Finding Longitude: How clocks and stars helped solve the longitude problem

Nowe some there be that be very inquisitive to have a way to get the longitude, but that is to tedious.

Seafarers have always needed to know where they are to avoid danger and ensure a successful voyage. First and foremost, this was about safety, although they appreciated that more precise navigation could increase speed and efficiency. To most, this meant pinpointing the ship’s latitude and longitude on a reliable chart. Latitude was fairly straightforward to measure from a ship. Longitude was the problem and good charts could only be produced when both could be measured.

As European vessels made longer and longer voyages from the fifteenth century onwards, navigation, including the determination of longitude, began to matter more. Long-distance trade, in particular, drove the desire for speed and reliability, and with it navigational certainty, to make voyages safer and more profitable. As international trading networks developed, and with them the need for stronger navies, navigational knowledge and training became more important to those with commercial and political power. Yet, despite this growing interest, the problem of determining longitude at sea would challenge seafarers, artisans and men of science for centuries before being solved, in principle at least, in the mid-eighteenth century. In the meantime, and, indeed, for long afterwards, seafarers relied on knowledge and techniques that had been developed over generations. Many voyages were successful, some ended in disaster.

... some difference arose between them about Latitude and Longitude; Mr. Kempthorne alledging that there was no such word as Longitude; after that, further angry words arose

Evidence at the trial of John Glendon, convicted of the manslaughter of Rupert Kempthorne at the Ship Tavern in Temple Bar, London in October 1692²

The importance of being able to measure longitude at sea was inextricably linked with wider issues of marine navigation and safety. For many seafarers, the main concern was not simply a matter of getting from place to place, since by the seventeenth century it was possible to sail to many parts of the world with some confidence of return. Rather, it was whether this could be done more predictably, more quickly and with less risk; in other words, could it be done more profitably?

Broadly speaking, the further people wished to sail, the greater the risks, whether along well-travelled routes with known hazards or into relatively unknown waters. The determination of longitude and other potential advances were of most interest, therefore, to nations investing in long-distance trade and outposts and settlements overseas (Fig. 2). Having opened up trade routes to the Pacific and Indian oceans, Spain and Portugal were the maritime superpowers of the sixteenth century. By the end of the seventeenth, the Netherlands, France and England were coming to dominate the oceans. It is no coincidence that the chronology of rewards for longitude solutions mirrored this sequence of maritime activity.

The expansion of global trade was linked to a progressive rise in the numbers and activities of chartered companies. Britain’s Muscovy Company (chartered in 1555), East India Company (1600), Royal Africa Company (1660) and Hudson’s Bay Company (1670) competed with similar institutions from other European countries, notably the Vereenigde Oost-Indische Compagnie or VOC (Dutch East India Company, 1602) and the Compagnie Française pour le Commerce des Indes Orientales (French East India Company, 1664). Subject to state supervision, each was granted the right to colonize, sign treaties, make and enforce laws, and hold a trade monopoly for specific territories overseas. The companies were largely free to do as they pleased but could draw on naval support and possibly, in times of crisis, government aid.

This was big business. In 1636–37, an inspection of the Spanish Manila galleons heading from the Spanish East Indies (Philippines) to New Spain (Mexico) valued their cargo at one million pesos (equivalent to £200,000 at the time and over £17 million today), while, in 1685, a French observer claimed that Dutch and English trade with Asia was making profits of between twelve and fifteen million livres (around £10,000,000, or more than £870 million today). This was exaggerated but English imports of tea, coffee, spices, textiles, chinaware and other commodities from Asia have been valued at just under £600,000 for that year, while the loss of five East India Company ships to privateers in 1695 cost the company £1,500,000. (Privateers were privately owned ships that had state permission to attack ships of enemy countries – and to keep the plunder.)

Privateers were just one of the risks. A ship’s high-value cargo was also in danger from natural hazards, such as storms, throughout a voyage, as were the lives of its crew. Between 1550 and 1650, one in five ships was lost between Portugal and India, and crews had a one in ten chance of dying during the voyages. It is no surprise that the safe arrival of a trading vessel at remote outposts was a cause for celebration, or that sailors looked to protective measures such as amulets to keep them from harm.

Each of the main trade routes – between Europe and America across the Atlantic; between Europe and Asia around the Cape of Good Hope; and between the Philippines and Mexico across the Pacific – presented its own challenges. Stormy passages in the Strait of Madagascar plagued Portuguese and Dutch vessels between Europe and Asia. The Dutch established an alternative route in the seventeenth century, sailing eastwards from the Cape of Good Hope until reaching the correct longitude and then turning north towards the trading posts of Indonesia. If they sailed too far east, however, they were likely to fall foul of the reefs of Australia’s western coast. It was a route on which knowing longitude really mattered.

Trading companies and the navies that supported them clearly had a vested interest in better charts and improved understanding of sea routes. As the famous diarist and naval administrator Samuel Pepys noted in 1683 in his Tangier Papers:

The companies encouraged their officers to gather data about weather patterns, currents, coastlines and sailing directions. It could be sensitive information. In the sixteenth century the Spanish monarchy prohibited the circulation of maps and descriptions of the Indies to protect their outposts in the Pacific. So it was a major coup when a British privateer took a book of sea charts and sailing directions from a captured Spanish ship. The charts were soon copied and made available by William Hack, a London chart maker, who presented a set to James II in 1685 (Fig. 3). By then, systematic chart provision had begun elsewhere in Europe, initially with impetus from the Dutch and French trading companies rather than their navies, while commercial chart makers like Hack led the way in England. The possibility of finding better ways to determine longitude was bound up with this interest, as the poet John Dryden suggested in his historical poem Annus Mirabilis in 1667:

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

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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

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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

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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.

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. Natural 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:

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

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:

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.

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.

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.

Almost forty years later, John Wood used eclipses of the Moon for on-the-spot longitude determinations when he was master’s mate on John Narbrough’s 1669–71 expedition to the Pacific, which was instructed to bring back geographical information and lay the foundations for future trade in South America. Observations at sea of a partial eclipse on 26 March 1670 gave the longitude of Cape Blanco (Cabo Blanco in southern Argentina) as 69° 16' W, while today’s value is 65° 45' W. Another observation a little further south on 18 September placed Port Desire (Puerto Deseado) at 73° W, the correct longitude being 65° 54' W. Wood also measured the position of the harbour of St Julian (Puerto San Julián, also in Argentina) from a conjunction of the Moon and Mars, calculating a longitude of 75° W, compared with a modern value of 67° 43' W. The observations showed significant errors by modern reckoning, not surprising given the instruments and data available, but they did demonstrate that determinations of longitude could be made while on expedition. While the infrequency of eclipses meant that they would never be routinely useful, other observations of the Moon had the potential to be used on a more regular basis and, as discussed in Chapter 2, some attempts to try them out were made in this early period.

Shipwrecks had many causes, just as they do today. Storms were a persistent problem but human error, including navigational mistakes, was also common. In many cases this was not simply about longitude determination but arose from a range of factors causing uncertainty as to a ship’s position and surroundings. Without proper charts, no amount of position fixing could prevent disaster.

Problems could easily arise in relatively unfamiliar parts of the world, and might be compounded by hostile weather and unknown currents. This was something that William Dampier, the first person to circumnavigate the world on three separate occasions, discovered repeatedly in a turbulent seafaring life. Dampier ventured into the Pacific for the second time in 1703 in command of the St George, as part of an ill-fated privateering party with the Cinque Ports. As the ships rounded Cape Horn, storms hit with their expected venom. The St George attempted to crawl its way around the Cape but its position was soon uncertain as the winds took it wherever they wished. What happened next depends on whose account one believes. According to William Funnell, an officer whom Dampier later accused of desertion, Dampier ordered the ship north once he believed they were to the west of Cape Horn but two days later it turned out, ‘contrary to all our expectations’, that they were still five leagues east of Tierra del Fuego.¹¹ Dampier saw it differently. While he conceded that there was some uncertainty about their east–west position, sighting Tierra del Fuego was not so unexpected:

Their troubles did not end there. Having separated from the Cinque Ports, the St George headed north towards the Juan Fernandez archipelago, off the coast of Chile, which was a regular rendezvous and watering spot for ships entering the Pacific. The typical approach to Juan Fernandez was to run down the latitude from the coast of Chile but, according to Funnell, the St George sailed right past because Dampier failed to recognize the islands. They finally returned after three days without sight of land, only to find the Cinque Ports safely anchored there. Dampier’s information and memory had led him astray. Incidentally, one of the sailors on board the Cinque Ports was Alexander Selkirk, the inspiration for Daniel Defoe’s Robinson Crusoe, who decided he would rather be abandoned alone on an uninhabited island in the archipelago than remain on the unseaworthy Cinque Ports. Despite the privations of life on the island, it proved to be wise decision as the Cinque Ports foundered later in its journey.

Mariners feared Cape Horn with reason, and the same was true of the western coast of Australia, which is littered with offshore reefs and islands that saw the demise of many ships plying their trade between Europe and Asia. The most notorious incident followed the loss of the VOC ship Batavia on its maiden voyage. Batavia sailed from the Netherlands in October 1628 and was in the southern Indian Ocean eight months later, heading along the recommended route eastwards before turning north for Java once it reached the correct longitude. By 4 June, it was approaching the Houtman Abrolhos, a known hazard off the west coast of Australia named ten years earlier by Frederik de Houtman, from the Portuguese abre os olhos, meaning ‘open your eyes’. The Batavia’s pilot knew he was approaching the reefs but seems to have ignored the danger signs and the ship struck. Of 322 on board, forty drowned during the shipwreck, and more than 110 men, women and children were killed as they awaited rescue in a tale of mutiny and murder that made for sensationalist reading back in Europe.

Remote, unknown waters presented obvious dangers but there were plenty closer to home as well. Indeed, the Royal Navy’s worst maritime disaster of this period occurred not hundreds or thousands of miles away, but off the Isles of Scilly. Having concluded naval operations in the Mediterranean, a fleet under the command of Admiral Sir Cloudesley Shovell set sail for England at the end of September 1707. It should have been a routine voyage in well-known waters, even though they hit gales as they headed home. Just over three weeks in, the Admiral ordered his ships to heave to and check their position, concluding that they were safely in the English Channel. On the evening of 22 October, however, five ships struck the outlying rocks of Scilly (Fig. 15). Within hours four had sunk and at least 1600 men, including Shovell, were dead. It was a national tragedy.

Many causes have been cited: weather; tides and currents; compass error; even longitude. What the surviving log-books show is that variable navigational abilities and unreliable data were the main culprits. The officers’ latitude determinations from backstaff observations, for instance, had an average spread of 25.5 nautical miles (47.2 km), those by dead reckoning a spread of 73 nautical miles (135.2 km). More dangerously, their geographical data was flawed. Most of the fleet took Cape Spartel at the entrance to the Strait of Gibraltar as their point of departure. Its latitude and longitude were listed in manuals such as Colson’s New Seaman’s Kalendar and Seller’s Practical Navigation, but their figures varied widely. Combined with inaccurate charts (see Fig. 11) and generally moderate navigational skills, poor data landed the fleet in its perilous position.

The known hazards of the sea and the resulting losses were a spur to improve all aspects of seafaring, including navigation. Among Europe’s maritime states, possible improvements were of obvious interest to those wielding commercial and political power as they sought to strengthen naval and trading operations. As will be seen in Chapter 2, the various rewards offered for longitude solutions from the sixteenth century onwards, and the foundation of state observatories in the seventeenth, arose within this context.

Identical motives lay behind initiatives to improve navigational training. State-backed schools to train and license navigators and pilots engaged in long-distance trade were founded in Spain and Portugal in the fifteenth and sixteenth centuries, and these inspired a number of French navigation schools in the second half of the seventeenth century. Britain was not far behind its rivals when, in 1672, Samuel Pepys, by then Clerk of the Acts of the Navy, led moves to create ‘a Nursery ... of Children to be educated in Mathematicks for the particular Use and Service of Navigacon’.¹³ Granted a charter by Charles II, the Royal Mathematical School at Christ’s Hospital took in forty boys each year, from 1673, to study mathematics and navigation to prepare them for life in the merchant service or Royal Navy.

Significantly, the school had the support of Isaac Newton (1642–1727) and the astronomers John Flamsteed and Edmond Halley (1656–1742), who saw this as a way in which their work could have tangible public benefit. Flamsteed, who taught some of the boys at the Royal Observatory, wrote to Pepys of the school’s value, foreseeing a time when trained seamen would fix longitudes from astronomical observations, ‘whereby the faults of our present Mapps and Sea Charts ... will be corrected and a halfe the Business of navigation perfected’.¹⁴ Another school initiated in 1712 as part of Greenwich Hospital for Seamen followed similar lines, with pupils first taught (from 1715) by Thomas Weston, assistant to the Astronomer Royal.

Pepys continued his campaign to improve standards after becoming Secretary of the Admiralty. Having observed naval navigation in action, his assessment was scathing:

The school solution had been one way to address the problem. Pepys anticipated that, with concerted state support and the help of astronomers and mathematicians, the painful situation he described might be alleviated to the benefit of the nation.

Up until the eighteenth century, longitude determination at sea was one of a number of challenges that faced naval and merchant fleets worldwide. As different nations became the dominant players in maritime affairs, so their political and commercial leaders were willing to give encouragement to anyone offering to solve any of the myriad problems that diminished profits and put lives in danger.

In Britain, the drive to improve navigational knowledge gained impetus as a result of the loss of Admiral Sir Cloudesley Shovell and his men. As an experienced and high-ranking naval officer who knew the dangers only too well, Shovell had had an interest in navigational improvements; for instance, he had met with Isaac Newton in 1699 to examine a proposal for finding longitude put forward by a Monsieur Burden. His death in 1707 alongside so many of his men was a national disaster and, though not solely (if at all) attributable to problems in determining longitude, would be cited in lobbying for a Longitude Act seven years later.

Since there were techniques allowing mariners to navigate with some confidence, one could argue that the measurement of longitude was not an insurmountable problem for them. Nonetheless, it was a practical issue whose solution was felt by some to be within reach and of obvious benefit. For mathematicians, astronomers and cartographers, in particular, it was an intellectual challenge and a practical conundrum in which the peculiarities of being at sea merely hindered elegant mathematical and astronomical solutions. To their way of thinking, here was an arena in which their skills might be called upon in the service of humanity, perhaps earning them fame, fortune and influence in the process. Longitude was a problem for which they believed they might have the answer, and it was they who would put it on the political agenda.

CHAPTER 1

THE PROBLEM