Science & Technology Studies
Annals of Science, 56 (1999), 331-356
1. Differing interpretations
Newton's retrospective claim to have discovered the law of gravity was made in June 1686 to Edmond Halley,1 in the context of a priority dispute. The first evidence for his use of an inverse square law of gravitational attraction appears in the De Motu documents dateable to November 1684; shortly after which, evidence that he had accepted and was using that law is found in his letter to Flamsteed of January 1685, concerning inequalities in the motion of Jupiter and Saturn.2 The last indication of adherence to his earlier ether-vortex theory of gravitation is an unpublished comment on cometary motion dated as spring 1681,3 affirming that ‘Materiam coelorum fluidam esse [et] circa centrum systematis cosmici secundum cursum Planetarum gyrare'.4
With remarkable unanimity, experts nowadays accept that the linkage of Kepler's first and second laws to an inverse-square centripetal force was accomplished by Newton in the winter of 1679/80, somewhat as a consequence of researches into unpublished Newton-manuscripts by Professor D.T.Whiteside. However, the latter's views on this subject have modified with time. Whereas in 1964 he wrote, concerning that period:
in 1991, he wrote,
We here explore the consequences of choosing not to take that word. This will bring us into accord with John Lohne's interpretation of events, whereby the linkage with Kepler's laws was accomplished after Halley's visit in the summer of 1684 and not before.7
The traditional view concerning the events of this period had been that Newton merely ‘repeated his calculations of 1666' over the winter of 1679/80, to quote from the essay of Rouse Ball,8 though with improved figures on the second occasion. Whiteside's re-casting of the traditional tale has since become widely accepted, though there has been some dispute over the radical position which he formulated in 1970: that there existed no Newtonian manuscripts dateable prior to 1684 showing use of centripetal force concepts in orbit theory, as in for example a Moon-test.9 Herivel had argued in 1961 that a document dateable to the period in question (winter of 1679/80) showed the computation, a view endorsed more recently by Westfall.10 Both Hall and Whiteside have firmly opposed this Herivel-Westfall position, viewing the document in question as rather belonging to the late 1680s; a view likewise taken by Bernard Cohen.11 We will not here adopt Westfall's view.
A fine account of the events in question, by Curtis Wilson in the General History of Astronomy,12 goes further than previous versions in conceding Newton's immersion in a quasi-alchemical ether theory of gravity during the 1670s; though claiming (improbably) that this formed a matrix for his development of an inverse-square law.13 It will here be argued that these two different modes of viewing gravity were inherently incompatible, and that the acceptance of one meant the rejection of the other. To accept such an account of these events would mean recreating a version of the two-Newton dilemma, as would be undesirable. Let us first review the development of Newton's gravity-ether theory.
2. The Early Gravity-Ether Theory
In Newton's student notes on Descartes (c. 1668) a rather Aristotelian downward impulsion of gravity is compared with the centrifugal force of the (Cartesian) solar vortex:
Descartes had spoken of a conatus a centro or conatus recedendi, an endeavour from the centre, possessed by such bodies as stones whirled around in slings.15 The ethers tending to move away from the Sun, in the solar vortex, were pulled away from it, Newton had mused to himself, by something resembling the pull of objects downwards on the surface of the Earth. Early thoughts on neo-Cartesian ether-vortex theories were also found in one of the ‘Questiones' of his student notebook under the heading ‘Of Gravity and Levity'.16
His belief at that time was that, to quote Westfall, ‘gravity (heaviness) is caused by the descent of a subtle invisible matter which strikes all bodies and carries them down'.17 His student notes showed him mulling over the design of a perpetual-motion engine to harness the downward flow of the gravity-ether.18 Later on in the 1670s he was to write to the Royal Society about its properties.
Some early notes by Newton on lunar theory appear on two folio sheets of his copy of Vincent Wing's Astronomia Britannica, published in 1669. They described how a terrestrial vortex, carrying the Moon round, was 1/43rd of the strength of the solar vortex.19 The pressure of the solar vortex deformed the lunar orbit within the terrestrial one, thereby accounting for certain known inequalities in its lunar motion. His notes queried whether the Earth's ‘endeavour of receding' from the Sun might affect the Moon's orbit, ‘unless the moon also shares in the same endeavour.'
These notes also describe how Kepler's third law applied to the orbits of Earth, Mars, Jupiter and Saturn, but only as a ‘weak first approximation' to those of Venus or Mercury.20 The orbits of these inner planets were perturbed by proximity to the solar vortex, so their endeavours of receding (‘vis centrifuga') were not deducible from the the inverse squares of their distances from the Sun. These notes should be compared with the somewhat better known computations performed by Newton a year or two earlier, on a sheet shown much later on to David Gregory, whereby an inverse-square ratio of the ‘conatus recedendi' for the planets was inferred from Kepler's third law.21
When in 1980 Rupert Hall published the text of this important but oft-misunderstood manuscript (c.1669) he concluded:
Unfortunately for the historian, the document offers no direct and conclusive evidence that Newton had yet entertained the conception of universal gravitation, nor does it contain a formulation of the inverse square law.22
It may be time to stop characterising such a situation as ‘unfortunate'. The document interpreted Kepler's third law in terms of an inverse square proportionality in the tendency which planets had to recede from the Sun - that which Descartes called their ‘conatus recedendi.' Curtis Wilson has well characterised the text as ‘Newton's test of the inverse square proportion in the 1660's'.23 He quoted Herivel's conclusion, that in this text ‘...there is apparently no indication whatsoever of the notion of universal gravitation',24 and objected to this on the grounds that Newton must have been assuming some counterbalancing, inward-pulling force. This was however two decades before anyone had formulated the principle ‘to every action there is an equal and opposite reaction' and one should be cautious of assuming that some such principle was then regarded as evident. Students will tend initially to picture a centrifugal force - as in Descartes' sling of 1664 illustrating the tendency to recede from the centre25 - and the less intuitively evident notion of a centripetal force tends to arrive at a later stage. Not until 1675 does Newton formulate an inward-pulling centripetal force, that is based on an ether-flow model.
A sea-change in scholarly opinion over this and related Newton documents of the period resulted from Whiteside's conclusion in 1970 alluded to above:
Let me iconoclastically suggest that what Newton in the 1660s had developed was not an hypothesis of universal centripetal attraction at all, and that therefore he had nothing of the sort to communicate.
In exact terms, what Newton found in 1666... was a law deducing that the centrifugal endeavours (outwards from the centre of motion) of planets travelling in pristine circular paths (wherein they were borne along by the deferent solar vortex) varied as the inverse square of their distance from the Sun; and similarly, mutatis mutandis, for other objects in particular the Moon caught up in the terrestrial whirlpool. Let me insist that Newton's extant manuscripts contain, before 1684, not a single reference, explicit or implied, to a centripetal attractive force used to account for the constraining of the vortical matter into a circular orbit from a straight line inertial path. Nor do they exhibit factual evidence for any Moon test made by Newton at any time before the middle 1680s in the simple numerical form suggested by Newton himself to Desmaizeaux in 1718 in context (of priority squabbles) where it was to his considerable advantage to assert that such a test had in fact taken place ...'26
More recently, Whiteside has described this paper as showing Newton's ‘first major discovery in dynamics', as a derivation, independently of Christiaan Huygens, of ‘the measure of force of outwards endeavour... which made precise the woolly notion held by Descartes of the conatus recedendi a centro' resulting from circular motion.27 A well-balanced review of this early document has also been provided by Cohen.28
In the following decade, and deriving from his alchemical studies,29 Newton came to develop his views on the workings of the gravity-ether. As communicated to the Royal Society in December of 1675 and written up in their History,30 it went as follows:
So may the gravitating attraction of the earth be caused by the continual condensation of some other such like aetherial spirit, not of the main body of phlegmatic aether, but of something very thinly and subtilely diffused through it, perhaps of an unctious, or gummy tenacious and springy nature.
The notion came to him while observing how a lens on his table when rubbed would attract little bits of paper: ‘yet would the papers as they hung under the glass recieve some new motion, inclining this way or that way, according as I moved my finger.' He surmised that there must be some subtle ether causing this, which was a fair enough way of referring to static electricity, and that the ether of gravity was of a different kind.
As ‘nature is a perpetual circulatory worker', so this gravitational ether circulated, thereby pulling things downwards. It was a rather vitalistic and alchemical theory:
the vast body of the earth, which may be everywhere to the very centre in perpetual working, may continually condense so much of this spirit as to cause it from above to descend with great celerity for a supply.
Its ‘gummy, tenacious nature' enabled it to get a grip on objects as it bore swiftly downwards, perhaps not easy for an invisible and intangible substance. A quantitative statement here appears, which in view of later claims he made about this theory should be noted. Following directly on from the previous quote, he asserts:
in which descent it may bear down with it the bodies it pervades with a force proportional to the superficies of all their parts it acts upon...
In other words, the larger the surface of body, the greater the force of gravity acting upon it. After condensing, this gravity ether descends into the bowels of the earth to be refreshed, and then arises until it ‘vanishes again into the aetherial spaces.' The Sun would ‘imbibe this spirit copiously, to conserve his shining, and keep the planets from receding further from him.' As well as explaining the pull downwards to which this sublunary realm is subject, and why the Sun kept shining, it could also account for the planetary orbits remaining apart: for, as oil and water did not mix,
... the like unsociableness may be in aetherial natures, as perhaps between the aethers in the vortices of the sun and planets.31
It should hardly be controversial to state, of this 1675 Hypothesis, that it was ‘...incompatible with universal gravitation' (Curtis Wilson).32 Yet, some have accepted Newton's retrospective claim that the 1675 Hypothesis encoded an inverse square principle.33 Newton averred to Halley in 1686, that:
Between ten and eleven years ago, there was an hypothesis of mine registered in your books, wherein I hinted at a cause of gravity towards the Earth, sun and planets, with the dependence of the celestial motions thereon; in which the proportion of the decrease of gravity from the superficies of the planet (though for brevity's sake not there expressed) can be no other than reciprocally duplicate of the distance from the centre.34
The Hypothesis had actually stated that gravity's pull on an object was proportional to its surface area (‘proportional to the superficies of all the parts it acts upon...'). If Halley was being asked to accept an allegedly implicit inverse-square notion - on the analogy of a flux density of particles converging towards a point increasing as 1/R² - then a certain consequence should follow. A uniform speed of motion of the gravity-ether is implied, as Rosenfield pointed out,35 as well as momentum transfer between the ‘gummy and tenacious ether' and the objects it bore downwards.
It was the nature of Newton's gravity-ether that it rushed downwards, into the bowels of the earth. Would not the force of gravity then (with the above assumptions) continue to increase by an inverse-square principle of attraction below the Earth's surface? Or, the body of the Earth being in ‘continual working' such that the gravity-aether ‘spirit' was there ‘condensed' and ‘refreshed,' would gravity's pull perchance cease below Earth's surface? Newton's letter to Halley of June 1686 began its case by saying:
I never extended the duplicate proportion lower than to the superficies of the earth....what he [Hooke] told me of the duplicate proportion was erroneous, namely, that it reached down from hence to the centre of the earth.
Newton's major criticism of the theory contained in Hooke's letters to him (of December 27, 1679 and January 6, 1680) was that it did just this; whereas in fact, the letters of Hooke had rather affirmed the converse.36
In an earlier letter to Hooke, of January 13th, 1679, Newton twice made the conjecture that the force of gravity inside the Earth would become greater nearer to its centre,37 a fact generally unmentioned by historians but concordant with his gravity-ether hypotheses of this period. The letter evaluated motion under a (hypothetical) friction-free condition and uniform forcefield within the Earth, as Hooke had postulated by way of discussion, then continued: ‘Thus I conceive it would be if gravity were ye same at all distances from ye centre. But if it be supposed greater nearer ye center...' It described how the figure drawn would change if Earth's gravity were to increase as one drew nearer to its centre. This theme is then reiterated: ‘For the increase of gravity in ye descent may be supposed such yt ye body shall by an infinite number of spiral revolutions descend ...'
A second gravity-ether hypothesis was proposed by Newton to Robert Boyle in February 1679, wherein ‘ye cause of gravity' was to be found, not as earlier in a flux of downward-rushing particles, but in a static gradient of texture in an aether, from grosser particles above to subtler ones below.38 The gradient extended to Earth's centre:
from ye top of ye air to ye surface of ye earth and again from ye surface of ye earth to ye centre thereof the aether is insensibly finer and finer.
Any body suspended in this aether-gradient would ‘endeavour' to move downwards. Two points should be noted about this second aether-gravity model communicated by Newton: if the 1675 version encoded an inverse-square principle, as was averred a decade later, then that principle has here been dispensed with; and, its gravity-field clearly continued down through Earth's crust as far as Earth's centre, a matter which remained equivocal in the earlier version.
In the letter to Halley of July 27th, 1686, Newton gave a final twist to his 1675 gravity-ether theory, by way of explaining how it had encoded an inverse-square principle: ‘...ye diminution of the aether's velocity in acting upon ye first parts of any body it meets with [is] recompensed by the increase of its density arising from that retardation,'39 ie the gravity-aether would increase its density when it slowed down.
The Principia's Book Two was primarily concerned to refute the theory of vortices, by demonstrating that no swirling ethers could possibly account for Kepler's third law.40 Are we to believe that the author of the Principia initially found them compatible, and that his ‘unguent and tactile ether', pulling objects downwards, encoded an early inverse-square viewpoint? His ‘Hypothesis non fingo' remark is here fairly pertinent, indicating a refusal to indulge in speculation on possible causes of gravitation. That refusal was grounded (I suggest) upon painful memories, of how very wrong had been his youthful speculations. A process of repression seems to have occurred, of all his earlier endeavours to discern a substantial cause for gravitation, before he could be satisfied with a mere mathematical description of the phenomena.
A huge comet appeared in the winter of 1680, and a correspondence ensued between Newton and the ‘King's Observator', John Flamsteed. This comet came closer to the Sun than almost any other since,41 within less than one solar radius at closest approach, and was thereby wrenched into a trajectory radically different from anything seen hitherto in the heavens. Nobody except Flamsteed at the time could believe that the comet in the November pre-dawn sky and that two weeks later in the evening sky, with a much larger tail, were one and the same.
Writing to the astronomer by way of ‘Ye question of ye two comets', Newton challenged the latter's belief that the Sun could swing a comet around so that it came back upon itself. It was by some magnetic force, replied the astronomer, who was not much given to theoretical speculations. That could not be, replied the mathematican, for magnetism is destroyed by heat, and the sun is hot.42 Then, accepting hypothetically the notion that there was just one comet, which had swung right around the Sun, he explained to Flamsteed that it must have gone behind the Sun, and not in front as the astronomer had supposed, because of the direction in which the solar vortex was rotating.
Scholars have omitted mentioning this fact when discussing this letter. Earlier in the letter, Newton had allowed ‘ye attractive power of ye Sun' as a valid possibility for changing the comet's direction, yet could not admit the astronomer's view that it had passed in front of the Sun at perihelion. He drew the diagram shown to explain the difficulty involved in such a trajectory, and continued:
Nor will ye motion of ye Vortex relieve ye difficulty but rather increase it. For that [ie, the direction in which the vortex was rotating] being according to ye order of ye letters & marks Aß? a would make the Comet verge from ye line gS rather towards ye line fq then towards h. The only way to relieve this difficulty in my judgmt is to suppose ye Comet to have gone not between ye [Sun] & Earth but to have fetched a compass about ye [Sun] as in this figure.
Figure 1: Newton's diagram for the 1680 comet
The reason here given by Newton, for that comet of 1680 having passed behind the Sun and not in front of it, was in terms of the direction of rotation of the solar vortex. When he writes, ‘the only way to relieve this difficulty,' the difficulty referred to is that of having the comet move in the reverse direction to the solar vortex. Flamsteed accepted this view, as shown in the delivery of his third Gresham lecture, in May of 1681, on this topic. The lecture alluded gratefully to a letter from ‘Mr Newton ye learned professor of Astronomy at Cambridge,'43 and described the comet as thrown around and carried on the far side of the Sun by its vortex: the first British account of a perihelion passage.
Curtis Wilson has concluded: ‘That Newton was entertaining the idea of universal gravitation after the correspondence with Hooke, and was uncertain of its truth, is the most plausible explanation for Newton's interest in the comet of the winter of 1680/81, and for the correspondence resulting therefrom'.44 A different view is advocated here, namely that, although this situation offered every opportunity for expressing the working of some principle of gravitation, little resembling such is to be found. As well as the above-mentioned explanation which Newton offered to Flamsteed, he had some further thoughts on the matter that were expressed in two unsent drafts of his next letter to Flamsteed,45 plus a further extensive outline of cometary motion which he wrote out for his own benefit, during or shortly after this correspondence. The opening paragraph of the present essay quotes from the latter, as being the start of a sixteen-point conclusion he wrote out about the nature of cometary motion,46 and the last clear statement from Newton's pen showing belief in the ether vortex theory.
Surprisingly, one of the unsent drafts of his letter to Flamsteed returns to the notion of magnetic attraction, even though he had earlier been fairly scathing about this to Flamsteed:
But all these difficulties may be avoyded by supposing ye comet to be directed by ye Sun's magnetism as well as attracted, and consequently to have been attracted all ye time of its motion,...the vis centrifuga [in perihelion] overpow'ring the attraction and forcing the Comet notwithstanding the attraction, to begin to recede from ye Sun.47
It is evident that Newton was re-considering a magnetical explanation, whereby the Sun directed the course of the comet as well as attracting it. To quote Eric Forbes:
Newton ... subsequently acknowledged that the solar magnetism could both direct and attract the comet and hence be the causal agent of its observed motion.48
What is here viewed as an a historical perspective has been advocated recently by Professor Nauenberg, whereby Newton in the 1670s had developed ‘his early ideas on orbital dynamics', including computation of curve path trajectories using second order differential calculus and the the inverse square principle of gravitational attraction. Nauenberg averred that in these 1681 letters to Flamsteed, ‘Newton explains the correct theory of the orbit of a comet around the sun.'50 This position is here viewed as incompatible with the historical texts. Apart from anything else, it cannot account for Newton's final flat denial that the ‘two comets' were one, contained in the letter of 16th April forwarded to Flamsteed. Barely more than a week separated the last sighting of the December 1680 comet and the first appearance of the January 1681 comet. Why could he not accept the well-argued thesis from the ‘King's Observator' that the two were one? Five weeks had passed by, since Flamsteed's last letter during which time he had composed two drafts, so the problem was hardly lack of concentration on the subject.
Newton had previously observed the 1664 comet, but astronomers had gathered little by way of useful data about it. Huygens had assigned to this 1664 comet a slightly curved path, whereas Kepler had said that comets followed rectilinear paths, and Cassini had put this comet in an orbit around Sirius.51 Its path had been ‘in a line almost straight,' Newton explained (in his second letter to Flamsteed, via Crompton) - though conceding that it could well be in orbit around Sirius. The path of the 1680 comet would need to be v shaped due to its unprecedentedly close approach to the Sun, were Flamsteed correct and the ‘two comets' one. As Lucasian Mathematics professor he ought not to be seen endorsing harebrained notions. Further, the sharp twist in its trajectory would have to come during the unobservable part of its orbit, making a continuous and dynamical account of its path quite tricky. Yet, the unsent draft of a letter to Flamsteed did contain the suggestion of a means of computing the cometary path, and proposition X of the notes he composed on the topic contained the pregnant phrase: ‘the curve is an oval if the comet returns in an orbit, if not is nearly a hyperbola.'52 And there things would doubtless have remained, had not another comet, equally remarkable in its implications though vastly different in its orbit, turned up two years later.
The letters sent to Halley in June and July of 1686, staking Newton's claim for originality in discovering the law of gravity, alluded thrice to views supposedly expressed in a letter which he had sent to Huygens in 1673. This letter had been sent via Oldenburg the Royal Society's Secretary, as was the custom, ie Huygens received the letter transcribed by Oldenburg. The comments in this letter were regarded as significant because they would have predated Hooke's notions on the subject. The first letter sent to Halley averred that the letter to Huygens had:
...added out of my aforesaid paper [ie, the 1675 letter to the Royal Society] an instance of their [the laws of motion] usefulness, in comparing the forces of the moon from the earth, and earth from the sun; in determining a problem about the moon's phase, and putting a limit to the sun's parallax, which shows that I had then my eye upon comparing the forces of the planets arising from their circular motion, and understood it'.
A copy of this 13-year old letter remained in Newton's files, or so Halley was informed five weeks later, when the latter part of its opening paragraph was quoted to him. Again its significance was explained: ‘Now from these words its evident yt I was at that time versed in the Theory of ye force arising from circular motion, & had an eye upon ye forces of ye planets'.53 On the third occasion of bringing this passage to Halley's attention, it was even suggested that Hooke could have derived his knowledge of gravity theory therefrom, by perusing the copy kept in the Society's correspondence.54
The passage alluded to was not present in the letter received by Huygens. The letter in Newton's handwriting as sent to Oldenburg for transcription is now in the Royal Society's archives.55 The two are identical, except for the omission of this key passage. The editor of the Huygens Oeuvres commented:
On voit que le principal argument de Newton en faveur de sa priorité vis-à-vis de Hooke consiste dans le passage de sa lettre à Huygens... On remarquera que ce passage manque dans notre texte, c'est-à-dire dans la copie qu'Oldenburg a transmise à Huygens. Il est difficile d'expliquer une omission aussi importante. Elle est absolument contraire aux habitudes d'Oldenburg. Toutes les copies de lettres qu'Oldenburg a transmises à Huygens ont été reconnues exactes. Ce n'est que dans de rares exceptions qu'Oldenburg omet une phrase.
The editors of Huygens' Oeuvres ruled out the possibility that Oldenburg had himself decided not to send the text, which constitutes the latter half of the opening paragraph of the letter, on the grounds that he only omitted odd phrases and some concluding remarks, as omissions which would have had Huygens' blessing. They concluded that some instruction must have been given to the Royal Society's secretary, of which no trace survives: ‘Quelle est la main qui a soustrait aux yeux de Huygens les reflexions de Newton sur la force centrifuge...?'56 What Oldenburg had written to Huygens a propos of this copied letter, was merely: ‘I find myself obliged to give you a copy of it, which I shall do in English as I received it,' which hardly sounds as if he had decided to omit the bulk of the first paragraph.57
The Editor of Volume I of the Correspondence noted the fact as a curiosity, a unique instance of the Royal Society's record of a Newton letter being at variance with that actually sent.58 Louise Patterson in 1950 wrote that ‘The Royal Society copy in which it [the gravity argument] does appear is an edited copy. The Huygens letter therefore... provides very dubious evidence on Newton's behalf'.59
What the letter which Newton had written to Oldenburg, to be forwarded to Huygens, actually said was: ‘I receiv'd your letters, with M.Huygens kind present, which I viewed with great satisfaction, finding it full of very subtile and useful speculations very worthy of the author. I am glad, that we are to expect another discourse of the Vis Centrifuga, which speculation may prove of good use in Natural Philosophy and Astronomy, as well as in Mechanics'.60 It cited as an example, that the Moon faced earthwards owing to ‘ye greater conatus of ye other side to recede from it' (a similar answer had been given to this question in his c.1669 document, discussed above). If this is the reason given for the Moon facing Earthwards, then this letter does indeed indicate something rather significant, about its author's grasp of gravity theory. This is however not readily compatible with what Newton later averred about it, to Halley.
7. The Correspondence of 1679-1680
I suggest that the much-analysed letters sent by Newton to Hooke over the crucial period, the winter of 1679/80, have I suggest a simpler meaning than is normally assigned to them, as from a writer who simply lacks interest in ‘philosophy' through being deeply immersed in theological and alchemic studies.61 It is hardly remarkable that a man fresh back from managing the funeral arrangements after his mother's death in Lincolnshire should confess to Hooke that he was:
almost wholly unacquainted wth what Philosophers at London or abroad have of late been imployed about. And perhaps you will ye more to believe me when I tell you yt I did not before ye reciept of your last letter, so much as heare (yt I remember) of your Hypothesis of compounding ye celestial motions of ye Planets, of a direct motion by the tangt to ye curve & of ye laws & causes of springyness, though these no doubt are well known to ye Philosophical world.62
The ‘hypothesis of springyness' was what is nowadays called Hooke's Law. We find other expressions of gratitude such as ‘I cannot but return my hearty thanks for your thinking me worthy of so noble a commerce & in order thereto francly imparting to me several things in your letter.' Or again,
If I were not so unhappy as to be unacquainted with your Hypothesis above mentioned (as I am wth almost all things which have of late been done or attempted in philosophy) I should so far comply wth your desire as to send you what Objections I could think of against them if I could think of any.
The letter repeatedly describes Newton's estrangement from natural philosophy or science, referred to as ‘philosophy':
...my affection to philosophy being worn out, so that I am almost as little concerned about it as one tradesman uses to be about another man's trade or a country man about learning.
It concludes by saying he may attempt a new design of his reflecting telescope mirror and promising that ‘If I do any thing you may expect to hear from me.' There is no trace of irritation, still less of superiority, in this correspondence, as historians (echoing the claim made by Newton in June, 1686) tend to find present. Hooke replied with a tactful and encouraging letter, hoping that his interest in ‘Philosophy' may revive by-and-by, adding ‘And I know that you that have soe fully known those Dilights cannot chuse but sumetime have a hankering after them and now and then Desire a taste of them'63 (The spelling mistakes are said to be due to his amanuensis).
It is seldom observed that Newton's letters both prior to and following this correspondence advocated the ether-gravity theory. The last letter recorded prior to those addressed to Hooke, was that to Boyle already discussed, in January of 1679. His next extant letter after the Hooke correspondence was a year later, to Thomas Burnet concerning the latter's forthcoming Telluris Theoriae Sacra of 1681, soon translated into English as the Sacred Theory of the Earth. Newton had evidently been sent a pre-publication draft, the text of which makes no allusion to vortex-motion and his first letter to Burnett suggested that the work take account of ‘ye pressure of ye vortex or of ye Moon',64 as having worked formatively upon the Earth over the course of time. The downward pressure exerted by the Moon was pictured as having formed hills and valleys in the course of time. ‘Note the allusion to the Cartesian theory of vortices', added the Editors.
Burnet's reply rejected this view. It quoted Newton's remark about formative processes as having taken place ‘by ye pressure of ye vortex of ye Moon upon ye waters', and suggested that Newton adopt a more bible-based, Mosaic account of Earth's early stages. A second letter to Burnet in January 1681 returned to this theme, despite Burnet's scepticism: ‘the pressure of ye Moon or Vortex etc may promote ye irregularities of ye causes of ye hills'.65 The letter carried on for six pages describing the exact manner in which the world was created, underscoring the way in which theological issues were uppermost in Newton's mind over this period. This correspondence does help us to appreciate how far from his mind was the modern ‘new philosophy' in these years, as he had confessed to Hooke. However, the letter tells us more than that, loth though Newtonian scholars have been to acknowledge its plain meaning.
One is reminded of Voltaire's immortal quip of four decades later, to the effect that in France the Moon overhead exerted a downward pressure (via the terrestrial vortex) to cause a low tide, while in England its gravity pull upwards caused a high tide. In 1681 Newton still envisaged a Cartesian Moon overhead, exerting a downward pressure via the terrestrial vortex.
The Hooke correspondence, and these letters, as well as the following correspondence with Flamsteed about ‘ye question of ye two comets', indicate a man still fully immersed in the Cartesian vortex theory, modified by his own alchemical notions on ether. One should remove from this picture any notion of a figure who has re-cast physics and astronomy on dynamical principles: it simply is not there. He was then a mathematican known for a telescope, colour theory and his binomial expansion, but otherwise had no inkling that he was destined to become known for a gravity theory, beyond his effort of 1675.66 His ardent endeavours were then going into chemical/alchemical experiments.
The tenor of these letters to Hooke is not well compatible with that assigned to them retrospectively by Newton's letter to Halley of June 1686. Being guided more by the former, we part company from the majority of scholars who have printed their views on the matter, excepting Lohne and Patterson in their studies of the 1950s.67 The July 1686 letter to Halley made out that Newton had then been long familiar with the inverse-square principle, and had merely been stimulated, through irritation from Hooke's presumptuous tone, to solve the great problem. Is one to believe that, returning to Cambridge after supervising his mother's funeral, he was suddenly stimulated to solve the relation of Kepler's first two laws to an inverse square principle, then put it aside and told no-one about it? This would lead us to a situation where, as Herivel complained, ‘Newton's loss of interest at this point would almost seem to argue an inability to appreciate the importance and significance of his own discoveries'.68 Such a view takes the concept of modesty beyond reasonable limits. This was, after all, the issue characterised by Westfall as ‘the great unanswered question confronting natural philosophy,'69 that the cognoscenti of Europe were pondering. Our view adheres rather to the historical record, that he solved this problem at Halley's prodding and did then communicate it to the Royal Society via Halley, at the end of 1684. The problem of elliptical orbits caught Newton's interest once he realised that a comet trajectory could have this form. After this revolutionary discovery - if the phrase may be excused - then the geometrical problem of computing the orbit, perihelion, nodes, and inclination to the ecliptic for a comet's path siezed a hold of him and he then began to reason in the manner of which history tells.70
The researches of Rob Iliffe have provided a relatively full picture of the ultimate issues with which Newton was grappling through the winter of 1679/80, such that he met the approaches of the Royal Society's Secretary with polite but firm declination to become involved in its doings, on account of his great distance from ‘philosophy.' He was busy interpreting the apocalypse, as was involving him in some quite intense discussions with his colleague Henry More (also from Grantham), the Cambridge Platonist.71
More composed his Apocalypsis Apocalypseos in the latter half of 1679, sending out some copies as New Year's gifts around the beginning of 1680. A letter which More wrote to John Sharp in August of 1680 alluded to his and 'Mr Newton's agreement in Apocalypticall notions.' It was by no means an uncommon idea in Restoration England, that themes in the books of Daniel and Revelation had political relevance, especially in relation to Roman Catholicism; added to which, in 1679 the strange hysteria of the Papish Plot had gripped the nation. More's letter to Sharp described his gift to Newton of a copy of his new book, and how in discussion Newton had seemed much to approve of his views, in the expression of which ‘...he seemed to be in a manner transported'.72
Newton returned from Woolsthorpe Manor on November 27th, 1679, two months after the start of Michaelemas term, starting his first response to Hooke on the next day, and over the next month or so read More. Iliffe reconstructs ‘at least three conversations' between More and Newton over this brief period, during which it became evident that More was greatly mistaken in supposing a concordance of views. The disagreement revolved around the seven vials and seven trumpets of the Book of Revelations, and their link with historical epochs of time. The extensive marginal comments which Newton added to his copy of More's book show him arguing against ‘synchronising the trumpets and the vials.' An in-depth debate about history, the apocalypse and the millenium was ongoing between thee two, which remained cordial although both had deeply held though differing convictions. Newton's was related to his disbelief in the Trinity, which he had carefully to conceal, and through which he became immersed in studying theological movements of the fourth century, as the period when the doctrine of the Trinity became established.
The early 1680s also found Newton continuously occupied with his alchemical researches that involved metal sublimations, especially involving the volatile metals tin and antimony, and ammonium chloride (sal ammoniac).73 The latter is a salt that will readily sublime on heating, and he viewed it as ‘the key to the art' and ‘an aid to the Elixir.'74 These considerations may help us to evaluate what did and did not transpire, over the crucial winter of 1679/80.
Hooke complained that his theory had been taken from him,75 a claim tersely dismissed by Halley in 1686 on the grounds that ‘nothing thereon appear[ed] in print, nor on the Books of the Society'.76 A comment by Sir David Brewster on Hooke's work is pertinent:
In this remarkable passage, [from Hooke's 1674 ‘Attempt to Prove the motion of the Earth'] the doctrine of universal gravitation, and the general law of planetary motions, are clearly laid down. The diminution of gravity as the square of distance, is alone wanting to complete the basis of Newtonian philosophy; but even this desideratum was in the course of a few years supplied by Dr Hooke. In a letter which he addressed to Newton in 1679, relative to the curve described by a projectile influenced by the Earth's daily motion, he asserted, that if the force of gravity decreased as the square of the distance, the curve described by a projectile would be an ellipse, whose focus was the centre of the Earth'.77,78
Brewster argued a case for independent but non-synchronous invention, in which two persons arrived at the same general theory; one being in advance of the other by over a decade.
Hooke's ‘Attempt to Prove the Motion of the Earth' of 1674 had proposed the notion that: ‘all Coelestial Bodies whatsoever, have an attraction or gravitating power towards their own centres...but that they do also attract all other Coelestial bodies that are within the sphere of their activity...' It was within this context that he formulated a principle of rectilinear inertia:
That all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a straight line, till they are by some other effectual powers deflected and bent into a Motion, describing a circle, ellipsis, or some other more compounded Curve line'.79
This may well have been the first clear statement of what came to be called ‘Newton's first law of motion,'80 as was the key to discerning centripetal acceleration in planetary motion: only by its use does acceleration towards the centre become evident. Earlier, astronomers could only discern a centrifugal force away from a centre. Figure (1) shows Hooke's diagram from his lecture of 23 May 1666, "Of ye Inflection of a Direct Motion
Figure 2: Hooke's diagram for centripetal force (see below)
There were several occasions on which Robert Hooke publicly proposed his conception of the inverse-square law of gravitation, prior to anyone else advocating it. As Secretary of the Royal Society, he inquired in November 1679 of Newton's view concerning his idea of ‘compounding the celestial motions of the planets of a direct motion by the tangent and an attractive motion towards the central body.' His next letter but one of January 6th, 1680 saw the formulation for the first time of the inverse square law of attraction:
my supposition is that the Attraction always is in a duplicate proportion to the distance from the Center Reciprocall...
That sentence concluded with an approximate version of Kepler's second law, for which he has been much censured by historians:
...and Consequently that the Velocity will be...as Kepler Supposes Reciprocall to the Distance.
In his Astronomia Nova Kepler had formulated his second law in this approximate manner.82 The correct formulation would have been, reciprocally as the perpendicular distance from the focus of the ellipse, of the tangent from the given point on the circumference - a cumbersome phrase for an orally dictated letter.
Historians of science tend not to be appreciative of Hooke's enunciation of the inverse-square law of gravitation.83 When the letter was first published by Alexandre Koyré in 1952, the latter endorsed Newton's claim of 1686, that Hooke had believed the inverse-square law would continue to apply under the Earth's surface: ‘Newton, therefore, is perfectly right in reproaching Hooke... for extending the inverse square proportion down to the centre of the earth.'84 In fact, however, as Curtis Wilson has noted of the January 6th letter, ‘Hooke rightly supposes that the force of gravity beneath the Earth's surface decreases with approach to the centre, and in much the same way that the force on a pendulum bob decreases with approach to the centre of its swing.'85 The other analogy employed in the January 6th letter was the centripetal force on a ball rolling in a bowl, where the acceleration diminishes on approaching the centre. It is remarkable that, when publishing an historic letter, Koyr_ should have apprehended, not the plain meaning of its text, but a different one averred by another six years after it was sent.
Bernard Cohen averred that the two different versions of Kepler's second law, the correct area law and its approximation, were both present together in the Hooke latter: ‘Hooke believed that these two laws of planetary speed could both be valid...Hooke seems to have had neither the mathematical ability nor the the mathematical insight to see that the two speed laws he had put forth in his letter to Newton could not be true simultaneously; he was apparently endowed with no mathematical censor to tell him right from wrong in a nonelementary problem.'86 However, no two such laws are conjointly present in that January 6th letter.
Even had Hooke been in the habit of using the approximate form of the Second Law, as did for example Christopher Wren,87 it is unlikely that it would have led to any detectable difference in the computing of planetary positions.88 Solutions to the Kepler equation for computing planetary anomalies then in use all involved approximation methods. For Cohen to describe the approximation used by Hooke as ‘false' and thereby imply incompetence in these matters, is rather severe. Hooke was being avant-garde in cognising this second law at all, and Newton was then hardly aware of it.89
Westfall found of Hooke's letter that: ‘its apparent derivation of the inverse-square law turns out to be a bastard demonstration resting on a deep confusion about dynamics and accelerated motion...combining his fallacious law of force with Kepler's fallacious law of velocities.'90 It is hardly historical to describe his proposed law of force and the approximate version of Kepler's law as ‘fallacious', nor will mere abuse dismiss the case. Hooke's letter included no derivation of the inverse-square law, presenting it as a ‘supposition': not until his 1682 lectures was a demonstration given, the first.
Curtis Wilson has characterised the proposals in the Hooke letter as ‘guesses', adding that Hooke had therein claimed that his two principles - of rectilinear inertia combined with an inverse-square attractive force towards a centre - would lead to an orbit which was ‘something other than the ellipse used by practically all the astronomers of his day', wherein he was ‘mistaken.'91 Hooke's published views on gravitation had started in 1664 with his ‘Micrographia', in which he observed that the shape of the lunar mountain ranges demonstrated that the Moon must have its own gravity field, and ever since then his lectures and publications had discussed the subject, twice addressing the Royal Society about how the planets ‘moved in circular or elliptical lines'.92 Historians of science are prone to describe his great conclusion, drawn from eighteen years of pondering the matter, as a ‘guess.'93 Curiously, they never describe Newton's binomial theorem as a ‘guess', though no proof was ever supplied.94
The purpose of Hooke's letter was to stimulate Newton to apply his mind to ascertaining the orbit resulting from these principles - unsuccessfully, in the short term. It would have been tactless for the letter to specify the answer required, viz. an ellipse. Huygens was then advocating egg-shaped ovals for the planetary orbits. The function of the Royal Society's secretary was to stimulate informed discussion. All the January 6th letter said about the resulting orbit, was that the resulting curve would have its two ‘auges' (ie its apogee and perigee positions) stable and opposite each other, in contrast with the subject of the previous letter, the path of a ball rolling in a bowl, where they kept altering. To infer from this letter that Hooke did not accept the theory of elliptical orbits seems excessive.
Hooke's bold hypothesis was that throughout the universe there existed an
active principle, which I conceive universal to all solid bodies in Nature, and that is, of a Gravitation or Power of attracting similar solid bodies towards their centres.
His argument wove between the physics of an earth which moves round the Sun, still a fairly new idea, to comets and why their tails point away from the Sun - quite a tricky matter to explain. His theory is shown to be better than the old theories of vortices or crystal spheres because of the way comets can move about the solar system, in a quite contrary direction than the planets.
Gravity applies to any body in proportion to its ‘weight' he explains, irrespective of shape or whether it is solid or liquid (today we would say ‘mass'). The attraction is as inverse square of distance simply because of the three-dimensional nature of space. Using the analogy of an effluvium radiating through space, he explained:
For this Power propagated, as I shall then shew, does continually diminish according as the Orb of propagation does continually increase, as we find the Propagation of the Media of Light and Sound do also...And from hence I conceive the Power thereof to be always reciprocal to the Area or Superficies of the Orb of Propagation, that is duplicate of the distance.'98
Robert Hooke developed his theory of gravitation between 1666 (when lowering masses down a well in Surrey he strove to measure their decrease in weight) to 1682, when his theory was fully formed.
This argument, the first public exposition of the universal inverse-square law of gravitational attraction, has been little acknowledged by historians of science, although Professor Theodore Brown, in his Introduction to the second edition of Hooke's Posthumous works, has stated that the real interest of the ‘comet' lectures lies in their comments upon gravity theory, with an inverse-square law derived from the analogy with light.99 The argument concerning the ‘Orb of Propagation' is analogous to that later used by Michael Faraday in comprehending electrostatic force and how it decreases as the square of distance. As the area of the surface of a sphere is 4pr², so in unit area of such a sphere's surface the concentration of lines of flux (or however one pictures it) must vary inversely as the square of the distance; for the same reason as light and sound intensity decrease through space inversely as the square of the distance.
These lectures on the comet were read to the Royal Society on 25th October, the 8th and 15th November, 1682.100 The discourse is recorded in the Posthumous works of Hooke, edited and published by Richard Waller in 1705. Waller was there in the habit of conflating several lectures at a time, delivered by Hooke at short weekly intervals, without dating the separate parts. He was elected FRS in May 1681, so would have been familiar with the lectures then delivered. The chapter of Hooke's posthumous works entitled, ‘A Discourse of the Nature of Comets' was cited by Waller as having been given ‘soon after Michelmas' of 1682. Hooke's Discourse ‘Of Comets and Gravity' starts on page 166, with the discussion of the theory of universal gravitation beginning at the bottom of page 176. It continues over nine pages and breaks off abruptly on page 185. It is introduced with phrases like, ‘These my conceptions (as being, I think, wholly new, and not yet asserted by any person whatsoever)...' His explanation as to why gravity diminished reciprocally as the duplicate of distance occurs on the last page.
The Royal Society's History, which consists of brief minutes of the meetings, says only that Hooke then gave two lectures on the subject of comets and does not mention gravity. Could the gravity discourse have been given at some other date, and merely appended by Waller to the comet lectures? In his introduction to the ‘Nature of Comets' discourse, Waller stated: ‘I shall only give some account of what is immediately annext to it, and which indeed the Thread of the Discourse led him to; that is, a short Treatise of Gravity.' Thus, as Waller stated, it was the logic of the comet lecture which led Hooke on to the theme of universal gravitation. This is confirmed by a later remark on another occasion,101 when Hooke was again discussing gravity, and remarked: ‘yet ‘tis very evident by many arguments I produced in my lectures about the Comet, that the Power thereof [ie, of gravity] is not limited with so small an extent...' He was there arguing against a popular notion that gravity terminated in the atmosphere and reached no higher. It is evident that within Hooke's mind, the overall context for that lecture-series wherein he argued extensively about the nature of gravity was ‘the Comet', viz that of 1682.
His exposition of the inverse-square nature of the gravity force followed on from his lecture-series on light nearly three years earlier, where he had derived the inverse square law for light intensity geometrically using conical space elements - an example of what Hooke called ‘Physics geometrically handled.'102 As Koyré pointed out, for Hooke the law was ‘deduced from an analogy with the inverse square law of the intensity of illumination.'103
Much would have been discussed by the coffee-house trio of Halley, Hooke and Wren, accustomed to meeting by St Paul's in the early 1680s, of which alas only a highly polarised account remains, after severe loyalty-tests had been imposed. Once Halley realised that he was in possession of a manuscript ‘that all future ages will admire,' viz the Principia, everything changed. For example, Halley did once claim that the inverse-square principle for centripetal attraction had occurred to him in January 1684;104 however, that claim only appears in a letter which was a masterpiece of diplomacy, sent to Newton in June 1686. This achieved its all-important goal, of preventing the threatened suppression of part III of the Principia - as would have left Halley personally committed to financing the publication of merely the first two volumes of a treatise on motion. The ploy in that letter was evidently successful, as a mollified Newton soon replied, with the (unlikely) suggestion that of the three of them, Hooke was the last to come by the duplicate proportion principle. The rather brutal comment Halley made, cited above, about his old friend Hooke's priority claim should also be seen in this light, as it was contained in that same letter.
Textbooks sometimes affirm that Wren arrived at the inverse-square principle of gravity in the late 1670s.105 Newton's first letter to Halley of June 1686 averred that he recalled discussing the matter with Wren and hearing him propose such a notion. Halley evidently went back to Wren after receiving this letter, for his tactful reply indicated that Wren had not confirmed the story.106 Hooke was the only person in Europe, up until the summer of 1684, on record as advocating the inverse-square law. It was difficult for him to relate it to elliptical motion,107 which was the reason for his approaching Newton about the matter. That, however, is an application of the law and not the law itself, and without relevance for the question of priority.
Newton constructed a proof to demonstrate that an elliptical orbit could be generated by an inverse square force of centripetal attraction, in the autumn of 1684, following Halley's visit, though is not easy to follow. Whiteside has inferred that even Halley did not understand it, from an error which he as its publisher made in an accompanying diagram.108 The proof depends upon a form of integral calculus, using volumes, ie cubic quantities. It is not something over which one remarks 'Aha!' upon perusing. To quote further from the essay by Lohne, with which this paper began,
But Halley had to wait three months till he got - not the deduction - but a tract containing material for a course of nine lectures ... We may indeed be grateful that there was a problem Newton could not solve, and so was forced to write and publish his Principia ...109
Lohne also pointed out the still controversial fact that, as Bernard Cohen later remarked,
What Newton proved, however, in De Motu was not that if the attractive force varies as inverse square of the distance, then the orbit will be an ellipse; rather, he proved the converse, namely, that if the orbit is an ellipse, then the attractive force must vary inversely as the square of the distance.110
The difficulty of this proof, and it being the converse of what he had apparently stated to Halley could be accomplished, argues against the usual tale of it having been done rapidly and somewhat casually in the winter of 1679/80, then put away and ignored.
The late E.J.Aiton, one of the few science historians who really understood the mathematics involved, described the proof of the Kepler area law given in De Motu as 'mathematically unsound' on the grounds that the summation of the infinitesimal changes was not accomplished rigorously. Concerning its inference that, in an elliptical orbit, the centripetal force varies as the inverse square of the distance, Aiton wrote: ‘Once again this argument leaves unresolved the logical difficulties inherent in the approximation of a continuous force by a sucession of impulses'111. Such difficulties, reflecting the limited range of integral calculus methods then available, may help us to discern that the proof was first accomplished, in a difficult and laborious manner, in the autumn of 1684 and not earlier.
The proof required as preliminaries such fundamental matters as the formulation of the concept of moments as small changes, his concepts of force and impulse, plus the expression of Kepler's second law in terms of what we would nowadays call the conservation of angular momentum, which was then far from evident. And, how could Newton have stopped there? Achieving this proof led him ineluctibly on to demonstrate that other conic section orbits, traced out by comets, were also generated by an inverse-square law of attraction. Thus, the embryonic subject that Leibniz was later to call dynamics had to be hatched, in order to formulate this proof. It was not a self-contained kind of thing, that one could just do and then leave (as the traditional tale has it). By accomplishing it, he was committed to a new beginning, which beginning was - De Motu.
12. Halley's Comet: the Trigger
Rupert Hall has argued that:
Newton's late discovery of the true power of the law of gravitation - after 1680 - was a blow to his aethereal hypothesis; for a Cartesian ether... it is difficult to see how it could agree with the unresisted motion of the planets. With the law came the interstellar vacuum.112
This thesis accords fairly well with the case here to be advocated, and would become identical with it merely by removal of the qualifying phrase, ‘...the true power of...'
Historians have hitherto had difficulty in locating the date when the truth of the theory of gravity dawned upon Isaac Newton. If we are now able to do this, it is at the cost of dispelling the myths of centuries. It may have dawned silently as he pondered the path of ‘Halley's comet' of 1682, while recalling the problems of interpreting that of 1680. The two comets had different but equally potent implications: that of 1680 had an orbit more or less ‘V' - shaped, coming within less than a solar radius to the Sun at its perihelion. The next, remembered by posterity as ‘Halley's comet', was tilted at a mere 18? to the ecliptic, in contrast with the 61? of the 1680 comet, and at perihelion was a respectable 0.6 A.U. from the sun, compared with the 0.006 A.U. of its predecessor.113
More significantly, the parabola of its trajectory passed close to the ecliptic, but in the reverse direction to the planetary orbits. As Newton watched it, all the ethereal matter of the huge solar vortex, that he had so long believed in, dissolved (I conjecture) into nothingness. That did not happen with the 1680 comet, which revolved in the same direction as the planets. The 1682 comet was more or less within the zodiacal region, and if the ether-vortex was working anywhere it had to be there. The comet moved in between Mercury and Venus at its perihelion. A tension built up between all that Newton had said publicly on the subject and the new testimony of the heavens. At last, the skies became for him empty. Only then was he moved to ponder the words Hooke had earlier addressed to him. His alchemical experiments continued, until in August of 1684 his furnace was allowed to expire, following the visit of Edmond Halley, and an entirely new phase of his life began. Claims that he had accepted or formulated an inverse-square law of gravitational attraction prior to that date are mere fabrications; of which Newton himself was the prime author.114
The comet appeared as a decisive counter-example to what had hitherto appeared as more or less axiomatic, namely that things orbiting around the Sun went one way. This meant that whatever explanation was required, it should not be directional, unlike Kepler's magnetic force or Descartes' vortices. It became evident to him that the nucleus of this comet had to be a solid body, even though the Sun's heat at its perihelion caused its tail to grow. Eventually, Newton's treatment of this comet ended up as a full twenty pages of Book III of his Principia.
By the early 1690s, the fact that all planets orbited in the same direction around the Sun, and did so in nearly circular orbits, was being promoted into propositions of theology. They appeared in the first set of Boyle lectures given by Bentley, and in Samuel Clarke's correspondence with Leibniz. That which a decade earlier had been part of natural science, explained by Descartes' ether-vortex, had since become unexplained and rendered problematic by the new gravity theory. Book Two of the Principia demolished the ethers that had been carrying them round, and instead a ‘divine arm' was invoked to set them rolling at the start. The path of Halley's comet, ‘the only known bright periodic comet,'115 as was discernibly a conic section, elliptical or parabolic, formed the turning-point.
Discussing a recollection by Newton around the year 1718 to the effect that in the years 1676-7 he had accomplished the linking of Kepler's laws to the inverse-square principle, Bernard Cohen commented: ‘Of course this is bogus history, created by Newton.'116 As Cohen rightly observed, once Newton had learnt to analyse orbital motion in terms of centripetal forces, ‘he interpreted his early calculations as if they were essentially the "moon test" described in the scholium to prop.4, bk. three, of the Principia.'117
A year prior to Newton's death, stories of the apple myth begin to appear. Rather surprisingly, Westfall has opined that the sixty-year gap between recollection and the supposed insight ‘does not seriously compromise acceptance of the incident itself.'118 But, if anything, the sequence of events is comparable to that recently discerned over the well-known dream-legend of August Kekulé. (A reevaluation of the legendary dream of Kekulé whereby he supposedly envisioned the benzene ring structure has emphasised its function in a priority dispute. The dream was only recalled a few years before Kekulé's death, when it was located in a comfortably distant past in order to predate a rival's priority claim. Scrutiny of the Kekulé notebooks failed to detect any such definite moment of insight, pointing rather to a later period, wherein he could have obtained the notion from another119; but, concluded the authors, ‘we have our doubts whether the truth will get in the way of a good story.')
Newton was loath to acknowledge that he owed central components of the Principia's scheme to others. As Bernard Cohen has observed, the Principia gave no acknowledgement to Kepler as a discoveror either of ellipses or the area law.120 Book Three opened with a discussion of Kepler's third law as shown in the motions of the satellites of Saturn and Jupiter, with no hint that Flamsteed had pointed out the fact. In a somewhat parallel case-study, Professor Hall referred to a ‘famous but delusive passage' composed by Newton in 1713, asserting that the Principia had been composed using fluxional methods, then afterwards re-cast into its geometrical format.121 Only after Whiteside's exhaustive researches established that no such preliminary notes existed, could realistic histories of the fluxional method begin to be composed. The historian should refrain from projecting back into past time, discoveries for which documentary evidence is lacking.
2) Ibid,, 412-3, 413 (sent 12 Jan 1685).
3) D.T.Whiteside, ‘The Prehistory of the Principia', Notes and Records of the Royal Society, 45 (1991), 11-61, 45, n. 43. Earlier he had dated this text a year later, in the spring of 1682: see D.T.Whiteside, ‘Before the Principia,' Journal for the History of Astronomy, I (1970), 5-19, 14, n. 42.
4) ‘The matter of the heavens is fluid, and revolves around the centre of the cosmic system in the direction of the courses of the planets' (Whiteside, note 3 (1970), 18, n. 42, ref. ULC Add MS. 3965, 14,f,613); Betty J.T. Dobbs, The Janus Faces of Genius: the role of alchemy in Newton's thought (Cambridge, 1991), 127-8.
5) D.T.Whiteside, ‘Newton's Early thoughts on Planetary Motion, A Fresh Look,' British Journal for the History of Science, 2, pt.2 (December 1964), 117-137 (135). For the first draft of De Motu in Autumn of 1684, see The Mathematical Papers of Isaac Newton, edited by D.T. Whiteside, VI (Cambridge, 1974), 37-80.
7) J.Lohne, “Hooke Versus Newton“, Centaurus, 7 (1960), 6-52, 35.
8) Rouse Ball, An Essay on Newton's Principia (London, 1893), 22.
9) Whiteside (note 3) 1970, p.11. For the Moon-test performed in 1685, see N.Kollerstrom, ‘Newton's two Moon-tests', British Journal for the History of Science, 24 (1991), 369-72.
10) J.W.Herivel, ‘Newton's First Solution to the Problem of Kepler Motion', British Journal for the History of Science, 2 (1965), 350-354; R.Westfall, Never at Rest (Cambridge, 1980), 387-8 and 403. For the Locke letter, see A.R.Hall & M.B.Hall, The Unpublished Papers of Isaac Newton, (Cambridge, 1962), 293-301; and J.W.Herivel, The Background of Newton's Principia (Oxford, 1965), 246-54.
11) For a rebuttal of the Herivel-Westfall case, see Whiteside (note 3) 1991, pp.53-4, n. 87. Brackenridge has claimed that the content of the text whose date is disputed supports the later dating, in ‘The Critical Role of Curvature in Newton's Developing Dynamics,' The Investigation of Difficult Things, Essays on Newton and the history of the exact sciences, in honour of D.T.Whiteside (Cambridge, 1992), Chapter 8, 242. The debate is reviewed in Brackenridge, ‘The Locke/Newton Manuscripts revisited: conjugates, curvatures & conjectures', Archives Internationales d'Histoire des Sciences, 43 (1993), 280-292, 282.
12) R.Taton and C.Wilson, editors, The General History of Astronomy, Vol 2A (Cambridge, 1989), Chapter 13, C.Wilson, ‘The Newtonian Achievement in Astronomy,' 234-254.
13) Ibid., 236.
14) ‘De gravitatione et aequipondio fluidorum (Newtonian text) in Hall & Hall (note 10), 121-156, 148-9. Dobbs has proposed a composition date of 1684, sixteen years later, straining credulity (note 4, 141).
15) For Descartes' view on how subtle matter revolving around the earth caused bodies to fall downward, see A. Koyr_, Galileo Studies (Hassocks, 1978), 92.
16) Wilson, note 12, 235.
17) Westfall, note 10, 91.
18) Ibid, 91.
19) The copy of Vincent Wing's textbook Astronomia Britannica (London, 1669), that belonged to Newton, is at Trinity College Cambridge, shelved at NQ.18.36. For Whiteside on Newton's comments inscribed therein, see chiefly: note (3) (1970), 9; ‘Newton's Lunar Theory: from High Hope to Disenchantment', Vistas in Astronomy, 19 (1976), 317-328, 318; and note (3) (1991), 12. Of the theory therein implied, Curtis Wilson initially commented: ‘It is likely that Newton is here merely reasoning in line with the vortical theory outlined by Wing' (‘From Kepler's laws...to Universal Gravitation', Archive for History of Exact Sciences, 6 (1970), 89-170 (142); reprinted in C.Wilson, Astronomy from Kepler to Newton (London, 1989, Chapter 8). More recently he views Newton as during the 1670s still accepting the vortex theory (note (12), 237).
20) Whiteside (note 3), 1970, 12; for relevant text of these notes (in Latin) see Whiteside (note 3, 1991), 45, n.42.
21) U.L.C. MS Add. 3958, sect.5,fol 87; Corr., I, pp.298-303. For a well-balanced assessment of what was contained in this early text, see I. Bernard Cohen, The Newtonian Revolution (Cambridge, 1980), 236-240 and 346, n. 4 & 5.
22) A.R.Hall, ‘Newton on the Calculation of Central Forces', Annals of Science,13 (1957), 62-71, 69.
23) Wilson (note 19), 1989, 143.
24) Herivel (note 10), 72, cited in Wilson (note 19), 140.
25) R_n_ Descartes, Principia philosophiae (Amsterdam, 1644), 56; Principles of Philosophy, translated by V.R.Miller and R.P.Miller (Dortrecht, 1983), 60: discussed by P.J.Pugliese in Robert Hooke, New Studies edited by M.Hunter and S.Schaffer (Woodbridge, 1989), 187.
26) Whiteside (note 9), 11.
27) D.T.Whiteside, The Preliminary Manuscripts for Isaac Newton's 1678 Principia, 1684-1685 (Cambridge, 1989), x.
28) Cohen (note 21), 238-240.
29) Dobbs (note 4), 96-106.
30) T.Birch, History of the Royal Society, 4 vols (London 1756-7; reprinted Brussels 1968), 3, 1756, 248-60.
31) The Correspondence of Isaac Newton, I (London, 1959), ‘An Hypothesis explaining the Properties of Light,' 362-389 (sent 7 December, 1675); E.Aiton, The Vortex Theory of Planetary motions (London, 1972), 106-7.
32) Wilson (note 19), 144.
33) L.Rosenfield, ‘Newton and the Law of Gravitation', Archive for History of Exact Sciences, 2 (1965), 365-386; Cohen (note 21), 1980, 348, ref. 8. The issue is further discussed in Curtis Wilson (note 12), 236-7.
34) The Correspondence of Isaac Newton, II (Cambridge, 1960), 446-7 (sent 27 July, 1686).
35) Rosenfield (note 33), 373.
36) Aiton (note 31), 106: ‘Hooke did not, in fact, make this assumption, as was clear from one of his letters in Newton's possession.' See also M. Nauenberg, ‘Hooke, Orbital Motion, and Newton's Principia', American Journal of Physics, 62 (1994), 331-350 (338).
38) Ibid, 288-295, 295 (sent 28 Feb. 1679); Dobbs (note 4), pp.117-9.
39) Ibid, 446-7 (sent 27 July, 1686).
40) Cohen (note 21), p.185.
41) E.Forbes, ‘The Comet of 1680-81', in N.Thrower, editor, Standing on the Shoulders of Giants (Los Angeles & Berkeley, 1990), 312-323; curiously, Forbes omitted to mention its very close approach to the Sun, 0.0062 AU at perihelion.
42) The Correspondence of Isaac Newton, II (Cambridge, 1960), 340-347, 341 (sent 28 Feb. 1681).
43) The Gresham Lectures of John Flamsteed, edited by E.G.Forbes (London, 1975), Lecture 3, 106-116,114; Introduction by Forbes, 1-78,32.
44) Wilson (note 19), 151-6.
45) The Correspondence of Isaac Newton, II (Cambridge, 1960), 358-62 (April 1681, not sent).
46) University Library Cambridge, Add. 3965 (14) f.613r. These propositions were first made known by J.Ruffner in his doctoral dissertation, The Background and Early Development of Newton's Theory of Comets (Indiana, Indianapolis, 1966); discussed by Domenico Meli, in Equivalence and Priority: Newton versus Leibniz (Oxford, 1993), 179, n.12.
47) The Correspondence of Isaac Newton, II (Cambridge, 1960), 361.
48) Forbes (note 41), 315. Forbes was alluding to the draft letter sent to Crompton of April 1681 (The Correspondence of Isaac Newton, II (Cambridge, 1960), 358-62), erroneously supposing that it had been sent.
49) Whiteside (note 3) 1970, p.14.
50) M.Nauenberg, ‘Newton's Early Computational Method for Dynamics', Archive for History of Exact Sciences, 46 (1994), 221-252, 252.
51) D.K.Yeomans, Comets, a Chronological History of Observation, Science, Myth and Folklore (New York, 1991), 70,89.
52) Newton manuscript (note 46), propn. X.
53) The Correspondence of Isaac Newton, II (Cambridge, 1960), 435-440, 436 (sent 20 June 1686); 446-7 (sent 27 July 1686).
54) The actual content of the inserted paragraph is not of great relevance: it contains an estimate of the ratio of the maximal distances Earth/Sun and Earth/Moon, as 10000:56, which underestimates the Earth/Sun distance by about 100%. Estimates of this ratio were then rapidly improving. Overall, the paragraph's connection with gravity theory is slight.
55) The Correspondence of Isaac Newton, II (Cambridge, 1960), 290-295: Royal Society Archives LBC.6.172, dated 23 June 1673.
56) The Hague copy of Huygens's letter is in the University of Leiden, published in the Oeuvres complètes de Christiaan Huygens, vol.7 (Hague, 1888), 325-8.
57) The Correspondence of Henry Oldenburg, vol.10 (London, 1975), 58-68 (68): Oldenburg to Huygens, sent 27 June 1673.
58) The Correspondence of Isaac Newton, I (Cambridge, 1959), Preface by W.Turnbull, xxxiii.
59) L.D.Patterson, ‘Hooke's Theory of Gravitation and its Influence upon Newton', Isis, 40 (1949), 327-341; 41 (1950), 32-45 (32).
60) The Correspondence of Isaac Newton, I (Cambridge, 1959), 290-5 (290) (sent 23 June 1673).
61) For the theological debates between Newton and Henry More around this time, as a result of the latter's Apocalypsis Apocalypseos appearing towards the end of 1679, see R.Iliffe, ‘Making a Shew: Apocalyptic Hermeneutics and the Sociology of Christian Idolatry in the work of Isaac Newton and Henry More', in The Book of Nature and Scripture, edited by J.Force and R.Popkin (Dortrecht, 1994), 55-88.
62) The Correspondence of Isaac Newton, II (Cambridge, 1960), 300-3, 302 (sent 28 Nov. 1679). Newton visited Woolsthorpe on July 28th and returned November 27th, his mother having been buried June 4th: Ibid, 303, n2.
63) Ibid, 304-6 (sent 9 December, 1697).
64) Ibid, 319 (sent 24 December, 1680).
65) Ibid, 329-334, 331 (sent January 1681).
66) For a different view, see M.Nauenberg, ‘Newton's Early Computational Method for Dynamics', Archive for History of Exact Sciences, 46 (1994), 221-252.
67) Lohne (note7) and L.Patterson (note 59).
68) Herivel (note 10) 1965, 23.
69) Westfall (note 10), 402.
70) P.Lancaster Brown, Halley's Comet and the Principia (Aldeburgh, 1986), 67-70.
71) Iliffe (note 61), 65-85.
72) Ibid, 69; Westfall (note 10), 349.
73) Cambridge University Library Add. MS. 3973 (Chemical experiments 1679/80).
74) Westfall (note 10), 364.
75) There are two extant texts where Hooke reviewed the situation, neither included in the posthumous Works: the first, undated, was published in manuscript form by R.T.Gunther, Early Science in Oxford, vol.10 (Oxford, 1931), 57-60: ‘A True State of the Case and Controversy between Sir Isaac Newton and Dr. Robert Hooke as to the Priority of that Noble Hypothesis of Motion of ye Planets about ye Sun as their center,' discussed in Nauenberg (note 36) p.346; the second (untitled) was a lecture read before the Royal Society in February 1690, in: A.R.Hall, ‘Two Unpublished Letters of Robert Hooke,' Isis, 42 (1951), 219-230, 224-7.
76) The Correspondence of Isaac Newton, II (Cambridge, 1960), 441-3 (sent 29 June 1686).
77) R.Hooke, ‘An Attempt to Prove the Motion of the Earth by Observations' (1674), in Lectiones Cutlerianae (London, 1670), the first of six Cutler lectures; reprinted by Gunter (note 75), VIII, 1-28. See J.A.Bennett, ‘Magnetical Philosophy and Astronomy from Wilkins to Hooke' in Taton & Wilson (note 12), 222-230 (229).
78) D.Brewster, Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton, I, (Edinburgh 1855, reprinted London, 1965), 287-8.
79) Hooke (note 77), 28.
80) Descartes' principles of inertia (Cohen, note 21, pp.183-4) resemble this principle, but lack a concept of uniform velocity; see Alan Gabbey, ‘Force and Inertia in Seventeenth-century Dynamics,' in Studies in History and Philosophy of Science' vol.2 (1971), 1-67 (59). As Descartes' space was full of matter, motion could only be that of the whole of matter in a closed path or vortex.
81) Royal Soc. Hooke MS XX,41, May 23 1666; reprinted in Gunther (note 75), VI, pp.265-8 as ‘Motion in a Curve, a Statement of Planetary Movements as a Mechanical Problem.' Patterson (note 49), p.333 commented: ‘Hooke's diagram ... in which he anticipated Huygens' first theorem on centripetal force.' See also Bennet (note 77), 229.
82) For the two versions of Kepler's second law in Astronomia Nova of 1609, see E.J.Aiton, ‘Kepler's Second Law,' Isis, 60 (19690, 75-90; J.Dreyer, A History of Astronomy from Thales to Kepler (New York, 1953), 388.
83) An exception here is V.L.Arnol'd, Huygens and Barrow, Newton and Hooke, (Berlin, 1990; 1989 in Russian).
84) A. Koyr_, ‘An Unpublished letter of Robert Hooke to Isaac Newton', Isis, 43 (1952), 312-337, 334.
85) Wilson (note 12), 245; for further discussion, see note 36.
86) Cohen (note 21), 54.
87) Ibid, 228.
88) Aiton (note 82), p.79, quotes Max Caspar as having computed the difference in mean anomalies for Earth's orbit, using both distance and area law, and finding its maximal value (at the octants) to be 9 arcseconds. For comparison, tables then had errors in planetary longitudes of tens of arcminutes: O.Gingerich and B.Welther, Planetary, Lunar and Solar Positions AD 1650-1805, Preface ‘The Accuracy of Historical Ephemerides' (Cambridge, Mass., 1983), pp.i-xxiii; partially reproduced in Wilson (note 12), 187-189.
89) Cohen (note 21), 250: ‘prior to this correspondence with Hooke in 1679-1680, the second law was not part of Newton's conscious armoury of astronomical principles;' 349, note 5 for Nature correspondence over this issue between Herivel, Whiteside and Cohen; Wilson (note 12), 238.
90) Westfall (note 10), 386-7.
91) Wilson (note 12), 245.
92) R.Hooke, Motion in a Curve, a Statement of Planetary Movements as a Mechancial Problem (lecture given on May 23, 1666), in Gunther (note 75), VI, 265-8 (265); 1670 Cutler lecture, An Attempt to Prove the Motion of the Earth, Birch (note 30), II, 90-92, 91, and Gunther (note 77).
93) Cohen (note 21), p.249.
94) D.T.Whiteside, “Newton's Discovery of the General binomial Theorem“, The Mathematical Gazette, 45 (1961), 175-180 (180).
95) Birch (note 30) vol.IV, 1.
96) T.M.Brown, Ed., The posthumous works of Robert Hooke... 1705 (2nd edn. Princeton 1971), ‘Of Comets and Gravity', 166-185.
97) Nauenberg (note 36), p.347, note 28.
98) Brown (note 96), 185.
99) Ibid, 7; see also, P.D.Lawrence and A.G.Molland, ‘David Gregory's Inaugural Lecture at Oxford', Notes & Records of the Royal Society, 25 (1970), 143-178 (152).
100) Birch (note 30), 162-5.
101) Brown (note 96), 202.
102) Brown (note 96), ‘Lectures on Light', p.73, delivered ‘about the beginning of 1680;' pp.79-80 (arguments for the inverse-square attenuation of light intensity), and pp.93,114 for other comments on the inverse-square ratio, alluding briefly to planetary motion.
103) Koyr_ (note 84) 336; also, Lawrence and Molland (note 99), 151.
104) Westfall (note 10), 402.
105) The Correspondence of Isaac Newton, II (Cambridge, 1960), 441-3, 442 (sent 29 June 1686). For a recent account averring that the inverse-square law had ocurred to both Halley and Wren in the early 1670s, who then told it to Hooke, see J.Balfour, Absolute or Relative motion? I, The Discovery of Dynamics (Cambridge, 1989), p.542. On the view here taken, this reverses the historical sequence.
106) The Correspondence of Isaac Newton, II (Cambridge, 1960), 442.
107) Nauenberg (note 36), reviewed Hooke's unfinished manuscript ‘The Laws of Circular Motion' kept at Trinity College Library, Cambridge (MS 0.11a 1/16), as to how a body moving in a central field of force would tend to trace out an ellipse. He disagreed with an earlier review of this manuscript by P.J.Pugliese (‘Robert Hooke and the Dynamics of Motion in a Curved Path', in Hunter and Schaffer (note 25), 181-205) which concluded that Hooke could not make much headway with the problem. His view is challenged by Herman Erlichson, in ‘Hooke's September 1685 Ellipse Vertices construction and Newton's Instantaneous Impulse Construction', Historia Mathematica, 24 (1997), 167-184.
108) Whiteside (note 3), 33.
109) Lohne (note 7), 36.
110) I.Bernard Cohen, ‘The Principia, Universal Gravitation, and the “Newtonian Style..."' Contemporary Newton Research, Ed. Z.Bechler (Dortrecht and London, 1982), 84.
111) E.J.Aiton (note 31), pp.103-4; criticised in H.Erlichson, ‘Newton's Polygon Model and the Second Order Fallacy', Centaurus, 35 (1992) 243-58.
112) A.R.Hall and M.B.Hall, ‘Newton and the Theory of Matter,' Texas Quarterly Journal, 10 (Autumn 1967), 54-68 (63).
113) B.Marsden & G.Williams, Catalogue of Cometary Orbits (International Astronomical Union, 1992), 7th Edn., 10.
114) For Newton's several recollections of events, see Cohen, Introduction to Newton's Principia, Supplement 1 (Cambridge, 1971), 289-298.
115) Richard Stephenson, ‘The Ancient History of Halley's Comet,' in Thrower (note 41), 231-253 (231).
116) Cohen (note 21), 248.
118) Westfall (note 10), 154. For recent belief in a c.1666 ‘Moon-test', see Balfour (note 105), 534; S.Chandrasekhar, Newton's Principia for the Common Reader (Oxford, 1995), Chapter 1.
119) J.H.Wotiz and S. Rudofsky, ‘Kekul_'s dreams: fact or fiction?' Chemistry in Britain (August, 1984), 720-3 (723); John Wotiz, Ed., The Kekul_ Riddle, A Challenge for Chemists and Psychologists (Illinois, 1997).
120) I.B.Cohen, ‘Kepler's Century, Prelude to Newton's' in ‘Four Hundred Years, proceeding held in honour of Johannes Kepler,' Vistas in Astronomy, 18 (1975), 3-36 (5).
121) A.R.Hall, Philosophers at War (Cambridge 1980), 229; challenged by Herman Erlichson in ‘Evidence that Newton used the Calculus to discover some of the Propositions in the Principia,' Centaurus, 39 (1997), 253-266. The issue is reviewed in F.de Gandt, Force and Geometry in Newton's Principia (Princeton, 1995).
rev: June 2003