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

While the leading astronomers at Paris and Greenwich had championed the use of Jupiter’s satellites, the founding of both observatories had been prompted by interest in what was known as the lunar-distance method. In France it was raised by a physician and Professor of Mathematics at the Collège Royal, Jean-Baptiste Morin, in 1634, and in London in 1674 by Le Sieur de St Pierre, another Frenchman, about whom almost nothing is known beyond his title. The method had advantages over Jupiter’s satellites in terms of what navigators would be required to observe at sea but it also had significant disadvantages with regard to the complexity of the Moon’s motions.

The method was already more than a century old, the first description having been published by Johann Werner of Nuremburg in 1514 and clarified in Peter Apian’s Cosmographica (1524) and Introductio Geographica (1533, Fig. 13), influential works that went through several editions. It made use of the well-known cross-staff (Fig. 14 (#litres_trial_promo)) to measure the Moon’s position as it moved against the background of stars. The crucial measurement – the lunar distance or ‘lunar’ – was the angle formed between the Moon and a star. With that, plus their altitudes, an accurate reference for the positions of bright stars distributed around the night sky and an almanac predicting positions of the Moon, a navigator could find the time at the place on which the tables’ data was based and subtract this from observed local time. This worked in theory but neither tables nor instruments were yet sufficiently accurate in practice, and the calculations required were actually more complex than those mentioned by Werner.

Fig. 13 – Title page of Introductio Geographica, Peter Apian (Ingolstadt, 1533)

{National Maritime Museum, Greenwich, London}

Fig. 14 – Decorated ivory cross-staff, by Thomas Tuttell, c.1700

{National Maritime Museum, Greenwich, London}

There were some surprisingly early attempts to determine longitude by versions of this method. In July 1612, the English Arctic explorer William Baffin observed the Moon’s transit, or passing, across his local meridian to determine longitude while in Greenland, but found it ‘somewhat difficult and troublesome’.

He took the observation from land, recognizing that it would be impossible from a moving ship. Three years later, on an expedition in search of the North-West Passage, he made observations from the ship to determine longitude from the angular distance of the Moon from the Sun. The range of observations Baffin made on these voyages suggests that he was quite unusual among English mariners. For most, these forays into the complexities of astronomical navigation would have been entirely unfamiliar.

Even in the seventeenth century, the method was not well known beyond mathematical circles. Thus, when Charles II heard of St Pierre’s claims to have solved the problem of longitude by using this method, a commission was appointed to examine their validity. The commissioners foreshadowed those appointed forty years later by the 1714 Act. They included the President of the Royal Society, the King’s Master of Mechanics, professors of astronomy and mathematics, including Christopher Wren (1632–1723) and Robert Hooke, and other Fellows of the Royal Society. Most of them had also been responsible for judging Henry Bond’s magnetic scheme the year before and it is likely that St Pierre hoped for a reward, given the commissioners’ recommendation that the King ‘grant some present support for Mr Bonde’.

However, as happened in France, it became clear that the method was unworkable without a vastly improved catalogue of stars and theory of the Moon’s motion. In both cases, the resulting recommendation was to found an observatory and appoint astronomers. Already co-opted to the Commission was John Flamsteed, a young astronomer who had impressed several Fellows of the Royal Society and had an influential patron in Jonas Moore, Surveyor-General of the Ordnance. On 4 March 1675, Charles II signed a royal warrant that appointed Flamsteed his ‘astronomical observator’ and charged him ‘to apply himself with the most exact Care and Diligence to the rectifying the Tables of the Motions of the Heavens, and the places of the fixed Stars, so as to find out the so much desired Longitude of Places for perfecting the art of Navigation’.

An observatory, designed by Wren and Hooke, was built at Greenwich (Fig. 15 (#litres_trial_promo)) and Flamsteed began his long series of observations there on 16 September 1676.

It was in the second of Flamsteed’s tasks that he had greatest success, although it was over a lifetime of observation and was the cause of some tribulation. His great legacy was a much larger and more accurate catalogue of ‘fixed stars’ than previously existed. On the way to producing this master-work, Flamsteed published tables of Jupiter’s satellites and other observations, calculations and commentaries. He also shared data with astronomers and mathematicians across Europe as part of a reciprocal, scholarly correspondence. His relationship with one of the most important figures of the period, Isaac Newton, broke down when he felt this scholarly etiquette was ignored. Newton, desperate to have access to as many observations as he could for the improvement of his theoretical work, demanded, in Flamsteed’s view, too much and gave too little in return.

Fig. 15 – Royal Observatory from Crooms Hill, British School, c.1696

{National Maritime Museum, Greenwich, London}

Fig. 16 – The effects of the Sun on the Moon’s motion, from Isaac Newton’s Philosophiae Naturalis Principia Mathematica (Cambridge, 1713) (detail)

{National Maritime Museum, Greenwich, London}

A serious quarrel took place over Flamsteed’s catalogue. Newton, as President of the Royal Society, urged its publication and Prince George of Denmark, Queen Anne’s consort and Lord High Admiral, agreed to pay. Newton, Halley and other Royal Society ‘referees’ for the publication gained the upper hand by persuading Queen Anne to appoint a Royal Society committee as a Board of Visitors to the Royal Observatory, with power to tell the Astronomer Royal what to observe and publish. In 1712, an edition of Flamsteed’s valuable catalogue was published prematurely, without his knowledge and to his lasting fury. The process of assembling his own edition took the rest of his life and, thanks to the dedication of his wife and two assistants, appeared posthumously in 1725.

Newton’s interest in Flamsteed’s observations had been particularly intense when he was struggling with the second edition of his Principia. The first edition, with its mathematically expressed laws, including the inverse square law of universal gravitation, provided a new and essential framework for predicting the motions of the planets. However, the complexity of the Moon’s motion, caused by the interplay of the gravitational influences of Earth, Sun and Moon, was great enough to defeat Newton. He struggled again with lunar theory and the so-called three-body problem for the book’s 1713 edition (Fig. 16 (#litres_trial_promo)), building on observational data from Flamsteed and others and recalling later that ‘his head never ached but with his studies on the moon’.

Newton wished to devise a theory, based on both mathematics and empirical observations, that was accurate to two minutes of arc (that is, to one-thirtieth of a degree). He felt that this high level of accuracy was necessary in the theory in order to achieve accuracy to within one degree in practical navigation observations. However, in this he failed. Despite his best efforts, his evidence to the parliamentary committee of 1714 had to state that the Moon’s ‘Theory is not yet exact enough’ to determine longitude at sea within one degree. Nevertheless, he gave the impression that this improvement would be forthcoming and that it was here that the long-awaited solution would lie.

‘a Watch to keep Time exactly’

The accuracy of Flamsteed’s observations depended on a recent revolution in timekeeping. One of the coordinates that indicates the position of stars is expressed as time: the moment at which a heavenly body passes, or transits, the observer’s local meridian (line of longitude). In order to record this accurately and precisely good clocks are required. Clocks had become capable of acting as scientific instruments, known as astronomical regulators, once they incorporated pendulums, the timekeeping properties of which had been observed by Galileo. It was left to the Dutch mathematician and astronomer Christiaan Huygens (1629–95) to apply this to a clock in 1657.

The Octagon Room of the Royal Observatory at Greenwich was designed around the pendulum clocks installed there (Fig. 17 (#litres_trial_promo)). Made by Thomas Tompion, London’s leading clockmaker, they were an experimental design with thirteen-foot pendulums suspended behind the room’s panelling and above the dials. They were accurate enough to help Flamsteed in his first task as Astronomer Royal: to demonstrate that the Earth itself is a regular timekeeper, a prerequisite of the positional astronomy he was appointed to improve.

The timekeeper method of finding longitude at sea – a shipboard clock that would keep the time at a known location throughout a sea voyage for comparison with observations of local time – was, as Whiston and Ditton said, ‘the easiest to understand and practice’. The huge strides made in the accuracy of pendulum clocks were encouraging but the technical challenges facing their application at sea were huge. Watches, less influenced by the motion of the ship, were much too inexact. As Whiston and Ditton’s 1714 pamphlet put it:

Fig. 17 – The Octagon Room at the Royal Observatory, Greenwich, by Francis Place, c.1676

{National Maritime Museum, Greenwich, London}

Watches are so influenc’d by heat and cold, moisture and drought; and their small Springs, Wheels, and Pevets are so incapable of that degree of exactness, which is here requir’d, that we believe all wise Men give up their Hopes from them in this Matter. Clocks, govern’d by long Pendulum’s, go much truer: But then the difference of Gravity in different Latitudes, the lengthening of the Pendulum-rod by heat, and shortening it by cold; together with the different moisture of the Air, and the tossings of the Ship, all put together, are circumstances so unpromising, that we believe Wise Men are almost out of hope of Success from this Method also.

It had ‘been so long in vain attempted at Sea, that we see little Hopes of its great usefulness there’.

Dependence on a single clock was also potentially dangerous if there were no means to check its performance.

Fig. 18 – Marine timekeeper, by Severyn Oosterwijck, c.1662 based on the designs of Alexander Bruce and Christaan Huygens

{National Maritime Museum, Greenwich, London, Private Collection}

Fig. 19 – Frontispiece to Thomas Sprat’s History of the Royal-Society of London (London, 1667); note the triangular maritime timekeeper at the top left and the two navigational instruments hanging on the column behind it

{National Maritime Museum, Greenwich, London}

One of those who had attempted to make functional sea-clocks was the same Christiaan Huygens who had had such success with pendulums. As with others in this story, his attempt to apply this work to the problem of longitude was immediate. Huygens had a deep theoretical understanding of the physical principles behind this practical work, making use of clockmakers and others to construct, test and develop his designs. These collaborations were fruitful but not always easy.

One individual with whom he became involved was Alexander Bruce, Earl of Kincardine, who tested a timekeeper on a voyage between Scotland and The Hague in early 1662. Its performance convinced Huygens to collaborate, and he joined Bruce in making and testing two further clocks on the same model, with the assistance of Severyn Oosterwijck, a clockmaker from The Hague (Fig. 18 (#litres_trial_promo)). Further trial results were sufficiently encouraging for work to be continued, now also in collaboration with Hooke. The clocks were approved at the Royal Society, especially after a very favourable (and probably untrue) report of them was given by Captain Robert Holmes after a voyage to Lisbon. Huygens was made a Fellow of the Royal Society when he visited London in 1663, patents were discussed and the Duke of York expressed interest in the clocks. One of these triangular clocks has been identified on the left of the iconic frontispiece of Thomas Sprat’s 1667 History of the Royal-Society of London (Fig. 19 (#litres_trial_promo)). Despite all this, the clocks were little used.

Huygens continued to develop his ideas. Much of this work was done in relative secrecy and, even once revealed, seems to have made little impact. However, by 1666 he was working within the Académie des Sciences for the French Crown and further sea trials were undertaken, some achieving good results. He published another design in Horologium Oscillatorium in 1673; this timekeeper was spring-driven, set on gimbals (devices designed to keep objects level in unstable conditions), and had a triangular pendulum that was forced to move in only one plane. A later version (Fig. 20 (#litres_trial_promo)) was tried, inconclusively, in the 1680s, this time in collaboration with the Dutch East India Company. Huygens was also one of those who, in the 1670s, were involved with the invention of the balance spring, crucial to the development of accurate watches. There are hints that Huygens saw this as a potential alternative for a timekeeper solution to the longitude problem but, because springs were too greatly affected by changes in temperature, it was not one he pursued.

Fig. 20 – Christiaan Huygens’ design for a marine timekeeper, originally drawn c.1685–86

{National Maritime Museum, Greenwich, London, Courtesy of Jonathan Betts}

Fig. 21 – Longitude timekeeper, designed by Lothar and Conrad Zumbach de Koesfelt, made by Franciscus le Dieu, 1749

{Museum Boerhaave, Leiden}

Fig. 22 – Plate from Henry Sully’s Description Abrégée d’une Horlorge d’une Nouvelle Invention (Paris, 1724)

{National Maritime Museum, Greenwich, London}

Huygens died in 1695, having made some huge practical and theoretical advances but without a clock having yet been taken up as a usable tool at sea. His influence on those who followed, through his publications, manuscripts or collaborators, was enormous. One follower was Lothar Zumbach de Koesfelt, a Dutch physician, mathematician and musician, who described a sea-clock in 1714. It was later improved by his son Conrad, who in 1749 also designed a clock that used a glass container to control its temperature (Fig. 21 (#litres_trial_promo)). Another was Henry Sully, who, trained in England and working on the Continent, experimented with a marine clock and watch (Fig. 22 (#litres_trial_promo)). Sully made ample use of both French and English networks, not least the Royal Society’s chief authority on instruments and timekeepers, George Graham (1673–1751). While Sully’s clock had mechanisms that made it portable and minimized the effects of temperature and gravity, Graham’s report and trials were to show that a ship’s motion in open sea would fatally influence its pendulum.

In 1714, then, there were several potential solutions to the problem of finding longitude at sea. Most of them were theoretically viable and had already been researched by mathematicians, astronomers, artisans and mariners. In many ways the ground had been prepared: the next, crucial step may not have seemed all that distant. However, all of the methods presented practical problems, most particularly due to the conditions under which observers or instruments had to perform at sea. It was a practical and technical set of problems, and the government hoped that these could be met so that the methods ‘true in theory’ might be made ‘Practicable and Useful at Sea’.

While much previous work had taken place in Spain, Holland, Venice and elsewhere, the momentum had decisively shifted towards Britain. Ideas and skills were available, particularly in London with its flourishing instrument trade, maritime interests, places of open discussion, such as coffee-houses, and widespread access to print. These opportunities were seized by many of those with ideas, mechanisms and projects relating to longitude. The Royal Society, Astronomer Royal and Commissioners of Longitude were marked out as the key figures from whom to seek interest, approval and, perhaps, a route towards one of the 1714 Act’s enormous rewards.

CHAPTER 3 (#ulink_d40b2641-4a97-50ad-a455-e6ca61df6443)

ON TRIAL (#ulink_d40b2641-4a97-50ad-a455-e6ca61df6443)

I understand not Mathematicks, but have been formerly troubled too much with Projectors of the Longitude to my great Mortification and some Charges by encouraging them ... One of my Projectors cut his Throat, and the other was found an Imposter.

Jonathan Swift, letter to John Wheldon, 27 September 1727

The likely effect of the Longitude Act must have been uncertain as it went through Parliament, but within weeks it was clear that it had caught the public’s attention. Schemes of all sorts came under public scrutiny – a mixed bag of ideas, some more plausible than others and many held up for ridicule. In an age awash with projects of all sorts, getting these ideas taken seriously and gaining support required tenacity and robust strategies.

It would be two decades before a genuinely promising scheme emerged in the work of John Harrison (1693–1776). From the mid-1730s, his sea-clocks began to garner praise and the support of the Commissioners of Longitude. Even so, it took him another twenty years to complete a watch that was ready for a decisive trial. Over the same period, two other contenders emerged in Tobias Mayer’s work on the Moon and Christopher Irwin’s marine chair for viewing Jupiter’s satellites. The three methods would finally go head-to-head in 1763–64 in a sea trial to Barbados, which established marine timekeepers and the measurement of lunar distances (or ‘lunars’) as the methods to back.