Out of the Shadow of a Giant

by John Gribbin

  Phew! After rambling on a bit more, Newton gets to the question of how the Sun and the planets stay in their separate places:

  So some fluids (as Oyle and water) though their pores are in freedome enough to mix with one another. Yet by some secret principle of unsociablenes they keep asunder, & some that are Sociable may become unsociable by adding a third thing to one of them, as water to Spirit of Wine by dissolving Salt of Tartar in it. The like unsociablenes may be in aethereall Natures, as perhaps between the aethers in the vortices of the Sun and Planets.

  Comparing those almost contemporaneous accounts, the modern reader is left in no doubt who was the forward-looking scientist with great insight, and who was the backward-looking mystic with a head filled with magical mumbo jumbo.fn4 But if this was the confused state of Newton’s thinking about gravity and planetary orbits in the second half of the 1670s, what does it tell us about the famous story of the falling apple, which according to Newton he saw in 1665 or 1666, and made him realise that the same force that pulls the apple to the ground holds the Moon in its orbit, and gave him the inspiration for his theory of gravity, including the inverse square law? Simple. He made it up, in order to ensure that posterity would not realise how much he got from Hooke.

  The story as it has come down to us dates from an anecdote he told in 1726, the year before he died. The story was told to William Stukeley, a much younger man who came from the same part of the country and collected anecdotes about Newton in a hero-worshipping and uncritical way. Although this particular story dates from 1726, it was not written down until 1752. The manuscript is in the Royal Society archive and can be accessed online, but the story appears in Stukeley’s Memoirs of Sir Isaac Newton’s Life, edited by A. H. White and published in 1936. According to Stukeley, on 15 April 1726:

  After dinner, the weather being warm, we went into the garden & drank thea under the shade of some apple tree; only he & myself.

  Amid other discourse, he told me, he was just in the same situation, as when formerly the notion of gravitation came into his mind. Why shd that apple always descend perpendicularly to the ground, thought he to himself; occasion’d by the fall of an apple, as he sat in contemplative mood.

  Why shd it not go sideways, or upwards? But constantly to the Earth’s centre? Assuredly the reason is, that the Earth draws it. There must be a drawing power in matter. And the sum of the drawing power in the matter of the Earth must be in the Earth’s centre, not in any side of the Earth.

  Therefore does this apple fall perpendicularly or towards the centre? If matter thus draws matter; it must be proportion of its quantity. Therefore the apple draws the Earth, as well as the Earth draws the apple. There is a power, like that we here call gravity, which extends its self thro’ the universe.

  This was clearly a story that Newton had rehearsed and polished. He also told it to John Conduitt, the husband of Newton’s niece, who recorded:fn5

  In the year 1666 he retired again from Cambridge to his mother in Lincolnshire. Whilst he was pensively meandering in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from Earth, but that this power must extend much further than was usually thought.

  Why not as high as the Moon said he to himself & if so, that must influence her motion & perhaps retain her orbit, whereupon he fell a calculating what would be the effect of that supposition.

  Apart from the evidence of Newton’s own letter to Oldenburg in 1675, which gives the lie to the account, there is an even more striking example of Newton’s attempt to rewrite history. In his correspondence with Halley, he refers to a letter sent to Oldenburg in June 1673, to be copied and sent on to Huygens, in which he spells out the idea of a centripetal gravitational attraction. Sure enough, the version of the letter in the archive of the Royal supports this claim. But, alas for Newton’s reputation, the letter in the Huygens archive does not contain the relevant material. The version held by the Royal has been faked.fn6

  So the fabled story of the fall of an apple in the plague year of 1665 giving Newton the inspiration for ‘his’ theory of gravity is just that – a fable. Until he received Hooke’s letter, Newton had not realised that gravity is a universal force that affects all objects, but had thought of orbital motion in terms of vortices or whirlpools in some mysterious fluid, carrying planets round the Sun (and the Moon around the Earth) like chips of wood floating in vortices in a river. This is not a system that readily explains the fall of an apple from a tree. By the time he came up with the apple story, Newton was an old man and the plague year was a distant memory (and, of course, Hooke was dead). There are two possible reasons why he told the story. The charitable version is that over the years he had first hit on the falling apple and the falling Moon analogy as a neat demonstration of universal gravity at work, then convinced himself that this must have been how he got the idea in the first place. Old men reminiscing about their youth do tend to make mistakes like this. But the evidence suggests that it would be a mistake to put a charitable interpretation on anything Newton said, especially where it concerned his priority vis-à-vis Hooke. The other possibility is that Newton deliberately made the story up, and told it to make sure that future generations would never guess that Hooke deserved the credit for the concept of universal gravity. This seems to us much more likely, given the clear evidence that Newton told lies about his priority claims on more than one occasion. Either way, we have only Newton’s word, the word of a known liar, that the falling apple story is true; which reminds us that there were good reasons why the Royal Society chose as its motto nullius in verba.

  Newton does not seem to have latched on immediately to Hooke’s ideas concerning a universal centripetal attractive force of gravity in 1680, but still clung to his idea of vortices. But a comet that appeared in 1682 did not fit that world-view, and is probably the reason why he started to take Hooke’s suggestion seriously. This is the object now known as Halley’s comet, which Hooke, like other astronomers, studied during August and September that year. As well as its later significance to our story (see Chapter Eleven), it has one important property: it goes round the Sun in the opposite way to the planets – a so-called retrograde orbit. This simply does not fit the image of all the bodies in the Solar System being swept around the Sun in a swirling fluid – the comet would have to be moving ‘upstream’, against the flow of the ‘aethereall Spirit’. So Newton was primed not only by the correspondence with Hooke but also by the fact of retrograde cometary orbits when Halley happened to visit Cambridge in 1684 and took the opportunity to ask Newton for his thoughts about orbits and the inverse square law.

  Newton’s personal circumstances had changed around this time. From his early days in Cambridge, Newton had shared a set of rooms in Trinity with another scholar, John Wickins, who among other things had acted as his scribe. Wickins resigned his Fellowship in 1683, became Rector of Stoke Edith in Hertfordshire, and married. Newton seems to have been somewhat disgruntled by the break-up of their friendship, but in 1685 Wickins was replaced by a young man just up from Grantham, Isaac’s namesake Humphrey Newton (neither of them ever claimed that they were related). Humphrey only stayed with Isaac for five years, but it is worth mentioning because, among other things, he wrote out the fair copy of Newton’s masterwork, the Principia, from which the printer worked.

  A few months after Wren had challenged Hooke and Halley to find a proof of the inverse square law, with the inducement of a book prize, Halley had to travel to Peterborough, in the summer of 1684, on the family business we discuss in Chapter Eight. He took the opportunity to take a slight detour to Cambridge to meet up with Newton, where he raised the subject that had been nagging at Hooke, Wren and himself since January. What is an undoubtedly embellished account of what happened next (but the only account we have) comes from Abraham de Moivre, a French Huguenot refugee who was an acquaintance of Newton and reported what Newton told him of the events:

&
nbsp; In 1684 Dr Halley came to visit him in Cambridge, after they had been some time together the Dr asked him what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it. Sr Isaac replied immediately it would be an Ellipsis, the Dr struck with joy & amazement asked him how he knew it, why saith he, I have calculated it, whereupon Dr Halley asked him for the calculation without any further delay, Sr Isaac looked among his papers but could not find it, but he promised to renew it, & then send it to him.fn7

  Just like Hooke in January, Newton was playing for time by pretending he had already made the calculation, and planning to do it once Halley was out of the way, so that he could then claim to have ‘found’ the missing piece of paper. But unlike Hooke, Newton did have the mathematical skills to carry out the proof, as well as both the opportunity and inclination to work single-mindedly (even obsessively) on one project, without being distracted by other activities.

  The initial result of this single-minded devotion to the problem of planetary orbits was a short paper titled De Motu Corporum in Gyrum (On the Motion of Bodies in Orbit), which Newton sent to Halley in November 1684. This was only an outline of Newton’s ideas, but enough to show Halley that Newton should be encouraged to flesh it out into a complete package. From our point of view, the most significant thing about De Motu, as it is usually known, is that in it Newton introduces the term centripetal force, having at last taken on board Hooke’s realisation that orbital motion is a result of the combination of the tendency of a body to move in a straight line and an inward (centripetal) pull of gravity. In De Motu, Newton showed that under the influence of a centripetal inverse square law planets would indeed follow elliptical orbits obeying Kepler’s First Law, that an imaginary line joining the planet to the Sun sweeps out equal areas in equal intervals of time.

  Halley returned to Cambridge to discuss the paper with Newton, and then, on 10 December, announced its existence, but probably not its detailed contents, to the Royal. He referred to it as a ‘curious treatise’, by which he meant that it invited curiosity, not that it was strange. Hooke was, therefore, at least aware of De Motu, and Halley may have given him a chance to read it. But he was not prompted by this to return to his own studies of orbital motion, and seems to have accepted that he had taken this as far as he could.fn8 But it must have been clear to him how much his ideas had shaped Newton’s thinking, and he no doubt expected credit for them in due course.

  Halley now became in effect the midwife for Newton’s masterpiece. Enthusiastically backed up by the Royal, he encouraged Newton to concentrate on writing what became Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy) – the Principia. Alchemy and theology were pushed to one side, while Halley encouraged Newton when he tired of the project and soothed his ruffled feathers when he got angry, particularly about Hooke’s claims. More than a year after Halley had started cajoling Newton to develop the ideas hinted at in De Motu, the first fruit appeared. On 21 April 1686, Halley, by then Clerk of the Royal, told the Society that Newton’s book was nearly ready for publication, and the following week the manuscript of Book One of the Principia arrived in London and was presented to them. It claimed to explain ‘all the phaenomena of the celestial motions by the only supposition of a gravitation towards the center of the sun decreasing as the squares of the distances therefrom reciprocating’. It all sounded very familiar to Hooke.

  We know of the immediate fallout from the meeting of 28 April 1686 from a letter that Halley later wrote to Newton. The meeting was chaired by Sir John Hoskins, who said that Newton’s book ‘was so much more to be prized, for that it was both Invented and perfected at the same time.’ We can imagine Hooke sitting there fuming, thinking that it may have been perfected by Newton, but it had been invented, years before, by himself. Exactly what he said to Hoskins we do not know, but Halley tells Newton (and us) that the two of them ‘who till then were the most inseparable cronies, have since scarce seen one another, and are utterly fallen out.’ At the usual coffee house gathering after the meeting, Hooke tried to press the point that he had long had both the inverse square law and the idea of a centripetal attraction, but to no avail.

  Halley was a good friend of Hooke, but his immediate objective was to see the Principia through to publication.fn9 When Halley wrote to Newton on 22 May 1686 to inform him that the Royal intended to pay for the cost of printing the book, he made an attempt to pre-empt trouble by giving an undramatic account of these events to Newton before some wilder story might reach him, with a carefully phrased attempt to maintain equilibrium between Newton and Hooke:

  There is one thing more that I ought to inform you of, viz, that Mr Hook has some pretensions upon the invention of ye rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center. He sais you had the notion from him, though he owns the Demonstration of the Curves generated therby to be wholly your own; how much of this is so, you know best, as likewise what you have to do in this matter, only Mr Hook seems to expect you should make some mention of him, in the preface, which, it is possible, you may see reason to praefix. I must beg your pardon that it is I, that send you this account, but I thought it my duty to let you know it, that you so may act accordingly; being in myself fully satisfied, that nothing but the greatest Candour imaginable, is to be expected from a person, who of all men has the least need to borrow reputation.

  At first, Newton responded as Halley had hoped. He agreed that Hooke had made a contribution to the understanding of planetary motion, and that Newton would give him credit where due. But in a blatant lie he said that nothing in the correspondence of 1679–1680 had contributed to Newton’s thinking, and had the chutzpah to say that if his recollection was at fault ‘I desire Mr Hooke to help my memory’. Perhaps Newton’s memory really was that bad. As he brooded in Cambridge, he seems to have grown increasingly angry about Hooke’s claims, an anger fuelled by a more colourful account of Hooke’s clash with Hoskins, supplied by Edward Paget, who was both a Fellow of the Royal and a Fellow of Trinity, Newton’s college. On 20 June 1686 Newton wrote a much more intemperate letter to Halley, incorrectly saying that Hooke had claimed the inverse square law operates all the way to the centre of the Earth (which Hooke had explicitly said was not the case) and making unjustified claims that Hooke had actually stolen his ideas, such as they were, from other people. But he did make one valid point, albeit in a rather over-the-top way. It was all very well having bright ideas, but somebody had to do the work of proving them.

  Now is this not very fine? Mathematicians that find out, settle & do all the business must content themselves with being nothing but dry calculators & drudges & another that does nothing but pretend & grasp at all things must carry away all the invention as well as of those that were to follow him as of those that went before. Much after this same manner were his letters writ to me … And upon this information I must now acknowledge in print I had all from him & so did nothing my self but drudge in calculating demonstrating & writing upon ye inventions of this great man.

  Of course, Hooke did not wish to ‘carry away all the invention’, but simply to have credit for his work, and if anyone, it was Newton who was carrying away the invention of ‘those that went before’.

  Halley did not read this letter out to the Royal, but filed it away quietly. Newton had also threatened to withhold Book Three of the Principia, which was already in draft form, from publication. So Halley went into soothing overdrive. He now (29 June) told Newton about the coffee house discussion of January 1684, the bust-up with Hoskins, and the circumstances surrounding Hooke’s claim, which, he said, had been ‘represented in worse colours than it ought’. Halley succeeded in soothing Newton to the extent that he admitted on 14 July 1686 that ‘he [Hooke] was in some respects misrepresented to me’, withdrew his threat to withhold Book Three, and conceded the minor point that the correspon
dence with Hooke had led him to seek a mathematical basis for an understanding of the motion of the planets. But the overall outcome of this brouhaha was that Hooke’s work was not acknowledged as fully in the Principia as it would have been if he had bitten his lip and kept quiet.

  In the draft of Book Three, which Halley had not yet seen, Hooke was mentioned as one of the discoverers of the importance of centripetal force, along with ‘others of our nation’; this was already minimising his contribution, since there were no such ‘others’, but in one of his fits of rage Newton crossed the reference out. He then went through the manuscript savagely erasing almost every reference to Hooke (he may have overlooked some of the ones that remain), and where he could not ignore Hooke’s contribution to observations of comets he reduced the reference from Clarissimus (‘the very distinguished’) Hookius to plain Hookius. But he did acknowledge that ‘our countrymen Wren, Halley and Hooke’ had been aware of the inverse square law.

  Newton also made some other changes to Book Three. He had originally drafted it in what he called ‘a popular method’ to make the ideas relatively easily accessible. But he changed it into a mathematical treatise of deliberately great complexity. He later told William Derham, who was a Fellow of the Royal and an acquaintance of Newton (and eventually edited some of Hooke’s papers for publication), that he had done this ‘to avoid being baited by little smatterers in mathematics’. We can guess which ‘little smatterer’ he had in mind. In the final version of Book Three Newton also added Proposition XIX, suggesting that the Earth bulges at the equator because of its rotation; Hooke, who had made this suggestion some time earlier (as Newton was well aware), received no acknowledgement. But, as ‘Espinasse has pointed out, after delivering the book to the Royal Newton took no interest in its publication, and as he had written to Oldenburg in 1676 did now ‘bid adieu’ to science.