ray of light is’. As Newton shied awayfrom public dispute over his theory, so his account of light became still more

23 Newton to Oldenburg, 11 June 1672, in Newton (1959–1977), Vol. I, pp. 171–193 (esp. pp. 173–174);my italics.24 Ibid., pp. 187–188 (and the discussion on p. 190 n. 18); Shapiro (1993), p. 23 n. 34.




abstract and was further clothed in a mathematical garb. In the autumn of 1672 hedrew up a list of experiments that would clarify his theory, and did so in a waythat reduced the theory to propositions—proving each proposition ‘from one or

more of those Expt

s by the assistance of common notions set down in the form of Definitions & Axioms in imitation of the Method by wch Mathematitians are wontto prove their doctrines’. At heart Newton believed that he had mathematicallydemonstrated his theory beyond cavil, but when even Christiaan Huygens failed toappreciate his approach to natural philosophy, he lost interest in playing the gameany further. He remained mired in what he took to be futile disputes with a groupof Liege Jesuits who were unable to reproduce the most basic features of hisexperiments.25

5. The development of Newton’s cosmology

Privately, Newton had long explored aspects of the nature of vision, the physical‘nature’ of light, and its role in a rich cosmology. In the 1666 essay on colours hecombined elements of the historical and instructional narrative styles with physicaland anatomical explanations of various phenomena. From this period he was com-mitted to the optical role played by a vibrating aetherial medium, and continued tobe so when he returned to analyse the periodicity of thin films in 1671. In 1672 hecomposed a dissertation on this topic (the ‘Discourse on observations’), which he

had promised to send to Oldenburg along with the ‘New theory’ and in an appen-dix to the 1672 essay, he described a physical ‘hypothesis’ involving light corpusclesexciting vibrations in the aether.26

In 1675, when he was much more keenly aware about the reasons for distin-guishing between hypothetical conjectures and knowledge that was mathematicallycertain, he sent Oldenburg a package containing his musings on the nature of lightas well as a revised ‘Discourse on observations’ composed of twenty-four observa-tions on thin plates along with nine ‘propositions’ that resulted from them. Anoriginal draft of the ‘Observations’ contained the view that his doctrine of hetero-

geneity had ‘met with the most universall & obstinate Prejudice’, although to Newtonit appeared as ‘infallibly true & certaine, as it can seem extravagant to others’.Neither this, nor a powerful statement to the effect that the science of coloursdeserved ‘rather to be esteemed Mathematicall then Physicall’ were included in theversion read out to the Royal Society over three weeks in early 1676 and indeed

25 Hooke to Lord Brouncker [?], late June 1672; Huygens to Oldenburg, 17 September 1672, Newton toOldenburg, 21 September 1672, Oldenburg to Newton, 18 January 1672/1673, Newton to Oldenburg, 3April 1673, in Newton (1959–1977), Vol. I, pp. 174, 198–205 (esp. pp. 201, 205 n. 21), 235–236, 237,

255–256, 264. For the replication of Newton’s ‘crucial experiment’ see Schaffer (1989) and Shapiro

(1996). For comprehensibility and intelligibility see Iliffe (2003).26 CUL Add. Ms. 3975 fols. 1–22; Newton (1983), pp. 466–489; Shapiro (1993), pp. 49–60; Iliffe (1995);

Bechler (1973). For contemporary matter theory see Henry (1986).




none of the main enclosures in the parcel sent to Oldenburg actually appeared inthe pages of the Transactions.27

The physicalist explanation of his views on the nature of light constituted a sub-

stantial enlargement of the ‘hypothesis’ appended to the 1672 paper. Newton toldOldenburg, as he had done three years earlier, that the discourse might have donebetter to have been accompanied by more diagrams and that he was sending the‘Hypothesis’ despite worries about becoming embroiled in ‘vain disputes’. In themain body of the text he expanded his reservations about hypotheses in generaland about releasing this one in particular, but complained that he had felt theneed to send his private views ‘because I have observed the heads of somegreat virtuoso’s to run much upon Hypotheses, as if my discourses wanted anHypothesis to explain them by, & found, that some when I could not make themtake my meaning, when I spake of the nature of light & colours abstractedly, havereadily apprehended it when I illustrated my Discourse by an Hypothesis’. Con-taining novel data gleaned from experiments with air-pumps, the new account of the natural world was substantially larger than that composed three years earlier.He supposed that there was an ‘ætheriall Medium’ of approximately the sameconstitution as air but rarer, subtler and more elastic; it could vibrate much fasterthan air and its vibrations were present in reflexion and refraction just as they werein fermentation, putrefaction and fire. This medium was composed of the ‘maineflegmatic body’ of aether but also other ‘ætheriall Spirits’, just as ‘air’ was‘compounded of the flegmatic body of Air intermixt with various vapours & exha-

lations’. This heterogeneous constitution of the aether could help explain electricity,magnetism and gravitation—the last caused by an aetherial spirit ‘very thinly &subtly diffused through it, perhaps of an unctuous or Gummy, tenacous & Springynature’—while another subtle spirit could be controlled by the soul to effect muscu-lar contraction and hence animal motion. Finally, light was a different entity fromthe aether and they acted mutually, light warming the aether, and aether refractinglight.28

Much of Newton’s depiction of the aetherial spirit can be plausibly related toanother programme of work on which he was engaged at the same time, a projectthat used a different language to describe the internal workings of nature. In a

paper that has been tentatively dated to the early/mid-1670s, Newton formulated acosmology that explicitly used standard ‘alchemical’ terminology. He argued thatmetals ‘vegetated’ and that this ‘vegetation’ could be promoted by art, but heaffirmed that it was ultimately ‘ye sole effect of a latent sp[iri]t & that this sp[iri]t isthe same in all things only discriminated by its different degrees of maturity & therude matter’. He went on to discuss processes such as putrefaction and nourish-ment, and linked the means by which metals grew or could be made to work on

27 Newton to Oldenburg, 7 December 1675, in Newton (1959–1977), Vol. I, pp. 362–92 (esp. pp. 385–386),

for extracts removed from the later versions.28 Newton (1959–1977), Vol. I, pp. 360–361, 363–372. For other treatments of these themes see Dobbs

(1991), pp. 89–121, and Kubrin (1967).




each other to the growth of an animal from the egg. Growth took place in both

cases by a slow nourishment or ‘imbibing’, and the connection between the two

kingdoms was shown by the fact that nothing had so great an influence on animals

as minerals. Minerals could only unite with our bodies and become part of them if they too had a ‘principle of vegetation’ within them, and when this happened the

two were ‘conjoyned like male & female’.29

Despite the overtly alchemical language in the ‘vegetation of metals’ manuscript,

Newton almost certainly drew from this work in the 1675 ‘Hypothesis’ and pub-

licly expressed his view that nature was ‘a perpetuall circulatory worker, generating

fluids out of solids, and solids out of fluids, fixed things out of volatile, & volatile

out of fixed, subtile out of gross, & gross out of subtile’. According to Newton,

some elements in this cyclical cosmos were made to rise and ‘make the upper jui-

ces, Rivers and the Atmosphere; & by consequence others to descend for a Requi-tall to the former’. Employing virtually identical concepts to those used in his

alchemical manuscript, he argued that the sun might also ‘imbibe’ this spirit to

conserve ‘his Shining’ and prevent the planets from careering off into space, while

he thought that it was likely that the spirit ‘affords or carryes with it thither the

solary fewell & materiall Principle of Light’.30

In February 1679 Newton wrote to Robert Boyle regarding a discussion that

they had conducted earlier, probably in spring 1675. He told Boyle that there was

‘diffused through all places an æthereal substance capable of contraction & dila-

tation, strongly elastick, & in a word much like air in all respects, but far more

subtile’. He claimed that by considering how from the ‘continual fermentationsmade in ye bowels of ye earth there are aereal substances raised out of all kinds of

bodies’, then the ‘true permanent Air’ might well be metallic. All of this could

serve towards explaining gravity, and indeed virtually any other phenomenon he

could think of. Outside his private sphere, proferious of caution were closely linked

to the neutralisation of entities such as ‘light’; in his letter to Boyle he told him

that he would only ‘set down my apprehensions in ye form of suppositions’, while

in the 1675 ‘Hypothesis’ he protested that his aetherial explanation was merely an

illustrative hypothesis:

Though I shall not assume this or any other Hypothesis, nor thinking it neces-

sary to concerne my selfe whether the properties of Light, discovered by me, be

explained by this or Mr Hook’s or any other Hypothesis capable of explaining

them; yet while I am describing this, I shall sometimes to avoyde Circumlo-

cution & to represent it more conveniently speak of it as if I assumed it & pro-

pounded it to be believed.

29 ‘Of nature’s obvious laws & processes in vegetation’, Dibner Ms. 1031B, Dibner Library of the His-

tory of Science and Technology, Special Collections Branch, Smithsonian Institution; reproduced in

Dobbs (1991), pp. 256–270, 258–259.30 Newton to Oldenburg, 7 December 1675 and 25 January 1675/1676, in Newton (1959–1977), Vol. I,

pp. 360–361, 362–389, 413–415.




Although he continued to apply these caveats when referring to aethers, spirits andactive principles in public, Newton retained an intense commitment to this generalcosmology throughout his life.31

6. From vortices to voids

The development of the dynamics of the Principia embraced a completely dis-tinct philosophical tradition and was expressed in a very different language fromthat used to describe the aetherial and spirituous cosmologies. In this parallelworld, the Principia represented as much a discursive and disciplinary transform-ation within mixed mathematics as it did a conceptual revolution in dynamics.However, his treatment of various natural phenomena in the Principia did not fun-

damentally change his private commitment to the basic cosmological accountsarticulated in the 1670s, which also included explanations of gravitation. Althoughthe dynamics of the Principia was unformed in the early 1680s, the resources forhis achievement were partly laid down by his momentous work in the mid-1660son determining g and on comparing the forces required to keep the Moon in itsorbit with Galileo’s law of terrestrial free fall. At the same time, he famously com-bined his discovery that the centrally-directed ‘force’ keeping a globe in orbit alonga circle of radius r (ignoring the ‘quantity of body’) was v 2/r with Kepler’s so-called Third Law to determine that the forces that kept planets in their orbits werereciprocally as the squares of their distances from the sun. Newton did not yet pos-sess the notion of Universal Gravitation, and equally significant clues were pro-vided by other natural philosophers in the early 1680s who provoked him toreconsider his cosmology and dynamics.32

At the end of 1679, Hooke famously wrote to Newton suggesting that the orbitalmotions of a planet could be compounded of rectilinear motion (‘direct motion bythe tangent’) and a centrally-directed attracting force (originally stated in hisAttempt to prove the motion of the earth of 1674 and recently reprinted in hisCutlerian Lectures). In reply Newton produced a model in which orbital motionswere accounted for according to an analysis in which deviation from a circular

orbit was caused by the ‘overballancing’ of either gravity or the countervailing viscentrifuga. More specifically, he argued that at any point on the badly drawn curvedescribed in his letter, motion of a body was compounded of the tangential motionat the start of the motion, ‘& of all ye innumerable converging motions successivelygenerated by ye impresses of gravity in every moment of it’s passage’. This impulse-model analysis, and indeed the precise interpretation of vis centrifuga, has receivedsubstantial attention in recent literature, not least because Newton appears to be

31 Newton to Boyle, 28 Feb 1678/1679 and ‘Hypothesis’, in Newton (1959–1977), Vol. II, pp. 288–295

(esp. pp. 288–289), and Vol. I, pp. 363–364.32 For the development of Newton’s dynamics between 1664 and 1687, see Herivel (1965) and

Whiteside (1989), pp. x–xvii. For the correspondence with Hooke, see Lohne (1960); Nauenberg (1994);Gandt (1995), pp. 151–161; Brackenridge (2001), esp. pp. 114–115.




ignorant of Kepler’s area law, which would have allowed him to equate time inter-vals to the area of orbital segments and which was the central dynamical insightunderlining the analysis in his ‘De motu corporum in gyrum’ of late 1684. What-

ever its underlying mathematical foundation, Newton said little or nothing aboutthe possible physical causes of motion despite later being asked by Hooke to sup-ply a ‘physicall Reason’ for planetary orbits.33

Newton remained wedded to a vortex, or at least a non-magnetic account of planetary motion. In early 1680, he responded to a request from Thomas Burnetfor his views concerning a philosophical explanation of Genesis and told Burnetthat the rugged nature of the Earth’s surface might have been caused by the heatof the Sun or the vortex of the Moon on the surface waters of the Earth. 34 InNovember of the same year a brilliant comet became visible to astronomers whileanother appeared the following month. In a letter passed on to Newton, the

Astronomer Royal John Flamsteed argued that these were the same object andthat the comet was turned from its original path by the magnetic attraction of thesun, but directed away from this path by the rotation of the solar vortex. Theattractive force ultimately overpowered the effect of the vortex but by the time thecomet was at perihelion it was travelling directly counter to the flow of the vortexand was in the process of turning around in front of the sun. Once twisted around,the opposite pole of the body would present itself to the sun and be repelled byit.35

Newton replied that he accepted that the sun exerted some centrally attractingforce ‘whereby the Planets are kept in their courses about him from going away intangent lines’, but that this could not be magnetic since hot loadstones (naturalmagnets) lost their ‘vertue’, or power. Even if the attractive power of the sun werelike a magnet, and the comet like a piece of iron, Flamsteed had still not offered amechanism whereby the sun would suddenly switch from attraction to repulsion.As with a mariner’s compass, the power of the sun to ‘direct’ (that is, influence theN or S alignment of) an object was greater than its power to attract or repel, sothat ‘once so directed the Comet will be always attracted by ye Sun & neverrepelled’.36 Newton later noted that if the comet were subject to a continuousdirecting and attracting force, the continuous attraction would serve to decelerate

the comet in its recess and make the comet travel along an orbit close to that

33 Hooke to Newton, 24 November 1679, Newton to Hooke, 28 November 1679; Hooke to Newton, 9December 1679, Newton to Hooke, 13 December 1679, Hooke to Newton 6 January and 17 January1679/1680; in Newton (1959–1977), Vol. II, pp. 297–298, 300–303, 304–306, 307–308, 309–310, 312–313.Borelli’s theory, relying on a balance between centrally attracting and centrifugal forces, is outlined inhis Theoricæ mediceorum planetarum ex causis physicis deductæ (Florence, 1666).34 Newton to Burnet, 24 December 1680 and January 1680/1681, in Newton (1959–1977), Vol. II,

pp. 319, 329–334.35 Flamsteed to Crompton for Newton, 15 December 1680, Flamsteed to Crompton, 12 February

1680/1681, Flamsteed to Halley, 17 February 1680/1681, in Newton (1959–1977), Vol. II, pp. 315–316,

336, 336–339. The observations in the ‘Waste Book’ are CUL Add. Ms. 4004 fols. 97r–101v.36 Newton to Crompton for Flamsteed, 28 February 1680/1681, in Newton (1959–1977), Vol. II,

pp. 340–347.




observed. At perihelion, the centrifugal force would then have ‘overpower’d’ theattraction, forcing the comet to recede from the sun despite the still acting mag-netic attraction. Again, something resembling the Borellian model was used to

model the forces operating on the orbiting body although magnetism would neversatisfy Newton as an adequate mechanism for explaining celestial motions. In avitally important exchange at the end of 1684 he asked Flamsteed for data con-cerning the deviation of planets from their positions in Kepler’s RudolphineTables and also for information on the possible effect of Jupiter on the orbit of Saturn. Flamsteed remarked that the distance between the planets was too greatfor any magnetic force to operate while he also noted that ‘in such yielding matteras our æther, I can not conceave that any impression made by ye one planet uponit can disturbe ye motion of the other’. In reply Newton spoke only generally of Jupiter’s ‘influence’ and of the fact that these effects of the planets on one another

seemed to be inadequate to explain observed deviations from Kepler’s Third Law.Flamsteed noted in return that determining Saturn’s deviation from its predictedorbit was beyond the limits of observational accuracy.37

By the time he wrote the early mixed mathematical papers that formed the basisof the Principia, Newton’s dynamical tools and techniques had been dramaticallyrecast. His first response to Halley’s request in 1684 to link elliptical planetaryorbits to an inverse-square force law was sent to the Royal Society in November of that year. In this first text, called ‘De motu corporum in gyrum’, he invoked thenotion of both rectilinear inertia and a centripetal force that varied according the

square of the distance. Newton termed centripetal force in Definition 1 as ‘that bywhich a body is impelled or attracted towards some point regarded as a centre’ andin Definition 3 he called the ‘resisting force’ ‘that arising from the steadilyimpeding medium’. While the theorems began with a simple set of two-body pro-blems, the scholia dealt with problems in the concrete world. The scholium toProblem 4 dealt with the fact that many observations taken over a long period of time might determine whether a comet was periodic, while in the scholium to Prob-lem 5 he mentioned that gravity was a type of centripetal force.38

In a revision of this text composed soon afterwards and entitled ‘De motusphæricorum corporum in fluidis’, Newton added two scholia that dealt more

directly with the consequences of both mutual gravitational attraction in the hea-vens, and the existence of a resisting medium. The addition of these scholia showsthat Newton was more explicitly trying to incorporate the observed phenomenainto his analysis, fine-tuning the mathematical model with novel empirical data. Inthe first scholium, he argued that the fact that the sun was not always at the centre

37 Flamsteed to Crompton for Newton, 7 March 1680/1681, Newton to Crompton for Flamsteed, ?April 1681, Flamsteed to Newton, 27 December 1684, Newton to Flamsteed, 30 December 1684,Flamsteed to Newton, 5 January 1684/1685 and Newton to Flamsteed, 12 January 1684/1685, Flamsteed

to Newton, 27 January 1684/1685, in Newton (1959–1977), Vol. II, pp. 348–358, 358–361, 403–405,

406–408, 408–412, 412–414, 414–415.38 Herivel (1965), pp. 277–289 (esp. pp. 277, 283, 285); Newton (1967–1981), Vol. 6, pp. 30–75 (esp. pp.

30–33); Newton (1962), pp. 214–228; Dobbs (1991), pp. 130–136.




of gravity of the solar system meant that planets carved out new orbits at each newrevolution, ‘and the orbit of any one planet depends on the combined motion of allthe planets, not to mention the action of all these on each other’. In the second, he

set out to determine the motion of celestial bodies in the aether, except that he nowremarked that the resistance of ‘pure’ aether was ‘either nothing or excessivelysmall’. Aether ought to resist more, as it could penetrate the inner parts of bodies,and yet it appeared to offer no sensible resistance; ‘comets are carried withimmense speed indifferently in all parts of our heavens yet do not lose their tail northe vapour surrounding their heads [by having them] impeded or torn away by theresistance of the aether’. Ignoring the fact that he had shown that planets alwaysdeviated from perfect elliptical trajectories (on the grounds that small deviationsfrom such orbits could be ignored), Newton also mentioned that the planets hadcontinued in their motion for thousands of years, ‘so far are they from experienc-ing any resistance’.39

Newton worked intensively over the next two years, expanding what at onepoint was a two book opus into its final tripartite form. As a work whose titleclaimed that it revealed the mathematical principles of natural philosophy, the veryrationale of the published Principia went boldly against the grain of most contem-porary approaches to natural philosophy. As an example of mixed mathematicsand mathematics, the Principia was the latest and perhaps the last in a genre whoseclosest antecedents included Galileo’s Two new sciences, and Huygens’s Horologiumoscillatorium. The bold disciplinary transformation that the work represented, the

substantial amount of pure mathematics that permeated Book One, and the math-ematical carapace that cloaked Book Three, all made it a difficult object to classifyfor contemporaries. However radically innovative the Principia was conceptually,its general mixed mathematical structure had been a staple of Newton’s naturalphilosophy since the ‘Waste Book’. As befitted such a text, the concept of force— even for short-range forces—was ruthlessly neutralised. In a partial draft of thePreface to the 1687 Principia, Newton wrote that he ‘suspected’ that chemicalphenomena were based on ‘certain forces by which the particles of bodies, throughcauses still unknown, either are impelled towards one another and cohere, or repeleach other and fly apart’. As in the published version of the Principia, he held out

the promise that there might be numerous forces of this kind, and what remainedfor philosophers was to devise experiments to find these forces and then theirproperties, causes and effects.40

By maintaining ontological neutrality, Newton could hedge over the precisecause of attraction or gravitation, yet even within the mathematical analysis thedimensional incompatibility between infinitesimal-impulse and continuous notionsof force created an abiding tension. In other ways too, the Principia itself was by

39 Herivel (1965), pp. 301–303; Newton (1962), pp. 214–228, 90–156 (esp. pp. 146–147); see in parti-

cular Dobbs (1991), pp. 136–145.40 Newton (1962), pp. 302–308, 320–347 (esp. pp. 333–334). The demolition of vortices occurs in Book

Two, Props. 51–53 in Newton (1999), pp. 779–790.




no means a coherent mixed mathematical opus. Newton constructed the Principiaso that it embodied the division between the abstract mathematical world of cen-tripetal attractions and inertia, and the more ‘philosophical’ discussion concerning

the real ‘system’ of the world that constituted Book Three. This distinction wasalso respected in other ostensibly mixed mathematical works. In ‘De gravitatione’for example, he suggested that there were two ways of treating the science of gravi-tation and hydrodynamics. In so far as the subject pertained to the mathematicalsciences ‘and was largely abstract[ed] from physical considerations’, Newton wrote,‘I have undertaken to demonstrate its individual propositions from abstract princi-ples, sufficiently well known to the student, strictly and geometrically.’ In so far asthe work could make clear many of the phenomena of natural philosophy how-ever, to confirm ‘the certainty of its principles’, he was prepared to deal with thetopic in the form of scholia that constituted a ‘freer form of discussion’ not to ‘be

confused with the former which is treated in Lemmas, propositions and cor-ollaries’.41

In the Preface to the Principia Newton commented that the moderns wereattempting ‘to reduce the phenomena of nature to mathematical laws’ and that thesubject of the work as a whole was ‘rational mechanics’, that is, ‘the science,expressed in exact propositions and demonstrations, of the motions that resultfrom any forces whatever and of the forces that are required for any motions what-ever’. Both here and at the start of Book Three, Newton clearly distinguishedbetween the principles of the first two books, which were ‘not philosophical but

strictly mathematical’ (not including the illustrative ‘philosophical’ scholia) and thefinal book, which ‘exhibited the system of the world from the same principles’. AsCohen points out, the physically neutralised term ‘gravitatio’ appears nowhere inthe first two books in any of the editions but rather Newton used the mathemat-ically neutralised term ‘attractio’. Despite this inherent distinction, he went on tosay that in the final book he had shelved the approach adopted in the more ‘popu-lar’ liber secundus (a draft of Book Three rejected in Autumn, 1685) and had‘translated the substance of the earlier version into propositions in a mathematicalstyle’. It was this—as much as mathematical treatment of the first two books andthe ontological neutrality observed throughout the work—that contributed to the

widely held view that the Principia as a whole was essentially mathematics.42

Although Newton described the first two books as primarily ‘mathematical’,partly because the geometry had already become ‘physicalised’ he occasionally usedontologically neutral expressions that were ostensibly about the material world butthat were nevertheless supposed to be read as pertaining to a virtual, mathematicalenvironment. All of these terms occurred outside the main propositional frame-work, and are to be found in the definitions or more ‘philosophical’ scholia. Asearly as Definition 8, for example, he remarked that he would not consider the‘physical causes and sites of forces’ involved in the basic concepts of his system,

41 Newton (1962), pp. 121–122.42 Newton (1999), pp. 381–382, 793; Cohen (1980), pp. 82–83; Gingras (2001).




since the concept of ‘force’ was purely mathematical: ‘let the reader beware of thinking that by words of this kind I am anywhere defining a species or mode of action or a physical cause or reason, or that I am attributing forces in a true and

physical sense to centres (which are mathematical points) if I happen to say thatcentres attract or that centres have forces’. In the introduction to Section 11, whenhe referred to centripetally attracting bodies at rest, he claimed that such a situ-ation could hardly exist in the real world because of the Third Law of Motion. Hestated that he was about to discuss centripetal forces as ‘attractions’ ‘although per-haps—if we speak in the language of physics—they might more truly be calledimpulses’. He remarked that his recourse to the language of impulses was because‘we are here concerned with mathematics; and therefore, putting aside any debatesconcerning physics, we are using familiar language so as to be more easily under-stood by mathematical readers’. In the scholium to Proposition 69 he repeated his

nescience about the cause of attraction, again dividing up between mathematics,which ‘requires an investigation of those quantities of forces and their proportionsthat follow from any conditions that may be supposed’, and a methodologicallydeferred process that would compare these ‘proportions with the phenomena’.Finally, in the scholium to Proposition 23 of Book Two, he cautioned that thequestion of whether the elastic fluids of which he had been speaking actually con-sisted of particles that repel one another was ‘a question for physics. We havemathematically demonstrated a property of fluids consisting of particles of thissort so as to provide natural philosophers with the means with which to treat thequestion’.43

7. Aetherial languages

Whatever the language deployed in the Principia, Newton continued to believe inthe existence of real non-Principia-type forces. Even in his masterwork, a decidedlynon-mathematical analysis appeared in Proposition 41 of Book Three where helaunched into a substantial excursus regarding the function of comets’ tails. Newtonhad broached the nature and function of comets with Flamsteed at the start of thedecade and in the Principia he determined that the tail arose from the heating bythe Sun of the comet’s head. Tails dissipated in aphelion and then grew again asthe comet approached the Sun, and the effluvia generated thereby would in time becaptured by the gravitating power of the planets. This efflux had a life-giving force,replenishing ‘whatever liquid is consumed by vegetation and putrefaction and con-verted to dry earth’. Without this ‘outside source of increase’, fluids would disap-pear entirely, while Newton also ‘suspected’ that comets supplied ‘that spirit whichis the smallest but most subtle and excellent part of the air’. Although Newton

43 Newton (1999), pp. 407–408, 560–561, 699; McMullin (1985), pp. 252–254; Cohen (1980), pp. 72–73;

Herivel (1965), p. 319. Newton proposed an analogy between the propagation of rays of light and themotion of bodies in Book One, Prop. 96, while ‘not arguing at all about the nature of the rays (that is,whether they are bodies or not)’; see Newton (1999), pp. 625–626.




might treat certain phenomena in terms of ontologically neutral short-range forces,here (with only a mild hesitancy) was a clear statement, using very different lan-guage, of a philosophical programme that was alien to that of mixed mathematics.44

Famously, despite being prompted to give a comprehensible physical explanationof gravitation by philosophers such as Huygens and Leibniz (who refused tounderstand ‘attraction’ phenomenalistically), Newton refused to do so. His publicmixed mathematical treatment of action-at-a-distance demanded such silence aboutits putative causes, but elsewhere he freely used the language of active principlesand aethers. In drafts for the 1706 Optice, for example, he argued that active prin-ciples were necessary for ‘conserving and recruiting’ motion, which was otherwiseprone to decrease. However, he went on to say that since bodies were intrinsically‘passive’, there had to be some other principle in the world other than the vis iner-tiae. Referring to the power humans had to move their own bodies, he noted that

‘by this instance & that of gravity it appears that there are other laws of motion(unknown to us) than those wch arise from Vis inertiae (unknown to us) wch isenough to justify & encourage our search after them’. ‘We cannot’, he concluded,‘say that all nature is not alive’.45

As it had done in his alchemical program, light continued to provide a source of agency for Newton and he dealt with the connections between light and matter insome of the ‘Queries’ to the 1704 Opticks. As remnants of private research pro-grammes such as alchemy, which had not been susceptible to mathematical treat-ment, these could only appear under the guise of questions. Accordingly,speculations that light might be the chief principle of activity in matter were sup-pressed before publication, expressed as ‘conjectures’ or recast in ontologically neu-tral terms. In print (Query 30 in the 1717/1718 Opticks) he remarked that as thesmallest particles, light might be the active principles described above, and heasked whether light and matter might be interconvertible. Nevertheless, in the firstOpticks and in Optice (1706) he remained deliberately vague about the presence of some intermediate entity between the two, referring only in a phenomenalistic wayto a vis (in Optice) or ‘Principle’ whose cause was not yet known.46

However, after 1707, experiments performed by Francis Hauksbee at the RoyalSociety suggested to Newton that short-range forces might be primarily electrical

in nature. Before the second edition of the Principia appeared in 1713 he referredto an electrical ‘spirit’ that caused electrical attractions and argued that it was‘unphilosophical’ to appeal to any other force. Harking back to his work on thevegetation of metals, he suggested that this force was implicated in the union of soul and body, as well as in generation, nutrition and the ‘preparation of nourish-ment’: ‘by being stronger in the particles of living substances then in others it may

44 Newton (1999), pp. 403–404, 918–927 (esp. p. 926); see also Cohen (1980), p. 315 n. 18; Kubrin(1967); Schechner Genuth (1985); Schaffer (1987).45 See McMullin (1978), pp. 6, 49–55; Dobbs (1991), pp. 218–230; McGuire (1996) (citations from CUL

Add. Ms. 3970 fols. 255r–56r and 620r).46 Dobbs (1991), pp. 218–222; Kubrin (1967); McMullin (1978), pp. 84–94; McGuire (1996), pp. 206,

208–209 (from CUL Add. Ms. 3970 fols. 235v and 620r).




preserve them from corruption & act upon the nourishment to make it of like form& vertue wth the living particles as a magnet turns iron to a magnet & fire turns itsnourishment to fire’. Even in the General Scholium to the 1713 Principia, Newton

accounted for various phenomena by means of a ‘certain most subtle spirit thatpervades and lies hid in all gross bodies’. Finally, in connection with the new Quer-ies to the second 1717/1718 English edition of Opticks, he introduced an ‘optical’aether to account for light and described it as an agent that could act (by whatevermeans) over both long and short distances. This was clearly distinguished from thesubtle matter that gave rise to electrical motions in Query 22.47

Aside from the question of how they relate to statements in the various editionsof the Principia, historians have found it difficult to explain these changes and toaccount for the fact that the various queries as found in the 1717/1718 Opticksappear to be deeply at odds with each other with regard to the nature of aethers,

spirits and ‘forces’ and the relationships between them. However one deals with theapparently unbridgeable gap between the aether- and spirit-dense world of his priv-ate natural philosophy, and the force-filled spaces of the Principia, Rod Home issurely right to say that Newton’s ideas about a quasi-mechanistic cause of elec-tricity and magnetism ‘changed scarcely at all from the 1670s to the end of his life[and] the consistency with which he maintained these particular opinions overmany years suggests a firm belief that they were nevertheless correct’. I haveargued that we should envisage him being capable of working simultaneously indifferent and largely incompatible fields. If it is true that the Principia project

remained publicly dominant after the late 1680s, nevertheless he continued to workon alchemy until about 1700 and indeed on more conventional natural philosophyuntil the 1720s.48

Educated in a Barrovian mixed mathematical culture, and attached to thisapproach throughout his career, he nevertheless pursued apparently incompatibleprojects in private. The distinctions between these fields, and even the differentways in which he deployed ontological neutrality—‘speaking generally’—are mani-fold and subtle. By the time Newton wrote the various forms of the Queries in theearly eighteenth century, he had a bewildering repertoire of techniques for present-ing his views to different audiences. Although the patchwork effect of some of these

writings can provoke the cry of confusion, this view is premissed on the notionthat Newton was in possession of an integrated ‘mind’, and that all of his researchwas essentially the same thing. In fact the obvious tensions in his work more likelyrepresent the junk residue of the audiences, projects, genres, disciplinary forma-tions and linguistic styles in and for whom they were first written. His creativeachievement was much more than the conceptual innovations that were containedwithin the Principia and Opticks. Since concepts were attached to specific disciplin-ary structures, all conceptual changes had implications for the nature of the disci-

47 Heilbron (1983), pp. 52–66; Dobbs (1991), pp. 222–225; Guerlac (1967); Home (1985), esp. p. 111(citation from CUL Add. Ms. 3970 fol. 241r); Home (1993), esp. pp. 195–198.48 Home (1985), pp. 99–101; (1993), pp. 197–198.




pline to which they were appropriate. I do not of course, rule out the importanceof finding conceptual links between different areas of Newton’s work, but suggestonly that an essentialised and psychologised ‘mind’ should not be thoughtlessly

invoked as the nescio quid that underpins the connectedness of his work. The intel-lectualist concentration on concepts, along with the continuing attachment to theunities of oeuvre and mind do scant justice to Newton’s subtle manipulations of discipline, setting and audience.

Acknowledgements

For comments on previous versions of this paper I would like to thank MichaelHawkins, Nick Jardine, Scott Mandelbrote, Moti Feingold, Stephen Snobelen and

Andrew Warwick.

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