by John Gribbin
On 13 September, which was also the day of Tom’s funeral, Hooke took over the Secretaryship on a caretaker basis, until a permanent replacement for Oldenburg could be appointed. The Secretary was the key person in the Royal, essentially responsible for running the Society, keeping records, and communicating with scientists across Europe. Hooke, along with Boyle, Wren, Aubrey and others, realised that this was an opportunity to restore the Royal to what it had been intended to be. Some of the founders had died, others had got old and lost interest, but there was a rising generation ready to take over. After much lobbying and behind-the-scenes manipulating, on 30 November 1677 the Fellows elected a new President, Sir Joseph Williamson (the Secretary of State), a new Treasurer, Abraham Hill (one of Hooke’s camp), a new Vice-President, Christopher Wren, and joint Secretaries, Hooke and Nehemiah Grew (another curator of experiments). Hooke and Grew were also elected to the Council, the governing body of the Royal. Significant though this coup was, both for Hooke and for the Royal, in scientific terms it was accompanied, coincidentally, by an equally significant development in microscopy, with Hooke revitalised and throwing himself wholeheartedly back into scientific work.
Earlier in the year, news had come from the Netherlands of Anton van Leeuwenhoek’s discovery of tiny living organisms wriggling about in droplets of water. Leeuwenhoek was very secretive about the methods he had used to observe these creatures, so that when Grew, in the spirit of nullius in verba, had tried to replicate the observations he had had no success. But on 10 November, using an improved microscope and the trick of trapping water in very thin tubes of glass, which themselves had a magnifying effect, Hooke saw in rainwater that had been standing for a week ‘great numbers of exceedingly small animals swimming to and fro’ and commented ‘nor could I indeed imagine that nature had afforded instances of so exceedingly minute animal productions’. On 15 November, he showed these microorganisms at the Royal.
Hooke followed this up by making his own single-lens microscopes (essentially very powerful magnifying glasses) of the kind Leeuwenhoek had hinted that he used. These are tiny droplets of glass, fixed in a hole in a thin metal plate, which are extremely difficult to make and equally difficult to use, involving such close focusing with the eye that the operator’s vision is likely to be damaged by long use (as, indeed, Hooke’s seems to have been). Significantly, and unlike Leeuwenhoek, Hooke was eager to pass on the details not only of what he had discovered but how he had discovered it. In an essay, Microscopium, published in April 1678, he wrote:
The manner how the said Mr. Leeuwenhoek doth make these discoveries, he doth as yet not think fit to impart, for reasons best known to himself; and therefore I am not able to acquaint you with what it is: but as to the ways I have made use of, I here freely discover that all such persons as have a desire to make any enquiries into Nature this way, may be the better inabled to do so.
Although he was generally so open about his discoveries, there was one secret that Hooke had, until now, hugged to himself, for reasons that were practical and understandable – his theory of springs. But with Oldenburg dead and the prospects of a patent for his watches remote, the time had now come for him to release that secret into the world. And it was far more than the seeming simplicity of ‘Hooke’s law’ might lead you to think.
A letter written by Hooke in January 1678, to Martin Lister, a botanist based in York, sums up the optimism with which he started the new year. The changes at the Royal, he said, had ‘very much revived us and put a new spirit in all our proceeding which I perswade myself will not only be beneficial and delightful to the members of the Society, but to the whole learned world.’ Hooke was now forty-two, and past his prime for making new scientific discoveries, but looking forward to life as an elder statesman of the Royal. In March that year, however, the edge was taken off his happiness by his brother’s suicide and Grace’s ‘trouble’. Preoccupied with sorting out the mess left by John Hooke, architectural work, and assisting a London publisher, Moses Pitt, with a new atlas, it was not until late July, just after his forty-third birthday, that Hooke got to grips with writing up his theory of springs for publication. The manuscript was delivered to the printer early in October, and finished books were ready by the end of November, with the title Lectures De Potentia Restititutiva: or of Spring. It is usually referred to by the English subtitle.
Hooke explained in the book that he had come up with the ideas it contained about eighteen years previously, ‘but designing to apply it to some particular use, I omitted the publishing thereof.’ The ‘particular use’, of course, was the spring-driven watch. The book explains how to make a simple spring balance, but goes on to point out that the same rule (or law) applies to any springy body, such as a wooden ruler placed over the edge of a table or desk and weighed down at its end: ‘the force or power thereof to restore itself to its natural position is always proportionate to the Distance or space it is removed therefrom,’ and ‘if one power stretch or bend it one space, two will bend it two, and three will bend it three.’ Twice the weight doubles the distance, three times the weight trebles the distance, and so on. This is important simply as an empirical law – early in the nineteenth century, Thomas Young refined Hooke’s work by introducing a term known as ‘Young’s modulus’, which has been described as ‘the most useful of all concepts in engineering’,fn3 although few engineers appreciate Hooke’s role in discovering it. Hooke himself, though, had an engineer’s turn of mind, and always looked for practical applications of his work. In this case, one example he offers is that ‘From this Principle it will be easie to calculate the several strengths of Bows, as of Long Bows or Cross-Bows, whether they be made of Wood, Steel, Horns, Sinews, or the like.’ He also explained how a vibrating spring beats time as regularly as a swinging pendulum, the key to his work with spring-driven watches. But he went beyond the everyday practicality of his discovery. In order to explain what he had found, Hooke came up with a whole new theory of matter, in effect developing the atomic and kinetic theories decades ahead of their time.
Hooke began with the premise that the ‘sensible Universe’ consists of ‘body and motion’, and supposes ‘the whole Universe and all the particles thereof to be in a continued motion’. Vibrating particles that shared the same ‘harmonious’ speed and amplitude of motion clung together and made up what he called ‘congruous’ bodies, but the size of these bodies depended on the speed with which they were vibrating, and on the pressure of their surroundings, harking back to his work with Boyle on air pressure. Hooke explicitly says that the particles are repeatedly colliding with one another, and that these collisions provide the outward pressure that stops them collapsing. ‘All springy bodies whatsoever consist of parts thus qualified, that is, of small bodies indued with appropriate and peculiar motion.’ But if the outside pressure could be increased to halve the size of the object, the frequency of the collision would be doubled, giving the object a tendency to spring back outwards. And if an object is stretched, the average distance between particles and the frequency of the collisions is correspondingly reduced, reducing the outward pressure and encouraging the object to shrink back to its original size because of the outside pressure of the air (or of the ether, a hypothetical fluid that in Hooke’s day was thought to fill the Universe). He also described something akin to modern molecules: ‘two or more of these particles joyned immediately together, and coalescing into one become of another nature and make a compounded particle differing in nature from each of the other particles’.
Within that framework, Hooke could also explain why bent objects tend to straighten up (because one side is stretched and the other is squeezed), and the way in which springs vibrate. Of course, the idea of atoms was not new; it went back to the time of Democritus. But the idea of atoms in random motion, colliding with one another and exerting an outward pressure that increased if they were compressed, was new, as was the suggestion in Micrographia that heat is simply ‘a very brisk and vehement agitation of the parts of
a body’. But it would be nearly two hundred years before the kinetic theory of matter became mainstream science, and by then everyone had forgotten that Hooke thought of something similar long before.
Of Spring ought to have been Hooke’s swan song and scientific memorial, ensuring him of a place in the pantheon of science (if his earlier achievements had not already done that). And for a few years his status as an elder statesman of seventeenth-century science did indeed seem assured. But it would prove the calm before the storm.
As you might expect for someone at this stage of his career, Hooke’s scientific work now largely consisted of refining and completing projects that he had been involved with for some time. One of the most impressive of these was a kind of automated weather station, or ‘weather clock’, which not only measured temperature, rainfall, air pressure and both wind speed and direction, all at the same time, but recorded the measurements by punching holes in a steadily unrolling strip of paper. The original idea went back to a suggestion by Christopher Wren in the 1650s, but it was Hooke who actually built such a weather station, drawing on his work with clocks, barometers, hygrometers and the like over the years. It was completed and demonstrated to the Fellows in May 1679. Although the device was ingenious and did work, it was rather impractical, and the punched paper recordings were difficult to interpret, so it remained just a curiosity, although a tribute to Hooke’s ingenuity and practical skill.
Tantalisingly, we have only hints of what might have been a much more useful practical idea. As part of his work with the mapmaker Pitt, Hooke became interested in the process of printing, and on 13 March 1679 he noted in his diary that he had told Pitt of a ‘new contrivance for printing books’. At that time, all printing presses used the flat-bed process, where each sheet of paper was laid out on a flat wooden base, with the print pressed into it by squeezing another flat piece of wood down on top of it. The process was slow, because each time the top part of the press had to be lifted, the printed page removed, and another blank page inserted before it could be printed in its turn. On 14 March, Hooke records discussing a ‘contrivance for tinplates for Rolling presse’, undoubtedly the idea he had mentioned to Pitt, with a friend. If this refers to a machine with a rolling cylinder pressing down on the sheet of paper being printed, Hooke was a hundred years ahead of his time: printing presses based on revolving cylinders were not developed until the 1780s. They speed things up enormously, because sheets of paper can be fed one after another into the gap between the rotating cylinder and the bed of the press, and out the other side, while the cylinder just keeps on rolling to and fro.
Although Hooke’s work as City Surveyor was now largely over, he had plenty of architectural work, and was closely involved in practical aspects of Wren’s work on St Paul’s Cathedral at this time. In the summer, he was distracted from all these activities when Grace contracted smallpox, but unlike little Tom Giles she survived. Even for Hooke, there was too much going on for one man to handle, and something had to give. That something was the Secretaryship of the Royal, the duties of which were not suited to his abilities, and which he neglected abominably. Things got worse when Nehemiah Grew, who had been handling the correspondence of the Royal, gave up his post as joint Secretary, and virtually gave up science, in 1679, as his medical practice prospered. But the Secretaryship drew Hooke back into contact with the man who would become his nemesis: Isaac Newton.
It all started when Sir Jonas Moore, who had been the patron of the first Astronomer Royal, John Flamsteed, died in August 1679. Worried that Moore’s heirs might try to claim the valuable scientific instruments at the Greenwich Observatory, the Royal quickly dispatched Hooke, along with his assistants Harry Hunt and Thomas Crawley, to recover the items, including several quadrants, which they regarded as having been loaned, not given, to the observatory. Flamsteed, left without some of his best instruments, including a quadrant made by Hooke, was livid, but could do nothing except let off steam in letters to his friends. The return of the instruments back to Gresham College, however, revived Hooke’s interest in the puzzle of planetary motion, which he discussed with Wren over the autumn of 1679. On 18 October, the pair mulled over ‘Elliptick motion’, and on the 21st developed the theme at Bruin’s coffee house. On 8 November, over coffee at Man’s, Hooke told Wren about his latest ideas concerning elliptical motion ‘about central attraction’. By this time, Hooke had the inverse square law clear, although he arrived at it from the point of view of a physicist, not a mathematician.
Hooke was not the only person to realise that gravity obeys an inverse square law, and he may not have been the first. But he developed a particularly neat practical explanation for why this should be the case. It is worth going into in detail because of the way it demonstrates the difference between the mind of a physicist and the mind of a mathematician.fn4
Hooke knew, of course, that the apparent brightness of a light, such as a candle flame, decreases as the square of its distance to the observer. A candle twice as far away appears to be only one quarter as bright. You don’t need very sophisticated equipment to measure this. You could just place a single candle a certain distance away, with four identical candles twice as far away, and note that the combined light from the four distant candles was the same as the single light from the one nearby candle. This inverse square law can be explained very naturally using the wave theory of light. Imagine the light spreading out as an expanding wave in all directions from its source. This advancing wave forms a spherical shell around the source, like the skin of an expanding spherical balloon, or a soap bubble. As the sphere gets bigger, the light has to be spread in some sense more thinly, so that it can still cover the entire surface. And we know from simple geometry that the area of the surface of a sphere is proportional to the square of its radius. So when the bubble is twice as big, the area is four times as great, and at each point on its surface there will only be one quarter as much light. Hooke extended this analogy to the idea of gravity as an influence spreading out from every material object in the Universe, including the Sun, to explain why gravity also obeys an inverse square law, with the force tugging on an object being one quarter as strong at twice the distance. This is the way the physicist thinks, picturing what is going on and making analogies with similar physical systems. The mathematician plays with equations and finds the ones that match the physical reality of our world. Science progresses when the equations and the physical insight come together in one package, which is what happened with the theory of gravity. But both components are equally important, so (getting ahead of our story a little) what has come down to us as Newton’s theory of gravity should really be known as the Hooke–Newton theory of gravity.
But it might not even have been known as ‘Newton’s’ theory of gravity, had it not been for a fateful letter that Hooke wrote to Newton on 24 November 1679, when, under pressure from the Council of the Royal, he was trying to fulfil his duties as Secretary more diligently, including keeping up a correspondence with other scientists. The letter begins:
Finding by our Registers that you were pleased to correspond with Mr Oldenburg and having also had the happiness of Receiving some Letters from you my self, make me presume to trouble you with this present scribble. Dr Grews more urgent occasions having made him Decline the holding Correspondence. And the Society, hath devolved it on me. I hope therefore that you will please to continue your former favours to the Society by communicating what shall occur to you that is philosophicall, and in returne I shall be sure to acquaint you with what we shall Receive considerable from other parts or find out new here. And you may rest assured that whatever shall be soe communicated shall be noe otherwise farther imparted or disposed of then you yourself shall prescribe. I am not ignorant that both heretofore and not long since also there have been some who have indeavourd to misrepresent me to you and possibly they or others have not been wanting to doe the like to me, but Difference in opinion if such there be (especially in Philosophicall matters where Interest hath l
ittle concerne) me thinks should not be the occasion of Enmity – tis not wth me I am sure. For my own part I shall take it as a great favour if you shall please to communicate by Letter your objections against any hypothesis or opinion of mine, And particularly if you will let me know your thoughts of that compounding the celestiall motions of the planetts of a direct motion by the tangent & an attractive motion towards the centrall body …
Note the reasonable tone of the letter. Note also, and even more significantly, that this is the first time that Newton was made aware of the importance of the idea of an inward (centripetal) force combining with a tangential (straight line) motion to make an orbit; previously he had subscribed to the idea of an outward (centrifugal) force being constrained by something (maybe ‘the ether’) to stop planets flying away into space. In his reply, dated 28 November, Newton said that he had given up natural philosophy for other studies, that he had not heard of Hooke’s work on springs, and that he had not come across the idea that a planetary orbit was a combination of a straight-line motion and a central attraction. ‘I have had no time to entertain philosophical meditations’, he wrote, and [am] ‘almost wholly unacquainted with what philosophers in London or abroad have of late been imployed about.’ As a result, ‘believe me when I tell you that I did not, before the receipt of your letter so much as heare (that I remember) of your hypothesis.’ Given Newton’s reclusive nature at the time, it seems entirely possible. On the other hand, he may have been dissembling. Hooke’s ideas had been published by the Royal,fn5 and Newton had possibly seen them – he certainly seems to have admitted this in 1686, in a letter to Halley. Either way, he certainly did not realise their importance until he received the 24 November 1679 letter. As Richard Westfall, a leading Newton scholar, has put it, before that date:
