Читать книгу Sextant: A Voyage Guided by the Stars and the Men Who Mapped the World’s Oceans - David Barrie - Страница 14

Day 7: Stayed in my bunk ’til 0745 and then sat in the sun reading Slocum while watching clouds building up – the barometer is falling and the weather is starting to break. The wind veered to W and increased to F 5 so we took down the main and ran on under genoa at 6–7 knots. Colin was still not comfortable though, so we went right down to the pocket handkerchief No. 2 stays’l which cut our speed to 4 knots.

After lunch – the usual sandwiches though the bread is getting mouldy round the edges – I went to sleep or tried to for two hours. Much rolling and rattling. It’s amazing how much the weather affects one’s mood out here. All the same, we’ve made good progress so far and today we’ve covered 144 miles, noon to noon. Our course is now 105° magnetic. Helped Colin work out our noon position: 42° 34' N, 46° 16' W.

Celestial navigation would be easy if the sun and all the other heavenly bodies stood motionless in the sky – as Polaris does, almost.^fn1 It would then be possible to fix your position by sextant sights without the need to know the time or even the date. The cosmos, however, is not that obliging. Not only does the earth rotate completely once every day, but its axis of rotation – currently inclined at roughly 23.5 degrees to the plane of its orbit around the sun – also changes gradually over a cycle of about 25,800 years.^fn2 To complicate matters further, the earth’s orbit around the sun is elliptical rather than circular, with the result that the interval between one passage of the sun over the observer’s meridian and the next is not quite constant. So not only do the heavens appear to be in motion, but that motion itself is also changeful. This is most obviously revealed by the variations in the path of the sun across the sky – which is measured by its declination to the north or south of the equator – the phenomenon that gives rise to the seasons. The behaviour of the planets and the moon is yet more complex.

The ancient Greeks and Romans, who leaned heavily on earlier Babylonian learning, had a well-developed understanding of the paths that the various heavenly bodies described, as did the Arab astronomers who followed them. They clung, however, to the view – associated with the astronomer Ptolemy (c.90–168 CE) – that the earth was at the centre of the universe, and this theory prevailed until the time of Copernicus (1473–1543).¹ Though Ptolemaic orthodoxy may have been misguided, it did not prevent astronomers producing accurate solar declination tables as far back as the end of the fifteenth century. These enabled mariners for the first time to adjust their observations of the sun to allow for the seasonal changes in its meridian altitude. Now they could determine their latitude at noon as the sun crossed their meridian, as well as after dark (from the height of Polaris), subject to the limitations of the instruments then at their disposal. Moreover, they could continue to find their latitude when south of the equator – when Polaris had disappeared below the northern horizon. This breakthrough helped the Portuguese to open up an enormously valuable trade route into the Indian Ocean round the Cape of Good Hope. Early in the sixteenth century the Portuguese also devised a rule for determining latitude by reference to the stars of the Southern Cross – which lie some distance from the south celestial pole.²

While latitude could be determined quite easily, the earth’s motions meant that the measurement of longitude was a much more difficult challenge. Early in the sixteenth century the astronomer Gemma Frisius (1508–55) realized that a promising approach to solving the longitude problem would be to find a way of measuring time accurately – whether on land or sea. An observer equipped with an accurate enough clock set to the time at a reference meridian could in principle compare the time of an event (such as sunrise or sunset) with the predicted time of the same event at a reference meridian – such as Greenwich.^fn3 The observer’s longitude could then be derived by converting the time difference in hours and minutes into a spatial displacement measured in degrees and minutes east or west – one hour being equal to 15 degrees of longitude (360 divided by 24).

It was not until the early seventeenth century that Copernican theory was firmly established on the basis of the observations of Tycho Brahe (1546–1601), Galileo Galilei (1564–1642) and Johannes Kepler (1571–1630). Galileo’s momentous discovery of the moons of Jupiter and, soon afterwards, of the changing phases of the planet Venus not only provided overwhelming evidence that the earth was not the centre of the universe but also opened the way to a proper understanding of planetary motion.³ The invention of the first pendulum clock in the 1650s by Christiaan Huygens (1629–95) also marked a great advance. It was now possible for astronomers to measure time with sufficient precision to predict with great accuracy the positions of all the major heavenly bodies day by day – though, as we shall see, there was one troublesome exception: the moon. The establishment of the two great Royal Observatories in Paris (1667) and Greenwich (1675) contributed notably to this process. These technical developments, coupled with major theoretical advances – of which the publication in 1687 of Newton’s laws of motion was the most significant – were crucial steps on the path to the eventual solution of the longitude problem.

By the end of the seventeenth century, the laborious observations of astronomers had yielded the first accurate ephemeris tables.⁴ An observer on dry land supplied with a pendulum clock could now regulate it by reference to the predicted events and thereby establish his or her longitude. French scientists were the first to apply the new technology to the making of accurate terrestrial maps and the results were sometimes surprising. In 1693 a new map of the coast of France based on an elaborate survey supervised by the astronomers Jean Picard (1620–82) and Philippe de La Hire (1640–1718) revealed that the kingdom had shrunk. The port of Brest, for example, had moved 50 miles to the east of its position on the best existing map. King Louis XIV is reputed to have complained that he had lost more territory to his astronomers than to his enemies.⁵

The French undertook much basic research – including heroic efforts to determine the precise shape of the planet, a knowledge of which was essential if maps were accurately to reflect reality. Scientists were sent all over the world in an attempt to decide whether Newton’s prediction that the earth bulged slightly around the equator was correct. If it did, the geographical length of a degree of latitude would increase as one moved away from the equator towards the poles. While one such expedition went to Finland and another to South Africa, a third, led by Louis Godin, set out in 1735 for the Andes to try to measure a degree of latitude at the equator. Godin and his team endured extraordinary hardships, first struggling through tropical jungles and then working at heights of over 16,000 feet on the freezing mountaintops, as they carefully measured baselines and extended a network of triangles along the mountain chain over a distance of some 200 miles.^fn4 Their efforts, combined with the work of the other expeditions, confirmed Newton’s prediction.⁶

The British were initially slow to learn from the French map-makers, but a growing awareness of the great military and commercial advantages conferred by good maps and charts prompted action. Murdoch Mackenzie Senior (1712–97) led the way with his pioneering marine survey of the Orkney Islands in the 1740s, based on a rigid system of triangulation using precisely measured baselines, the first of which was laid out on the frozen surface of a lake.⁷ Mackenzie’s were the first accurate British charts, and he also invented the system of symbolic abbreviations that survives to this day. His Treatise on Maritim Surveying (published in 1774) was to set the pattern for every hydrographic survey conducted over the next hundred years, and in it he listed the quadrant and sextant as essential items of the marine surveyor’s equipment. Of the sextant he had this to say:

This instrument may be used with great Advantage in Maritim surveys, on most Occasions; being more portable, more readily applied to the taking of Angles, and generally more accurately and minutely divided than Theodolites are: an Observer is less liable to make mistakes with it; and, which is a very material advantage, he can take angles with it at sea, as well as on Land.⁸

Mackenzie is also credited with the invention of the ‘station pointer’ – an invaluable instrument that enables the coastal navigator quickly to fix his position by taking horizontal sextant angles between three or more fixed points.

Not until the 1790s did the newly established Ordnance Survey follow Mackenzie’s example and begin mapping Britain by triangulation. In 1797 the intricate network of triangles was extended from Land’s End to the Scilly Isles and, to general consternation, it emerged that the position of the islands shown on contemporary charts was out by the astonishingly wide margin of 20 nautical miles.⁹ Cold comfort for poor Shovell.^fn5

*

For all the progress that was being made in mapping the land, accurate position-fixing at sea still remained an impossible dream in the early eighteenth century. In fact it was no closer to reality than it had been 150 years earlier when the Spanish, conscious of the vital commercial importance of their overseas colonies and the difficulties surrounding accurate and therefore safe navigation, began to seek a shipboard solution to the longitude problem. In 1567 King Philip II offered the first cash prize to anyone who could crack it, and in 1598 his successor, Philip III, raised the stakes: the winner would receive a one-off payment of 6,000 ducats together with an annual pension of 2,000 ducats. So important was the goal that this princely annuity was promised even to the heirs of the eventual winner.¹⁰ Other prizes were later announced by the Dutch and Venetian Republics, by France and, eventually, by Britain. Under the terms of the British Longitude Act of 1714, a sum of up to £20,000 was offered as ‘a due and sufficient Encouragement to any such Person or Persons as shall discover a proper Method of Finding the said Longitude’. This would now be worth several million pounds.

The Longitude Act, however, imposed high standards of accuracy: to win the maximum amount the successful method had to be capable of determining longitude within a margin of error not exceeding half a degree of a great circle (equivalent to 30 nautical miles). Half the maximum prize would be payable when the Commissioners of the new Board of Longitude were satisfied that the proposed method extended to ‘the Security of Ships within Eighty Geographical Miles from the Shores, which are Places of the greatest Danger’, while the balance would be paid ‘when a ship … shall actually Sail over the Ocean, from Great Britain to any such Port in the West-Indies, as those Commissioners … shall Choose or Nominate for the Experiment, without Losing their Longitude beyond the Limits before mentioned’. Moreover, the reward would be paid only ‘as soon as such method for the Discovery of the said Longitude shall have been Tried and found Practicable and Useful at Sea, within any of the degrees aforesaid’. The words ‘Practicable’ and ‘Useful’ were to give rise to bitter disputes. Lesser rewards were available for proposals that the Commissioners judged of ‘considerable Use to the Publick’.¹¹

Though pendulum clocks coupled with the new ephemeris tables permitted land-based observers to determine their longitude accurately, nobody had yet managed to devise a time-keeper that could be relied on at sea. Existing spring-driven clocks and watches were hopelessly erratic, and despite valiant attempts it proved impossible to make pendulum clocks work reliably on board ship. Strenuous efforts were therefore made to find methods of determining longitude that did not rely on astronomical observations and which could therefore be employed without the need to know the time. Mapping the geographical variations in the direction of the earth’s magnetic field seemed to offer some hope, but in the end this line of enquiry proved abortive and the heavens became the exclusive focus of scientific attention among those seeking to solve the longitude problem. If sea-going clocks were not to be relied on, then perhaps the sailor could find the time from observations of the sun, moon and stars. The challenge was to identify a frequently occurring astronomical event the precise time of which could be both accurately predicted and easily observed on board ship, anywhere in the world. Published tables of the predicted times of such events would in principle enable the navigator to find the time at a given reference meridian (such as Greenwich or Paris) wherever he happened to be – providing the skies were clear. Comparison with the local time – derived from astronomical observations – would then reveal the observer’s longitude.

Various methods of achieving this goal had already been suggested. For example, in 1616 Galileo opened discussions with Spanish officials about the possibility of using observations of the appearance and disappearance of the moons of Jupiter (the four largest of which he had recently discovered) as a means of determining the time at the reference meridian. In return for a large fee for travelling to Spain to demonstrate his method to King Philip III, an annual royalty both for himself and his heirs, as well as appointment to the chivalric Order of Santiago, he proposed to draw up the necessary tables and update them annually; he even invented a telescopic device to be worn on the head that was supposed to permit making the necessary observations at sea.¹² But the Spanish lost interest and in 1635 an ageing Galileo turned to the Dutch, this time with improved tables and a mechanical device for representing the motions of the Jovian satellites that he called the ‘Jovilab’.

The Dutch States General responded enthusiastically and even appointed an astronomer to act as a technical go-between, but Galileo – who was by now going blind – was unable to generate the orbital parameters of the moons on which sufficiently precise predictions could be based.¹³ In any case, a fairly powerful telescope was required to observe the moons of Jupiter and such an instrument could not be held steadily enough on board ship. And there was another problem lurking in the background: without an accurate shipboard time-keeper, how exactly was the navigator supposed to compare local time (derived most easily from sun sights) with the time obtained from the tiny Jovian moons – visible only after the sun had set? Galileo claimed he knew how to make a sufficiently accurate pendulum clock but he had not succeeded in doing so by the time he died, and anyway it would have been of no use at sea.¹⁴

Jupiter’s moons were, however, very useful to land-based observers equipped with pendulum clocks – once the necessary tables had been produced at the Paris Observatory. In the 1680s a French expedition established the longitude of the Cape Verde Islands, Guadeloupe and Martinique using this technique,¹⁵ and Picard and La Hire also employed it when making their map of France. Eclipses of the sun were among the other possibilities, but they were too infrequent to be of much use, and it was not until the invention of the sextant that it was possible to observe them with sufficient accuracy on board ship. Spanish navigators and astronomers had experimented with the technique in the sixteenth century, but the results, even at land-based observatories, were of no value.^fn6

So it is not surprising that when the Longitude Act was passed in 1714, few observers expected that anyone would soon succeed in claiming the big money. Many bizarre and frankly ludicrous proposals were put forward, and in consequence the quest became something of a standing joke. William Hogarth included a cheerful lunatic searching for a solution to the longitude problem in the background of the scene from the madhouse in the Rake’s Progress of 1735.

Such scepticism was misplaced. After a struggle lasting hundreds of years, two radically different solutions to the problem of finding the time on board ship emerged almost simultaneously in the 1750s – one mechanical, the other astronomical. Both, however, relied on accurate angular measurements made with a quadrant or, better still, a sextant. As we shall see, one method was based on a new kind of clock, while the other depended on the first accurate tables of the motions of the moon. In practice, however, the two techniques were to be mutually dependent for many years to come.

*

The extraordinary story of the development by John Harrison (1693–1776) of the first accurate shipboard time-keeper – and his long struggle for official recognition of his feat – is by now well known. In 1759, after more than thirty years of experimentation, he produced a highly innovative ‘watch’ (known as ‘H4’). It was not regulated by a pendulum and exploited the ingenious principles of compensation he had developed in earlier experimental devices; it was also a great deal smaller and more practical. H4 easily passed the second (and possibly also the first)¹⁶ of two rigorous sea trials – a voyage to Barbados and back in 1763. But the Longitude Board were cautious about recognizing Harrison’s remarkable technical breakthrough. Rigorously interpreting the wording of the Longitude Act they demanded to be convinced that the new watch’s exceptional performance had been more than a fluke and that the mechanism itself could be reliably replicated at an affordable price. Arguments about whether H4 and its maker had or had not satisfied the precise terms of the Act were to drag on for years. The elderly Harrison, vigorously supported by his son, William, was enraged by the apparently perverse delays in awarding him the full prize of £20,000, and by adjustments to the terms of the Act that – in his view – seemed designed to deny it to him. His tactless and explosively ill-tempered behaviour alienated many members of the Board, which had by the end of 1762 already funded his labours to the tune of £4,750 – a very substantial sum.

As guardians of public funds the Board were understandably anxious not to expose themselves to charges of waste. But their reluctance to reward Harrison in full was also influenced by the belief – which Newton had shared – that the only reliable solution to the longitude problem must be astronomical not mechanical. After all, watches could go wrong, and seemed very likely to do so in a damp and bumpy ship at sea – especially if the temperature varied a good deal, as it would on a voyage from Europe to the tropics. How would the navigator be able to tell if the watch started to misbehave? Who was going to fix it if it stopped? How could any errors be corrected?

These were perfectly fair questions, and as experience subsequently showed many chronometers did indeed perform poorly, often running irregularly or stopping altogether for no obvious reason. Even their own makers did not understand exactly what they were doing: they were artists as much as engineers, and they relied heavily on trial and error. The sun, moon and stars, by contrast, were the very embodiment of perfection – and indeed the basis of time itself. Until the invention of the ‘atomic clock’ in the mid-twentieth century, the movements of the sun and stars remained the fundamental indices of time. Harrison’s watch may well have seemed inelegant to the more mathematically minded members of the Longitude Board – a questionable, brute-force solution to a problem they regarded as essentially astronomical in nature.

Harrison’s great achievement was the invention of a radically new watch movement that could keep time accurately – not just in stable conditions on land, but also in the wildly variable environment of a ship at sea. He was certainly a difficult and irascible man, as was his son, but he was highly ingenious and extremely determined, and in 1773, following a powerful speech in the House of Commons by Edmund Burke, and a sympathetic intervention by King George III himself, Parliament (rather than the unbending Longitude Board) awarded him a further £8,750.^{17 fn7} The practical marine chronometers (as these ‘time-keepers’ were eventually to be known) that relied on Harrison’s pioneering work were not, however, mere duplicates of H4. They owed much to the inventive skills of other watchmakers like Pierre Le Roy and Ferdinand Berthoud in Paris and Larcum Kendall, John Arnold and Thomas Earnshaw in London.¹⁸

The chronometer we carried aboard Saecwen was a descendant of those developed in the last decades of the eighteenth century and probably differed little from them. It sat luxuriously in a pretty mahogany box with brassbound corners, secured by strong elastic cords in a safe corner of the cabin near the mast. Lifting the lid, a circular brass case was revealed, with a plain but elegant dial and thin, spear-shaped hands, the whole mechanism supported in a gimballed cradle that isolated it quite effectively from the motion of the boat. Colin alone undertook the delicate task of winding it, a ritual performed at the same time each day in order to maintain an even tension in the mainspring. The chronometer’s lovely, silky tick was like a breathless heartbeat. With the sextant, it was a thing of beauty.

The ‘PZX’ Triangle

The ‘PZX’ triangle is at the heart of celestial navigation and can be used to solve a variety of navigational problems.

The angle XPZ is the key to finding the ‘local time at ship’. P is the North Pole, X the ‘geographical position’ of the sun, and Z the position of the ship. The arc XA is the declination of the sun (tabulated in the Nautical Almanac); the arc ZB is the ship’s latitude (typically obtained from a ‘mer alt’). We can calculate the lengths of sides PX and PZ: PX is 90 degrees minus the sun’s declination, while PZ is 90 degrees minus the ship’s latitude. The third side, ZX, is equivalent to the ‘zenith distance’ of the sun, which is obtained by subtracting its altitude (observed with the sextant) from 90 degrees.

Using spherical trigonometry we can now derive the angle XPZ, which is the sun’s Local Hour Angle or LHA – in this case a measure of the time elapsed since the sun crossed the ship’s meridian. The time that has passed since the sun crossed the Greenwich Meridian (revealed by the chronometer) is its Greenwich Hour Angle or GHA. By subtracting the LHA from the GHA the navigator can obtain the required ‘local time’ and thereby the ship’s longitude. Similar calculations can be performed using other celestial bodies.

*

Using our chronometer (duly set to Greenwich time) I learned from Colin a rough-and-ready method of determining Saecwen’s longitude. When the weather was clear I would time the moment of sunrise or sunset and compare the results with the times of these events tabulated in the Nautical Almanac. If, for example, the disc of the sun appeared over the eastern horizon at 0600 GMT according to the chronometer while the tabulated time of the same event at Greenwich was 0400, it followed that we were two hours or 30 degrees west of Greenwich. The results I obtained were – at best – accurate to about half a degree either way. In principle the same technique could be used to obtain the longitude by comparing the local and Greenwich times of a heavenly body’s transit across our meridian.

In practice, however, it is difficult to determine the exact moment of sunrise or sunset because atmospheric refraction, which is strongest at low angles, has the effect of ‘lifting’ the sun’s disc so that it remains visible for some time after it has actually dipped below the horizon. The timing of a meridian passage at sea is also problematical as heavenly bodies pause for a significant interval at the height of their arc. One way of doing so is to take two, timed ‘equal altitude’ observations of the relevant body on either side of the meridian and to halve the time difference between them. A major drawback of this method is that clouds may obscure the crucial second sight. It also requires a reasonably accurate clock. And precision is vital: an error of just one minute in the measurement of either local or Greenwich time can result in a positional error of as much as 15 miles.

How then is the navigator to obtain an accurate longitude, even if he or she has an accurate clock? Knowing the exact time at the reference meridian by itself is no help. There has to be something with which that time can be compared. The solution lay in discovering the local time at ship from sextant observations – usually altitudes of the sun in the morning or afternoon, though other heavenly bodies could be used. Mathematicians developed a variety of techniques for achieving this objective, all of which involved solving what came to be known as the ‘PZX’ triangle – see diagram above. These methods – which, as we shall see, relied on knowing the ship’s latitude – remained at the heart of celestial navigation until the emergence of the ‘new navigation’ in the 1870s.