Out of the Shadow of a Giant

by John Gribbin

  A couple of years later, Halley picked up on the demographic studies that he had begun with his analysis of births and deaths in Paris during his Grand Tour. He obtained similar data for the city then known as Breslau (now Wrocław). He was particularly interested in these data, because as far as he knew the population of Breslau was steady; the equivalent figures for London were distorted because the population was rising as people moved into the city. By looking at how many people of each age died in an interval of five years he was able to work out, among other things, the probability that somebody of a certain age would live on for a certain number of years. This kind of calculation produces actuarial tables that have been used as a basis for calculating life insurance premiums and annuities ever since. In one of Halley’s own examples, he showed that for this particular population the cost of an annuity at a rate of 6 per cent for a man aged forty should be 10.57 years’ premium. Some would live longer than average and do well out of such an annuity; some would die sooner and receive less. But on average the insurance company would balance its books. It was Halley who put life insurance on a scientific basis.fn3

  In September 1691, in a presentation to the Royal Society, Halley discussed the possibility of measuring the distance to the Sun using a transit of Venus, but at that time he did not follow this up with a detailed analysis. At about that time, in spite of his continuing interest in astronomy and demonstrated skill as an astronomer, Halley suffered a setback in his astronomical career. That year, the post of Savilian Professor of Astronomy at Oxford became vacant, and Halley applied for the job. In purely scientific terms, he was an ideal candidate, but other considerations intervened, and there was also another worthy candidate.

  The suitability of Halley for the post had been recognised in some quarters as early as 1678, when his career was taking off on the strength of the trip to St Helena. In that year, when Edward Bernard, who held the chair at the time, mentioned to Flamsteed that he was thinking of resigning, Flamsteed had recommended Halley as his successor, writing:

  He is very ingenious, as I found when he talked with me; and his friends being wealthy, you may expect that advantage [that is, financial reward] by a resignation to him …

  But by the time Bernard actually did resign, in 1691, a lot of water had flowed under the bridge, not least concerning Flamsteed’s views about Halley. In the summer of 1691, Halley was busy with attempts to salvage the cargo from a ship, the Guynie, that had sunk off the Sussex coast. This threatened to interfere with his application for the professorship, and on 22 June, in a letter to Abraham Hill, one of the governors of the company that owned the ship, Halley not only brought him up to date with the salvage work but went on:

  This business requiring my assistance, when an affair of great consequence to myself calls me to London, viz, looking after the Astronomy-Professor’s place in Oxford, I humbly beg of you to intercede for me with the Archbishop Dr. Tillotson, to defer the election for some short time ’till I have done here, if it be but for a fortnight: but it must be done with expedition lest it be too late for me to speak. This time will give me an opportunity to clear myself in another matter, there being a caveat entered against me, till I can show that I am not guilty of asserting the eternity of the world.

  The Archbishop was one of the Electors for the Savilian Chair, and it was essential that a candidate should be of orthodox religious views (or at least be thought to be; Newton got away with his unorthodoxy by keeping it secret); Halley’s modest suggestions about the Flood seemed to be about to cause problems.

  In the event, the election was not held until December, because Bernard did not get around to formally resigning his post until the beginning of November 1691. This gave Halley time to get an endorsement from the Royal Society, where at the meeting of 11 November it was his no doubt pleasant duty as Clerk to record that:

  It was ordered that the Society doe give a recommendatory Letter to Mr Halley signifying their opinion of his abilities to perform the Office of Professor of Astronomy in Oxford now vacant, as likewise to testifye, what he has done for the advancement of the said Science, and that Dr Gale be desired to draw up the Testimoniall.

  It was to no avail, and nor were Halley’s protestations that he did not claim that the age of the Earth was infinite. The post went to the Scot David Gregory (not to be confused with James, inventor of the Gregorian telescope) who, ironically, had been ejected from his position in Edinburgh on religious grounds. There are no contemporary accounts of exactly what happened at the election, only later stories based on half-truth and rumour. There isn’t even any direct evidence that Halley’s ideas about the age of the Earth were held against him. But it is clear that one powerful voice in particular spoke up in opposition to Halley being appointed. On a letter he received from Wallis at the end of 1698, which referred to some work by Gregory, Flamsteed wrote:

  Dr Gregory is a freind of Mr Halleys tho he was his competitor but I perceive by this transaction he is no freind of mine tho I showed him more freindship than he could reasonably expect on yt occasion & Mr Halley as much enmity …

  Quite a turnaround from 1678! Regardless of Flamsteed’s animosity and any other caveats, though, Gregory was an excellent candidate who thoroughly deserved the post, so the result of the election should be regarded as his success rather than as Halley’s failure. But the ‘failure’, such as it was, meant that Halley was available for another unusual career move in the 1690s. First, though, he made more contributions to astronomy, including his ground-breaking study of comets.

  Before he carried out his comet studies, Halley made another astronomical investigation, which demonstrates both the breadth of his own knowledge and his willingness to embrace new ideas. He had a long-standing interest in ancient history, and found that this interest combined with his interest in astronomy in the work of the Arab al-Battani, also known as Albategnius, who lived from about 858 AD to 929 AD. Al-Battani had made observations of the Moon, which had come down to Halley’s day in a Latin translation made by Plato Tiburtinus. Halley commented that, judging by this translation, Tiburtinus knew neither astronomy nor Arabic, and Halley used his knowledge of both to revise the text and draw out the correct astronomical information. Halley was something of a linguist, as this example shows. He studied Latin and Greek at school, knew some Hebrew as well as Arabic, and wrote letters in French and Italian while he was Clerk (as well, of course, as in Latin) and on other occasions. Contemporaries also said that he spoke German. With the correct data, Halley was able to work out the latitudes of al-Battani’s observing sites, and then to compare his observations from those sites with seventeenth-century observations from London. What he found was dramatic.

  As well as his routine observations of the Moon and other objects, al-Battani had observed solar eclipses in 891 AD and 901 AD, and lunar eclipses in 883 AD and 901 AD. The precise timing of all these events, combined with his ‘modern’ data, showed Halley that in the eight centuries between the Arab observations and his own the Moon had been speeding up in its orbit. We now know that this is a result of tidal influences: the rotation of the Earth slows down, while the Moon accelerates in its orbit. But the details of the physics do not matter here. What matters is that Halley had observed that the heavens are changing, and changing on a timescale noticeable to humankind. Hooke, as we describe shortly, had shown that the Earth evolves; Halley discovered that the heavens evolve. It was a profound, even revolutionary, idea that was essentially ignored at the time, and which gets only a passing mention in most books about Halley today.

  In 1692, Halley published his ideas about terrestrial magnetism, which he had been mulling over, off and on, for some time. He suggested that the way the Earth’s magnetic field varied could be explained if the interior of the planet was made up of an outer shell and an inner core, separated by a fluid layer, so that they could rotate at different rates. On this picture, each of the two parts of the Earth had its own magnetic field, with north and south magnetic poles, so th
ere would be four magnetic poles in all, and the variations would be explained by the differential rotation of the two parts of the planet changing the geographical relationship of the two sets of magnetic poles. It was, he said, an ‘Hypothesis which after Ages may examine, amend or refute.’ It did, indeed, turn out to be wrong. But it was a reasonable and genuinely scientific attempt to explain a natural phenomenon, using the still-new idea of offering hypotheses based on past observations, which could be tested by further observations and experiments.

  Halley was also, like Hooke, happy to apply his intellectual powers to more down-to-earth matters. Around the same time that he was investigating the orbit of the Moon, he was asked by one of the Fellows, James Houghton, how to work out the acreage of land in each English county. Halley’s ingenious solution is an early example of lateral thinking. He took a large map of England, and cut out the largest complete circle he could from the map. The circle covered a diameter representing 691⁄3 miles, with an area corresponding to 9,665,00 acres. He then weighed both the circle and the complete map. Since the circle weighed only one quarter as much as the whole map, he concluded that the area of England was 36,660,00 acres. This differs by only a little over 1 per cent from the modern figure. He then worked out the area of each county by cutting their outlines out and weighing them.

  Halley solved that problem without using any mathematical skill beyond the simple arithmetic he learned in school. But when he turned his attention to comets in the mid-1690s, he used the most sophisticated mathematical toolkit of the time, the technique, now known as calculus, which Newton had invented.fn4 Halley was, indeed, the first person apart from Newton to apply calculus to the study of the Universe.

  Newton himself had worked out the behaviour of things discussed in the Principia using calculus, but had not yet revealed the technique and knew that his contemporaries would not understand the calculations. So he recast all the calculations as geometrical examples, which was itself something of a mathematical tour de force. But Halley does not seem to have used geometrical methods at all in his attack on comets, since he wrote to Newton as early as 21 October 1695 that he was ‘ready at the finding a Cometts orb by Calculation’ – the calculation referred to being the techniques of calculus.

  Although Halley began his detailed study of comets in the mid-1690s, and corresponded with Newton about his results, he continued to work on the problem intermittently over the next ten years, interrupted by other activities, and published most of his results in the Philosophical Transactions in 1705; the final version, with some relatively minor further tweaks, appeared in 1726. But we shall describe all of the comet work together, rather than scattering it piecemeal through the rest of our book. The calculus technique was essential for calculating the orbits of comets accurately, because of the need to extrapolate from the relatively few observations that could be made while the comet was near to the Sun, and bright enough to be visible. The key question that Halley set out to answer was whether any comets are on elliptical orbits, which might take them far out from the Sun, but which were closed, so that those comets would eventually (and predictably) return to the inner part of the Solar System. Such orbits are much more elongated versions of the orbits of the planets, which, although elliptical, are nearly circular. The main alternative was that comets might follow parabolic orbits. These are open, in the sense that a comet in such an orbit falls towards the Sun from the depths of space, swings round the Sun, and disappears off into the void, never to return. There was also the possibility that they might follow hyperbolic orbits, which are also open and from our point of view can be regarded as extreme parabolas. One of the spin-offs from Newton’s proof of the relationship between orbits and the inverse square law was that it showed that these kinds of orbits are also allowed by the same inverse square law. This confirmed Hooke’s suggestion that comets are ordinary members of the Solar System, subject to the same laws as the planets, and opened up the possibility of predicting their orbits.fn5 The problem was that in the parts of these orbits close to the Sun, where comets are visible, all three kinds of orbit follow very similar paths, and look very similar. You would need very accurate observations and very detailed calculations to distinguish one kind of orbit from another. That was (just) what Halley had, although in the Principia Newton himself had concluded that cometary orbits were parabolic.

  One reason for Halley’s success was that he went back over the historical records and used every scrap of information he could lay his hands on, as well as the more or less contemporary seventeenth-century records from people such as Hevelius and Flamsteed, and his own observations. He was lucky to have so much data: compared with twentieth-century observations, and the twenty-first century so far, an unusually large number of bright comets had been visible in the sixteenth and seventeenth centuries. Halley had enough observations to compute the orbits of twenty-four comets, each one, as he put it, an ‘immense labour’. And two of the sets of calculations had to be redone when he found that some adjustments were necessary. One of these was for the comet of 1682, now known as Halley’s Comet. Halley suspected that this was the same as a comet that had appeared in 1531 and one seen in 1607. If that were the case, it must be following an elliptical orbit. But when he first calculated the orbit, it came out as a parabola. He needed more data, and the way he got it shows something of the scientific politics of the time.

  Flamsteed had made detailed observations of the comet, which were just what Halley needed, but which, characteristically, Flamsteed had not published. Flamsteed was not speaking to Halley, and there was no chance of getting the data directly from him. So Halley was forced to write to Newton:

  I must entreat you to procure for me of Mr Flamsteed what he has observed of the Comett of 1682 particularly in the month of September, for I am more and more confirmed that we have seen that Comett now three times, since ye Yeare 1531, he will not deny it you, though I know he will me.

  Newton got the observations from Flamsteed, and passed them on to Halley, who re-computed the orbit and found that it was indeed elliptical, with a period of about seventy-six years. That made it possible, in principle, to predict exactly where the comet would appear on its next return. But it wouldn’t be easy.

  In order to predict exactly where on the sky the comet would reappear, Halley needed to calculate the gravitational influence of the giant planets Jupiter and Saturn on the comet when it passed through the outer Solar System, following Hooke’s insight that all astronomical objects exert a gravitational influence. Even Halley needed help with this. He wrote to Newton:

  I must entreat you to consider how far a Comets motion may be disturbed by the Centers of Saturn and Jupiter, particularly in its ascent [return] from the Sun, and what difference they may cause in the time of the Revolution of the Comett in its so very Elliptick Orb.

  Newton replied to the effect that the perturbing influences of the planets on a comet could not be calculated without a lot more information about the particular orbit. Neither Newton nor Halley ever worked out a satisfactory way to deal with the perturbation problem. Even with that aid, he would have had to work out where Jupiter and Saturn would be at the relevant time to get an approximate indication of their distance. Finally, having adjusted the orbital calculation for the comet accordingly, he would have had to work out where the Earth would be in its orbit at the appropriate time, so that he could tell astronomers on Earth where to point their telescopes to catch an early sight of the comet. It was left for Halley’s successorsfn6 to predict, building on his work, not just that the comet of 1682 (and 1607 and 1531) would reappear in 1758, but that it would first be seen in a particular part of the sky around Christmas 1758. We shall return to this famous prediction, and its consequences, in Chapter Eleven. But now it is time to look at some of the distractions that kept Halley occupied and largely away from astronomy between 1696 and 1703.

  Just a year after his letter to Newton claiming to be ‘ready at the finding a Cometts orb’, on 21 Oct
ober 1696 Halley informed Newton that:

  I have almost finished the Comet of 1682 and the next you shall know whether that of 1607 were not the same, which I see more and more reason to suspect.

  Around the same time, in an undated letter, he wrote:

  I will waite on you at your lodgings to morrow morning to discourse the other matter of serving you as your Deputy.

  Newton was by now, of course, Warden of the Royal Mint, and living in London. The post of ‘Deputy’, which Halley refers to, was an invitation, which he accepted, to take charge of the recoinage that Newton was overseeing at one of the regional mints, at Chester. It was not to prove a happy experience.

  The recoinage was necessary because the practice of ‘clipping’ silver coins – snipping off small pieces to melt down and turn into forged currency – had become so widespread that the value of the currency was sliding and inflation was setting in. The solution was to call in all the old silver coins and replace them with new coins with milled edges that could not be clipped without this being obvious. The Chancellor of the Exchequer at the time was Charles Montagu (later the Earl of Halifax), a Fellow of the Royal Society and a friend of Newton, which explains Newton’s appointment to the Mint in 1696. Halley was not actually Newton’s deputy in Chester, although he was appointed at Newton’s suggestion. In fact, he was Deputy Comptroller there, the Comptroller being one William Molyneux, who was responsible to the government.

  Newton must have thought he was doing Halley a favour by finding the post for him, perhaps as a mark of gratitude for his work on the Principia, but it is not clear what the reason was, nor why Halley accepted the offer. One possibility is that it was a way to raise Halley’s profile as a public servant and gain favour with the King, but this seems unlikely given Halley’s already high reputation. Another suggestion is that Halley was temporarily short of money, and needed the income, which was £90 a year. In 1693, English and Dutch merchants had suffered a large financial loss when a fleet of ships was intercepted by the French off Lagos, in the south of Portugal. This became known as the Lagos disaster. Speculators who had invested in cargoes carried by the ships lost everything. Halley, who had contacts among those traders, seems to have been one of the investors; Hooke’s diary entry for 24 July 1693 tells us ‘2 East India ships said to be taken by French in India. Hot, clear. Hallys trade taken by French.’ The presence of the weather report in between the other two sentences suggests that Hooke is referring to two separate incidents, and that Halley’s loss was not related to the ships taken by the French in India, but to the Lagos disaster, news of which reached London on 24 July. Or maybe (unlikely, in view of his meticulous record-keeping), Hooke confused two separate events. But would Halley have still been in financial need three years later? Surely he would have sought an income sooner if he had been badly hit by the Lagos disaster. We shall never know, but for whatever reason, Halley did take up the appointment, and managed to carry out his duties as Clerk at the same time.