Although the two designs differed in the details, Godfrey’s plainly used the same principle as Hadley’s. After considering the matter, the Royal Society decided that it was a case of independent invention. Meanwhile, Hadley took out a patent to bolster his own claim and deter competition in the commercial navigational market. Rivals included new reflecting instruments and improved backstaffs, such as John Elton’s design with an artificial horizon for use when the natural one was obscured (Fig. 21).
Fig. 21 – Backstaff with artificial horizon, designed by John Elton and made by Jonathan Sisson, c.1732
{National Maritime Museum, Greenwich, London}
Fig. 22 – A seaman with an octant, log and line, compass and other equipment, from ‘Book of Drafts and Remarks’, by Archibald Hamilton, 1763
{National Maritime Museum, Greenwich, London}
Fig. 23 – Tobias Mayer, by an unknown artist, mid-eighteenth century
{Private Collection / Photo: Tobias-Mayer-Verein}
Instruments to Godfrey’s design were manufactured in America for a while, but Hadley’s design came to dominate there as it did in England and elsewhere in Europe. Indeed, it would remain popular to the end of the nineteenth century. Later called the octant because the frame was one-eighth of a circle, it was initially known as the Hadley quadrant (since it could actually measure angles up to 90°, or a quarter of a circle). Good connections had ensured that Hadley’s name became synonymous with the instrument. And although it found its greatest use for latitude and local time determinations (Fig. 22), the Hadley quadrant would soon be bound up in other attempts to improve astronomical methods for finding longitude.
Mayer, the Moon and Maskelyne
In May 1756, John Elliot, recently promoted to lieutenant in the Royal Navy, was penning a letter home. ‘There is no News here worth troubling you with’, he wrote, ‘only the discovery of the longitude by a Hanovarien ... The obs[ervatio]n is simple & easey but the Calculation is extreamly perplexd’.29 It was a wonderfully understated revelation. The Hanoverian in question was an astronomer named Tobias Mayer (1723–62, Fig. 23). It is said that he had never seen the sea, yet he made possible an astronomical method for determining a ship’s longitude. In doing so, he succeeded where Newton had failed, mastering the three-body problem and showing how to predict the Moon’s movements.
Fig. 24 – ‘Germaniae atque in ea Locorum Principaliorum Mappa Critica’, by Tobias Mayer, 1750. Mayer’s map compared three sets of co-ordinates – in green, yellow and pink – to show how much they differed
{The British Library Board}
Mayer’s motivation came from a background in cartography, which relied on accurate observations of lunar eclipses and occultations (when one heavenly body obscures another) to measure terrestrial longitudes. Mayer soon realized that existing data was unreliable and drew a map of the German lands to show how uncertain the locations of even the major cities were (Fig. 24). This led him in two directions. First, he wanted to create a better map of the Moon, so that observers could correctly identify specific features to allow more accurate comparisons between data from different places on Earth. So he began a long series of lunar observations, from which he hoped to produce a detailed globe. At the same time, he began to investigate lunar theory and how it might be improved to predict the Moon’s motions accurately. This occupied him more and more after his appointment at the University of Göttingen in 1751.
As Newton himself knew, the Principia’s theories failed to describe the Moon’s motions. Such a conspicuous flaw in the Newtonian system stimulated some of the finest mathematicians of the eighteenth century, including Leonhard Euler, Jean d’Alembert and Alexis Clairaut, to tackle the problem and apply new forms of mathematical analysis in an attempt to model the Sun’s effect on the Moon’s orbit around the Earth. Such was the crisis that Euler and Clairaut even considered abandoning Newton’s inverse square law of gravity to help their models match the observed results. Mayer drew on this work, in particular Euler’s techniques, but soon came to believe that part of the problem lay in the astronomical observations on which the theories were based. He confirmed this through a detailed analysis of historical observations and the best modern data from James Bradley, now third Astronomer Royal at Greenwich. This allowed Mayer to apply corrections to the mathematical models and derive an improved theory and new lunar and solar tables, which Bradley found to be impressively accurate.
Mayer did not believe that determining longitude from a ship would ever be possible but, at Euler’s urging, he reconsidered and drew up another set of lunar tables and a method for using them at sea. At the same time he designed an instrument for shipboard observations: a circular device that operated on the octant’s principle of double reflection but which used repeated measurements around the full circle to reduce the effect of errors in the divided scale (Fig. 25). It all seemed so promising that Euler was soon urging him to submit his ideas to the Commissioners of Longitude, even though Mayer doubted that they would reward a foreigner. Eventually, Mayer gave in and allowed his friends and colleagues to promote his interests in Britain. Thereafter, discussions with the Commissioners passed through diplomatic channels, via Johann David Michaelis, Secretary of Hanoverian affairs in Göttingen, and his cousin William Philip Best, a private secretary of George II. Negotiations were helped by the fact that the King was also the Elector of Hanover.
Discussions of Mayer’s ideas were taking place in England by the end of 1754, and James Bradley commissioned the London instrument maker John Bird (1709–76) to make a brass copy of Mayer’s repeating circle. This was tested with the lunar tables early in 1757 by Captain John Campbell, who, as a master’s mate on the Centurion during Anson’s traumatic voyage around Cape Horn, knew what issues were at stake. In his tests, Campbell found the circular instrument rather cumbersome and proposed an alternative design comprising just one-sixth of a circle and able to measure up to 120°. This, the first marine sextant, was also made by Bird and was tested by Campbell in 1758–59. It was a success, Bradley reported, concluding that Mayer’s tables and a good instrument of this sort (Fig. 26) could determine a ship’s longitude to within 1°, a result that brought Mayer’s proposal within the limits of the 1714 Act.
While Campbell’s trials were promising, they were over short distances during blockade duty as part of the war with France. However, tests over a longer distance were soon underway. One set was carried out by Carsten Niebuhr, astronomer and cartographer on the Royal Danish Expedition to Arabia in 1761–67. Having studied at Göttingen for the post, Niebuhr had persuaded Mayer to teach him the lunar-distance method and sent back his first results within a few months. Mayer was ecstatic: the observations were ‘more accurate than I ever could have hoped for. You have barely taken your first steps at sea and you already can determine longitude better than 80-year-old navigators.’30
Fig. 25 – Mayer’s design for a repeating circle, from Tabulae Motuum Solis et Lunae Novae (London, 1770)
{National Maritime Museum, Greenwich, London}
Fig. 26 – Marine sextant, by John Bird, c.1758
{National Maritime Museum, Greenwich, London}
Fig. 27 – Nevil Maskelyne, by John Russell, c.1776
{National Maritime Museum, Greenwich, London}
That same year Mayer’s ideas were trialled on a longer British voyage. The opportunity was an expedition to the Atlantic island of St Helena to observe the transit of Venus across the face of the Sun in 1761, a rare event that astronomers hoped to use to determine the distance between the Earth and the Sun and hence the scale of the Solar System. Among other things, the results would help refine the mathematical models of the problematic three-body system. Nevil Maskelyne (1732–1811, Fig. 27), a mathematics graduate from Cambridge who was already working with Bradley, was appointed to make the transit observations and used the voyage to St Helena to test Mayer’s ideas. Departing in January 1761, he and his assistant, Robert Waddington, spent eleven weeks on the East India Co
mpany ship Prince Henry with a Hadley quadrant, Mayer’s tables and copies of the French astronomical almanacs, the Connaissance des Temps. By the time they anchored, Maskelyne was able to report that his longitude reckoning by lunars was only 1½° in error compared with errors of up to 10° from dead reckoning.
Once he returned from an otherwise frustrating scientific expedition, Maskelyne became a vociferous advocate of lunars. He told the Royal Society that anyone with sufficient time and ability could now determine their longitude at sea. He also published The British Mariner’s Guide (Fig. 28), which contained new versions of Mayer’s tables and instructions for observing and calculating longitude. He did acknowledge that there might be one objection, however: the ‘difficulty and nicety of the calculations’, as he gently put it. In fact, the calculations were decidedly lengthy, although he added that they required no knowledge of spherical geometry, only ‘care in the computer’.31 They would be even simpler if precomputed tables of the Moon’s future positions were produced, an idea Maskelyne got from the Connaissance des Temps for 1761, which included example tables of this sort and a method for using lunar distances to determine longitude at sea. The method was devised by the French astronomer Nicolas Louis de Lacaille (1713–62), who had used it on a voyage from the Cape of Good Hope in 1754 and published it in full the following year, although his proposal was not fully taken up in France.
Fig. 28 – The British Mariner’s Guide, by Nevil Maskelyne (London, 1763)
{National Maritime Museum, Greenwich, London}
Around the same time, Robert Waddington also published a book on lunar distances and began teaching East India Company officers. Lunars had come of age and had active disciples in Britain. Maskelyne would become their most prominent champion and would be a key player in the forthcoming sea trial to the West Indies.
‘Erwin’s Easy Chair’
While Mayer’s negotiations with the Commissioners of Longitude took place through diplomatic channels and international correspondence, other more public strategies could be successful. Christopher Irwin was a master of these. Indeed, most of what is known of him, including the fact that he was from Roscommon in Ireland, comes from his self-publicity in newspapers and other publications.
Irwin came to the attention of London readers in the late 1750s, when he began promoting a scheme for finding longitude from Jupiter’s satellites. His proposal was for a marine chair with counterweights hanging underneath, to hold the observer steady as they viewed the satellites through a telescope. The idea of building such a contraption predated even the discovery of Jupiter’s satellites (Fig. 29). In that sense, Irwin was only repeating what had gone before, but he did incorporate the latest telescopic innovations. More notable was his use of newspapers to convince the public and the Commissioners that his design worked.
Fig. 29 – A sixteenth-century design for a marine observing chair, from Le Cosmolabe, by Jacques Besson (Paris, 1567)
{National Maritime Museum, Greenwich, London}
In 1759, Irwin persuaded the Navy to lay on shipboard trials of the chair. Within days, The London Magazine reported that he had discovered the longitude and printed a certificate from the ‘brave lord Howe’, a hero from the Seven Years War, testifying that the chair could be used to determine longitude to within fifteen miles. The report added that the king’s brother was much taken with it and that his mathematical teacher had cried, ‘This will do, this will do’.32 Irwin was presumably responsible for other flattering reports in London’s press, including a letter from a ‘Francis Drake’, who applauded ‘the excellency of the design, and the masterliness of the execution’ and urged the government to reward its inventor.33 Not everyone was taken in: the Busy Body ran a fictional autobiography of a would-be projector, whose scheme had obtained ‘a pompous certificate, signed by an admiral, three captains of men of war, and a mathematical Professor, who repeated to me these flattering words, this will do, this will do.’34
Whoever the authors, the publicity caused quite a stir. In October, a Swedish astronomer named Bengt Ferrner saw the chair at the workshop of Jeremiah Sisson, who had it mounted above his house with a hole through the roof for the counterweight. Ferrner was not convinced it would work: while it was certainly ‘artful and comfortable’, a ship’s movements would probably disturb it too much.35 Around the same time, one of Tobias Mayer’s supporters scribbled a concerned note to Göttingen about the rival invention, which was being called ‘Erwin’s Easy Chair’.36
Irwin’s publicity drive seems to have impressed the Commissioners, since they met him during 1762 and, swayed by Lord Howe’s report, offered £500 for further experiments. Irwin made sure the papers reported it, one praising ‘the intense labour and unrebukeable perseverance of a fellow subject indued with great candor and modesty’.37 The next year, Irwin told the Commissioners that he had made further improvements but wanted more money. Eventually, they agreed another £100 for him to join the sea trials being discussed with Harrison. All was set for the Easy Chair to go to the West Indies.
Trial by water
With three longitude methods ready by 1763, the end of the Seven Years War allowed a full trial to go ahead and the Commissioners finalized the details in August. The destination was to be Barbados, with Maskelyne appointed as the astronomer in charge, assisted by Charles Green, an astronomical assistant at the Royal Observatory. On the way out, Maskelyne and Green were to test Irwin’s marine chair and Mayer’s newest tables, which his widow had sent after his death in 1762. Once at Barbados, they were to determine the island’s longitude by observations of Jupiter’s satellites in order to assess the two astronomical methods and the performance of H4, which would travel separately with William Harrison.
Fig. 30 – ‘View of Bridgetown and part of Carlisle Bay in the Island of Barbadoes’, by Edward Brenton, late eighteenth century
{National Maritime Museum, Greenwich, London}
Maskelyne, Green and Irwin departed England on the Princess Louisa in September 1763, arriving in Bridgetown (Fig. 30) in early November. The two methods had fared very differently. The astronomers had made many successful lunar-distance observations, Maskelyne noting that the results of his final set were within ½° of the truth. ‘My friend Irwin’s machine’, he confided to his brother, however, ‘proves a mere bauble’.38 Even in calm waters, Jupiter and its satellites moved too rapidly across the field of view, although Green did manage at least one successful observation. For the second half of the voyage, they abandoned the chair and focused on the Moon.
William Harrison left the following March on the Tartar. The watch performed well throughout and impressed the ship’s captain. William had reason to feel confident, therefore, until he came ashore in mid-May. According to his later account,
he was told that Mr. Maskelyne was a Candidate for the Premium for discovering the Longitude and therefore they thought it was very odd, that he should be sent to make the Observations to Judge another Scheme Mr. Maskelyne having declared in a very Public manner that he had found the Longitude himself ...39
Harrison claimed that Maskelyne was so discombobulated when challenged on the matter that his observations became sloppy and worthless. Maskelyne’s actual thoughts are unknown, but it is worth noting that Harrison junior was hardly an objective advocate for his father. Nor is there evidence that the young astronomer sought a reward, since it was Mayer’s work that was on trial, not his. Nonetheless, the incident was symptomatic of deteriorating relations between the Harrisons, the Commissioners and the astronomical community represented by Maskelyne.
Harrison and Maskelyne returned to England separately the same year. The Commissioners sent the results for processing and were ready to consider them on 9 February 1765, Maskelyne having been appointed as fifth Astronomer Royal only the day before. No doubt to the consternation of the Harrisons, he was now a Commissioner too.
There was much to discuss at the meeting. In the light of Maskelyne’s testimony that lunar distances could find
longitude to within 1°, the Commissioners recommended that Mayer’s widow receive up to £5000 in recognition of her husband’s work. They also confirmed that John Harrison’s watch had kept time within the most stringent limits of the 1714 Act, its error being just 39.2 seconds or 9.8 miles (15.8 km) at the latitude of Barbados. They pointed out, however, that he
hath not yet made a discovery of the Principles upon which the said Timekeeper is constructed, nor of the method of carrying those principles into Execution, by means whereof other such Timekeepers might be framed of sufficient correctness to find the Longitude at sea ... whereby the said Invention might be adjudged practicable and usefull in terms of the said Act & agreeable to the true Intent & meaning thereof.40
Their recommendation was that Parliament award Harrison £10,000 when he demonstrated the principles of the watch, with the remaining £10,000 (less payments already made) to be awarded once it was proved that ‘his method will be of common & general Utility’; in other words, once it was shown that other makers could produce similar timekeepers.41 This would set the terms of a series of increasingly heated debates with the Harrisons, who considered that the full reward was already due under the terms of the 1714 Act and that the Commissioners had unfairly changed the rules.
The recommendations went before Parliament and became law in a new Longitude Act of 10 May 1765. This confirmed the conditional payments to Harrison, but awarded only £3000 to Mayer’s heirs, as well as £300 to Leonhard Euler for theoretical work that underpinned the development of accurate lunar tables. In addition, the Act proposed that £5000 might be paid to anyone who improved Mayer’s tables in the future and instructed the Commissioners to begin publishing a nautical almanac. The trials were over. It was up to the Commissioners to bring the new methods into practice.
Finding Longitude Page 8
