Sextant: A Voyage Guided by the Stars and the Men Who Mapped the World’s Oceans

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 …

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)

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.

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.

Fig 6: Hadley’s reflecting ‘quadrant’.

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.

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.

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.

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.

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).

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 sea – at last became a practical possibility.

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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 degrees 30 minutes 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 centre coincides with the centre 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 humour, though its actual origins remain mysterious. 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!’

Chapter 4 (#ulink_b6e7de6b-7fb7-562b-905f-cc56744553fb)

Bligh’s Boat Journey (#ulink_b6e7de6b-7fb7-562b-905f-cc56744553fb)

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 caused 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.