Out of the Shadow of a Giant

by John Gribbin

  But all of Hooke’s scientific activities in the 1680s would soon be overshadowed by Newton’s greatest triumph. It all started innocently enough, when Hooke, Wren and Halley were discussing the inverse square law, on one of their convivial visits to a coffee shop, following a meeting of the Royal in January 1684. By then, they all knew that the inverse square law of gravity could explain the orbits of the planets. But they did not know if this was the only law that would do the job, or if anything more might be required to explain orbital dynamics. In modern parlance, was the inverse square law of gravity both necessary and sufficient to do the job? In their parlance, could Kepler’s laws of planetary motion be derived from the inverse square law? Hooke said they could, but that he had not completed the calculation. Halley explained what happened next in a letter to Newton written a couple of years later:

  Sir Christopher to encourage the Inquiry sd, that he would give Mr Hook or me 2 months time to bring him a convincing demonstration thereof, and besides the honour, he of us that did it, should have from him a present of a book of 40s. Mr Hook then sd that he had it, but that he would conceal it for some time that others triing and failing, might know how to value it, when he should make it publick; however I remember that Sr Christopher was little satisfied that he could do it, and tho Mr Hook then promised to show it him, I do not yet find that in any particular he has been as good as his word.

  Hooke seems to have been sure that he could solve the problem, given time, so pretended that he had already solved it. In this, as we shall see, he would not be alone. But he never did solve the problem. There the matter rested, until, as we discuss in Chapter Seven, Halley raised it on a visit to Newton later in 1684. Meanwhile, Hooke worked on telescopes, barometers, his weather clock and, of course, his activities as architect and builder. He served on the Council again from December 1684 to November 1685;fn11 at that time most of the demonstrations at the Royal were carried out by Denis Papin, who had returned from Venice, but Hooke made many contributions to the discussions. In the autumn of 1685, however, a storm in a teacup brewed up, which although initially seemed to end in Hooke’s favour, would cast a long shadow.

  At that time, Francis Aston and Tancred Robinson were joint Secretaries of the Royal, and responsible for the publication of the Philosophical Transactions. In the September–October issue of the journal they published an anonymous review of the letters of Hevelius, which raked over the old controversy with Hooke, whom the reviewer roundly criticised for:

  making it his business, to carp at all [Hevelius’] Instruments, and render them suspected; to blacken and disparage to the Learned World, all his Observations

  and repeated Hevelius’ own disparaging remarks about Hooke:

  That he makes it his own business to perswade him and all the world, that his own way is the best, safest, and most exquisite, which ever can be invented by any; reproaching this Author all along for not obeying him and following his dictates, (as if this Author were one under his command;) Bragging only of what he can do, but doth nothing.

  In the matter of open sights versus telescopic observations, of course, Hooke’s way was indeed ‘the best, safest, and most exquisite’. The attack on Hooke was so unjustified that it led to a blazing row, culminating in the resignation of Aston and Robinson, and their replacement by John Hoskinsfn12 and Thomas Gale, both friends of Hooke. In the aftermath of this brouhaha the Royal also established the post of Clerk, with Halley, as we discuss in Chapter Eight, as the first incumbent. So far, so good, as far as Hooke was concerned. But although Newton was at that time still in his reclusive hideaway in Cambridge and never attended meetings of the Royal, he did read the Philosophical Transactions, and took the review at face value. This would have a damaging effect on his already shaky relationship with Hooke; the letter of 1686 mentioned above, with its reference to ‘a man of a strange unsociable temper’, suggests the influence of the Hevelius comments on Newton. It is time to cut to the chase and tell the story of gravity from Hooke’s perspective.

  CHAPTER SEVEN

  A MISSION OF GRAVITY

  The study of gravity was one of the most important scientific missions of Hooke’s life – arguably, the most important mission. Which is why he was so upset when Isaac Newton picked up what Hooke regarded as ‘his’ ball and ran off with it. Hooke experimented with and studied gravity for decades, developing a sound theoretical understanding of what was going on. Then Newton came along and did a few sums that, from Hooke’s point of view, confirmed what Hooke had discovered and were just the icing on the cake; and yet Newton got credit for baking the whole cake. At that time, and with some justification, the mathematical side of science was not so highly regarded as the ideas side; you need ideas, after all, before you can find the appropriate equations, as even Albert Einstein’s investigation of gravity proved. So let’s look at the whole story of gravity from Hooke’s perspective.

  Hooke’s interest in gravity went back to his childhood. His early obsession with the possibility of flight – attempting to overcome gravity – was one manifestation of this, and part of his interest in developing spring-driven clocks and watches was because he knew that a pendulum clock would beat time at a different rate in places where the force of gravity was different, such as (he surmised) on top of a mountain. In the early days of the Royal Society, Hooke proposed different ways to measure gravity using falling objects, and carried out experiments with mixed results. In one series of experiments, carried out in 1663, lead weights were dropped from different heights on to one pan of a beam balance, while the other pan, which contained a heavier weight, was held in place by a light spring, to see how much what he called the ‘force’ of the falling object moved the balance. Descartes had argued as a principle that if an object (in physicists’ language, a body) is at rest, then the impact of a smaller body will never move it, no matter how fast the smaller body moves. Hooke showed by experiment that ‘the least body by an acquired celerity may be able to move the greatest’. This was the beginning of an understanding of the idea of conservation of momentum.

  The next step was to measure how fast falling objects moved: in places where gravity is weaker, they would be expected to fall more slowly, so this might provide a way to measure how gravity differs from place to place. This required an accurate timekeeper, which Hooke duly built. We don’t have a complete description of it, but the discussion of the experiments and their results reveal that it was a pendulum some 9¾ inches long (roughly 250 mm) which beat once every half-second. By the summer of 1664, Hooke had found that a lead ball starting from rest would drop 15½ feet in the first second of its fall. But these experiments were not followed up, partly because Hooke was kept so busy by the Royal on various projects, and partly because his investigation of gravity now took another turn.

  At that time, the tallest building in London was the steeple of the old St Paul’s Cathedral, and this seemed a natural place for Hooke to carry out experiments involving studies of gravity and atmospheric pressure. The cathedral had been badly damaged by fire in 1561, and in the rebuilding (completed in 1566), the steeple had been topped off with a pyramid-shaped roof, instead of a spire. A wooden platform under that roof was reachable by ladders, with a long, clear drop beneath it. Hooke went to investigate the possibilities in August 1664, and on the 25th of that month wrote to Boyle with news of his initial observations:

  One was, that a pendulum of the length of one hundred and eighty foot did perform each single vibration in no less time than six whole seconds, so that in a turn and return of the pendulum, the half second pendulum was observed to give twenty four strokes or vibrations … I with a plum line found the perpendicular height of [the tower] two hundred and four foot very near, which is about sixty foot higher than it was usually reported to be. In which place I shall, with some other company, this week try the velocity of the descent of the falling bodies, the Torricellian experiment, and several experiments about pendulums, and weighing.

  Hooke’s ambiti
ous experimental programme was hindered rather than helped by the presence of several Fellows. But in spite of this – and in spite of the dangers and difficulties of working in a crumbling tower 200 feet above the ground balanced on an incomplete floor made of partly rotten century-old timbers, Hooke carried out many experiments over the next few weeks. His studies of gravity were inconclusive. In an earlier investigation at Westminster Abbey in November 1662, for example, he had tried weighing a piece of iron and a ball of string in a balance at ground level, then set up the balance on the roof of the abbey and used the string to lower the iron seventy-one feet while still attached to the balance, to see if its weight changed with height. He did sometimes record a small difference in weight, but nothing that could not be explained by such influences as the absorption of moisture from the air by the extended line. Similar experiments carried out a couple of years later at St Paul’s also failed to find any change in the influence of gravity with height. Like his results with timing falling bodies in the tower, the results, he reported, were ‘so imperfect, that I shall not, till we make them more accurate, trouble you with an account of them.’

  But the opportunity to make them more accurate never arose. By October, the fading autumn light and increasingly inclement weather brought an end to the experiments. It was intended to restart the programme in the spring of 1665, but first plague and then fire meant that old St Paul’s would never again be the site of scientific experimentation, and it would be a long time before the old cathedral was replaced.

  As we have mentioned, by the time Micrographia was published in 1665 Hooke had already realised that the Moon – and by implication other celestial bodies – exerted its own gravitational influence, and during the plague year he carried out the experiments at deep wells, which we described earlier. His work so far on gravity was summarised in the report On Gravity that he presented to the Royal in February 1666. This concentrated on his experimental work, but was supplemented by a presentation describing his theoretical ideas about orbits, or, as he put it, ‘concerning the inflection of a direct motion into a curve by a supervening attractive principle.’

  I have often wondered why the Planets should move about the Sun according to Copernicus his supposition, being not included in any solid orbs (which the Antients possibly for this reason might embrace) nor tied to it, as their Center. by any visible strings; and neither depart from it above such a degree, nor yet move in a streight line, as all bodies, that have but one singular impulse ought to doe: But all the Coelestiall bodies, being regular to solid bodies … must have some other cause, besides the first imprest Impulse, that must bend their motion into that Curve.

  Hooke dismissed the idea that a planet trying to move in a straight line is constantly being nudged sideways by the resistance of some fluid through which it is moving, preferring the idea that the deflection is caused by:

  an attractive property of the body placed in the center; whereby it continually endeavours to attract or draw it to itself. For if such a principle be supposed, all the phaenomena of the planets seem possible to be explained.

  This was written in May 1666, long before Newton said anything similar; the paper is in the archive of the Royal and reprinted by Birch. It was at this time that Hooke demonstrated, using conical pendulums, how a straight-line motion could be bent into a curve by a central force.

  Hooke continued to think about gravity and to make astronomical observations (among other things) even during the hectic period immediately following the Great Fire. In what became the first of his Cutlerian Lectures to be published, in 1670 Hooke described An Attempt to Prove the Motion of the Earth. The attempt was based on making observations at different times of year to try to detect the apparent shift in the positions of stars (the parallax) by comparing observations made on opposite sides of the Earth’s orbit. The underlying principle was sound – parallax measurements are a cornerstone of modern astronomical distance measurements – but the effect is too small for Hooke to have been able to measure it with his equipment. The fact that the parallax effect is so small means that the stars are very far away, and therefore, in order to be visible at all, comparable in size to the Sun. But from our point of view, the interesting thing about this lecture is that when it was published, in 1674, Hooke included at the end a more detailed exposition of his thoughts on planetary motion. He promises that at some future time he will describe:

  a System of the World differing in many particulars from any yet known, answering in all things to the common Rules of Mechanical Motions: This depends upon three Suppositions. First, That all Coelestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the Earth to do, but that they do also attract all the other Coelestial Bodies that are within the sphere of their activity; and consequently that not only the Sun and Moon have an influence upon the body and motion of the Earth, and the Earth upon them, but that Mercury also Venus, Mars, Jupiter and Saturnfn1 by their attractive powers, have a considerable influence upon its motion as in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodies whatsoever that are put in a direct and simple motion, will so continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipsis, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified; but it is a notion, which if fully prosecuted as it ought to be, will mightily assist the Astronomer to reduce all the Coelestial Motions to a certain rule, which I doubt will never be done true without it.

  Michael Cooper has commented that this ‘resembles very closely Newton’s world-view as it eventually appeared seventeen years later’. It would be more accurate to say that the world-view presented in the Principia resembles very closely Hooke’s world-view as it appeared seventeen years earlier!fn2 There is everything here except the inverse square law, and Hooke soon had that, as well. As we have seen, by about 1676 Hooke, Halley and Wren were aware that an inverse square law of gravity would do the trick (at least for circular orbits; the more general application was tricky to prove). In 1677, Hooke observed a comet and at the behest of the Royal published a paper the following year,fn3 drawing on this and his earlier observations for comets. Quoting from his lecture notes for 1665, Hooke posed the key questions concerning the orbit of a comet:

  What kind of motion it was carried with? Whether in a straight or bended line? And if bended, whether in a circular or other curve, as elliptical or other compounded line, whether the convex or concave side of the curve were turned towards the Earth? Whether in any of those lines it moved equal or unequal spaces in equal times? [and] Whether it ever appears again, being moved in a circle; or be carryed clear away, and never appear again, being moved in a straight or paraboloeical line?

  He reached the conclusion that cometary nuclei contain solid matter that possesses its own ‘gravitating principle’ so that it is attracted towards the Sun and deflected (as he put it, ‘incurvated’) from a straight line into a curved path around the Sun, although in this case ‘it were not wholly stayed and circumflected into a circle’.

  The scene was set for the correspondence that Hooke initiated at the end of 1679 in his capacity as Secretary, culminating with his statement to Newton in the letter of 6 January 1680 that ‘the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall.’

  So by 1680 Hooke had not only worked out, but had presented to Newton, a complete world-view incorporating the idea of universal gravitation, the first law of motion (that every body stays at rest or proceeds in a straight line at constant speed unless deflected
by a force) and the centripetal inverse square law. He pointed out that the force of gravity should be calculated in accordance with the inverse square law as if it acted from the centre of a body such as the Earth or the Sun, but that the inverse square law did not work below the surface of such a body. He knew that the Universe was governed by physical laws, the same laws that applied here on Earth, and not by mystic powers. Before he received this package of ideas, Newton’s world-view was very much what you would expect from a mystic alchemist and crackpot theologian. He thought that the planets were kept apart by ‘unsociableness’ and referred to vortices in the ether. On 7 December 1675, a year after the publication of An Attempt to Prove the Motion of the Earth, he wrote to Oldenburg spelling this out:

  So may the gravitating attraction of the Earth be caused by the continual condensation of some other such like ethereal Spirit, not of the maine body of flegmatic aether but of something very thinly and subtily diffused through it, perhaps of an unctuous or Gummy, tenacious & Springy nature, and bearing much the same relation to aether, we the vital aereall Spirit requisite for the conservation of flame & vitall motions (I mean not ye imaginary volatile saltpeter), does to Air. For if such an aethereall Spirit may be condensed in fermenting or burning bodies, or otherwise inspissated in ye pores of ye earth to a tender matter wch may be as it were ye succus nutritious of ye earth or primary substance out of wch things generable grow (or otherwise coagulated, in the pores of the earth and water, into some kind of humid active matter for the continuall use of nature. adhereing to the sides of those pores after the manner that vapours condense on the sides of a Vessell subtily set); the vast body of the Earth, wch may be every where to the very centre in perpetuall working, may continually condense so much of this Spirit as to cause it from above to descend with great celerity for a supply.