Finding Longitude Read online

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  What is longitude?

  Latitude and longitude are the coordinates normally used to specify locations on Earth. The system was already established by the second century BC in the cartographic work of Hipparchus of Nicaea and enshrined by the second century AD in Ptolemy’s Geographia, which described the mathematical concepts of a grid for mapping the world.

  Latitude is the distance north or south of the Equator, measured as an angle from the centre of the Earth, and runs from 0° at the Equator to 90° at the North and South Poles. Each degree of latitude corresponds to roughly sixty nautical miles (111 km) on the Earth’s surface. Lines of latitude run parallel to the Equator.

  Longitude is the distance east or west, also measured as an angle from the Earth’s centre. Lines of longitude, called meridians, run between the poles, where they converge. So, 1° of longitude on the Earth’s surface is almost the same length as 1° of latitude at the Equator but diminishes to nothing at the poles. By convention, longitude is now measured from the Greenwich Meridian, and runs from 0° through Greenwich to 180° east and west on the other side of the globe. Until there was international agreement on this, whoever was measuring longitudes could choose any meridian or reference point they wished: Ptolemy, for example, used the island of Ferro (El Hierro) in the Canary Islands, as does the chart in Fig. 1, but London, Paris and many other places were used on different charts. Since it was difficult to measure with certainty, before the eighteenth century many charts did not show lines of longitude.

  When plotting geographical positions, latitude and longitude are divided into degrees (°), minutes (') and seconds (″), with sixty minutes in a degree, and sixty seconds in a minute. The Empire State Building in New York, for example, lies at a latitude of about forty degrees, forty-four minutes and fifty-four seconds north of the Equator and at a longitude of about seventy-three degrees, fifty-nine minutes and ten seconds west of Greenwich. Its position is written as 40° 44' 54″ N, 73° 59' 10″ W.

  Fig. 4 – Longitude lines are imaginary lines on the Earth’s surface that run from pole to pole around the globe and give the distance east or west from the Prime Meridian

  {CollinsBartholomew Ltd 2014}

  Fig. 5 – Latitude lines are imaginary lines on the Earth’s surface. They run east and west around the globe and give the distance north or south of the Equator

  {CollinsBartholomew Ltd 2014}

  Latitude relates to a definable reference (the Equator) and can be determined from the position of heavenly bodies such as the Sun or the Pole Star, but longitude is more difficult to determine because there are no natural references from which to measure. Since longitude is a distance in the direction of the Earth’s daily rotation, the longitude difference between two places can be thought of as being directly related to the difference between their local times as defined by the Sun’s position, local noon occurring when the Sun is highest in the sky. The Earth rotates through 360° in twenty-four hours, so one hour of time difference is equivalent to 15° of longitude; or, put another way, the Earth turns through 1° of longitude every four minutes.

  Most longitude schemes were based on this principle and relied on an observer determining the time both where they were and, simultaneously, at a reference point with a known geographical position. The difficult part was knowing what time it was at the reference location. It was the same problem whether on land or sea, although a ship’s movements made any observations much more difficult. Also, for marine navigation, the determination of longitude should not take so long that it became pointless, and any observations had to be possible on most days; that is, they could not be based on infrequent celestial phenomena.

  There is another important issue related to this; as John Flamsteed (1646–1719), the first Astronomer Royal at Greenwich, noted in 1697, ‘Tis in vain to talk of the Use of finding the Longitude at Sea, except you know the true Longitude and Latitude of the Port for which you are designed.’4 In other words, navigators had to know exactly where their destination was and needed accurate charts on which to plot their position. So the story of finding longitude at sea is bound up with those of determining longitude on land and of creating better charts and maps.

  Fig. 6 – For places separated by 30° of longitude, the local time is two hours different – two hours later towards the east and two hours earlier towards the west. For places separated by 45° of longitude, the local times are three hours different

  {CollinsBartholomew Ltd 2014}

  Instructed ships shall sail to quick Commerce;

  By which remotest regions are alli’d:

  Which makes one City of the Universe,

  Where some may gain, and all may be suppli’d.5

  Instruction, a footnote explained, was to be by ‘a more exact knowledge of Longitudes’.

  Though highlighted by Dryden and others, determining longitude was just one of many maritime problems for which solutions had long been sought. Seamen’s health, including the control of scurvy, ensuring supplies of fresh water, understanding weather patterns, and building ships that were seaworthy, fast and, in the case of trading vessels, able to hold as much cargo as possible, would also tax the minds of seafarers, artisans and men of science for centuries to come. Yet it was longitude that would attract government attention.

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  The practice of navigation

  Mariners were plying the oceans for centuries before the longitude ‘problem’ was solved. Many voyages were over relatively short distances and along familiar routes, often reasonably close to land, where being able to plot one’s position with precision would have counted for little, but longer voyages often passed without incident too. This was because there were well-developed techniques for navigating a ship successfully that worked right across the globe.

  Essentially, a mariner needed to know which way their ship was heading and how fast, where it had come from, where they were intending to go, how the sea and weather might affect them, and whether any hazards lay ahead. Tracking the ship’s movements was the key and relied on the chip-log (or ship-log) for measuring speed in knots, and the magnetic compass for direction (Fig. 7). Throughout the voyage, the officers supervised regular observations of speed and direction, noting them down and later transferring the information to a written log (Fig. 8), together with wind direction and other remarks.

  This information was used to fix the current position of the ship by plotting its direction and distance travelled from one point to the next – a procedure known as ‘dead reckoning’. By applying the latest measurements to the previous day’s position, and adjusting for the effects of wind and currents, the ship’s navigator could plot the new position on the chart and note it in the written log. This was fairly straightforward over short distances. Over much longer distances, printed tables were used to convert the ship’s various diagonal courses into changes of position north–south and east–west.

  Latitude could be measured directly from the maximum height of the Sun or the Pole Star above the horizon. A range of instruments for these observations had been devised over the centuries, with those in use by the late seventeenth century including the cross-staff (see Chapter 2, Fig. 14) and, particularly among English sailors, the backstaff (Fig. 9). Each measured an angle between the celestial body (usually the Sun) and the horizon, from which latitude could be derived with a few simple calculations. Until the perfection of techniques described in later chapters, however, longitude could only be derived from dead reckoning, which was indispensable on long-distance voyages. On days when the weather allowed an astronomical observation for latitude, the difference between that and the latitude calculated by dead reckoning could be used to adjust the longitude estimate, hopefully improving its accuracy.

  Constant vigilance was also essential – ‘the best navigator is the best looker-out’, Samuel Pepys noted.6 This included watching for additional clues to check the ship’s position, in particular when relatively close to the coast. Natura
l and man-made features, such as a headland, a church tower or a deliberately placed marker, were obvious signposts. As they headed ‘north up the Yorkshire coast’, for instance, Whitby sailors recalled that:

  When Flamborough we pass by

  Filey Brigg we mayn’t come nigh

  Scarborough Castle lies out to sea,

  Whitby three points northerly.7

  This local knowledge was also written down or published in books known as pilots or rutters (from the French routiers), which included descriptions and sketches of distinctive coastal features. When land was out of sight, birds, marine animals and plants could reveal its proximity and direction. On a voyage to Philadelphia in 1726, Benjamin Franklin was reassured that they would soon arrive, having seen

  Fig. 7 – A mariner’s compass made by Jonathan Eade in London, c.1750. The compass is mounted on gimbals to keep it steady on a moving ship. North is indicated by a fleur-de-lys

  {National Maritime Museum, Greenwich, London}

  Fig. 8 – A page from the log of the Orford by Lieutenant Lochard, October 1707, showing the observations and results of calculations for latitude and longitude. There is also a column for general comments (detail)

  {National Maritime Museum, Greenwich, London}

  Fig. 9 – A backstaff, used to measure the angle between the Sun and the horizon; made of lignum vitae and boxwood by Will Garner, London, 1734

  {National Maritime Museum, Greenwich, London}

  Fig. 10 – A seaman with a lead and line (right), from The Great and Newly Enlarged Sea Atlas or Waterworld, by Johannes van Keulen (Amsterdam, 1682) (detail)

  {National Maritime Museum, Greenwich, London}

  Fig. 11 – ‘The Islands of Scilly’, from Great Britain’s Coasting Pilot, by Greenvile Collins (London, 1693). The lighthouse on St Agnis (St Agnes) was nine miles out of position (detail)

  {National Maritime Museum, Greenwich, London}

  Fig. 12 – The Indian Ocean, from The Great and Newly Enlarged Sea Atlas (Amsterdam, 1682), showing Europeans’ incomplete knowledge of the coastline of Hollandia Nova (Australia) (detail)

  {National Maritime Museum, Greenwich, London}

  Fig. 13 – Navigation instruments used in the late seventeenth century, from Practical Navigation, by John Seller (London, 1672) (detail)

  {National Maritime Museum, Greenwich, London}

  [an] abundance of grampuses, which are seldom far from land; but towards evening we had a more evident token, to wit, a little tired bird, something like a lark, came on board us, who certainly is an American, and ’tis likely was ashore this day.8

  The lead and line (Fig. 10) – a lead weight attached to a long rope that was dropped at regular intervals to check the depth and nature of the seabed – gave further help. North Sea sailors, for example, boasted that they could tell west from east from the pebbles that came up with the lead (which had a hollow base ‘armed’ with tallow to pick up seabed samples): those in the west could be broken between one’s teeth.

  Lead, log and lookout worked well for coastal and short journeys, but might not be sufficient for longer ones. As European navigators embarked on increasingly ambitious voyages, often spending months in water too deep for sounding, they began to look to other methods for fixing their position. Being able to fix latitude and longitude with some degree of accuracy became more important.

  One consequence of being unable to measure longitude directly was that seamen sensibly chose quite conservative routes. For example, if a ship set out on what the officers believed to be a direct course to its destination, there was the real danger that they would arrive at the correct latitude but find they had missed the destination. Unfortunately, they would not know whether they had sailed too far to the east or too far to the west, and so would not know which way to turn. The usual practice became to aim well to the east or west at the outset. Once the ship reached the latitude of their destination, they would ‘run down the latitude’ on a westerly or easterly heading, confident that landfall lay ahead. The buccaneer and explorer William Dampier (1651–1715) recorded using this method of latitude sailing on the Batchelor’s Delight in 1684:

  we steered away N.W. by N. intending to run into the latitude of the Isles Gallapagos, and steer off West, because we did not know the certain distance, and therefore could not shape a direct Course to them. When we came within 40 minutes of the Equator we steer’d West ...9

  It was a longer journey but they arrived safely a couple of weeks later.

  On some routes, latitude sailing was a matter of safety. Approaching the south-west coast of India from the Cape of Good Hope, for example, trading vessels needed to avoid the dangerous waters near the Maldives and the Laccadive Islands (Lakshadweep). The recommended course was to keep west to a latitude of 8° or 9° North, where there were safe channels running east to the Indian coast. Ironically, the predictability of latitude sailing made it dangerous in wartime, when enemy ships simply waited at the appropriate latitude for victims to sail to them, a tactic employed by French privateers off the Windward Islands of the Caribbean.

  Mariners’ knowledge and skills, and the quality of their instruments, were crucial for effective navigation, as was the accuracy of charts and geographical data in printed manuals. However, these could be in error, even for areas close to home. Greenvile Collins’s 1693 chart of the Isles of Scilly from his Great Britain’s Coasting Pilot (Fig. 11), for example, placed the St Agnes lighthouse nine miles out of position, while the Philosophical Transactions, the Royal Society of London’s journal, warned in 1700 that the information normally issued for ships heading into the English Channel was dangerously misleading. In less familiar waters, charts were likely to be even more unreliable or incomplete: it would not be until the nineteenth century that Australia’s coastline would be fully drawn on European charts (Fig. 12).

  Nonetheless, mariners had a set of methods that brought together centuries of accumulated seafaring knowledge with instruments and techniques that could be used to fix a ship’s position and course, and navigate it safely from A to B and back again (Fig. 13). The staple was dead reckoning, the only routine method of determining longitude until the end of the eighteenth century, and the dominant one long after that. It was straightforward, used a relatively inexpensive suite of instruments and worked well enough in most situations.

  Early attempts to measure longitude

  While most mariners could not determine their longitude at sea with the tools normally available, there were occasional attempts to do so, since the theories were sound. The most obvious approach was to use eclipses, which were predictable and simultaneously visible from different locations. By comparing the local time of the eclipse on a ship with the predicted time at a specific place, noted in astronomical tables such as Regiomontanus’ Ephemerides or Zacuto’s Almanach Perpetuum, a mariner could work out the longitude difference from that place.

  Eclipses had long been used for observations on land, including an ambitious project of the 1570s and 1580s to fix the positions of different parts of the Spanish empire and improve the maps and charts held secretly by the Council of the Indies, the governing body for the Spanish colonies in America. The scheme relied on local officials building a simple moondial and marking the position of the Moon’s shadow on the dial when the eclipse began and when it ended. They then copied the marks onto paper and sent them with details of the length of the Sun’s shadow at noon back to Spain for analysis. It was perfect for keeping sensitive cartographic information secret but the data was fiendishly complex to process and was riddled with error. A more successful project was Philipp Eckebrecht’s world map of 1630, which used lunar eclipse data to plot many of the locations and was the first to equate one hour of time, astronomically determined, to 15° of longitude.

  Fig. 14 – Two English ships wrecked in a storm on a rocky coast, by Willem van de Velde the Younger, c.1700

  {National Maritime Museum, Greenwich, London}

  Eclipses could not provide a
routine solution at sea, however, since they occur infrequently, although they could be tried out occasionally. Christopher Columbus made observations twice in the Caribbean, in 1494 and again in 1503, although his results were not impressive in terms of accuracy. That said, his observations were more in the way of experiments and were taken at anchor, rather than as part of routine navigation at sea, for which he used dead reckoning. Nonetheless, he did believe that ‘with the perfecting of instruments and the equipment of vessels, those who are to traffic and trade with the discovered islands will have better knowledge’.10

  Alternatively, eclipse observations from a ship could be compared with observations taken at another location, but only when the results could be brought together at a later date. On 29 October 1631, a Welsh explorer, Thomas James, viewed a lunar eclipse from Charlton Island in what is now Nunavut, Canada, during a voyage in search of the North-West Passage. Meanwhile, the mathematician Henry Gellibrand observed it at Gresham College, London, and was later able to calculate the longitude difference from James’s figures as 79° 30' (a modern reckoning would place James’s position as 79° 45' west of Gresham College). Gellibrand considered this an impressive result that augured well for future advances in the art of navigation.