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

Another is by the Eclipses of Jupiter’s Satellites. But by reason of the length of Telescopes requisite to observe them & the motion of a ship at sea, those Eclipses cannot yet be there observed.

A third is by the place of the Moon. But her Theory is not yet exact enough for this purpose. It is exact enough to determine her Longitude within two or three degrees, but not within a degree.

A Fourth is Mr Ditton’s project. And this is rather for keeping an account of the Longitude at sea than for finding it if at any time it should be lost, as it may easily be in cloudy weather ...

The first three methods on this list were, to Newton, the most promising. All were a means of carrying or finding a reference time against which to compare observations of local time on board ship. If practicable, they would allow difference in longitude to be established anywhere in the world. The last method, ‘Mr Ditton’s project’, as Newton said, targeted particular circumstances rather than being a universal solution to the problem. It is, however, of particular interest to the story, being the cause of parliamentary interest in the issue of longitude in 1713.

‘Mr Ditton’s project’

The Mr Ditton to whom Newton referred was Humphry Ditton (1675–1715), Master of the Royal Mathematical School at Christ’s Hospital. In reality, it was Mr Ditton’s and Mr Whiston’s project, but the latter was an individual with whom Newton, once close, had now broken ties. Perhaps Newton could not quite bring himself to write the name, despite the presence of William Whiston (1667–1752, Fig. 3 (#litres_trial_promo)) at the parliamentary committee. Whiston had been Newton’s chosen successor as Lucasian Professor of Mathematics at Cambridge in 1702, but was expelled from the university in 1710 for his unorthodox theological views. Those views were largely shared by Newton but he was anxious to avoid a public accusation of heresy. Whiston blamed their rupture on Newton’s ‘fearful, cautious, and suspicious Temper’.

After 1710, Whiston made his living as a scientific and theological lecturer, author and, he hoped, longitude projector – that is, someone who sought backing for a scheme, or project, intended to solve the longitude problem. He had lectured with Ditton from at least 1712 and they were promoting their longitude scheme the following year, through newspaper advertisements and letters drumming up English support by asking questions about foreign longitude rewards. In 1714, two petitions to Parliament appeared: one in April from Whiston and Ditton, and another in May recorded as being from ‘several Captains of her Majesty’s Ships, Merchants of London, and Commanders of Merchant-men’. The latter petition suggested that public ‘Encouragement’ would aid the search for a longitude solution.

It was this, in which Whiston may also have had a hand, that instigated the parliamentary committee at which Newton presented his evidence. Prominent Whig politicians, whose patronage Whiston enjoyed, were to steer the new legislation.

Claiming inspiration from the extraordinary display of fireworks on the Thames that celebrated the end of the War of the Spanish Succession in 1713, Whiston and Ditton proposed that vessels moored at known locations could fire shells vertically to 6440 feet at set times. Navigators would keep a look out for the lights and gauge their bearing and distance relative to the moored vessel by compass and by timing the difference between the flash and sound of the shell, or by measuring its elevation. Whiston and Ditton thought large shells might be visible for a hundred miles and that, where deep seas meant hulks could not be moored, ships might run down the latitude until they neared the next signal post. Newton seemed disinclined to comment more than necessary: ‘How far this is practicable & with what charge, they that are skilled in sea affairs are best able to judge’.

Fig. 3 – William Whiston, by an unknown artist, c.1690

{The Master, Fellows and Scholars of Clare College, Cambridge}

Fig. 4 – The limits of viewing the flash from a mortar fired at Shooter’s Hill, near Greenwich, from William Whiston’s The Longitude Discovered (London, 1738) (detail)

{National Maritime Museum, Greenwich, London}

Fig. 5 – A terrella (or ‘little earth’), a spherical lodestone used to model the Earth’s magnetic field, c.1600

{National Maritime Museum, Greenwich, London}

Whiston and Ditton presented their scheme more fully in a pamphlet addressed to the newly appointed Commissioners of Longitude. They offered it as a practical idea that, without universally solving the problem, would make a material difference. It was ‘easy to be understood and practis’d by Ordinary seamen, without the Necessity of any puzzling Calculations in Astronomy’ but would ‘prevent the Loss of abundance of Ships and Lives of Men’. The signals could provide both latitude and longitude, might be used to give exceptional warnings of bad weather, and would have most success in the areas of greatest danger – that is, near coasts. Here they invoked the maritime tragedy that occurred off Scilly in 1707, claiming their scheme ‘would certainly have sav’d all Sir Cloudsly Shovel’s Fleet, had it been then put in Practice’.

To put the idea into effect, Whiston, who continued the project after Ditton’s untimely death in 1715, relied on the skills of London’s firework makers and gunners as he began trials on Hampstead Heath and Blackheath (Fig. 4 (#litres_trial_promo)). There was merit in the idea, and explosives were later occasionally used to measure distances in survey work, but there were serious practical problems. Not least was the difficulty of mooring vessels in deep water, despite a claim that anchors might be secured by reaching down to supposedly still layers of water far below the surface.

It was all too easy for the firework scheme to be ridiculed, particularly by Tory satirists, who connected it to Whiston’s fiery and suspect theology, and cast the whole concept of longitude rewards as a Whig folly. Nevertheless, projecting, publicizing and finding patronage for longitude schemes remained one of Whiston’s major activities and sources of income. He explored all the accepted avenues of research, including one not mentioned by Newton: the Earth’s magnetism.

Magnetic variation and inclination

The idea that patterns in the Earth’s magnetic field might be a means of fixing position at sea had a long history and continued to be investigated in the eighteenth century and even into the nineteenth. It is interesting that Newton did not mention it in his evidence to the parliamentary committee, especially since he was joined there by Edmond Halley, an experienced astronomer, mathematician and navigator who had investigated these phenomena himself. As with Whiston’s signals, this method was about finding position relative to known locations rather than finding longitude itself. Presumably Newton and Halley therefore considered it discounted as a universal solution.

Most of the incoming proposals to the Spanish and Dutch longitude reward schemes were based on patterns in the Earth’s magnetic field, and many would be put to the British Commissioners of Longitude. There were two patterns that were investigated, with the hope that they were regular enough to be mapped and used. One was magnetic variation (also known as magnetic declination), which is the angular difference between magnetic north, shown on the compass, and true north, determined by the Sun or stars. A positive variation shows that magnetic north is east of true north, a negative one that it is to the west. The other was magnetic inclination, or magnetic dip, which is measured by the compass needle’s vertical rather than horizontal deviation. This is caused by the needle aligning itself with the Earth’s curving lines of magnetic force.

These were phenomena that had long been observed and investigated: variation had to be understood by navigators to correct steering directions, if not for position finding. In trying to make sense of the patterns of observational data, natural philosophers attempted to describe the Earth as, or containing, a giant magnet. One of the most famous of these accounts was De Magnete, published by William Gilbert, a London physician, in 1600. He undertook much of his research with spherical lodestones: known as terrellae, meaning ‘little earths’, these magnetic rocks were used to model patterns of geomagnetism (Fig. 5 (#litres_trial_promo)).

Magnetic inclination was also explored as a means of finding latitude, which, given that the Earth’s lines of magnetic force run north–south, had some plausibility. However, experiments had shown that the variations were too irregular and the observations too difficult to make at sea. In any case, astronomical observations were becoming much more effective for determining latitude. Thus, while schemes relating to magnetic inclination for latitude or longitude did not disappear, and even occasionally recurred in navigational textbooks, it was magnetic variation that had more impact. It involved significantly easier on-board observations and had a more plausible theoretical underpinning. This too was challenged, however, when it was demonstrated that the patterns change over time as well as place.

Fig. 6 – An amplitude compass, used for measuring magnetic variation from the apparent bearing of the Sun’s rising or setting; made by Ferreira, Lisbon, 1780

{National Maritime Museum, Greenwich, London}

Fig. 7 – Edmond Halley, by Thomas Murray, c.1690

{The Royal Society}

Nevertheless, navigation by magnetic variation was actually achieved, albeit in restricted locations or on familiar routes. The necessary tools were an amplitude compass (Fig. 6 (#litres_trial_promo)), to measure variation from observations of the sun and a chart recording previously observed lines of equal variation, against which to plot the ship’s position. This could be effective in specific circumstances, where the charting was detailed, and the lines ran nearly north–south and were reasonably close together. Some Portuguese navigators, for example, and those on Dutch East Indiamen, put the method into practice at various times during the seventeenth and eighteenth centuries, many apparently satisfied with the results.

Research into magnetism was a serious interest at the Royal Society, with demonstrations by their curator of experiments, Robert Hooke (1635–1703), who developed his own magnetic theory. Between 1668 and 1716, annual predictions by Henry Bond, a teacher of mathematics and navigation, were published in the Society’s journal, with the aim of encouraging magnetic observations against which his theory might be tested. Bond’s claims were investigated by a Royal Commission in 1674 and, although there was some doubt, he was paid £50 and given licence to publish his book The Longitude Found. On the basis that the six Commissioners were all Fellows, the book claimed the Royal Society’s approval, to which its President, Viscount Brouncker, objected strongly.

The Society’s interest nevertheless continued and was instrumental in persuading the government and the Navy to fund and equip a scientific voyage that would, among other things, chart magnetic variation as widely as possible. Edmond Halley (Fig. 7 (#litres_trial_promo)) was, very unusually for a civilian, given command of a specially built naval vessel, the Paramore, and set sail on two voyages in 1698 and 1699. He published charts of magnetic variation in 1701 and 1702 (Fig. 8 (#litres_trial_promo)), noting that they might be useful both for rectifying courses where compass readings might be unreliable, and for estimating longitude in places where the lines of similar variation were almost parallel to a meridian, provided that such charts were kept up to date to reflect change of variation over time.

While Halley did not produce updated charts, others did and they were put to use. However, the fact that this inexact, localized, practice-based and changeable method was not mentioned at the 1714 parliamentary committee underlines Newton’s view at the time that Parliament should be looking for a more complete solution. While Whiston and Ditton’s scheme had to be mentioned – and, by Whiston’s account, Newton’s initial ignoring of it risked the complete rejection of the proposed legislation – it perhaps served as a contrast to the great aim of finding a method that could be applied confidently at any location. It was, Newton suggested, only the astronomical and timekeeper solutions that held out that promise.

‘the Eclipses of Jupiter’s Satellites’

While rocket signals and magnetic schemes were about finding a means of fixing position relative to a known location (a moored hulk or charted magnetic feature), the other methods focused on the long-understood relationship between time and longitude. These were the only universal solutions to finding longitude at sea and, as Newton explained more than once to the Admiralty, only astronomical methods could be used to find longitude if it had been lost. The downside of astronomy was that observations could usually only be done at night, and sometimes irregularly if the target object was not in the right position, which meant that dead reckoning and other techniques were still required. Observations could also be also hampered by clouds, although this was equally true for calculating latitude and local time, without which neither astronomical nor timekeeper methods were effective.

The use of lunar and solar eclipses was the earliest of several potential astronomical methods for finding longitude. One key branch of research was to find ways of using the Moon’s position on a more regular basis, while the discovery of the moons (satellites) of Jupiter, with much more frequent eclipses, opened up new opportunities. The satellites were discovered in 1610 by Galileo Galilei (1564–1642, Fig. 9 (#litres_trial_promo)) with the use of a new instrument – the telescope. It revealed that Jupiter was orbited by four satellites that would disappear and reappear with useful regularity as they passed in front of or behind the planet (Fig. 10 (#litres_trial_promo)). They provided, in essence, a celestial timekeeper, visible at the same time from different points on Earth.

Galileo quickly realized that this was a potential means of finding longitude and, having drawn up provisional tables to predict the satellites’ motions, he attempted in 1616 to interest the Spanish in a proposal to make 100 telescopes and teach navigators the method. Having failed to convince them, he began protracted negotiations with the Dutch government in 1636, which only ended with his death six years later. The scepticism of the Spanish longitude committee was undoubtedly related to the practicalities of the method. Observing objects as small as Jupiter’s satellites with a telescope from a moving ship was clearly going to be very difficult. Even a century later, when the production of telescopes and lenses had vastly improved, Newton noted that ‘by reason of the length of Telescopes requisite to observe them & the motion of a ship at sea, those Eclipses cannot yet be there observed’.

Galileo recognized this problem and looked for a means of steadying the observer. He designed a helmet, the celatone, which supported a telescope that could be adjusted continually to counteract the ship’s movement. At least one was made and tried on board a ship in the harbour at Livorno. It impressed a member of the powerful Medici family, who apparently ‘judged this invention more important than the discovery of the telescope itself’.

Another idea was a hemispherical vessel in which the observer could sit and which would, in theory, be kept level by floating in a bath of oil (see Chapter 3, Fig. 29 (#litres_trial_promo)). Given the small number of telescopes at this time that could show Jupiter’s satellites at all, let alone a sharp image, such adaptations for use at sea were perhaps premature. Nevertheless, chairs, platforms and other devices that would ease shipboard observations continued to be explored.

Fig. 8 – Edmond Halley’s world sea chart on two sheets, showing lines of equal magnetic variation, 1702

{National Maritime Museum, Greenwich, London}

Fig. 9 – Galileo Galilei, attributed to Francesco Apollodoro, c.1602–07

{National Maritime Museum, Greenwich, London}

Fig. 10 – Galileo’s journal of the observations of Jupiter and its satellites, 1610

{Biblioteca Nazionale Centrale di Firenze}

Ongoing attempts to make the method workable at sea were encouraged by the successful use of Jupiter’s satellites to establish longitude on land. This method began to flourish with the availability of improved telescopes and the publication of more accurate tables by Giovanni Cassini (1625–1712) in 1668. As director of the newly established observatory in Paris (Fig. 11 (#litres_trial_promo)), Cassini promoted the use of his tables on expeditions and in the mapping of France. In 1693, the Académie des Sciences published a map that compared the position of France’s coastlines on the new maps with the old (Fig. 12 (#litres_trial_promo)). Although Louis XIV, it is said, complained that the astronomers had taken more territory from him than his enemies, he and the Académie continued to finance the method and ambitious expeditions to map the nation and her empire.

Cassini’s method and tables were taken up elsewhere, including Britain. There, the new observatory at Greenwich focused on longitude, and its first director, John Flamsteed, produced his own tables of Jupiter’s satellites, published by the Royal Society in 1683. He doubted their use could be made practical at sea but encouraged sailors to learn the method for use on coastal surveys (or, rather, berated them for having not already begun to do so). By the early eighteenth century, it was clear that the use of simultaneous observations of Jupiter’s satellites to establish longitude on land could, with the best equipment and careful observers, be extremely effective. The main focus of research into astronomical methods for use at sea, meanwhile, moved elsewhere.

Fig. 11 – Paris Observatory, 1729. An astronomical quadrant with a telescopic sight and a large telescope with a mast and pulley for raising it are shown

{National Maritime Museum, Greenwich, London}

Fig. 12 – Map of France that compares the position of its coastlines on maps using new astronomical data with older maps, from Recueil d’Observations (Paris, 1693)

{National Maritime Museum, Greenwich, London}

‘the Place of the Moon’