Out of the Shadow of a Giant

by John Gribbin

  Newton’s papers reveal no similar understanding of circular motion … Every time he had considered it, he had spoken of a tendency to recede from the centre, what Huygens called centrifugal force.’fn6

  and:

  I do not know of any document in which Newton employed either the word [centripetal] or the concept before Hooke instructed him to do so … Hooke’s suggestions exercised a profound influence on Newton’s speculations [and] prepared his mind for the conception of universal gravitation.fn7

  – A conception that Hooke had already had!

  As these comments highlight, the correspondence initiated by this exchange of letters triggered the development of what was to become the most significant package of ideas in British (and world) science – what we know now as Newtonian physics. In 1679, Newton really had given up natural philosophy for other studies, having found the real world uncongenial after the reaction given to his ideas about light, and was devoting his time to alchemy and to his bizarre theological studies.fn8 Even after Oldenburg had persuaded him not to resign his Fellowship, he had asked the Secretary not to forward any correspondence to him because he intended ‘to be no further solicitous about matters of Philosophy’. He might have kept to this intention had it not been for Hooke’s letter. But in his reply, even after reiterating that he had given up science, Newton could not resist offering his thoughts on an old puzzle.

  Ever since it had been recognised that the Earth rotates, philosophers had argued about what would happen to an object such as a bullet, or a cannonball, dropped from a height – say, from the top of a very tall tower. Would it carry with it the forward motion associated with the rotation of the Earth, and fall at the foot of the tower? Or would it fall straight towards the centre of the Earth, get left behind by the rotation, and fall behind the tower? In fact, the question had been partially answered in 1640, when the Frenchman Pierre Gassendi arranged for balls of different weights to be dropped from the mast of a galley being rowed flat out across the Mediterranean. The balls all fell at the foot of the mast, showing that they shared the forward motion of the ship – and by implication, that they ‘remembered’ the motion due to the rotation of the Earth. But Newton offered another suggestion. Gassendi certainly showed that the falling balls shared the forward motion of the ship, but a mast is too short for testing the effects of the rotation of the Earth directly. The surface of the Earth at a great height, such as at the top of a mountain, is moving faster than the surface at sea level, in order to complete one revolution of a larger circle in the same time, twenty-four hours, as the lower surface. So Newton suggested that if objects could be dropped from a great enough height, and fell in a vacuum, so that there was no air resistance, they would reach the surface lower down a little further to the east, ahead of where they started. So far, so good. But Newton included in his letter a hastily drawn diagram to illustrate his point, with the trajectory of the falling object carrying on below the surface of the Earth and making one turn of a spiral path before reaching the centre.

  After reading the scientific parts of Newton’s letter out to the Royal, Hooke wrote back to Newton, trying to persuade him not to give up natural philosophy, and, perhaps in an attempt to encourage further correspondence, pointing out what he saw as a minor error in Newton’s diagram. If his intention was indeed to stir Newton into scientific activity, he succeeded beyond his wildest dreams.

  In this letter, written in his capacity as Secretary and duly read out to the Royal on 11 December, Hooke suggested that if it were possible for an object to fall to the centre of the Earth, it would make several ellipsoidal orbits before reaching the centre; in addition, if the falling object started out from a great height at the latitude of London it would hit the ground slightly to the south-east, not due east. This was a straightforward example of the kind of friendly scientific debate that the Royal Society encouraged, and Hooke concluded with the exhortation that Newton should ‘goe on and Prosper’ in natural philosophy.

  But Newton was not straightforward, and reacted angrily to the letter and to the fact that Hooke, entirely in accordance with his role as Secretary, had made its content known to the Royal Society. He was still fuming about it years later, and in 1686 wrote to Halley about how it had affected him:

  Should a man who thinks himself knowing, & loves to shew it in correcting & instructing others, come to you when you are busy, & notwithstanding your excuse, press discourses upon you & through his own mistakes correct you & multiply discourses & then make use of it, to boast that he taught you all he spake and oblige you to acknowledge it & cry out injury and injustice if you do not, I beleive you would think him a man of a strange unsociable temper.fn9

  In truth, Newton was the man ‘of a strange unsociable temper’. He could not bear to be criticised or corrected, and anything that hinted at public criticism roused him to passion. Hooke, by contrast, was merely doing his job, and making a special effort to be seen to be doing it in the light of the justified criticism of other Fellows that he had been neglecting his duties as Secretary.

  Newton’s next letter, dated 13 December, was addressed not to ‘my ever Honoured Friend’, the form he had used before, but simply to ‘Mr Robert Hooke’. In it, he went into mathematical details to show that Hooke’s ellipsoidal path was also wrong. Intriguingly, a modern analysis of Newton’s mathematical methodology, carried out by Michael Nauenberg and discussed by Michael Cooper, shows that Newton used the idea of combining a tangential motion and a centripetal force in his calculation, even though he had claimed to be ignorant of Hooke’s work. The fact that he went to some trouble to disguise this suggests how (un)reliable a reporter he is. In the same letter, Newton made the assumption that ‘gravity be supposed uniform’. Hooke, of course, knew perfectly well that gravity obeyed an inverse square law. On 6 January, he wrote again to Newton, seemingly blissfully unaware of the hornets’ nest he was poking, pointing out that the attraction of gravity falls off ‘in a duplicate proportion to the Distance from the Centre’, but suggesting that this inverse square law would no longer operate beneath the Earth’s surface – ‘not that I believe there really is such an attraction to the very centre of the Earth’ – and mentioning various experiments he had carried out with pendulums and falling objects.

  This gives us another insight into Newton’s reliability as a reporter. In one of his letters to Halley in 1686,fn10 he scornfully wrote that what Hooke ‘told me of the duplicate proportion was erroneous, namely that it reached down from hence to the centre of the Earth.’ Hooke had actually said the exact opposite; it is difficult to see this as mere forgetfulness on Newton’s part, given the importance of the idea.

  On 17 January 1680 Hooke wrote again in friendly fashion asking Newton to address the question of the kind of planetary orbits that would be required by an inverse square law of gravity. He seems to have been encouraging collaboration, rather than stirring up rivalry:

  It now remains to know the proprietys of a curve Line … made by a central attractive power which makes the velocitys of Descent from the tangent Line or equall straight motional all Distances in a Duplicate proportion to the Distances Reciprocally taken. I doubt not that by your own excellent method you will easily find out what that Curve must be, and its proprietys, and suggest a physicall Reason of this proportion. If you have any time to consider of this matter, a word or two of your Thoughts of it will be very gratefull to the Society.

  Newton did not reply, and Hooke gave up the attempt to entice him back into the scientific fold. But in another letter to Halley in 1686 Newton grudgingly acknowledged that:

  his correcting my Spiral occasioned my finding the Theorem by wch I afterward examined the Ellipsis; yet I am not beholden to him for any light into yt business but only for ye diversion he gave me from other studies to think on these things & for his dogmaticalnes in writing as if he had found ye motion in ye Ellipsis, wch inclined me to try it after I saw by what method it was to be done.

  ‘Only for ye diver
sion he gave me from other studies’. Overall, Hooke’s time as Secretary was not a success. Administration was not his forte. But it turned Newton away from alchemy and loony theology, and back to science. Because this correspondence with Newton had such a profound influence on the development of British (and world) science, Hooke’s appointment as Secretary was arguably the most significant event in his, and Newton’s, life. And Newton was indeed ‘beholden to him’ for other ideas, not least the idea of an orbit as a combination of a straight-line motion with a centripetal attraction. It is Hooke who emerges from a reading of the correspondence as a reasonable, friendly man, eager to work with others to solve the mysteries of the Universe. As for Newton, we cannot improve on a summing up offered by Stephen Inwood:

  He was neurotic, self-centred, ambitious, intolerant, oversensitive, secretive, unforgiving and highly argumentative. It is hard to imagine Newton spending his evenings drinking coffee with a large group of congenial companions, or forming lifelong friendships with laundresses, sea captains, clerks and scientists.

  With Newton having gone back into his shell at the beginning of 1680, although Hooke was now distracted, as he would have put it, from his ‘other studies’ and working again on science, his life settled into its usual routine. His building and mapmaking activities continued; although the details need not concern us, this meant that he was now financially independent, but his life was still centred on Gresham College and the Royal Society. From the end of 1679 to the spring of 1680, his main scientific activity involved preparing various alloys and measuring their density (or specific gravity). He found that a mixture of tin and lead is in this sense lighter than the average density of the two metals, which he explained as due to ‘an aversion in the joyning of those two bodys’, whereas an alloy of copper and tin was heavier than the average of the two metals because the particles (what we would call atoms) had an ‘affinity’ and penetrated one another. The actual measurements are less interesting to us than the emphasis Hooke put in describing them: ‘Nature it selfe then is to be our Guide and we are to spend some time in her school with attention & silence before we venture to speak and teach’. In other words, experiments come first, theories afterwards.

  In April 1680 Hooke made one of his rare excursions outside London to visit Lord Conway at Ragley, in Warwickshire. Hooke was designing a house for him, which is worth mentioning because although Ragley Hall was altered in the eighteenth century the basic structure remains very much as Hooke planned it.

  In the summer of 1680, we get another insight into Hooke’s diligence. Exasperated by the failure of the Gresham lecturers to do their duty, the authorities demanded that they should all evict their tenants, take up residence and give the lectures they were being paid for. To encourage this, they suspended all salaries. Hooke, as the only Gresham Professor who had actually been living in the college and giving his lectures (preparing them even when there was no one to hear them), appealed, and got his salary restored (with arrears paid up) because, in the words of the committee ‘he only of all the lecturers hath bin constantly resident, & for ought that appears hath bin ready to read when any auditory appeared, and besides hath printed many of his lectures for the common benefit.’

  The lectures presented for the common benefit in 1680 and on various occasions over the next two years concerned light; as it happens, they were not published until after Hooke’s death, but in them he developed his wave theory, discussed the inverse square law for light (suggesting that this also applied to magnetism and gravity), and reiterated the importance of basing theories on experiment. It is particularly noteworthy, given the subsequent dispute with Newton, that Hooke presented the inverse square law for gravity in a public lecture in February 1680. In November that year, he spelled out his idea that the Sun exerts a gravitational force which shows up ‘on the Motions of all the other primary Planets, whose Motions as I have many years showed in this Place, are all influenced and modulated by the attractive Power of this great Body’. The key words, of course, being ‘attractive power’, an idea that Hooke indisputably gave to Newton. In a later lecture, he said that gravity is a universal force with infinite range, acting ‘on all bodies promiscuously, whether fluid or solid’. He also noted that ‘comparative to the other Powers of Nature, tis weak’. After all, a child can throw a stone up into the air, against the pull of gravity.

  At the end of 1680, Hooke, while still acting as Curator, was confirmed as joint Secretary of the Royal and as a Council member, while Wren was elected President, Boyle having declined the position on grounds of ill health. Around the same time, a bright comet became visible, and Hooke monitored it until it disappeared on 10 February 1681. Inevitably, this gave him the inspiration for a lecture on the history of comet studies. His workload at the Royal increased when a fellow Curator, Denis Papin, left to work in Venice, and was not replaced. But he found a new friend in the sea captain Robert Knox, who had just returned after many years in Sri Lanka (then known as Ceylon). Knox was a source of the kind of travellers’ tales that Hooke loved, and Hooke helped him prepare a book, Historical Relation of the Island Ceylon; the two remained friends until Hooke’s death two decades later.

  In May 1681, Hooke lectured on the role of air in sustaining life. He had shown that a fire is only sustained by a supply of fresh air ‘and without a Constant supply of that it will go out and Die’. He had also shown that fresh air, not the movement of the lungs, is essential for life: ‘whether the lungs move or not move, if fresh Air be supplied, the Animal lives, if it be wanting it dies’. He was on the edge of explaining respiration as a form of combustion, a century ahead of Pierre Laplace and Antoine Lavoisier.

  In the same year, Hooke studied the structure of the eye, designed an improved telescope, and built a machine with a toothed wheel that would strike a piece of metal or card and make it vibrate as the wheel turned. Changing the speed of the wheel changed the note produced by the vibration, which meant the frequency of the note could be measured. As so often with Hooke’s ideas, it was soon forgotten and reinvented, this time by a Frenchman, after whom it is called ‘Savart’s wheel’.

  With all this going on, something had to give. The diary was kept less frequently and then entries stopped altogether, and the quality of Hooke’s work as Secretary also declined. There were other irritations. Flamsteed, no friend of Hooke, had become Gresham Professor of Astronomy in June 1680, providing ample scope for him and Hooke to rub each other up the wrong way during the coffee house discussions they both participated in. Flamsteed was particularly enraged when it turned out that he was wrong and Hooke was right in an argument about the behaviour of a plano-convex lens. But Hooke was not the only recipient of his wrath: Flamsteed was so disputatious that he was forced to resign in 1684, when the other professors had had enough of him. In November 1682, Hooke was not reappointed as Secretary, and he also lost his place on the Council, although that was part of the normal rotation in which ten out of the twenty-one Council members left each year, and he would be elected to the Council again in later years. But for the time being, as far as his relationship with the Royal was concerned, at the beginning of 1683 he was once again ‘only’ Curator of experiments, a role he carried out alongside two other Curators, Edward Tyson and Frederick Slare. But it soon turned out that they were providing the bulk of the demonstrations, and in June Hooke’s status was altered. Instead of receiving a salary, he was to be paid on results, with a quarterly assessment of what he had contributed over the previous three months.

  Part of the reason Hooke had been remiss in his duties (as the Council saw it) was that his long-running dispute with Sir John Cutler had been dragging through the Courts. The tedious business resulted in Hooke receiving a payment of £200 in January 1683 and £475 in February 1684, although even then Cutler did not pay for the lectures Hooke continued to give. Freed from the hassles associated with the Secretaryship, and (at least for the time being) those associated with Cutler’s reluctance to pay, Hooke once again be
came more active as Curator, providing experiments and demonstrations to the Fellows as before. There was nothing particularly dramatic about these, although a couple are worth mentioning. In the winter of 1683–84 he demonstrated several different kinds of accurate weighing machine, and in 1685 he carried out a detailed study of wheel design and friction, concluding that narrow wheels with a large diameter were best for the conditions of the time, rather than the wide-rimmed wheels favoured by the government and approved by regulation. He was right, but was once again ignored.

  Hooke also carried out a study into the properties of ice. The second half of the seventeenth century was a period of such intense cold in Europe that it has become known as the Little Ice Age, and the winter of 1683–84 was the coldest and longest of a series of severe winters. The Thames at London froze hard enough to bear substantial weight from just before Christmas 1683 until mid-February 1684, so that it became the site of a Frost Fair, with tents and stalls laid out in streets, and both sledges and horse-drawn coaches using it as a highway. John Evelyn described it thus: ‘[there was] sliding with skates, a bull-baiting, horse and coach-races, puppet-plays, and interludes, cooks, tippling, and other lewd places, so that it seemed to be a bacchanalian triumph, or carnival on the water.’

  Hooke left no diary for the period, so we cannot be sure that he attended the Frost Fair, but it is unlikely that he could have resisted such an attraction on his doorstep. What we do know is that he prepared a bar of ice fifteen inches long, three and a half inches thick and four inches wide, which he stood on supports placed twelve inches apart and loaded it with weights to find its breaking point. It only gave way when the load reached 350 pounds. At the meeting of the Royal on 13 February 1684, Hooke described how he had found that a piece of ice weighs only seven-eights as much as the same volume of water, so that floating ice exposes just one-eighth of its volume above the surface. This refuted the widely held notion that ice sank to the bottom when a thaw set in – the break-up of the ice on the Thames soon confirmed Hooke’s assessment.