Newton's ‘De Aere et Aethere’ and the introduction of interparticulate forces into his physics

ABSTRACT

As well as the mathematically-supported celestial mechanics that Newton developed in his Principia, Newton also proposed a more speculative natural philosophy of interparticulate forces of attraction and repulsion. Although this speculative philosophy was not made public before the ‘Queries’ which Newton appended to the Opticks, it originated far earlier in Newton’s career. This article makes the case that Newton’s short, unfinished manuscript, entitled ‘De Aere et Aethere’, should be seen as an important landmark in Newton’s intellectual development, being the first work in which Newton assumed there are repulsive forces operating at a distance between the particles of bodies. The article offers an account of how Newton came to write ‘De Aere et Aethere’ and why. It also outlines its relationship to the ‘Conclusio’, with which Newton briefly intended to finish the Principia, and to the ‘Queries’ in the Opticks. The date of the manuscript is disputed, and the article also aims to settle this dispute. Claims that the ‘De Aere et Aethere’ must have been written before the ‘Hypothesis... of Light’ of 1675 are dismissed, and it is suggested, following R. S. Westfall, that it was written after a well-known letter Newton wrote to Boyle early in 1679.

KEYWORDS:

• Action at a distance
• aether
• attraction
• Isaac Newton
• repulsion

‘De Aere et Aethere’, a turning point in Newton’s physics?

As well as the unparalleled achievement of his Philosophiae naturalis principia mathematica (1687), in which Newton immeasurably improved the understanding of what he called ‘rational mechanics’, and invented what Leibniz called the science of dynamics, and seemed to have finally grasped the physics underlying the ‘System of the World’, Newton also proposed a much more speculative natural philosophy.¹ His speculative physics was based on the assumption that the invisibly small particles which he held to constitute all bodies interacted with one another, not just by colliding with one another (as in the strict versions of the mechanical philosophy which had been developed by Descartes, Hobbes, and others), but also by means of repulsive and attractive forces operating at a distance between them. This more speculative physics of interparticulate forces was first made public in the various ‘Queries’ successively added to the first two English editions of the Opticks (1704, 1717), and the intervening Latin Optice (1706).² It was in the final ‘Query 31’, for example, that Newton wrote:

Have not the small Particles of Bodies certain Powers, Virtues, or Forces, by which they act at a distance, not only upon the Rays of Light for reflecting, refracting, and inflecting them, but also upon one another for producing a great Part of the Phaenomena of Nature? For it’s well known, that Bodies act upon one another by the Attractions of Gravity, Magnetism, and Electricity, and these Instances shew the Tenor and Course of Nature, and make it not improbable but that there may be more attractive Powers than these.³

Newton signalled the conjectural nature of this interparticulate physics not only by presenting it in the form of queries, but also by stating at the beginning that he proposed them ‘in order to a further search to be made by others.’⁴ Newton’s reputation, following publication of the Principia, was so great that there was no shortage of natural philosophers willing to engage in that ‘further search’, and arguably his speculative physics of interparticulate forces proved to be as influential throughout the long eighteenth century as his more rigorous ‘System of the World’, especially among those with little or no aptitude for mathematics.⁵

Although Newton’s second great book was the place where he finally made his speculative physics public, and where he developed it in most detail, it was not first conceived as he was preparing the Opticks for the press. Nor did it grow out of the work he did for the Principia, even though the attractive force of gravity between all bodies was a fundamental aspect of the mathematically-supported dynamics he developed there. In fact, the origins of his speculative physics of interparticulate attractive and repulsive forces can be seen in a brief unfinished manuscript where he first supposes that there may be repulsive forces operating at a distance between particles of air, and indeed between the particles of all bodies. Known by the headings of its two chapters, this is Newton’s abandoned manuscript, ‘De Aere et Aethere.’⁶

The next time Newton wrote in the same terms, assuming repulsive forces between the particles which constitute all bodies, was in Proposition 23 of Book II of the Principia, and its scholium, where Newton gave a mathematical account of what we now call Boyle’s Law by assuming ‘particles that are repelled from one another by forces that are inversely proportional to the distances between their centres.’⁷ Additionally, during the final stages of preparing the Principia, Newton penned a ‘Conclusio’ for it which discussed repulsive forces between particles more generally, and combined them with discussion of attractive forces between particles. He was careful, however, to signal the distinction between these conjectures and the more rigorous approach of the main body of the Principia:

I am far from affirming that my views are correct, and I acknowledge their great imperfections, nevertheless they are simple and easy to conceive, and of the same kind as the natural philosophy of the cosmic system which depends on the attractive forces of greater bodies.⁸

Similarly, as he was to do later in the Opticks, he expressed a hope that others would take up these ideas: ‘I wished here to touch lightly upon them [these interparticulate forces] in order to give an opportunity to others for cultivating this kind of philosophizing more fully … ’⁹

Had Newton finished off the Principia with these pages, arguably it would have altered the whole tone of the book. In the end, however, he thought better of it, and confined some of these ideas instead to a draft preface.¹⁰ Even this did not make it into print. We will consider the similarities between ‘De Aere et Aethere’ and Proposition 23, as well as these two abandoned manuscripts in due course. It is clear, however, that the manuscripts were not suppressed because Newton had changed his mind about the possible existence of interparticulate forces. We can be sure of this because he alluded to this theory, albeit briefly, in the version of the Principia’s preface which did make it into print:

For many things lead me to have a suspicion that all phenomena may depend on certain forces by which the particles of bodies, by causes not yet known, either are impelled towards one another and cohere in regular figures, or are repelled from one another and recede. Since these forces are unknown, philosophers have hitherto made trial of nature in vain. But I hope that the principles set down here will shed some light on either this mode of philosophizing or some truer one.¹¹

Furthermore, he continued to offer an explanation of the behaviour of ‘elastic fluids’ in terms of repulsive forces operating between its particles in Proposition 23 of Book II. And, of course, he returned to these speculations about interparticulate forces in the Queries appended to the Opticks.

Given the longevity of these ideas in Newton’s thought, surely indicating his commitment to them, and given their subsequent importance in eighteenth-century Newtonianism, it might be expected that ‘De Aere et Aethere’, where these ideas first emerged, should be seen as an important turning point in Newton’s natural philosophizing. Dating from before Newton even dreamed of embarking on composition of the Principia, and maintained through to his late writings, especially as presented in the Queries he added to his Opticks, he evidently cherished this highly original, though entirely speculative, philosophy which proposed ubiquitous attractive and repulsive forces operating between the small particles of bodies.¹² Newton wrote in ‘De Aere’, for example, that the extreme rarefaction of air, which had been achieved in experiments with the air-pump, could be explained ‘by some principle acting at a distance’, which caused the particles of air ‘to recede mutually from each other’.¹³ It seems reasonable, therefore, to see this document as an early foreshadowing of the entirely new kind of physics that Newton presented in unpublished drafts temporarily intended for the Principia, and subsequently in print in the ‘Queries’, in which a wide variety of phenomena were explained in terms of attractive or repulsive forces operating between particles.

This was clearly the way R. S. Westfall thought about it. As he wrote of ‘De Aere et Aethere’:

The thrust of my interpretation of Newton holds that he started with aethereal mechanisms – the established philosophic orthodoxy – and that he finally rejected them in order to assert the radical concept of forces at a distance.¹⁴

Arguably, Westfall should have written not of ‘the’ but of ‘a philosophic orthodoxy’; there were many who rejected the concept of an aether. Even so, no contemporary of Newton’s would have been surprised to see him invoking aethers to explain physical change, as he did in his earliest works. Recourse to aethers, after all, was common, especially as Cartesianism continued to flourish. As Westfall suggested, however, contemporaries would have been taken aback to see Newton invoking the completely unheard-of physics of interparticulate forces acting at a distance.

As a matter of historiographical fact, however, the ‘De Aere et Aethere’ is by no means acknowledged as a turning point in Newton’s physics; on the contrary, it is seen as merely a minor speculative piece about the role of air and aether in physical change, which was quickly superseded by Newton’s (supposedly) later speculations relying on the concept of aether. The unimpressive historiographical fortunes of this under-rated document largely stem from the date attributed to it by A. Rupert Hall and Marie Boas Hall in their first edition of it (in their Unpublished Scientific Papers of Isaac Newton), and from the reasons they adduced for assigning that date.¹⁵ It was the Halls who suggested ‘De Aere’ was written before subsequent works where explanations are presented chiefly in aetherist terms. According to their dating, then, the appearance of interparticulate forces in ‘De Aere’ is a mere aberration, a flash in the pan, which led nowhere.

It is now clear that the Halls’ date, which goes hand-in-hand with the view that the ‘De Aere’ is an insignificant work which was soon superseded by Newton’s later philosophizing about aethers, is succeeding over Westfall’s assessment. This has recently become clear because two major studies of Newton, which are both set fair to become classics in the field, and therefore highly influential, have both endorsed the Halls’ proposed date. William R. Newman’s definitive study of Newton’s alchemy, and Dmitri Levitin’s magisterial ‘Study in the History of Knowledge’, have evidently accepted the Halls’ arguments for dating the ‘De Aere’ to before 1675, but they have also added new arguments, not found in the Halls’ introduction to the ‘De Aere’.¹⁶ In what follows, I want to argue on behalf of Westfall’s later date, 1679 or soon after, and therefore to suggest that the ‘De Aere’ should be recognized as an important turning point in the development of Newton’s unique and completely original speculative philosophy of interparticulate forces. Before going any further, however, it is important to critically reconsider how the Halls arrived at their date for the composition of ‘De Aere et Aethere’, and why Newman and Levitin have favoured it over Westfall’s date.

Dating the ‘De Aere et Aethere’

The Halls, in their first edition of the ‘De Aere et Aethere’ in Unpublished Scientific Papers, suggested that it must have been written between 1673 and 1675. Newton’s manuscript refers to experiments by Boyle which were published in 1673, and so it cannot have been written before then.¹⁷ It is easy to agree with this. The reasons they give for the last possible date of composition, 1675, are much less persuasive, however.

Comparing ‘De Aere et Aethere’ with the ‘Hypothesis explaining the Properties of Light’ of 1675, and a letter to Boyle of February 28, 1678/9 in which Newton tries to explain ‘the actions of Menstruums upon bodies’, the Halls focus on Newton’s use of ‘the repulsive force of air particles’.¹⁸

The feature of the De Aere et Aethere [they write] that immediately distinguishes it from Newton’s other discussions of phenomena of attraction and repulsion (the examples here are capillary attraction, the lack of cohesion in a dry powder, the difficulty of pressing two surfaces together, the walking of flies on water – all to be used repeatedly again) is that he here finds the cause of the effect in the repulsive force of air particles.¹⁹

They go on to argue that in the ‘Hypothesis’, some of these effects continue to be attributed to the ‘repulsion of air’, while others are said to be caused by the aether. By the time we get to the letter to Boyle, however, ‘the aether is made responsible for all the phenomena of attraction and repulsion, even capillary attraction.’²⁰ They conclude:

If we suppose that Newton’s ideas changed consistently, the Hypothesis of 1675 must mark a half-way stage in his thinking, and thus be later than De Aere et Aethere; in modifying his hypothesis Newton has transferred the repulsive force from the particles of air to the particles of aether in certain cases, as he was later to do in all cases.²¹

So, what we have, according to the Halls, is a steady progression from the exclusive use of the repulsive force of particles of air in ‘De Aere’, to the mixed use of the repulsive force of air particles and the repulsive force of aether in the ‘Hypothesis’, and finally to the exclusive use of the repulsive force of aether in the letter of 1679. Accordingly, the ‘De Aere et Aethere’ must be earlier than the ‘Hypothesis’.

Superficially, this might seem reasonable (although there might be lingering doubts as to whether Newton’s thought really did ‘change consistently’ like this). There is a major problem with the Halls’ argument, however. It depends upon the assumption that ‘repulsive force’ is invoked in all three of these documents. But in fact, although ‘repulsive force’ between particles is a prominent feature of the ‘De Aere et Aethere’, there is no mention whatsoever of any supposed ‘repulsive force’ in the other two documents. So, the progression of changes that the Halls’ argument relies upon turns out to be a complete figment.

It is not possible, of course, to demonstrate by carefully selected quotations that ‘repulsive force’ is nowhere mentioned in either the ‘Hypothesis’ or the letter to Boyle. I can only urge readers of this article to turn to these pieces and read them for themselves. In spite of what the Halls say, it is impossible to find anywhere in the ‘Hypothesis’ where Newton can be said to be transferring the notion of repulsive force of the air to repulsive force between particles of aether ‘in certain cases’. Consider, for example, the place in the ‘Hypothesis’ where Newton discusses the examples which, as we have seen above, the Halls say were ‘to be used repeatedly again’. Newton writes:

So, if two well polished convex glasses, ground on very large spheres, be laid one upon another, the air between them easily recedes, till they almost touch; but then [the air] begins to resist so much, that the weight of the upper glass is too little to bring them together so as to make the black, mentioned in the other papers I send you, appear in the midst of the ring of colours: and if the glasses be plain, though no broader than a two-pence, a man with his whole strength is not able to press all the air out from between them, so as to make them fully touch. You may observe also, that insects will walk upon water without wetting their feet, and the water bearing them up; also motes falling upon water will often lie long upon it without being wetted: and so, I suppose, aether in the confine of two mediums is less pliant and yielding than in other places, and so much the less pliant by how much the mediums differ in density … ²²

These effects, then, Newton supposes in the ‘Hypothesis’, are brought about not by repulsive forces but by the unyielding nature of the air and the aether (‘less pliant and yielding’). A man cannot press all of the air out from between two planes of glass, Newton says, but he makes no mention of a repulsive force operating.

We can compare this directly with ‘De Aere’, where Newton prefaces his discussion of these examples by saying that ‘air does not only seek to avoid bodies, but bodies also tend to fly from each other.’²³ Admittedly, a little later, when offering alternatives ‘concerning the cause of this repulsion’, he includes the possibility that the ‘intervening medium may give way with difficulty or not suffer itself to be much compressed.’²⁴ So, although Newton repeats in ‘De Aere’ the explanation for these phenomena given in the ‘Hypothesis’ (an intervening medium), nowhere in the ‘Hypothesis’ do we see so much as a hint that bodies might repel each other. Surely, this suggests the ‘Hypothesis’ was written first, not the other way around?

The case is entirely similar with regard to the letter to Boyle of February/March 1678/79. There is no suggestion that the phenomena discussed might be due to repulsive forces operating between particles. For the most part, as in the ‘Hypothesis’, Newton bases his conjectural explanations on the assumption that the aether ‘pervades all gross bodies, but yet so as to stand rarer in their pores than in free spaces, & so much the rarer, as their pores are less [i.e. smaller]’.²⁵ This can be directly compared with the ‘Hypothesis’: ‘so I suppose aether, though it pervades the pores of crystal, glass, water, and other natural bodies, yet it stands at a greater degree of rarity in those pores, than in the free Aethereal spaces, and at so much a greater degree of rarity, as the pores of the body are smaller.’²⁶

Unlike the ‘Hypothesis’, however, there are one or two places in the letter where Newton almost seems to come close to invoking forces acting at a distance. Consider, for example,

… when two bodies approaching one another, come so near together, as to make the aether between them begin to rarefy, they will begin to have a reluctance from being brought together, & an endeavour to recede from one another: which reluctance & endeavour will encrease as they come nearer together, because thereby they cause the interjacent aether to rarefy more & more.²⁷

The ‘reluctance from being brought together’ here might sound, superficially, like a repulsive force operating between the bodies. But there is no mention of such a force. The resistance is brought about by the process of causing the intervening aether to rarefy. Unfortunately, at this point, as in the ‘Hypothesis’, it is impossible to know how Newton understands rarefaction. It seems clear from both these two pieces, though, that he believes rarefaction, like condensation, requires some kind of effort, and that aether will resist rarefaction just as it is presumed to resist compression. To read into this passage the notion of a repulsive force operating between particles is to read it in the knowledge that Newton’s physics would subsequently invoke such repulsive forces. No contemporary reader, however, seeing it before the Principia was published, would have read it this way. It is not safe to assume that Newton was already thinking in terms of interparticulate repulsive forces when he wrote this letter to Boyle.

Similarly, a little later in the letter we read:

… the particles of vapors exhalations & air, do stand at a distance from one another, & endeavour to recede as far from one another as the pressure of the incumbent atmosphere will let them: for I conceive the confused mass of vapors air & exhalations which we call the Atmosphere to be nothing els but the particles of all sorts of bodies of which the earth consists, separated from one another & kept at a distance, by the said principle.²⁸

The ‘said principle’ here is, of course, the same supposed resistance to rarefaction of the intervening aether. So, we are being invited by Newton to imagine a scenario where particles of air, say, are made to recede from one another by the resistance to rarefaction of the aether between them, but that their endeavour to recede is countered by the constricting pressure of the incumbent atmosphere. Although the phrase ‘at a distance’ appears twice, it seems clear that Newton simply meant that particles of air, vapour, and so forth were each spread out with the various other exhalations between them, including of course the all pervading aether. Particles of salt sprinkled on a table top could be said to stand at a distance to one another in the same way.²⁹

In spite of the talk of things being ‘at a distance’, there is no suggestion here that there is in operation an actio in distans of the kind which Huygens and Leibniz later recognized as implicit in the Principia, and rejected as untenable.³⁰ Their objection was to the idea that one body could act upon another body without making contact with it, or without having its action transmitted to the other body by some intervening material means (such as streams of effluvial particles, or an aether). By contrast with these two aetherist documents, however, Newton was indeed proposing in ‘De Aere et Aethere’ that material particles could act upon one another across an intervening empty space without making contact, either directly or indirectly. At one point, for example, he writes of particles in an array expanding to take up more space as a result of vibrations of the particles. Newton makes it clear that the particles do not have to collide with one another as they vibrate – the vibrations of one particle are passed on to neighbouring particles at a distance by their repulsive forces.³¹ There is a marked contrast here with both the ‘Hypothesis’ and the letter to Boyle, where there is not the slightest suggestion that he was thinking about actions of bodies capable of operating on each other without making material contact.

Even so, it was presumably these parts of Newton’s discussions in the letter to Boyle, where he wrote of an ‘endeavour to recede’, which led the Halls to believe that ‘repulsive force’ featured in them in the same way that it did in ‘De Aere’. If so, the Halls were certainly taking two and two and coming up with five. At one point the Halls write that the action of air particles in ‘De Aere’ ‘in virtue of their intrinsic repulsive force’, is transferred, in the letter to Boyle, to aether particles, which are now said to possess ‘intrinsic repulsive force’.³² This simply is not true. There is absolutely no mention of a repulsive force between particles in either the ‘Hypothesis’ or the letter. The fact that ‘De Aere’ does draw explicitly on particles endowed with repulsive force sets it apart from either of the other two documents. Paradoxically, at one point the Halls even acknowledge this themselves:

He [Newton] used aether-language in the Hypothesis of 1675, the Letter to Boyle, and certain of the Quaeries. He attributed forces directly to material particles without the interposition of an aether, in De Aere et Aethere, the whole text and the printed preface of the Principia, the suppressed Conclusio and draft preface and certain other Quaeries. It is significant that when dealing with some of the most obscure – because not directly observable – phenomena of attraction and repulsion, in chemical reaction, Newton never introduced the aether at all, but always spoke of forces between the reactive particles.³³

It seems hard to reconcile this passage with the Halls’ assumption elsewhere in the same discussion that ‘intrinsic repulsive force’ appears not only in ‘De Aere’ but also in the ‘Hypothesis’ and the letter to Boyle. It might also be added, that it is surely significant that Newton explicitly invoked action at a distance in ‘De Aere’, with nothing material holding the particles of air separated from one another, but simply assuming the particles are held apart by repulsive forces operating between them. Again, this seems to show a marked similarity between the ‘De Aere’, and (as we shall see shortly) the suppressed ‘Conclusio’ and draft preface of the Principia, and ‘the whole text’ of the Principia where, as the Halls remind us, actions at a distance were implicit, much to the disgust of Huygens, Leibniz and other critics.³⁴

In fact, this passage from the Halls’ introduction to ‘De Aere’ actually seems to come close to Westfall’s position. The ‘De Aere’ now appears in the Halls’ list of Newton’s writings as the first in a sequence with the Principia and related drafts, and so can be seen as a turning point between the ‘aether-language’ of his early career, and the use of what Westfall rightly saw as the more ‘radical concept’ of interparticulate forces in his later career.³⁵ Clearly, the Halls saw this sequence as merely notional and not as chronological, and by continuing to insist on their early date for the ‘De Aere’ they ensured that it could hardly be accorded an important place in Newton’s intellectual development. If ‘De Aere’ was written before the aetherist ‘Hypothesis’ and his attempts to develop a revised aetherist natural philosophy in his 1679 letter to Boyle, then it cannot be seen as a turning point in Newton’s thinking, the beginnings of a commitment to interparticulate forces, but must be regarded merely as a false start.

Noting a slight inconsistency in their own attempts to reconstruct the order of composition of these three early documents, the Halls were forced to insist that the existence of ‘De Aere’ ‘belies Newton’s own statement to Boyle [in the letter] that his ideas would never have been committed to paper but for the latter’s persuasion’.³⁶ But, it only belies Newton’s statement if the ‘De Aere’ had indeed been written before the letter to Boyle. In view of what has been said here, however, it seems fair to appropriate this statement by Newton as further evidence in favour of the claim that the ‘De Aere’ was written after the letter to Boyle. We come back, then, to the view of R. S. Westfall, who suggested that Newton began to write ‘De Aere’ shortly after the letter, as a way of improving upon what Newton himself referred to as the ‘indigested’ thoughts in the letter to Boyle, so much so that he was ‘ashamed to send them at all’.³⁷

Of course, dating Newton’s papers is notoriously difficult; in the absence of a date or a clear temporal landmark of some other kind in the content, the way is fraught with uncertainty. One thing is certain, however, and that is that the Halls’ reasons for placing ‘De Aere’ at an earlier date than the ‘Hypothesis of Light’ cannot stand. Based as it is on the false assumption that repulsive force occurs in the ‘Hypothesis’ and the 1679 letter to Boyle, as well as in ‘De Aere’, their argument is completely invalid. Contrary to what the Halls claim, there is no progression from repulsive force between air particles (in the ‘De Aere’), to repulsive forces between air and aether particles (in the ‘Hypothesis’), to repulsive forces between aether particles only (in the letter to Boyle), because there is no mention of repulsive forces at all in either the ‘Hypothesis’ or the letter.³⁸ Clearly, in neither of those works was Newton thinking in terms of repulsive forces operating between particles. Among these three documents, this was an idea that was introduced for the first and only time in the ‘De Aere’. Moreover, as far as we know, it was introduced for the only time in Newton’s writings, until we get to Proposition 23, and the draft ‘Conclusio’ and preface, written for the Principia, where interparticulate forces between particles are explicitly invoked again.

Indeed, in view of what has gone before, it might be argued that there does seem to be a rather different progression through these three documents (different from the ‘progression’ foisted on them by the Halls). The ‘Hypothesis’ relies on aetherist explanations; the letter to Boyle does likewise but sometimes seems to come close to suggesting there are forces of recession acting at a distance (which, as we suggested earlier, may have misled the Halls into thinking of repulsive forces at work); and ‘De Aere’, in a marked change of approach, explicitly bases its explanations on the assumption that there are forces of repulsion operating across the empty distances between particles. Again, this ‘progression’ seems to suggest ‘De Aere’ came last in the sequence, not first.

So far, anyway, I would suggest that there is no reason to suppose ‘De Aere et Aethere’ was written before 1675. We need to take pause, however, before concluding that the Halls’ early date was wrong. It is possible, after all, that they hit upon the right date, even if for the wrong reasons. Certainly, the Halls’ pre-‘Hypothesis’ date for ‘De Aere’ has been endorsed by two leading scholars, who have added further reasons for insisting upon its early location in Newton’s oeuvre, and have explicitly rejected Westfall’s later date. Again, we must assess these new reasons, not adduced by the Halls.

Trouble with narrow pipes and atmospheric pressure

The first of these reasons for insisting that the ‘De Aere’ must be regarded as an early work is comparatively easy to assess. William R. Newman in his authoritative study of Newton’s alchemy has argued that Newton’s naïve understanding of capillary action in the ‘De Aere’ reveals the ‘juvenile status’ of the work. Similarly, Dmitri Levitin, in his magisterial study of early modern attitudes to metaphysics, Kingdom of Darkness, has repeated Newman’s point: ‘the explanation of capillary action as being due to air pressure that is given in the text cannot have been held by Newton by 1679.’³⁹ The claim arises from Newton’s comment that

… water ascends within a very narrow pipe whose lower end is immersed in stagnating water higher than the external level, and ascends the higher in proportion to the narrowness of the pipe, so that it will rise several inches in the narrowest pipes. This is a thing that does not happen when the water and the pipe are placed in an exhausted glass vessel.⁴⁰

Although Newton does not develop the problematic final sentence here, he does go on to develop an account of capillary action which ultimately depends upon atmospheric pressure. Newton simply states that in cases of air in capillary tubes, and other situations where air is closely surrounded by other bodies, ‘the air seeks to avoid the pores or intervals between the parts of these bodies’. Accordingly, he goes on:

and so, since in these [pores] the air is more rare than in wider spaces, the water can penetrate into them, [the air in the pores] pressing the surface of the incoming [water] less than the external atmosphere presses the surface of the stagnant water, and thus not sustaining the pressure of the external air.⁴¹

Clearly, as Newton wrote a few lines earlier, none of this could happen in a vacuum, where there is no external atmosphere to push the water into the capillary tube.

However, as we now know, capillary action is not caused by differential pressure, inside and outside capillary tubes, and does occur in a void space. Newman and Levitin insist that Newton never would have made the error of supposing atmospheric pressure was involved in capillary action as late as 1679, because in that very year he had been, as Newman says, ‘in deep communication with Boyle about the nature of matter’, and Boyle had already established in 1669 that capillary action still took place inside an evacuated air-pump.⁴²

We need to consider this carefully. Presumably, Newman’s claim that Newton had been in ‘deep communication’ with Boyle in 1679 stems from the fact that, in the letter of 1679, he wrote that he was sending Boyle his thoughts ‘about the physical qualities we spake of’. We also know that ten years before, in his Continuation of New Experiments Physico-Mechanical Touching the Spring and Weight of the Air, Boyle had confirmed in ‘Experiment XXVII’ that he had established that capillary action still took place inside the evacuated chamber of the air-pump.⁴³

Even before talking with Boyle in 1679, Newton might have read Boyle’s Continuation. If he did, however, he evidently failed to note its significance. Leaving ‘De Aere’ aside for the moment, we can see that in the ‘Hypothesis’ of 1675, Newton put forward the idea that capillary action was due to rarefaction of air inside the capillary tube, thereby making it easy for the air outside the tube, which is not rarefied, to push water into the tube. Newton wrote:

As the air can pervade the bores of small glass pipes, but yet not so easily as if they were wider; and therefore stands at a greater degree of rarity than in the free aereal spaces, and at so much a greater degree of rarity as the pipe is smaller, as is known by the rising of water in such pipes to a much greater hight than the surface of the stagnating water, into which they are dipped … ⁴⁴

We know that the air is rarer in the bore of the pipe, Newton says, precisely because the water rises up the pipe. Newton either believes that the water is sucked into the pipe because nature abhors a vacuum, or he believes the water ascends because the pressure of the external air is greater than the rarefied air in the pipe. It is inconceivable that Newton would have been subscribing to the old scholastic notion of the fuga vacui, so it is safe to assume that atmospheric pressure is involved in the ‘Hypothesis’ account, even though it is not made obviously explicit.

Newman implies that this erroneous account of capillary action (in which atmospheric pressure is falsely held to play a role) has been corrected by 1679, because, in the letter to Boyle, ‘Newton explicitly attributes capillary action in thin tubes to the ether, not the air.’⁴⁵ What Newman overlooks, however, is that the mechanics of Newton’s explanation in the letter to Boyle remains exactly the same, and therefore remains just as erroneous as the ‘Hypothesis’ account – capillary action is held to take place because the aether is rarefied inside small pipes, thus making it easy for the external aether, which is not rarefied, to push water into the pipe:

I suppose this aether pervades all gross bodies, but yet so as to stand rarer in their pores then in free spaces, & so much the rarer as their pores are less. And this I suppose (with others) to be the cause … of the rising of water in small glass pipes above the surface of the stagnating water they are dipt into: for I suspect the aether may stand rarer, not only in the insensible pores of bodies, but even in the very sensible cavities of those pipes. And the same principle may cause Menstruums to pervade with violence the pores of the bodies they dissolve, the surrounding aether, as well as the Atmosphere, pressing them together.⁴⁶

What we have here then is a clear example of what the Halls noticed: ‘in the Letter to Boyle, Newton makes no mention of air at all in this connexion; the aether is made responsible for all the phenomena … even capillary attraction.’⁴⁷ Nonetheless, the explanation of capillary action is effectively the same as the explanation in the earlier ‘Hypothesis’ – reduced pressure inside the tube due to the rarefaction of the surrounding medium results in the rising of water into the tube – not sucked into the tube, but pushed into it by the unrarefied aether outside it. Indeed, it should also be noted that although Newman writes that, in the letter to Boyle, ‘Newton explicitly attributes capillary action in thin tubes to the ether, not the air’; in fact Newton actually adds ‘as well as the Atmosphere’. So, contrary to what Newman writes, Newton explicitly attributes capillary action in the 1679 letter to both ‘the surrounding aether, as well as the Atmosphere’ (my emphases).

Newman’s point, when he writes that ‘Newton explicitly attributes capillary action in thin tubes to the ether’, is by no means clear. He certainly does not acknowledge that Newton’s aetherist account depends on differential pressure, inside and outside the tube, but nor does he offer any alternative account of how the aether is supposed to explain capillary action. Fortunately, we do not have to second-guess what putative account Newman might have had in mind. We can still assess the strength of Newman’s argument that the ‘De Aere’ could not have been written as late as 1679, even if we leave the aetherist account of the letter to Boyle out of our reckoning altogether.

The undeniable fact is that Newton was still upholding essentially the same theoretical explanation of capillary action – in terms of atmospheric pressure – in 1687 when he was writing the ‘Conclusio’ with which he was intending to finish the Principia. We read there:

particles of air in the narrow cavities of glass tubes flee from the glass, so that air seems to be more rare there than in free spaces and if the lower orifice of the tube is immersed in stagnating water it ascends quickly (as a certain person has ingeniously remarked following an hypothesis of his own) and fills the cavity from which the air tries to recede. And from the similar ascent of liquids in the small passages of sponges and other bodies it is learnt that the small particles of air endeavour to recede from all bodies universally.⁴⁸

Newton has by now reverted to air in his explanation, having completely excluded aethers from the Principia, and he is now explaining the rarefaction of the air in terms of repulsive forces operating between the particles, but essentially, the explanation of capillarity depends, as it did in the ‘Hypothesis’ over a decade earlier, on the assumption that there is reduced pressure inside a capillary tube due to the rarefaction inside the tube of the ambient medium. Whether that rarefaction is said to be due to the difficulty of ingress into narrow spaces (as in the ‘Hypothesis’), or whether it is merely ‘supposed’ axiomatically (as in the letter to Boyle), or whether it is due to air particles’ ‘endeavour to recede’ (as in the ‘De Aere’, and later the ‘Conclusio’), the explanation remains essentially the same: and implicitly, if not explicitly, depends upon the pressure of the surrounding atmosphere. Liquids ascend rapidly in a capillary tube because there is reduced pressure of the surrounding medium inside the tube, and so the standard pressure of the medium outside the tube pushes the liquid into the tube. Given that Newton was using this same atmospheric pressure account of capillarity in 1687, it can hardly be argued that he could not have written ‘De Aere’ as late as 1679.

We cannot know precisely when Newton realised that capillary action took place even in a vacuum, but we know that he pointed this out in print in the 1717 edition of the Opticks. He added into Query 31:

And if slender Pipes of Glass be dipped at one end into stagnating Water, the Water will rise up inside the Pipe, and the height to which it rises will be reciprocally proportional to the Diameter of the Cavity of the Pipe … And these Experiments succeed after the same manner in vacuo as in the open Air, (as hath been tried before the Royal Society,) and therefore are not influenced by the Weight or Pressure of the Atmosphere.⁴⁹

We learn shortly after that Newton is referring here to experiments performed by Francis Hauksbee, erstwhile chief experimenter for the Royal Society.⁵⁰ In fact, these experiments had been performed some years earlier, around 1712, and in an unpublished draft of the ‘General Scholium’, which Newton was preparing for the second edition of the Principia (1713), he had already noted that capillary action ‘succeeds in the Boylian vacuum and so does not depend on the weight of the incumbent atmosphere.’⁵¹ We cannot be sure, but these comments by Newton seem to suggest that he first realised that capillary action took place in a vacuum as a result of the work of Hauksbee, in 1712 or 1713, rather than through ‘deep communication with Boyle about the nature of matter’ in 1679, as Newman suggested.⁵²

Be that as it may, it seems unsafe to conclude, on the grounds that it mistakenly attributes capillary action to atmospheric pressure, that ‘De Aere et Aethere’ must have been written before 1675. As we have seen, Newton was still making the same mistake in the ‘Conclusio’ of 1687, and may well have continued in his false belief about capillary action until Hauksbee put him right.

Clearly, the ‘De Aere’ seems closest in its argumentation on this issue to the ‘Conclusio’. Both assume that there are repulsive forces between particles which result in the rarefaction of the ambient medium inside capillary tubes. In spite of the Halls’ false assumption that repulsive forces are at work in the ‘Hypothesis’ and the letter to Boyle, neither of these invoke interparticulate forces. Such forces are hypothesized for the first time in ‘De Aere’, and subsequently become a mainstay of the speculative physics that is most familiar to us from the ‘Queries’ added to the Opticks. If we take into account the fact that interparticlate forces were also discussed in the abandoned ‘Conclusio’ and the extended preface written for the Principia in 1687, Westfall’s claim that the ‘De Aere’ was written after the letter to Boyle, at a time when Newton was dropping aether-language (to use the Halls’ phrase), and indeed the very concept of an aether, from his natural philosophy seems highly plausible.

Between Newton’s ‘Alchemical Cosmology’ and the ‘Hypothesis’?

Being chiefly concerned with Newton’s alchemy, William R. Newman is fully aware that if the ‘De Aere’ was written before the ‘Hypothesis’ of 1675, it must have been written around the same time, or very shortly after, a remarkable alchemical work by Newton, known by its incipit as ‘Of Nature’s obvious laws’, which is securely dated to between 1670 and 1673.⁵³ The evident importance of this work for Newton has long been acknowledged by scholars because he repeated some of its ideas in the ‘Hypothesis’. Accordingly, Newman considers these three works together, seeking to establish that ‘De Aere’ sits neatly between ‘Of Nature’s obvious laws’ and the ‘Hypothesis’. Consequently, Newman talks of a ‘very significant point of convergence between’ the alchemical manuscript and ‘De Aere’.⁵⁴

It turns out, however, that Newman’s comparison of ‘De Aere’ with ‘Of Nature’s obvious laws’ shows ‘how Newton’s theory has progressed’ in ‘De Aere’.⁵⁵ Having introduced his readers to Newton’s suggestion in ‘De Aere’ that there are ‘three chief kinds’ of air, Newman points out: ‘Neither the emphasis on repulsion nor the clear tripartite division into permanent air, exhalations, and vapours is found in Of Nature’s obvious laws.’ However, Newman does not concede that, these things being so, the ‘De Aere’ might well have been written some years after his ‘alchemical cosmology’. Instead, he brings in a new comparison with another work included in the same alchemical manuscript, known as ‘Humores minerales’.

The claimed similarity here is with the suggestion in ‘De Aere’ that ‘permanent air’ is ‘nothing else than a collection of metallic particles which subterranean corrosions daily disperse from each other.’⁵⁶ This is compared with the suggestion in ‘Humores minerales’ that ‘some of the [subterranean] metallic fumes escape to the surface, where they “wander over the earth and bestow life on animals and vegetables. And they make stones, salts, and so forth.”’⁵⁷ As Newman notes, however, there are difficulties with this comparison which strongly suggest the originality of ‘De Aere’. As Newman writes, ‘there is no trace of the theory that true ‘permanent air’ is merely a congeries of unaltered metallic particles in either of the early texts preserved in Dibner 1031B’, which is the alchemical manuscript in question. He concludes, therefore:

It appears that Newton’s metallic theory of the air was a new concept when it appeared in De aere et aethere, and it may well have been suggested to him by his theory of repulsion between particles when they are separated from one another.⁵⁸

This last comment is surely correct. Whereas the talk in the alchemical manuscript is of dissolved metals being volatilized, and metallic fumes arising from fermentations and the like, in ‘De Aere’ all that is required for ‘the generation of air’ is ‘a certain action or motion which tears apart the small parts of bodies; since when separated they mutually flee from one another.’⁵⁹ Permanent air, as distinct from more transient exhalations or vapours, Newton says a little further on, must be generated from equally permanent metals.

Given that Newman himself admits that in ‘De Aere’ we are ‘in very different territory from the alchemical cosmology presented in Of Nature’s obvious laws’, and that the ‘De Aere’ shows how Newton’s thinking ‘has progressed’ from the earlier alchemical work, it seems fair to say that nothing he writes can be used to confirm ‘De Aere’ must have been written shortly after ‘Of Nature’s obvious laws’, and before the ‘Hypothesis’.⁶⁰

Additionally, the impression that the ‘De Aere’ cannot be made to fit in between these other two documents is reinforced when we remember the striking similarity in both their accounts of the nature of aether. After waxing lyrical about the aether as ‘Natures universall agent’ in ‘Of Nature’s obvious laws’, Newton goes so far as to suggest that ‘perhaps a great part if not all the moles of sensible matter is nothing but Aether congealed & interwoven into various textures … ’⁶¹ Although the language is somewhat toned down in the ‘Hypothesis’, Newton still muses that, ‘Perhaps the whole frame of nature may be nothing but various contextures of some certain aethereal spirits, or vapours, condensed as it were by precipitation … Thus perhaps may all things be originated from aether.’⁶² There is nothing remotely like this kind of ‘aether-language’, to use the Halls’ phrase, in ‘De Aere’.⁶³ Where the aethers in ‘Of Nature’s obvious laws’ and the ‘Hypothesis’ are presented in a distinctly vitalistic manner, the aether in ‘De Aere et Aethere’ is entirely mechanistic.⁶⁴ Once again, the differences between ‘Of Nature’s obvious laws’ and ‘De Aere’ are striking and undeniable, rather than any supposed ‘convergence’ between them.

I hope I have said enough by now to at least cast serious doubts on the claims that have been made for dating ‘De Aere’ to before the ‘Hypothesis … of Light’ of 1675. The Halls’ supposed progression from a physics which invokes repulsive force between air particles in the ‘De Aere’, to one that invokes repulsive forces between both air and aether particles, in the ‘Hypothesis’, through to a physics which assumes repulsive forces only between aether particles in the letter to Boyle, does not work for the obvious and undeniable reason that repulsive forces make no appearance at all in either the ‘Hypothesis’ or the letter. The claim of Newman and Levitin that the naïve theory of capillary action in ‘De Aere’ could not have been held by Newton as late as 1679 does not work because he clearly held effectively the same theory as late as 1687, and probably later than that. Finally, Newman’s exposition of a ‘convergence’ between ‘Of Nature’s obvious laws’ and ‘Humores minerales’ on the one hand, and ‘De Aere’ on the other, seem to bring out the marked differences between them, rather than any supposed indications that they were written at around the same time.

It seems much more likely, therefore, that Westfall was correct to see Newton’s thought evolving from aetherial accounts of physical change in his early career to the much more radical concept of interparticulate forces acting at a distance.⁶⁵ The very fact that Newton assumes the existence of repulsive forces operating between the particles of bodies, and that he explicitly declares them to be acting at a distance, indicates that the ‘De Aere’ should be seen as a staging post on the way to the new speculative physics of interparticulate forces that he subsequently developed in unpublished drafts for the Principia and finally made public in the ‘Queries’ appended to his Optice, and Opticks.⁶⁶ Asking us to believe the ‘De Aere’ was written before 1675 means that we are expected to believe that Newton came up with these innovative aspects of his later natural philosophy, interparticulate forces acting at a distance, very early in his career, but then quickly abandoned them to develop a highly unoriginal aetherist natural philosophy, only to return to his more original way of thinking in 1687, when he composed the ‘Conclusio’.⁶⁷ On the face of it, this seems highly implausible. Westfall’s suggestion, therefore, that ‘De Aere’ was written in 1679, or a bit later, seems to be a much better bet.⁶⁸

In what follows, I will take the liberty of assuming that the ‘De Aere’ was written after the letter to Boyle of February/March 1678/79. I want to try to reconstruct how it came to be written, and why it was abandoned unfinished. I will pursue this as a standard exercise in scholarly exegesis, although, unavoidably, I will sometimes have to indulge in speculation.

Newton’s spontaneously rarefying aether

When Newton finally relented of his reluctance to speculate in natural philosophy, ‘where there is no end of fansying’, as he later wrote to Boyle, and composed his ‘Hypothesis explaining the Properties of Light, discoursed of in my several Papers’, he did not restrict himself to explaining light. Before turning to light he introduced his ideas about the existence and nature of an all-pervading aether, as well as its role in a wide variety of phenomena.⁶⁹

The most significant aspect of these speculations for our purposes is that Newton often bases his explanations on the condensation and rarefaction of the aether. As well as the famous suggestion that aethereal spirits may be condensed and ‘after condensation wrought into various forms’, terrestrial gravity is explained in terms of the ‘continual condensation’ of the aether, while the rarefaction of the aether, brought about by rubbing the glass in which the aether was previously condensed, is invoked to explain electrical effects. Similarly, the unexplained supposition that aether is rarer in the pores of bodies than it is in free spaces is called upon in the explanation of a number of effects.⁷⁰

These speculations clearly had some hold over Newton’s mind because in his next piece of speculative natural philosophy, in the letter to Boyle of 1679, Newton drew almost exclusively on the rarefaction of the aether in his attempts to account for various chemical phenomena, and (additionally) gravity.

Newton begins the letter with five numbered starting suppositions, and all five seek to make use of the rarefaction of aether:

And first I suppose that there is diffused through all places an aethereal substance, capable of contraction and dilatation, strongly elastick …

1 I suppose this aether pervades all gross bodies but yet so as to stand rarer in their pores than in free spaces, & so much the rarer, as their pores are less … 

2 I suppose the rarer aether within bodies & the denser without them, not to be terminated in a mathematical superficies, but to grow gradually into one another … 

3 When two bodies moving towards one another come neare together, I suppose the aether between them to grow rarer than before … 

4 Now from the 4th supposition it follows, that when two bodies approaching one another, come so neare together as to make the aether between them begin to rarefy, they will begin to have a reluctance from being brought nearer together, & an endeavour to recede from one another … ⁷¹

‘From these principles’, Newton went on, ‘the actions of Menstruums upon bodies may be thus explained.’⁷² Essentially, these suppositions enable Newton to explain how particles of matter can break free from bodies and move independently. Consider, for example:

In the solution of metals, when a particle is loosing from the body, so soon as it gets to that distance from it, where the principle of receding described in the 4th & 5t suppositions begins to overcome the principle of acceding, described in the second supposition: the receding of the particle will be thereby accelerated, so that the particle shall as were with violence leap from the body, & putting the liquor into a brisk agitation, beget & promote that heat we often find to be caused in solutions of Metals.⁷³

This seems to be an advance on the speculations about similar phenomena in the ‘Hypothesis’, where too much is simply attributed to ‘active matter’, an unexplained incessant vibration of the aether, and the claim that denser aether in free spaces ‘which surrounds … bodies, must croud and press their parts together … ’⁷⁴

Newton was deeply dissatisfied with these speculations, however, to the point of being ‘ashamed to send them’ to Boyle.⁷⁵ The letter begins and ends with Newton’s expression of regret about the inadequacy of his efforts to explain the phenomena he tries to cover.⁷⁶ It is easy to see why. The whole argument depended entirely upon the ‘supposed gradual subtility of the parts of the aether’ (gradual in accordance with supposition 3), but this taken-for-granted gradual rarefaction of the aether was then used to explain the rarefaction of other bodies. But if rarefaction is explained by the action of something that is assumed to spontaneously rarefy itself, there seems to be some begging of the question.

Newton may only have come to recognize this as a problem while actually writing this letter. At one point, for example, he uses ‘the principle in the 4th & 5t suppositions’ to explain the transmutation of ‘gross compact substances into aereal ones.’⁷⁷ Such a transmutation, of course, involves changing a condensed substance into a rarefied substance. One way of doing this, Newton accepts, is by heat, but another is by this ‘principle’. Using the formation of vapour from water as his example, Newton writes to Boyle:

For as fast as the motion of heat can shake off the particles of water from the surface of it: those particles, by the said principle, will flote up & down in the air at a distance both from one another & from the particles of air, & make that substance we call vapor.⁷⁸

The rarefaction of water into vapour is a matter of spreading the water particles out from one another – no longer confined within the surface of the body of water, these particles float in the air at a distance from one another. But why do they spread themselves out? The particles of vapour have ‘an endeavour to recede from one another’ because, by supposition 5, their presence in the aether causes ‘the aether between them … to rarefy’. It is the rarefaction of the aether which caused the water particles’ ‘endeavour to recede from one another’, but the rarefaction of the aether is said to be caused by the water particles’ presence. Which came first, the chicken or the egg?

Effectively, Newton seems to have used the merely supposed rarefaction of aether to explain the rarefaction of water into vapour, and by extension the process of rarefaction in general. The ‘said principle’, that aether is rarefied as it is crowded in by encroaching bodies, is used to explain how other bodies become rarefied. Furthermore, the rarefaction of other bodies is seen in terms of spreading their constituent particles further apart from one another, and taking up a greater space; but the rarefaction of aether, which creates this ‘endeavour to recede from one another’ in other bodies, is itself supposed to take place in narrower spaces. No wonder Newton had his doubts as to the value of what he had written.

Another difficulty presented by this letter is that it is impossible for us to know just how Newton understood rarefaction. It may even have been the case that Newton realised, as he wrote, that he was unclear about what it might mean for a body to rarefy. We saw above that he seemed to understand the rarity of water vapour as an increased distance between the particles. Indeed, he even wrote of the particles of vapour floating ‘at a distance both from one another, and from the particles of air’. The implication of this statement is that air particles are already separated from one another, allowing room for water vapour particles to be separated not just from each other, but also from the particles of air. Clearly, if particles of air are in contact with one another, maintaining a continuum, particles of vapour in the air would also have to be in contact with air particles.

If, however, air particles are held to stand at a distance from one another, we have to confront the problem of what Aristotle had called (as an objection to the theories of the ancient atomists) ‘self-determined voids’.⁷⁹ How do air particles maintain distances from one another, rather than collapsing together? Readers might imagine there is no problem here, intuitively thinking of the kind of scenario familiar to us from our modern kinetic theory of gases – in which particles of air are in such rapid random motions that they only make contact with each other momentarily in collisions, and otherwise there is always void space between them. Early modern thinkers did not think in these terms, however. For them, the assumption was that air particles would be essentially static. Certainly, it was recognized that air particles could be put into motion by heat, but these motions were seen as vibrating motions, back and forth, but still centred on the original starting positions of the particles.⁸⁰ So, if air particles were held to be standing apart from one another, the question immediately arose as to what kept the particles standing apart? These were the self-determined voids to which Aristotle objected. This is also what Francis Bacon was referring to when he wrote that ‘whoever maintains the theory of the atom and the vacuum … necessarily implies the action of the virtue of the atom at a distance.’⁸¹

Within the context of the letter to Boyle, however, Newton could simply say the particles of air were kept apart because they were floating freely in the aether. However, since Newton’s account required the particles of air to be the cause of the increased rarefaction of the aether, and the aether was itself said to be, right from the outset, ‘far more subtile’ than air, this might have given Newton pause for thought. Was aether far more subtle because its particles stood even further apart than particles of air? If so, did we have to suppose a still rarer aether in which the particles of aether were suspended, and so on ad infinitum? As he apologized to Boyle that his thoughts were ‘so indigested that I am not well satisfied my self in them’, he might well have been wondering what it meant to say aether was rarer than air, or how the rarity of aether could be understood.⁸² Perhaps he began to think about self-determined voids?

‘De Aere et Aethere’ and repulsive forces

This brings us to ‘De Aere et Aethere’. Westfall’s surmise that this manuscript was written shortly after the letter to Boyle, in an attempt to improve on what he evidently saw as his earlier disastrous failure, seems entirely plausible.⁸³ The opening words of his fresh attempt indicate he had been thinking about rarefaction: ‘Among the properties of air its great rarefaction and condensation are remarkable.’⁸⁴ As we have already noted, however, he remained committed to the idea, invoked in the ‘Hypothesis’ and the letter to Boyle, that rarefaction somehow takes place in confined spaces:

Those who philosophize rightly know that all of these effects occur because the air seeks to avoid the pores or intervals between the parts of these bodies … ⁸⁵

In a new move, however, Newton now says that it is not only air which seeks to avoid bodies, but that all bodies ‘tend to fly from each other.’⁸⁶ Presumably, Newton takes this line because he holds the corpuscles constituting bodies to differ only in size, shape, and motions – the matter of all bodies is held to be the same, and so if air particles have repulsive forces, so must all other particles.⁸⁷ After providing various examples illustrating the tendency of particles to fly apart, Newton then reverts back to the ‘remarkable’ rarefaction and condensation of air. Referring to experiments with the air-pump reported by Robert Hooke in his Micrographia, Newton points out that air can expand to fill ‘a thousand times its normal space’.⁸⁸ As Newton immediately points out, this ‘would hardly seem to be possible if the particles of air were in mutual contact’.⁸⁹ In a second new move, Newton now introduces the idea of repulsive forces ‘acting at a distance’ to explain these extreme rarefactions.⁹⁰

There can be no denying that this is an extremely radical move by Newton. The concept of ‘action at a distance’, implying that bodies can interact with one another without making physical contact, had always been regarded as completely untenable. Just one manifestation of this was the fact that rarefaction had always been regarded as highly problematic, summed up, as we’ve just seen in Aristotle’s objection to ‘self-determined voids’. Although Newton wrote in ‘De Aere’ of air filling a thousand times its normal space, Boyle had claimed in his Discovery of the Admirable Rarefaction of Air (even without Heat) of 1670 to have rarefied air by 520,000 times.⁹¹ In spite of this, Boyle resolutely remained noncommittal as to how this might be possible, sticking to his earlier claim that his concern was not ‘to assign the adequate cause of the Spring of the Air, but onely to manifest, That the Air has a Spring, and to relate some of its effects.’⁹² Given that the ‘spring’ of the air was its ability to spontaneously disseminate itself through space, it is evident that Boyle was not ready to accept (or maybe just not willing to explicitly admit to) actions at a distance, but the Newton who wrote ‘De Aere et Aethere’ clearly was.

Interestingly, as well as the acceptance of action at a distance, there is another foreshadowing of the Principia in ‘De Aere’. At one point, Newton seems to undermine his own innovatory philosophy, just as he did in the scholium to Section 11 of Book I of the Principia, where he says that attraction may be brought about ‘from the action of aether or of air or of any medium whatsoever’.⁹³ ‘Many opinions may be offered concerning the cause of this repulsion’, he wrote in ‘De Aere’, before going on to provide three examples:

The intervening medium may give way with difficulty or not suffer itself to be much compressed [the assumption in the ‘Hypothesis’]. Or God may have created a certain incorporeal nature which seeks to repel bodies … Or it may be in the nature of bodies not only to have a hard and impenetrable nucleus but also [to have] a certain surrounding sphere of most fluid and tenuous matter which admits other bodies into it with difficulty. About these matters I do not dispute at all … Or lastly it may be that two or more of these causes sometimes operate together.⁹⁴

In the Principia, Newton was able to justify this kind of blatant equivocation by claiming that he was not concerned with the ‘physical properties’ of forces but only with their ‘mathematical proportions’.⁹⁵ He could not use the same justificatory tactic in ‘De Aere’, however, because it is not in the least mathematical. His contrasting response in this earlier work, evidently, was simply to stick to his guns, and so he simply deleted this whole passage. It is impossible to know what was going through Newton’s mind here, first reverting to aetherist speculations and then deleting them; but it is surely significant that just after he wrote ‘About these matters I do not dispute at all’, he added in square brackets an unequivocal affirmation of his radical new approach:

But as it is equally true that air avoids bodies, and bodies repel each other mutually, I seem to gather rightly from this that air is composed of the particles of bodies torn away from contact, and repelling each other with a certain large force.⁹⁶

It is easy to see that this comment directly contradicts two of the three alternative accounts in the same passage. Having undermined the idea of interparticulate forces acting at a distance with the suggestion that an unyielding medium may be involved, or that bodies might be surrounded by a hard-to-penetrate aethereal fluid, Newton now completely undermines those aetherist suggestions by reasserting that he gets things right when he says particles repel each other. Clearly, Newton could not let such juxtaposed contradictory comments stand. The result would simply be nonsensical. Consequently, he chose to strike out the whole passage in which he offered alternative causes for the repulsive forces between particles, including the undermining final reaffirmation of mutually repelling particles.

We have to assume that Newton initially wrote the first part of this passage in anticipation of objections from putative readers to the supposedly untenable concept of action at a distance. It is surely significant, however, that he quickly decided to remove this would-be exonerating passage. The important thing to note, then, is that in ‘De Aere’ Newton, in spite of a momentary dither indicated by the aetherist speculations he struck out, assumed throughout the existence of repulsive forces operating across the distance between the particles which were held to constitute all bodies. This is undeniably a highly radical and innovatory view (actions at a distance were generally held to be a complete no-no). Presumably, the dithering was the result of a moment of diffidence on Newton’s part – seeking to retreat back to more standard views, which of course involved aethers. Clearly, he overcame his diffidence, crossed out the aetherist speculations, and stuck to the radical suggestion (assumed throughout the whole of ‘De Aere’) that particles might repel one another at a distance. In the process of editing, he also crossed out the reaffirmation of actions at a distance that he had added in square brackets to his diffident qualifications (after all, he did not need a reaffirmation of his belief in interparticulate forces after he had deleted the aetherist shilly-shallying). What remains, in ‘De Aere’, therefore, are the several other places throughout the document where he suggests that there are repulsive forces acting at a distance between particles.

Newton goes on to propose that the repulsive force is also at work when air is expanded by heat. Particles of air, when agitated by heat, are assumed to vibrate, ‘and, by vibrating, propel hither and thither the neighbouring parts.’ It might be supposed that the propulsion of neighbouring parts was simply brought about, mechanistically, by the initial vibrating particle crashing into them. But no, Newton insists again on the reality of repulsive force acting at a distance. He even supplies a diagram in which it is clear that the middle particle of a depicted threesome only moves part of the way toward the surrounding particles as it vibrates. It sets the surrounding particles moving, therefore, not by colliding with them, but just by approaching nearer (and therefore exerting a greater repulsive force) as it vibrates back and forth.⁹⁷

Newton wraps up his discussion of the air by explaining how it is generated. Air is nothing more, or less, than ‘the small parts of bodies’ separated from their original bodies. Once separated, the particles flee from one another and become air. According to Newton, then, ‘every vehement agitation (like friction, fermentation, ignition and great heat) generates the aerial substance’.⁹⁸

The Aether in ‘De Aere et Aethere’, and the abandonment of the manuscript

Chapter 2 of this short manuscript is entitled ‘De Aethere’, but it consists of a single paragraph which ends in an unfinished sentence. Following on from the end of chapter 1, the aether is said to be just another kind of air:

And just as bodies of this Earth by breaking into small particles are converted into air, so these particles can be broken into lesser ones by some violent action and converted into yet more subtle air which, if it is subtle enough to penetrate the pores of glass, crystal and other terrestrial bodies, we may call the spirit of air, or the aether.⁹⁹

It is clear from the set-up in two separate chapters, that Newton is still under the impression that there must be such a thing as an aether. Or, at least, he was when he first decided to write this manuscript. Having stated that the aether is a more subtle kind of air, he goes on to show that ‘such spirits [of air] exist’.¹⁰⁰ As we have just seen, he has already mentioned perhaps the major reason for believing it to exist, namely, the fact that air-pump experiments have shown it can penetrate glass. The alternative would be to accept, with Boyle and others, that there is in fact a vacuum, or at least a partial vacuum, inside the glass chamber of an evacuated air-pump. But Newton goes on to support the existence of aether by pointing to the increase in weight of metals heated in a ‘hermetically sealed glass’, again showing there is a ‘saline spirit’ which can penetrate glass. Similarly, the motion of a pendulum in the chamber of an evacuated air-pump is damped almost as quickly as it is in the open air. Accordingly, Newton points out, there must be something in the chamber ‘much more subtle [than air] which damps the motion of the bob.’¹⁰¹

None of these examples, showing that aether must be capable of penetrating glass, are original to Newton; on the contrary, they are entirely standard and unoriginal arguments used to deny any claims that void space is a real possibility. If there is any originality in the discussion in ‘De Aethere’ at all, it is the supposition that aether is simply a subtle form of air, as opposed to the more usual assumption, that it was a subtler substance in its own right.¹⁰² Given that Newton has just been describing the behaviour of air in terms of repulsive forces operating between its particles, we might expect him to already – four sentences in – be having second thoughts about the behaviour of ‘spirit of air’.

There is a suggestion of original thinking, too, in the final words of ‘De Aethere’. Newton now suggests that magnetism, and likewise, ‘the attraction of glass, amber, jet, wax and resin and similar substances seems to be caused in the same way by a most tenuous matter of this kind’.¹⁰³ The mention of attraction might well have brought Newton back to his earlier discussion of repulsion. It was at this point, anyway, that Newton dropped the whole enterprise.

It is impossible to know, of course, why Newton dropped this project at this point. It seems perfectly plausible, however, that one factor might have been a sudden realisation that, in view of what he had written in the first chapter, Newton’s speculative physics no longer had any need, or any use, for an aether.¹⁰⁴ After all, the concept of an all pervasive aether was developed specifically to avoid acknowledging that void space might be possible, because void space was seen as likely to entail recourse to actions at a distance. What might look like action at a distance could always be attributed instead to an invisible and otherwise undetectable, but nonetheless material, aether. This is what aethers were for – to provide a supposedly material all pervasive medium for transferring action between bodies at a distance from one another. The fact that these supposed aethers were agreed to be completely undiscoverable was considered to be less problematic than the alternative, namely, accepting action at a distance by immaterial means, say, by virtues, forces, or occult ‘influences’.

It would seem, anyway, that Newton’s original plan for this document, following on from the failed aetherist philosophy he had tried to develop in the letter to Boyle, was to try again to develop a more convincing account of the role of air and aether in physics. Perhaps to his surprise he found himself introducing in the first chapter the idea of interparticulate forces capable of acting across empty space (which seemed to him to be the only plausible way to explain the extreme rarefactions of air that had been produced in the air-pump experiments). Turning to the second chapter, he begins (we have to suppose, unthinkingly) by calling upon standard aetherist tropes, but almost immediately realises he is undoing the potential of the original ideas he had just developed in ‘De Aere’, and so he stops himself after five and a half sentences.

This is necessarily speculative, of course. It might be objected that the reading suggested here is implausible because it involves Newton rejecting recourse to aethers in his first chapter, in the passage he crossed out (which we discussed above), but nevertheless carrying on to discuss aethers immediately after in ‘De Aethere’. The first thing to note, in response to this, is that they are undeniable matters of fact that the first chapter has a passage recurring to aethers which is crossed out, and that the second chapter does little more than very briefly rehearse a few standard claims about aethers. There is nothing implausible in the assumption that an author might decide to write two chapters comparing and contrasting the role of air in physics followed by the role of aethers. Having completed the first chapter, the author might then automatically start to write the planned second chapter, before shaking themselves, and realising that they were thoughtlessly repeating the error which had led them to delete a brief aetherist excursion in the first chapter. In both chapters, the evidence suggests recourse to aethers was quickly dismissed. This suggests a writer who is in two minds about what he is writing – either he is unsure about the proposed interparticulate forces, or he is uncertain about aethers. Either way, this is not an implausible scenario.

It should be borne in mind also that aethers were briefly introduced in the first section merely as a putative way of explaining ‘the cause of this repulsion.’ There is no inconsistency in rejecting the idea that aether might be a cause of repulsive force, but still continuing to think that aethers may be responsible for other phenomena (such as the damping of pendulums inside an evacuated air-pump). It seems to me to be perfectly plausible, therefore, that Newton’s plan to write two chapters, one on air and one on aether, might have still seemed viable to him, even though he had rejected the idea that aether might cause repulsive force. The plan to write these two chapters would only have been scuppered when he recognized the wider point: that his second chapter was superfluous after what he had written in the first (because aethers were not required to explain away putative actions at a distance, if repulsive forces acting at a distance had actually been proposed as explanatory phenomena in the first chapter).

So much for speculation; what we know for certain, anyway, is that Newton did not simply reject what he wrote in ‘De Aethere’, but he abandoned the whole manuscript. For all we know, it might well have been the case that Newton had no thought of ever returning to ‘De Aere et Aethere’, or even to its more fully considered first chapter, ‘De Aere’. It was, after all, entirely dependent upon the near unanimously rejected concept of actio in distans.¹⁰⁵ Newton might well have thought better about trying to pursue this crazy idea, and simply cast the manuscript aside without any thought of ever returning to it. He might also have been somewhat bemused to find himself thinking twice about the role of aethers, which up to that point had been a prominent feature of his natural philosophical theorizing, as we can see in ‘Of Nature’s obvious laws’, the ‘Hypothesis’, and the letter to Boyle of 1679.

Reviving interparticulate forces

Newton could not have known, when he discarded ‘De Aere et Aethere’, that within a few years he would find himself, quite unexpectedly, working towards his greatest achievement, the Principia mathematica. The story of the composition of the Principia has exercised leading Newton scholars for decades and we do not need to immerse ourselves here in his development, from 1684 to 1687, of a new mechanics and dynamics, ‘mathematically demonstrated’ at almost every step of the way.¹⁰⁶ Suffice it to say, however, that one of many remarkable features of this great work was the establishment of an attractive force of gravity, operating between all bodies. Furthermore, although Newton was careful to avoid any explicit suggestion that gravity operated at a distance, the fact that, on Newton’s account, it seemed to do so, was immediately recognized by contemporary readers of sufficient philosophical acuity.¹⁰⁷ Furthermore, as is well known, as Newton worked on the Principia, he began to develop arguments, backed up by experiments and astronomical observations, against the existence of an aether.¹⁰⁸

This being so, Newton seems to have been inspired to revive his earlier speculations on repulsive forces operating between particles of air. We can see this clearly in Proposition 23 of Book II:

Particles that are repelled from one another by forces that are inversely proportional to the distances between their centres constitute an elastic fluid whose density is proportional to the compression. And vice versa, if the density of a fluid composed of particles that are repelled from one another is as the compression, the centrifugal forces of the particles are inversely proportional to the distances between their centres.¹⁰⁹

As Cohen pointed out in his ‘Guide to Newton’s Principia’, ‘Book 2 of the Principia does not on first reading appear to have the homogeneity of book 1 or book 3 and seems rather to be a collection of loosely amalgamated topics.’¹¹⁰

Be that as it may, Newton repeats here in more elaborate form his comment in ‘De Aere’ that ‘by an easy computation it is discovered that the expansion of the air is reciprocal to the compressive force.’¹¹¹ Evidently, Newton has been giving more thought to his earlier, abandoned, speculations. He notes in the scholium to Proposition 23, for example, that he is supposing that the repulsive forces of particles ‘are terminated in the particles which are next to them or do not extend far beyond them.’¹¹² There is nothing like this in the ‘De Aere’. Although this suggests he has been treating his earlier speculations seriously before introducing them into the Principia, Newton is nevertheless careful to point out to his readers that, with regard to these matters, he is writing conjecturally: ‘Whether elastic fluids consist of particles that repel one another is, however, a question for physics.’¹¹³ Newton was alluding here to a distinction made earlier, in Book I, Section 11, where he declared himself to be concerned ‘in this treatise not [with] the species of forces and their physical qualities but their quantities and mathematical proportions … ’¹¹⁴ The point Newton is making, therefore, is that the supposition of repulsive forces accounts for the behaviour of elastic fluids, as the mathematics confirms, but whether particles really do repel one another in this way can only be established by physical investigations.

Newton’s return to speculations about repulsive forces between particles did not stop here. Remarkably, it seems that, for a while at least, Newton intended to add a highly speculative ‘Conclusio’ to the Principia. This was written in the spring of 1687, as the Principia was nearing completion. Had he persisted with this, it would have completely changed the character of the Principia. It seems fair to say that if the ‘Conclusio’ had been made the culmination of Newton’s great work, the main body of the Principia would have been seen as a consummate and protracted example of the new kind of physics of interparticulate forces which, though only implicit in the main body of the text, was made explicit in the ‘Conclusio’.¹¹⁵

Certainly, reading the ‘Conclusio’ gives one the impression that, when he wrote it, Newton wanted to extend the Principia beyond its treatment of gravity, and its critique of the hydrostatics of Cartesian vortex physics, and to introduce his speculative physics of attractive and repulsive forces between microparticles. This is clear even from its opening words, where Newton writes that if anyone should discover the innumerable motions of minute bodies, ‘I might almost say that he will have laid bare the whole nature of bodies so far as the mechanical causes of things are concerned.’ Newton goes on to present the analysis of gravity, that has been the main objective of the body of the Principia, as an example of the kind of more general physics he has in mind:

Whatever reasoning holds for greater motions, should hold for lesser ones as well. The former depend upon the greater attractive forces of larger bodies, and I suspect that the latter depend upon the lesser forces, as yet unobserved, of insensible particles. For, from the forces of gravity, of magnetism and of electricity it is manifest that there are various kinds of natural forces, and that there may be still more kinds is not to be rashly denied. It is very well known that greater bodies act mutually upon each other by these forces, and I do not clearly see why lesser ones should not act on one another by similar forces.¹¹⁶

Later, he presents the search for such forces as the way for physics to proceed:

I have briefly set these matters out, not in order to make a rash assertion that there are attractive and repulsive forces in bodies, but so that I can give an opportunity to imagine further experiments by which it can be ascertained more certainly whether they exist or not. For if it shall be settled that they are true it will remain for us to investigate their causes and properties diligently, as being the true principles from which, according to geometrical reasoning, all the more secret motions of the least particles are no less brought into being than are the motions of greater bodies which as we saw from the foregoing [books] derived from the laws of gravity.¹¹⁷

And, towards the end of his conclusion he repeats the point: ‘Thus almost all the phenomena of nature will depend on the forces of particles, if only it be possible to prove that forces of this kind do exist.¹¹⁸

Even after Newton thought better of concluding the Principia in this prescriptive way, he wrote in similar terms in a draft Preface:

It remains therefore that we inquire by means of fitting experiments whether there are forces of this kind in nature, then what are their properties, quantities and effects. For if all natural motions of great or small bodies can be explained through such forces, nothing more will remain than to inquire [into] the causes of gravity, magnetic attraction and the other forces.¹¹⁹

Since Newton had already hit upon the idea, in his ‘De Aere’, that some phenomena might be explained by interparticulate forces operating at a distance, when he completely unexpectedly found himself developing the universal principle of gravitation, which assumed a force acting at a distance, it is hardly surprising that he saw all these ideas, arrived at in completely different ways, as going hand in hand.¹²⁰

It seems clear, anyway, that the interparticulate forces which first appeared in ‘De Aere et Aethere’, sufficiently excited Newton that, for a while at least, he wanted to make them a prominent feature of the Principia. So much so, that even in the final recension of the text, the version that appeared in print, the ‘Author’s Preface to the Reader’ included the suggestive assertion that ‘all phenomena may depend upon certain forces’ of attraction and repulsion.¹²¹

It seems safe to assume, therefore, that the ideas about interparticulate forces, first adumbrated in the ‘De Aere et Aethere’, remained with him even though he did not finish that earlier work. Although he thought better of presenting these ideas publicly in the Principia, he subsequently published all of them in the ‘Queries’ he added to the Optice of 1706, and later editions. The link between the ‘greater attractive forces of larger bodies’ and ‘the lesser forces … of insensible particles’ was also brought out in the ‘General Scholium’ added at the end of the second edition of the Principia: ‘Gravity toward the sun is compounded of the gravities toward the individual particles of the sun’.¹²² As has been suggested before, Newton’s speculative physics of interparticulate forces, as it was presented in the ‘Queries’, was in many ways more influential than the complex mathematical dynamics of the Principia, especially among natural philosophers who were less adept at mathematics. Although this more speculative aspect of Newton’s thought was first developed at length in the ‘Conclusio’ of 1687, and more fully in the Opticks at the beginning of the eighteenth century, its origins can be found in the ‘De Aere et Aethere’ of 1679.

Conclusion

Newton’s speculative philosophy of interparticulate forces of attraction and repulsion proved immensely influential throughout the eighteenth century and into the nineteenth. Enlightenment natural philosophers first learned about it through the Queries appended to the Opticks, especially the rich and protracted Query 31. It was not newly minted, here, however. Many of the essential features of it had already been developed for the ‘Conclusio’ that Newton intended to append to the first edition of the Principia. As we have seen, however, this speculative natural philosophy did not grow out of the Principia. The apparent similarities between gravity acting at a distance and interparticulate forces acting at a distance was evidently recognized by Newton as he completed the Principia, but the speculative philosophy of interparticulate forces, at least in a preliminary and tentative form, pre-dated the Principia.

Newton could not have known, when he abandoned ‘De Aere et Aethere’, that he would soon find himself, for a second time thinking about action at a distance between bodies, as he worked out in detail that there must be an attractive force of gravity operating between all bodies. Newton set to work on what became the Principia at the importuning of Edmond Halley, and prior to that it had never been a part of his plan for future work. We can only assume that Newton was excited to realise that the speculations involving actio in distans which he had abandoned a few years before might not be as outlandish and unworkable as he had thought. Accordingly, he resurrected these speculations for a projected conclusion to the Principia. We cannot know why he changed his mind about including this conclusion, but we know he did not abandon his speculative philosophy for a second time. He simply bided his time, and made his conjectures about interparticulate forces public in the Optice.

It was suggested earlier that the stimulus which led to the idea of repulsive forces between particles in ‘De Aere’ was the seemingly intractable problem of the ‘spring’ of the air. How could air spontaneously disseminate itself through space the way it could be seen to do in the air-pump experiments? In ‘De Aere’ Newton wrote of air being able to take up ‘a thousand times its normal space’, and going on to point out that this ‘would hardly seem to be possible if the particles of air were in mutual contact’. By the time he wrote Query 31, the problem was seen to be even greater, but the solution was the same:

The Particles … as soon as they are beyond the reach of the Attraction of the Body, receding from it, and also from one another with great Strength, and keeping at a distance, so as sometimes to take up above a Million of Times more space than they did before in the form of a dense Body. Which vast Contraction and Expansion seems unintelligible by feigning the Particles of Air to be springy and ramous, or rolled up like Hoops, or by any other means than a repulsive Power.¹²³

It seems unlikely that Newton would have adopted this vacuist account of rarefaction of the air – assuming, as he does, that rarefaction was a matter of particles being spread out through a greater void space – in between writing ‘On Nature’s obvious laws’ and the ‘Hypothesis of Light’. In both of those early works Newton does not simply assume that the aether is a material means of transferring action between bodies, but gives it cosmic significance as the fundamental essence of all things (‘matter is nothing but Aether congealed & interwoven into various textures … ’).¹²⁴ Clearly, this way of thinking was continuous between those two early documents. The clearly contrasting assumption in ‘De Aere’ that extreme rarefaction implied action at a distance seems to be incompatible with this early way of thinking.

‘De Aere’ seems to be from a later, significantly different, part of Newton’s intellectual career. And certainly, as we have seen, there is no valid reason to suppose it was written before the ‘Hypothesis’ of 1675. The arguments of the Halls are invalid because they depend upon the mistaken claim that the ‘repulsive force of air particles’ are invoked in both the ‘Hypothesis’ and the letter to Boyle of 1679. In fact, considering just these three documents, the concept of repulsive force occurs uniquely in ‘De Aere’. The claims of Newman and Levitin that ‘De Aere’ could not have been written as late as 1679 (Westfall’s suggested date) because he assumes there that capillary action is caused by atmospheric pressure, are also insecure. As we have seen, Newton was using essentially the same explanation of capillarity up to 1687 – claiming it was caused by differential pressure inside and outside the capillary tube.

In ‘De Aere’ Newton wrote only of repulsive forces, but at some point in his thinking attractive forces were added to the mix (as we can see in the ‘Conclusio’). We can only speculate, but this might have been as a result of Newton writing in the last sentences of the abandoned ‘De Aethere’ about magnets, and ‘the attraction of glass, amber … and similar substances’; or it might possibly have been a result of his thinking about gravity, for the Principia.¹²⁵

Be that as it may, the ‘De Aere et Aethere’, in spite of its brevity, and its unfinished state, should be recognized as a crucially important landmark in Newton’s intellectual development. It was here that Newton first hit upon the essential feature of his speculative natural philosophy, which proved so influential throughout the Enlightenment, namely, the idea that between the particles of all bodies there might be ‘certain Powers, Virtues, or Forces, by which they act at a distance’.¹²⁶

Acknowledgements

I am extremely grateful to Dmitri Levitin, whose fair-minded and penetrating criticisms helped me to greatly improve upon earlier versions of this article.

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Notes

1 Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, translated by I. B. Cohen and Anne Whitman (Berkeley: University of California Press, 1999). ‘The System of the World’ is the sub-title of the culminating third book of the Principia. Hereafter cited simply as Newton, Principia. See also I. B. Cohen, ‘A Guide to Newton’s Principia’, included in his and Whitman’s translation, pp. 1-370, at p. 11.

2 Isaac Newton, Opticks, or a Treatise of the Reflections, Refractions, Inflections, & Colours of Light (London: Royal Society, 1704); Optice … libri tres (London: Royal Society, 1706); Opticks (London: Royal Society, 1717). Except where necessary, I have used the Dover edition: (New York: Dover, 1979), hereafter cited as Newton, Opticks. There were 16 Queries appended to the first edition. Seven more were added in the Optice, Finally, a group of 8 more were interpolated after the original 16, in the second English edition.

3 Newton, Opticks, pp. 375-76.

4 Newton, Opticks, p. 339.

5 On eighteenth-century speculative Newtonianism two classic studies have still not been superseded: Robert E. Schofield, Mechanism and Materialism: British Natural Philosophy in an Age of Reason (Princeton: Princeton University Press, 1970); and Arnold Thackray, Atoms and Powers: An Essay on Newtonian Matter-Theory and the Development of Chemistry (Cambridge, Mass.: Harvard University Press, 1970).

6 Isaac Newton, ‘De Aere et Aethere’, in A. R. Hall and M. Boas Hall, Unpublished Scientific Papers of Isaac Newton (Cambridge: Cambridge University Press, 1962), pp. 223-24, original Latin, pp. 216-17. Hereafter cited simply as ‘De Aere’, with the page reference to the Halls’ edition. It is difficult to imagine how repulsive forces between particles could act other than at a distance. The repulsion between two particles would make them move away from one another. At that point we would either have to assume the particles would immediately cease to act on one another, or we have to assume the repelling force continues across the distance between the particles. Action at a distance, therefore, seems to be even more bound up with the assumption of repulsive force than it does with the assumption of attraction. Alexandre Koyré showed long ago that for early modern thinkers a force of ‘attraction’ implied action at a distance. See his, ‘Gravity an Essential Property of Matter?’ in Newtonian Studies (London: Chapman & Hall, 1965), pp. 149-69.

7 Newton, Principia, pp. 697-99.

8 Hall and Hall, Unpublished Scientific Papers of Isaac Newton, pp. 321-47; p. 345; original Latin, p. 331-32. Hereafter cited as ‘Conclusio’.

9 ‘Conclusio’, p. 345; Latin, p. 332.

10 Hall and Hall, Unpublished Scientific Papers of Isaac Newton, pp. 302–08 (‘Partial Draft of the Preface’).

11 Newton, Principia, pp. 382-83. This appeared in the first edition of 1687 and remained unchanged in subsequent editions. Newton, Philosophiae naturalis principia mathematica (London: Royal Society, 1687), sig. A3v.

12 Readers may note the overlap between a speculative physics based on interparticulate forces of attraction and repulsion, and the Principia, which establishes attractive forces between all bodies, including invisibly small ones. The existence of the ‘Conclusio’ indicates that Newton came to see it too. In spite of this obvious overlap, however, I wish to make it clear that my focus in this paper is Newton’s speculative physics of interparticulate forces, as most clearly seen in the ‘Queries’ appended to the Opticks, and only briefly considered as a possible addition to the Principia. I am not making any would-be revisionist claims about the historical development of the Principia. I fully endorse the histories of the writing of the Principia as told by John Herivel and others, up to George E. Smith, which is a story of mathematics, mechanics, and dynamics, not a story of speculative matter theory. Literature along these lines is extensive and well established; see, for example, John Herivel, The Background to Newton’s Principia: A Study of Newton’s Dynamical Researches in the Years 1664–84 (Oxford: Clarendon Press, 1965); and George E. Smith, ‘The Principia: From Conception to Publication’, in Eric Schliesser and Chris Smeenk (eds), Oxford Handbook of Isaac Newton (Oxford: Oxford University Press, 2019), pp. 1-30, published online: https://doi.org/10.1093/oxfordhb/9780199930418.001.0001

13 ‘De Aere’, p. 223; Latin, p. 217.

14 R. S. Westfall, Never at Rest: A Biography of Isaac Newton (Cambridge: Cambridge University Press, 1980), p. 374n. Westfall declines to defend his interpretation, preferring to let it ‘stand by itself’. This paper is an attempt to defend his interpretation, and his dating of ‘De Aere et Aethere’, to some time after the letter Newton wrote to Robert Boyle, dated February 28, 1678/79.

15 Hall and Hall, Unpublished Scientific Papers, pp. 187-89.

16 William R. Newman, Newton the Alchemist: Science, Enigma, and the Quest for Nature’s Secret Fire (Princeton: Princeton University Press, 2019); Dmitri Levitin, The Kingdom of Darkness: Bayle, Newton, and the Emancipation of the European Mind from Philosophy (Cambridge: Cambridge University Press, 2022). Both of these works are models of excellent scholarship and their importance is hardly affected by my criticisms of this small matter, which has no impact on the power of their main theses. My aim is not to expose their errors but to better understand Newton’s intellectual development.

17 Robert Boyle, New Experiments to Make Fire and Flame Stable and Ponderable (London: M. Pitt, 1673) in Boyle, Works, ed. M. Hunter and E. B. Davis (London: Pickering & Chatto, 1999), vol. vii, pp. 299-322. See Hall and Hall, pp. 187-88.

18 Letter from Newton to Boyle, February 28, 1678-9, in I. B. Cohen (ed.), Isaac Newton’s Papers and Letters in Natural Philosophy, (Cambridge: Cambridge University Press, 1958), p. 251. Hall and Hall, p. 188. These other two documents are published in Isaac Newton’s Papers and Letters in Natural Philosophy, pp. 178–99 (‘An Hypothesis explaining the Properties of Light’), and pp. 250–53 (Letter from Newton to Boyle, February 28, 1678-9). These are also available online, thanks to the Newton Project, at https://www.newtonproject.ox.ac.uk/view/texts/diplomatic/NATP00002 (‘Hypothesis’), and https://www.newtonproject.ox.ac.uk/view/texts/diplomatic/NATP00275 (Letter). Hereafter cited as ‘Hypothesis’, and Letter respectively, followed by page reference in the Newton Project and, secondly, the page reference in Cohen (ed.), Newton’s Papers and Letters.

19 Hall and Hall, p. 188.

20 Hall and Hall, p. 188.

21 Hall and Hall, pp. 188-89.

22 ‘Hypothesis’, p. 257, p. 187. The reference to the ‘black’ is to a dark centre spot which appears where the lenses should be at their closest (but, according to Newton, do not quite touch). See also, ‘Hypothesis’, p. 264, p. 194.

23 ‘De Aere’, p. 222, Latin, p. 215.

24 ‘De Aere’, p. 223; Latin, p. 216. There is more to say about this comment in ‘De Aere’, which was in fact crossed out. We shall return to it.

25 Letter, fol. 62r, p. 250.

26 ‘Hypothesis’, p. 252, p. 182.

27 Letter, fol. 62v, p. 251.

28 Letter, fol. 63r, p. 251.

29 The same goes for the other mention of ‘particles at a distance from one another’, Letter, fol. 64r, p. 253.

30 Older historical scholarship on Newton, even by leading experts such as Alexandre Koyré and I. B. Cohen, has tended to deny that Newton believed in the possibility of action at a distance, in spite of the fact that he explicitly invokes it not just in ‘De Aere’, the draft preface for the Principia, and the Opticks. Evidently, Huygens and Leibniz were not so easily fooled even though they only had access to the Principia, which deliberately avoids any explicit mention of action at a distance. For a survey of the role of actions at a distance in Newton’s work, see John Henry, ‘Newton and Action at a Distance’, in Eric Schliesser and Chris Smeenk (eds), Oxford Handbook of Isaac Newton (Oxford: Oxford University Press, 2019), pp. 1-30, published online: https://doi.org/10.1093/oxfordhb/9780199930418.013.17

31 ‘De Aere et Aethere’, p. 224, Latin, p. 217. The first part of ‘De Aere et Aethere’ strongly suggests that Newton is thinking like an atomist – supposing that individual particles of air are separated from one another with void space in between. Certainly, in the examples he provides, the particles are said to be separated and to interact by means of a repulsive force operating between them: there is no suggestion that really their interaction is mediated by an intervening aether. Indeed, the superfluousness of an aether which was implicit in the first section of the manuscript, entitled ‘De Aere’, might be one reason why Newton, almost immediately after beginning, stopped writing the following section, ‘De Aethere’. This is necessarily speculative, but we shall discuss it further in due course.

32 Hall and Hall, p. 189.

33 Hall and Hall, p. 191.

34 See Koyré, Newtonian Studies, pp. 115-38; and I. B. Cohen, The Newtonian Revolution (Cambridge: Cambridge University Press, 1981), pp. 79-83.

35 Some readers might object at this point that Newton used aether-language in the ‘Queries’ appended to the Opticks, as this passage from the Halls’ introduction makes clear, and that it is therefore wrong to suggest a chronological divide with aether-language confined only to his early career. As a matter of historical fact, however, Newton rejected the use of aethers in his physics at least from the Principia, only to re-introduce them in a group of Queries added to the second English edition of the Opticks in 1717. This is the one and only appearance of this aether, however. It was introduced into the Opticks for specific restricted purposes, but never developed any further by Newton, and certainly never made the basis of a generalised physics to replace the physics developed in the Principia; or even the more conjectural physics promoted elsewhere in the Opticks. It was not introduced into the third edition of the Principia in 1726, for example, which remained as resolutely opposed to the concept of an aether as the earlier editions. Accordingly, these aether Queries of 1717 had no impact on wider aspects of his physics. To all intents and purposes, Newton’s speculative physics (as opposed to the more rigorous and mathematical physics of the Principia) continued to depend upon interparticulate forces operating at distances, and not on an aether. Indeed, even this aether of 1717 was held to consist of particles separated from one another by repulsive forces (see Henry, ‘Newton and Action at a Distance’). Newton did not revert back to ‘aether-language’ in 1717 except within the confines of these eight new Queries; nor did he rescind any of the objections to the concept of aethers which appeared elsewhere in the Queries (for example, Query 28), or anywhere else in his post-Principia works. In short, Newton’s physics continued to be radically different from the physics of his contemporaries, by virtue of its emphasis upon interparticulate forces, and it is wrong (and does Newton a great wrong) – the aether Queries notwithstanding – to imagine him reverting in 1717 to the kind of aetherist physics professed by Cartesians, Leibniz, and others.

36 Hall and Hall, p. 187. In the letter, Newton wrote: ‘had not your encouragement moved me to it, I should never, I think, have thus far set pen to paper about them.’ Letter, fol. 65r, p. 253.

37 Letter, fol. 62r, p. 250. For Westfall’s view, see his Never at Rest, p. 374. See also, Westfall, Force in Newton’s Physics (New York: American Elsevier, 1971), pp. 377-78, and 409-10. Westfall’s date has been accepted in Henry, ‘Newton and Action at a Distance’.

38 See Hall and Hall, pp. 188-89.,

39 Newman, Newton the Alchemist, p. 437; Dmitri Levitin, The Kingdom of Darkness, p. 556n.

40 ‘De Aere’, p. 221, Latin, p. 214.

41 ‘De Aere’, p. 221, Latin, pp. 214-15.

42 Newman, Newton the Alchemist, p. 438n.

43 Robert Boyle, A Continuation of New Experiments Physico-Mechanical Touching the Spring and Weight of the Air (1669), Experiment XXVII, in Boyle, Works, edited by M. Hunter and E. B. Davis (London: Pickering & Chatto, 1999), vol. vi, p. 105.

44 ‘Hypothesis’, p. 252, p. 182.

45 Newman, Newton the Alchemist, p. 438n.

46 Letter to Boyle, fol. 62r, p. 250.

47 Hall and Hall, p. 188.

48 Hall and Hall, ‘Conclusio’, p. 339, Latin, p. 326. The Halls suggest that the ‘certain person’ might be Boyle, but this seems doubtful, especially in view of the fact that Boyle is mentioned by name, in connection with another matter, just a few lines before this. It might be Robert Hooke who discusses capillarity in ‘small canes’ in his Micrographia (London: Royal Society, 1665), pp. 11-12. Hooke’s account, in which differential pressure within the cane and outside it, is explained in terms of Hooke’s concept of incongruity, is rather similar to Newton’s account. On Hooke’s concept of incongruity, see John Henry, ‘Robert Hooke, The Incongruous Mechanist’, in Robert Hooke: New Studies, edited by Michael Hunter and Simon Schaffer (The Boydell Press, Woodbridge, Suffolk, 1989), pp. 149-80.

49 Newton, Opticks, p. 391.

50 Newton, Opticks, p. 393. See Henry Guerlac, “Francis Hauksbee: Expérimentateur au profit de Newton,” in Archives internationales d’histoire des sciences, 16 (1963), 124–127; and A. Rupert Hall, All Was Light: An Introduction to Newton’s Opticks (Oxford: Clarendon Press, 1993), pp. 146-47.

51 Hall and Hall, p. 354, Latin, p. 351.

52 Newman, Newton the Alchemist, p. 438n.

53 The text of ‘Of Nature’s Obvious Laws & Processes in Vegetation’ (Washington DC, Dibner MS. 1031 B, The Dibner Library of the History of Science and Technology, Smithsonian Institution Libraries, Smithsonian Institution) is available online via The Chymistry of Isaac Newton website: https://webapp1.dlib.indiana.edu/newton/mss/norm/ALCH00081/query/field1=text&text1=Of%20Nature's%20obvious%20laws. In older works on Newton, this is sometimes referred to as ‘The Vegetation of Metals’. On its date, see Newman, Newton the Alchemist, p. 139n.

54 Newman, Newton the Alchemist, p. 438.

55 Newman, Newton the Alchemist, p. 439.

56 ‘De Aere’, p. 227, Latin, p. 220.

57 Newman, Newton the Alchemist, p. 439, quoting from Dibner 1031B, fol. 6r.

58 Newman, Newton the Alchemist, p. 440.

59 ‘De Aere’, p. 226, Latin, p. 219.

60 Newman, Newton the Alchemist, p. 438.

61 ‘Of Nature’s obvious laws’, fol. 3v.

62 ‘Hypothesis’, p. 250, p. 180.

63 Hall and Hall, p. 191.

64 ‘De Aere’, pp. 227-28, Latin, p. 220.

65 Westfall, Never at Rest, p. 374n.

66 See Hall and Hall, pp. 305, 306 (draft Preface), Latin, p. 303; ‘Conclusio’, pp. 336, 338, Latin, pp. 324, 325. We will return to these. Newton also hinted at interparticulate forces in some of the first sixteen ‘Queries’ appended to the first edition of the Opticks in 1704 (e.g. Newton, Opticks, pp. 339, 343). He developed his physics of interparticulate forces in more detail in the seven Quaestiones he added to the Optice in 1706, which became Queries 25 to 31 in the Opticks of 1717. For the English text, see Newton, Opticks, pp. 339-406.

67 Many of the features of Newton’s aetherist speculations in the ‘Hypothesis’ can be seen to have derived from earlier ideas propounded by Robert Hooke, as even Newton admitted: ‘Hypothesis’, pp. 248-49, pp. 178-79. See also, Newton’s letter to Henry Oldenburg, of December 21, 1675, in Papers and Letters, pp. 208-09. It might also be added that Newton’s aether theory was not only unoriginal, it was also far from convincing. Consider, for example his somewhat risible theory of gravity in the ‘Hypothesis’, p. 251, p. 181.

68 Westfall, Never at Rest, 374.

69 Letter, fol. 62r, p. 250; ‘Hypothesis’, pp. 250-51, 180-81.

70 ‘Hypothesis’, p. 250, p. 180.

71 Letter, ff. 62r-62v, pp. 250-51.

72 Letter, fol. 63r, p. 251.

73 Letter, fol. 63v, p. 252.

74 ‘Hypothesis’, pp. 251, 181; 252, 182.

75 Letter, fol. 62r, p. 250.

76 Letter, fols. 62r, and 65r, pp. 250, 253.

77 Letter, fol. 64r, p. 252.

78 Letter, fol. 64r, p. 252.

79 Aristotle, Physics, IV, 9, 216b, 30-35.

80 Clearly, they made allowance for windy days and other situations where air was put in motion, but there was nothing remotely like a kinetic theory of gases among early modern thinkers. On the importance of vibrating matter in early modern natural philosophy, see Xiaona Wang, Handling ‘Occult Qualities’ in the Scientific Revolution (Leiden: Brill, 2023), Section 4.2.

81 Francis Bacon, ‘Cupid, or the Atom’ [1609], in The Works of Francis Bacon, edited by J. Spedding, R. L. Ellis, and D. D. Heath (Cambridge: Cambridge University Press, 2011), vol. vi, p. 731.

82 Letter to Boyle, fol. 62r, p. 250.

83 Westfall, Never at Rest, p. 374.

84 ‘De Aere’, p. 221, Latin, p. 214.

85 ‘De Aere’, p. 221, Latin, p. 214.

86 ‘De Aere’, p. 222, Latin, p. 215.

87 Newton was no Antoine Lavoisier, and no John Dalton. He did not think in terms of qualitatively different particles of gold, mercury, etc. The particles constituting gold were materially the same as particles constituting water, differing only in size, shape, and how they were packed together – the matter of which both were made was the same. As the densest substance, gold might be presumed to consist of particles so closely packed together as to be touching; while the particles constituting water must be assumed to be spread further apart, allowing for bigger intervening pores. This way of conceiving things already raised problems for early modern thinkers – could air particles be in contact with one another, air being so much rarer than gold, or must there be self-determined voids between them? See, Newton’s discussions in ‘De Aere’, ‘Conclusio’, pp. 337 and 341; and in Queries 21 and 22, Newton, Opticks, pp. 350-53.

88 ‘De Aere’, p. 223, Latin, p. 216. See Robert Hooke, Micrographia (London, 1665), pp. 226-27.

89 ‘De Aere’, p. 223, Latin, p. 217.

90 ‘De Aere’, p. 223-24, Latin, p. 217.

91 Robert Boyle, Works, vol. vi, p. 387.

92 Boyle, Works, vol. i, p. 166.

93 Newton, Principia, p. 588. It is not clear to me how a surrounding medium could bring about an attraction, and if it did, whether the attracting bodies would obey the inverse square law. A number of Newton scholars have taken this and similar comments by Newton at face value and have therefore suggested he did not really believe in actions at a distance. I have never seen any of these scholars show how this could work mathematically. Newton never showed it either – it is almost as if he did not really take this comment seriously.

94 ‘De Aere’, p. 223, Latin, p. 216. Interestingly, the only one of these opinions that allows action at a distance involves God. When Newton defended interparticulate forces acting at a distance in the Queries appended to the Opticks, he also relied on God. See, for example, Query 28, and Query 31, Newton, Opticks, pp. 369-70, and pp. 400-403. See also, John Henry, ‘Newton, the Sensorium of God, and the Cause of Gravity’, Science in Context, 33 (2020): 329-51.

95 Newton, The Principia, p. 588. See also ‘Definition 8’, p. 408, where he also says the opposite of what he says throughout the rest of the Principia. For discussion, see Cohen, Newtonian Revolution, pp. 68-78, and passim.

96 ‘De Aere’, p. 223; Latin, p. 216. It is not obvious why Newton chose to put this comment in square brackets. Perhaps this was because it was saying the opposite of what had just been said before, and he wished therefore to signal that he was now making a contrasting (and contradicting) point? Be that as it may, it is of little consequence, since he struck out the foregoing passage and this contradiction of it.

97 ‘De Aere’, p. 224; Latin, p. 217. Again, it should be remembered that there was no equivalent of our conception of the kinetic theory of gases. So, heat did not simply increase the motion of already moving particles, for Newton. On the contrary, he seems to have envisaged air particles standing stationary apart from one another. Heat would cause the particles to vibrate, more or less vigorously, but always around the point where they were originally standing stationary.

98 ‘De Aere’, p. 226, Latin, p. 219.

99 ‘De Aere’, p. 227, Latin, p. 220.

100 ‘De Aere’, p. 227, Latin, p. 220.

101 ‘De Aere’, pp. 227-28, Latin, p. 220.

102 This view is largely associated with the Cartesian insistence that empty space is impossible, and therefore, there must be a very subtle form of matter which can, and does, fill all the gaps in nature between larger particles of matter (for example, the gaps unavoidably left between close-packed spherical particles). Since there was only one kind of matter in Cartesianism (as there was in atomism), different substances were distinguished in terms of size, shape, and arrangement of their particles. So, gold differed from iron, or air, by virtue of these differences. In this scheme, aether was therefore different from air, in the same way air was different from water, even though only one kind of matter was involved. There was some originality, therefore, in Newton’s claim that aether was simply ‘spirit of air’; although the distinction between this and Cartesianism was certainly a fine one.

103 ‘De Aere’, p. 228, Latin p. 220.

104 I say that this seems plausible. In fact, I am inclined to add that, in the light of what Newton had just written in ‘De Aere’, he ought to have quickly abandoned ‘De Aethere’ – which he did.

105 It was only nearly unanimously rejected because of the revival of natural magical traditions, inaugurated largely by Marsilio Ficino and other Renaissance thinkers enthralled by occult sciences. See Henry, ‘Newton and Action at a Distance’.

106 The quoted words are Roger Cotes’s in his Preface to the second edition (1713), Newton, Principia, p. 388. Literature on the composition of the Principia is already vast and still growing. See, for example, Herivel, The Background to Newton’s Principia; Cohen, The Newtonian Revolution; and George E. Smith, ‘The Principia: From Conception to Publication.’

107 For discussion of this point, see, for example, Alexandre Koyré, ‘Huygens and Leibniz on Universal Attraction’, in Newtonian Studies, pp. 115-38; and Cohen, Newtonian Revolution, pp. 79-83.

108 See, for example, Herivel, The Background to Newton’s Principia, pp. 96-102; Cohen, ‘Guide to Newton’s Principia’, in Newton, The Principia, p. 180-81; and George E. Smith, ‘Newton’s Numerator in 1685: A Year of Gestation’, Studies in History and Philosophy of Modern Physics, 68 (2019), 163–77.

109 I have slightly modified Cohen’s and Whitman’s translation in Newton, Principia, p. 697. As Cohen points out, the order of these two sentences are reversed in the second edition, which they quote. I have presented them as they appear in the first edition, Newton, Principia (London: The Royal Society, 1687), p. 301.

110 Cohen’s ‘Guide’ appears in Newton, Principia, pp. 1-370, see p. 164.

111 ‘De Aere’, pp. 223-24; Latin, p. 217.

112 Newton, Principia, p. 698.

113 Newton, Principia, p. 699.

114 Newton, Principia, p. 588.

115 Edited and translated in Hall and Hall, pp. 333-47; Latin, pp. 321-33. Hereafter cited simply as ‘Conclusio’.

116 ‘Conclusio’, p. 333, Latin, p. 321.

117 ‘Conclusio’, p. 341, Latin, p. 327.

118 ‘Conclusio’, p. 345, Latin, p. 331.

119 Hall and Hall, ‘Partial Draft of the Preface’, p. 307, Latin, p. 304.

120 As we have seen, the interparticulate forces hypothesised in ‘De Aere’ seem to have arisen as a way of understanding the extreme rarefactions developed in the air-pump. The force of gravity, by contrast, was arrived at through the attempt to provide a mathematical proof that Kepler’s laws of planetary motion were the result of the inertial tangential motion of planets being attracted to the sun by an attractive force varying inversely as the distance between them. During the course of the latter enterprise, Newton found himself rejecting the concept of an aether, and implicitly establishing gravity as a force acting at a distance. Remarkably, therefore, Newton recurred to actions at a distance twice, but through completely different routes. Small wonder that he should be led to link them together, as he seemed to be trying to do in the ‘Conclusio’.

121 Newton, Principia, pp. 382-83.

122 Newton, Principia, p. 943.

123 ‘De Aere’, p. 223, Latin, pp. 216-17; Newton, Opticks, pp. 395-96.

124 See ‘Of Nature’s obvious laws’, fol. 3v, and cf. ‘Hypothesis’, p. 250, p. 180.

125 In the ‘De Aethere’, p. 228 (Latin, p. 220), Newton wrote glibly about magnetism and electrical attraction as evidence for the existence of aether. It was at this point, however, that he stopped dead in his tracks. We can only speculate, but it may have been at this point that he realised he had further evidence for interparticulate forces, but this time attractive, rather than repelling. At the very least, it might have been the mention of attractions which brought repulsions back to the forefront of his mind, and caused him to realise aethers were therefore redundant.

126 Newton, Opticks, pp. 375-76.