Sextant Read online

  As this diagram makes clear, the height of Polaris above the northern horizon is equivalent to the observer’s latitude. Thus if Polaris is vertically overhead, you must be at the geographical North Pole, while if it appears right on the horizon you must be on the equator. In this diagram, its height above the horizon is 50 degrees and it follows that you must be 50 degrees north of the equator—in other words your latitude is 50 degrees North.*

  So vital was Polaris to the seafarer that the English simply called it “the Star,” and Shakespeare knew enough to press it into service in Sonnet 116:

  Let me not to the marriage of true minds

  Admit impediments. Love is not love

  Which alters when it alteration finds,

  Or bends with the remover to remove:

  O, no! it is an ever-fixèd mark,

  That looks on tempests and is never shaken;

  It is the star to every wandering bark,

  Whose worth’s unknown, although his height be taken. . . .*

  In medieval Latin, Polaris was Stella Maris—“star of the sea”—a term that was applied also to the Virgin Mary, whose sky-blue cloak is emblazoned with a star in many early European paintings. The theologian Alexander Neckham (1157–1217) likened Mary to the Pole Star standing at “the fixed hinge of the turning sky” and by which the sailor at night directs his course. Polaris must have seemed a perfect symbol of the Mother of God, the immaculate spiritual guide and intercessor. The name Stella Maris was sometimes also applied to the ship’s steering compass on which the thirty-two “points” are still often marked in the form of a star.7 Even today Stella Maris is a common name for fishing boats and “true north”—solidly reliable, unlike its variable magnetic cousin—was marked on old charts with a star. (True north marks the direction of the geographical north pole, which is fixed,* whereas the magnetic north pole—like its southern counterpart—wanders and is at present several hundred miles distant from it.)

  BEFORE THE END of the thirteenth century, the Venetian explorer Marco Polo recorded that he had measured the altitude of Polaris on the coast of India, though how he did so is unclear. The earliest references to the measurement of the height of Polaris by Portuguese navigators date from the mid-fifteenth century, but it seems unlikely that they were using purpose-built instruments to make their observations.8In theory they could have used the astronomer’s astrolabe, an elaborate device that permitted the observer to find the time of day, as well as solving other astronomical problems. It had by then achieved a high level of sophistication but it is doubtful that many ordinary sailors would have known how to operate one, and such a complicated and costly instrument would not have been required merely for the purpose of measuring the altitudes of heavenly bodies.

  A radically simplified version, known as the mariner’s astrolabe, was, however, widely adopted for use at sea during the sixteenth century,9 by which time solar declination tables were available. It was a metal disc or hollow circle with a scale of degrees engraved on its circumference. While it was suspended from its ring, the navigator would adjust the “alidade” (a revolving bar with peephole sights) so that it was aligned either with the sun or with Polaris and its height could then be read off from the scale. The motion of the ship, however, and the effects of the wind limited the usefulness of any instrument that had to be freely suspended, and it would have been much easier to obtain accurate readings from it on dry land.

  The Portuguese poet Luís Vaz de Camões (c. 1524–80), who sailed out to India in 1553, witnessed the use of an astrolabe at first hand—though it is not clear which kind—after his ship anchored off the west African coast. In his great epic The Lusiads (first published in 1572), he describes the scene:

  Like clouds, the mountains we spied

  Began to reveal themselves;

  The heavy anchors were readied;

  Now arrived, we took in the sails.

  And so that we would better know

  Where we were in these remote parts,

  Using that new instrument, the astrolabe,

  An invention of subtle skill and wisdom.

  We then landed on an open shore

  Where the crew scattered, wishing

  To see strange things in the land

  Where no other people had trod.

  But I, with the pilots, on the sandy beach

  To find out where I was,

  Remained to take the height of the sun

  And measure the painted universe.

  We reckoned that we had already passed

  The great circle of the Tropic of Capricorn

  Being between it and the frozen southern

  Circle, the most secret part of the world. . . .10

  The seaman’s quadrant, an even simpler device that was probably in use at a much earlier date than the mariner’s astrolabe, relied on a plumb-line, so it too would have been of limited utility on the open sea. Later developments included the cross-staff (first mentioned in 1545)11 and the more sophisticated back-staff (invented by the English navigator John Davis in the late sixteenth century). These were much more practical than the astrolabe and quadrant, but they were hardly precision instruments. In the latter part of the seventeenth century, as the scientific revolution fast gathered momentum, astronomers started to explore ways in which more accurate sights could be obtained from the moving deck of a ship. It was from this process that the sextant eventually emerged.

  Fig 4: Back-staff (left) and cross-staff (right).

  Fig 5: Diagram of a sextant, showing the double-reflection principle.

  Fig 6: Hadley’s reflecting quadrant.

  The sextant employs the principle of double reflection to enable the user simultaneously to observe the horizon and a chosen heavenly body, and to measure the angular distance between them with great accuracy. Its key virtue is that it marries the two in a single, steady image that is completely unaffected by the movement of the observer (or the deck on which he or she is standing) so long as the instrument is kept pointing in the right direction. The sextant is also versatile. Unlike the astrolabe or quadrant it can be used for measuring angles in any plane—for example, between two heavenly bodies, or between two objects on the surface of the earth.

  The sextant was the offspring of an earlier invention, the so-called reflecting quadrant. Sir Isaac Newton can take credit for designing the first device of this kind, plans for which were shown to the Royal Society in 1699.12 Another Fellow of the Royal Society, John Hadley (1682–1744), came up with two designs, similar to Newton’s though apparently not derived from them, which he presented to that institution in May 1731.13 One of these was widely adopted following successful sea trials conducted the following year by the Oxford professor of astronomy John Bradley, who was later to become Astronomer Royal.14 By one of those strange coincidences that seem common in the history of science, an American—Thomas Godfrey—independently came up with a similar design almost simultaneously.15

  Confusingly, the reflecting quadrant is actually an octant—its arc is one-eighth of a circle (45 degrees) rather than one-quarter. It is capable of measuring angles up to 90 degrees, thanks to the double-reflection principle. The invention of “Hadley’s quadrant” marked a revolution in the history of marine navigation. For the first time, it was possible to measure the altitudes of heavenly bodies from the moving deck of a ship at sea with great precision—in fact, with the help of a vernier scale, quadrants permitted readings to the nearest minute of arc (one-sixtieth of a degree).16 Its larger cousin, the sextant, which was later to become the instrument of choice for accurate offshore navigation, could measure angles up to 120 degrees. Both the quadrant and the sextant were far superior to any instruments previously available for measuring angles at sea, in terms of both precision and ease of use. The sextant’s original design was so perfect that it has to this day remained essentially unchanged, and with its introduction the solution of the greatest problem of celestial navigation—the accurate determination of longitude at s
ea—at last became a practical possibility.

  HAVING LEARNED HOW to do a mer alt, I could, in theory, have found my way home to England simply by following the right parallel of latitude: 49°30' North brings you nicely into the English Channel—halfway between Ushant and Scilly.* Mariners relied entirely on “latitude sailing” of this kind for hundreds of years before the longitude problem was solved, but it is subject to one potentially disastrous drawback: unless you know how far east or west you have travelled, and the coordinates of your destination, you cannot be sure when you are going to arrive. Latitude sailing also suffers the disadvantage that the shortest distance between two points on the surface of a sphere is a “Great Circle” (a circle whose center coincides with the center of the earth), not a parallel of latitude.* The difference can be significant if the voyage is a long one.

  You might suppose that it would be a simple matter for the sailor to work out his position in mid-ocean just by measuring the distance he has travelled on a particular course. This is known as “dead reckoning” (DR), a term that could well have been chosen by someone with a black sense of humor, though it is actually said to derive from “deduced reckoning.” Even today, when it is possible to measure speed and distance travelled through the water with great accuracy, DR is an imprecise science. Many factors affect a vessel’s rate of progress “over the ground” (that is, relative to the seabed), some of which are very hard to assess. Ocean currents are one example. These can be strong, but they are fickle, seldom running steadily in one direction or with a constant strength. Steering an accurate course is also much trickier than the landsman might suppose: it is nothing like driving a car down a road. Leaving aside human error, and the tendency of sailing vessels to “sag” (drifting sideways—or making “leeway”—when heading to windward, or “close-hauled”), the magnetic compass itself is subject to large errors—which were not well understood until the nineteenth century. Unless correct allowances are made for all these effects, the navigator will soon be lost. DR is, in practice, highly unreliable and especially so over long distances because the errors tend to accumulate—as Álvaro de Mendaña’s experiences in the sixteenth century vividly showed.

  There is an extraordinary passage in Moby-Dick where Herman Melville contrasts the reliability of celestial navigation with the uncertainties of DR in order to dramatize Captain Ahab’s descent into madness. Consumed by hatred for the white whale that has cost him his leg, Ahab takes his last mer alt seated in the bows of one of the open whaleboats in which he hopes to hunt it down.

  At length the desired observation was taken; and with his pencil upon his ivory leg, Ahab soon calculated what his latitude must be at that precise instant. Then falling into a moment’s revery, he again looked up towards the sun and murmured to himself: “Thou sea-mark! Thou high and mighty Pilot! Thou tellest me truly where I am—but canst thou cast the least hint where I shall be? Or canst thou tell where some other thing besides me is this moment living? Where is Moby Dick?”

  Ahab gazes thoughtfully at the quadrant, handling its “numerous cabalistical contrivances” one after another, and then mutters:

  “Foolish toy! babies’ plaything of haughty Admirals, and Commodores, and Captains: the world brags of thee, of thy cunning and might; but what after all canst thou do, but tell the poor, pitiful point, where thou happenest to be on this wide planet, and the hand that holds thee: no! not one jot more! Thou canst not tell where one drop of water or one grain of sand will be to-morrow noon: and yet with thy impotence thou insultest the sun! Science! Curse thee, thou vain toy. . . . Curse thee, thou quadrant!”

  To the astonishment of his crew, Ahab then dashes the instrument to the deck:

  “no longer will I guide my earthly way by thee: the level ship’s compass, and the level dead-reckoning, by log and by line: these shall conduct me, and show my place on the sea. Aye,” lighting from the boat to the deck, “thus I trample on thee, thou paltry thing that feebly pointest on high; thus I split and destroy thee!”17

  Chapter 4

  Bligh’s Boat Journey

  Day 5: Took the 0400 watch again. Another brilliant day with southerly force 2–3 wind, occasionally 4. Scarcely any cloud except on the southern horizon, where there always seems to be a patch of cumulus.

  After breakfast we checked our DR, which puts us somewhere near the Tail of the Bank. I did another mer alt and Colin plotted our exact position using an earlier timed sun sight*—latitude 42°42' N, longitude 52°13' W. Still on a course of 120° at about 5 knots.

  Over supper I mentioned how I had first heard of the sextant when I saw Mutiny on the Bounty. This triggered a string of reminiscences from Colin, who recalled the mutiny that broke out in 1931 at Invergordon in Scotland aboard some of the Royal Navy’s greatest ships—including the famous battle cruiser HMS Hood. Pay cuts were blamed at the time, but low morale on the big ships was the main factor, he thought. The smaller, more tightly knit crews of destroyers and frigates had experienced fewer problems. I asked what he thought of Bligh. Colin did not think the film had painted a fair portrait of him: Bligh had been a great seaman and navigator and, like Cook, had risen from the ranks. Maybe his explosive temper reflected some kind of social insecurity. Colin also objected that, since Bligh was in his mid-thirties when he commanded the Bounty, Trevor Howard had been far too old to play him.

  Colin was right about Bligh’s skills as a navigator. Bligh had sailed with Cook as master of the Resolution, a post to which he was appointed at the unusually early age of twenty-one. He seems to have enjoyed Cook’s approval; he certainly demonstrated great skill as a surveyor and draftsman. But he was a difficult man. J. C. Beaglehole, in his magisterial life of Cook, says that he “saw fools about him too easily,” and that even at this early stage in his career he displayed “the thin-skinned vanity” that was always to be his curse: “Bligh learnt a good deal from Cook: he never learnt that you do not make friends of men by insulting them.”1

  Bligh was actually involved in not one but three mutinies. These tempestuous events did not stop him reaching the rank of vice admiral,* but they have overshadowed his substantial achievements. Of these the most remarkable was his voyage in an overloaded twenty-three-foot open boat after being set adrift by the Bounty mutineers in the Tonga Islands. The mutineers, led by the master’s mate, Fletcher Christian, comprised more than half the Bounty’s crew, and they were—in Bligh’s words—“the most able men of the ship’s company.”2 Bligh later speculated that the temptations of Tahiti were the main cause of the mutiny. The crew had just spent twenty-three lazy weeks there while the gardener prepared the breadfruit seedlings for transplantation to the West Indies, and discipline had inevitably suffered.

  Bligh was not surprised that “a set of sailors, most of them void of connections,” should wish to “fix themselves in the midst of plenty on one of the finest islands of the world, where they need not labour, and where the allurements of dissipation are beyond anything that can be conceived.” However, he claimed to be aware of no discontent and bitterly complained that he had thought himself to be on the friendliest terms with Christian. So he felt not only shock but also a personal sense of betrayal when, just before sunrise on April 28, 1789, Christian, accompanied by three other men, came into Bligh’s cabin, tied his hands behind his back, and threatened him “with instant death” if he made the least noise. While Christian held a bayonet to his throat, the members of the crew who had refused to join the mutiny were put over the ship’s side into the launch. The captain’s clerk tried to save Bligh’s surveys and drawings, but was forbidden to do so. Nor was Bligh allowed to take the chronometer or any charts. At last he himself was forced to board the open boat, which was promptly cast adrift. Equipped only with a sextant and compass,3 and very limited supplies of bread, pork, water, rum, and wine, Bligh now faced the almost overwhelming challenge of bringing to safety the eighteen men who accompanied him.4

  Bligh decided first to lay in a supply of breadfruit and water at the
nearby island of Tofoa (now Tofua), but this plan went badly wrong. They were able to obtain very little in the way of provisions, and the natives—some of whom recalled Bligh from his visit to the Tongan archipelago with Cook fifteen years earlier—turned hostile when they realized the sailors were poorly armed and quite alone. Eventually they gathered on the beach, menacingly knocking stones together, and Bligh—who had witnessed Cook’s death—saw that an attack was imminent. He ordered all his men to get aboard the boat as quickly as possible, but stones began to fly and a member of the crew who had run back up the beach to cast off was clubbed to death. Bligh cut the painter and they escaped, under a barrage of well-aimed missiles, leaving their unfortunate comrade behind.

  Despite the desperate shortage of supplies, Bligh and his companions decided not to risk landing on any of the neighboring islands. Instead they headed west for Timor, in the Dutch East Indies, some 3,600 nautical miles away, as it was the nearest place where they could be sure to find help—and report the mutiny. To give some sense of the scale of this voyage, that is roughly the distance from Land’s End to the northeast coast of Brazil.

  Shortly after leaving Tofua they were caught in a heavy gale:

  The sea ran very high, so that between the seas the sail was becalmed, and when on the top of the sea it was too much to have set: but we could not venture to take in the sail for we were in very imminent danger and distress, the sea curling over the stern of the boat, which obliged us to bail with all our might. A situation more distressing has perhaps seldom been experienced.5

  Everything now depended on Bligh’s exceptional navigational skills and remarkable memory. Taking observations with the sextant to determine their latitude—a difficult feat in an overcrowded boat often tossed about in heavy seas—while keeping track of their westerly progress with the help of a makeshift log-line,6 * Bligh sailed toward the Great Barrier Reef, setting their course in accordance with his apparently detailed recollection of the charts he had been forced to leave behind. The food and water now had to be very strictly rationed. Such was Bligh’s devotion to duty that, even in these desperate circumstances, he continued to keep careful notes of the islands they passed—including the Fiji group, which they were the first Europeans to discover—recording their latitudes and estimating their longitudes as best he could. In addition to their growing hunger and thirst, the lack of space made life on board the boat “very miserable.” Bligh kept half the crew sitting up on watch while the other half lay down in the bottom, or on the chest in which they kept their small supply of bread: