History topic: English attack on the Longitude Problem

The early history of the longitude problem is discussed in our article Longitude and the Académie Royale. The present article discusses the attack on the longitude problem in England which began around the middle of the 17th century.

Groups of scientists began meeting in London and Oxford from 1645 and certainly the longitude problem was one of the main problems which they discussed. A poem written in 1661 described the work going on at Gresham College (see [6]):-

The Colledge will the whole world measure,
Which most impossible conclude,
And Navigators make a pleasure
By finding out the longitude.
Every Tarpalling shall then with ease
Sayle any ships to th'Antipodes.
[Tarpalling is old spelling for tarpaulin which, in addition to its meaning as a piece of material used for protecting exposed objects, means a sailor ]

In 1662 the group from Gresham College, which included John Wilkins, John Wallis and Robert Hooke, and other groups of scientists, became the Royal Society of London for the Promotion of Natural Knowledge. The Royal Society was granted its charter by Charles II and another member of the Gresham College group, Christopher Wren, wrote the preamble to the Royal Society's charter. One of the stated aims of the newly founded Royal Society was Finding the longitude.

Jonas Moore, a mathematics teacher and surveyor who was greatly in favour with Charles II, became a patron of John Flamsteed in 1670 after he met Flamsteed during a visit Flamsteed made to the Royal Society in London. Jonas Moore was able to provide Flamsteed with instruments to carry out astronomical observations. Three years later Moore, together with the famous diary writer Samuel Pepys, founded the Royal Mathematical School within Christ's Hospital. This School was set up with the specific aim of training boys in navigation techniques so that they could serve the King at sea.

Proposals were being made to solve the longitude problem and in 1673 one based on magnetic declination was proposed by a certain Henry Bond, see [9]. Charles II set up a committee to examine the proposal, the committee included among its members Brouncker, the President of the Royal Society, John Pell and Robert Hooke.

Hooke had long been interested in clocks and whether they might be used to solve the longitude problem. After investigating the difficulties he concluded that getting a clock to keep sufficiently accurate time at sea to solve the longitude problem was virtually impossible:-

Difficulties were proposed from the alteration of climates, airs, heats and colds, temperature of springs, the nature of vibrations, the wearing of materials, the motion of the ship ...
Nevertheless Hooke had lectured in 1664 on 20 different ways to use a spring to make the balance of a clock more uniform and said that he had a few tricks up his sleeve that might let him produce a sufficiently accurate clock. Hooke, therefore, like almost all scientists of that time was a biased judge of longitude solutions since he hoped to solve the problem himself.

Jonas Moore, although keen to see a solution of the longitude problem, seems to have seen his role as making it possible for others to solve it rather than himself. He persuaded Charles II to grant a warrant so that Cambridge could award an M.A. to Flamsteed in 1674. That same year the Royal Society began to plan to set up an observatory which Moore offered to finance but another proposal came from a Frenchman Le Sieur de St Pierre claiming to have solved the longitude problem using astronomical data. Charles II set up a Royal Commission to examine these new proposals from St Pierre consisting of Brouncker, Pell, Hooke together with Wren and three others.

In February 1675 Flamsteed arrived in London to stay with Moore and Moore arranged that Flamsteed be appointed assistant to the Royal Commission just set up to examine St Pierre's longitude proposals. Flamsteed quickly made observations which indicated that St Pierre's method of predicting the position of the moon, the lunar distance method of solving the longitude problem, was of little use. Of course if the exact position of the moon could be predicted then the longitude problem was solved and the English began to treat this as their main attack on the longitude problem in contrast to the French who worked largely on the moons of Jupiter method.

Moore also arranged for Flamsteed to visit the King and tell him of Jean Picard's work in the Paris Observatory and the French attack on the longitude problem. Flamsteed, playing the 'national pride' card, stressed to the King how the French had a Royal Observatory for this work and the King quickly moved so that England could match France. On 4 March 1675 he appointed Flamsteed his astronomical observer by Royal Warrant. From his salary of £100 he had to pay £10 taxes and also provide all his own instruments so that he might:-

... apply himself with the most exact care and diligence to rectifying the tables of the motions of the heavens, and the places of the fixed stars, so as to find the so-much-desired longitude of places for perfecting the art of navigation.
Flamsteed was informed of his appointment by Moore but was far from excited by the salary proposed, particularly when he learnt that he had to give lessons to two boys at the Royal Mathematical School at Christ's Hospital as part of his duties. Within two days of Flamsteed's appointment, Greenwich had been accepted as a site for the new observatory, the site being chosen by Wren. The building the Royal Observatory at Greenwich began in 1675 designed by Wren and directed by Hooke. Flamsteed and Halley advised on the requirements for the instruments and observing began in 1676.

One of Flamsteed's first projects at the Royal Observatory was to attempt to prove that the Earth rotated on its axis at a constant rate. This had been assumed by Copernicus when he first put forward his theory of the solar system but it had never been proved. It was also a vital ingredient in all proposed methods of determining the longitude which made the assumption that the Earth rotates a fixed amount in each minute.

Moore purchased two clocks for Flamsteed with pendulums 4 m long which were hung above the dials of the clocks. The Sun could not be used as a timekeeper since the fact that the Earth's orbit is not circular means that the sundial time would be ahead of accurate clock time for part of the year and behind it at other times. This variation between clock time and sundial time is known as the Equation of Time or the Equation of Natural Days and had been known to the Greeks and Arabs many centuries earlier (although of course the reason for the variation was not then understood).

Flamsteed used the star Sirius as a timekeeper correcting the sidereal time obtained from successive transits of the star into solar time, the difference of course being due to the rotation of the Earth round the Sun. Flamsteed wrote in a letter in 1677:-

... our clocks kept so good a correspondence with the Heavens that I doubt it not but they would prove the revolutions of the Earth to be isochronical...
He required a year to complete the experiment but this would only be possible if the Ordnance who paid his salary:-
... starve me not out, for my allowance you know is but small and now they are three quarters in my debt. I fear I must come down into the country to seek some poor vicarage, and then farewell to one experiment.
However Flamsteed did not starve and by March 1678 he had proved the isochronus rotation of the Earth. One part of the longitude problem was thus solved although nobody really doubted that the Earth rotated at a constant rate. (Of course we now know that with more accurate measurements we can detect that the Earth's rate of rotation does change and leap seconds are added on various occasion to correct for this.)

The Greenwich Royal Observatory had to provide large amounts of data and Flamsteed spent 15 years from 1689 to 1704 compiling tables of the moon for the lunar distance method of finding the longitude. Newton also required data on the moon so that he could perfect his understanding of the orbit in terms of his new theory of gravitation.

Between 1690 and 1707 there were a number of incidents in which English naval ships were lost at sea because they had lost their positions. In the most serious incident in 1707 over 2000 men were lost when four ships ran aground on the Scilly Islands while returning to England. More and more pressure was mounting for a solution to the longitude problem as the continuing failure to solve it was costing England vast sums of money. Everyone believed that mathematicians and astronomers would provide the solution but it is not to be. However both ingenious serious proposals as well as comical ones continued to come forward.

One comical proposal, based on the correct understanding that a knowledge of universal time would allow the longitude to be calculated, is described in [1]:-

[The proposal] involved the use of ... the 'powder of sympathy'. ... the powder of sympathy was applied, not to the wound but to the weapon that inflicted it. ... before sailing every ship should be furnished with a wounded dog. A reliable observer on shore, equipped with a standard clock and a bandage from the dog's wound would ... every hour, on the dot, immerse the bandage in a solution of the powder of sympathy and the dog on shipboard would yelp the hour.
A more serious proposal came from William Whiston and Humphrey Ditton in 1714. They proposed, see [1]:-
... a number of lightships be anchored in the principal shipping lanes at regular intervals... The lightships would fire at regular intervals a star shell timed to explode at 6440 feet. Sea captains could easily calculate their distance from the nearest lightship merely by timing the interval between the flash and the report.
Parliament set up a Committee whose members included Newton and Halley to examine the Whiston - Ditton proposals and report in general on the longitude problem. Newton reported to the Committee that most longitude proposals were correct in theory but fell down in practice. Newton did not favour the French method of using Jupiter's moons and noted that the Whiston - Ditton method did not allow longitude to be found at sea if ever it was lost. Newton did consider the clock method which was to eventually to succeed:-
One is, by a watch to keep time exactly: but by reason of the motion of the ship, the variation in heat and cold, wet and dry, and the difference in gravity at different latitudes, such a watch had not yet been made.
Parliament thought the time had come to make a radical move and, on 16 June 1714, they passed an Act:-
... for providing a publick reward for such person or persons as shall discover the longitude... to a sum of ten thousand pounds, if it determines the said longitude to one degree of a great circle, or sixty geographical miles, to fifteen thousand pounds, if it determines the same to two thirds of the distance, and to twenty thousand pounds, if it determines the same to one half of the same distance...
To understand the value of this prize one has only to remember poor Flamsteed's annual salary of £100 to provide both a living and to buy his instruments. Commissioners were appointed, known as the Board of Longitude, to judge whether proposals had met the conditions and to provide cash advances for promising proposals. The Commissioners included members of the Admiralty, the Astronomer Royal, the Savilian, Lucasian, and Plumian professors of mathematics in Oxford and Cambridge and ten members of Parliament.

Of course there was a flood of hopeful proposals submitted, one from Wren being among them. The Commission employed a secretary to deal with the huge number of impossible suggestions and met three times a year to consider those which the secretary thought just might be worth the Commission studying further. Many small awards were made but no proposal of real merit came along.

Before describing John Harrison's contribution to the longitude problem, and his finally solving the problem, there is one other important ingredient which should be mentioned. John Hadley, who was vice-president of the Royal Society, described in a communication to the Society in May 1731, two new instruments which were based on the principle of double reflection. These instruments allowed, see [6]:-

... both bodies (for lunar distances) or the body and the horizon (for altitudes) to be seen by the observer simultaneously, making observations in a moving ship practicable.
In fact Thomas Godfrey in Pennsylvania had made the same invention at almost exactly the same time as Hadley, and it was later discovered in Halley's papers that Newton had a similar idea in 1700 but Halley had told him it was not practical.

John Harrison built his first clock in 1715, the year after the Longitude Act was passed. By 1727 he had made a very fine clock with a 'gridiron' pendulum which consisted of nine alternating steel and brass rods to eliminate the effects of temperature changes. In 1730 Harrison visited London, taking with him his gridiron pendulum and the grasshopper escapement which he had developed, and there he learnt exactly what was required to win the longitude prize. He spoke with Halley, the Astronomer Royal, who advised him not to seek finance from the Board of Longitude, but rather first to seek money from other sources.

This Harrison did and was given money to enable him to make his first clock, specially designed to keep accurate time at sea. Halley advised him to approach the Board after his clock was built. Harrison completed the clock, now called H1, in 1735. It was a large clock weighing about 35 kg, looking far from beautiful but with many ingenious features. He took it to London where it was examined by five members of the Royal Society, including Halley, and they were enthusiastic about the clock and gave Harrison a certificate which basically meant that the Board of Longitude had little option but to order a sea trial.

Harrison accompanied H1 on board H M S Centurian to Lisbon and returned on H M S Oxford. It was a strange choice of a route since it was largely north/south but H1 behaved well and Harrison was able to tell the captain on the return voyage that the ship was 150 km further west that the captain believed.

However Harrison was not happy with H1 and he approached the Board of Longitude in 1737. The minutes of the Board record:-

Mr John Harrison produced a new invented machine, in the nature of clockwork, whereby he proposes to keep time at sea with more exactness than any other instrument of method hitherto known... and proposes to make another machine of smaller dimensions within two years, whereby he will endeavour to correct some defects which he hath found in that prepared...
H2 was built with £250 from the Board of Longitude (with the promise of another £250 when it was delivered for testing), but despite the intention, it turned out to be heavier than H1. It did however have a number of further innovative features. Harrison completed H2 in 1739, as promised, but spent two years testing it himself. Sea trials were difficult since England was at war with France: the Seven Years War certainly disrupted scientific advance.

Harrison decided to build a third clock, H3, and wrote to the Board of Longitude in 1741. He was awarded another £500. Clearly the Royal Society were impressed with Harrison's work since they awarded him their Copley Medal in 1749, a remarkable event considering the fact that Harrison had no academic background or training. The Royal Society proclaimed Harrison to be:-

... the author of the most important scientific discovery or contribution to science by experiment or otherwise...
Work on H3 did not go as well as Harrison had hoped and he received a number of further advances from the Board of Longitude before he eventually decided in 1757 not to test H3 but to build a much smaller clock.

H4 was started in 1757 and completed in two years.

It was about 12 cm in diameter and Harrison himself was perfectly correct when he said:-

I think I may make bold to say, that there is any other mechanical or mathematical thing in the World that is more beautiful or curious in texture than this my watch or time-keeper for the longitude ...
In 1761 Harrison requested a trial at sea for H4. Since 1741 he had received £3000 from the Board of Longitude to help him complete his work and they now gave him another £500 to complete adjusting H4.

Although up to this stage Harrison had been treated pretty well by the Board of Longitude he was now to find it almost impossible to convince them that H4 satisfied the conditions for the award of the £20000 prize. A trial was organised and H4 was put on the Deptford with John Harrison's son, William Harrison, looking after it. The conditions of the prize were completely met when the Deptford reached Jamaica, H4 having only lost 5 seconds on the whole journey. On the return, which was not part of the trial, H4 with William Harrison were on the sloop Merlin. The weather was extremely bad and the Merlin was buffeted throughout the journey yet H4 still performed within the conditions set down for the £20000 prize.

The Royal Society and the Board of Longitude were unwilling to give Harrison the £20000 he deserved for meeting the conditions. There were a number of reasons for this. In the first place the conditions had been set up when there was little prospect that they would be met so they had not been carefully thought out. Now it was argued that it could have been chance which meant that H4 satisfied the conditions. Perhaps more significantly there were still many members of the Royal Society who still hoped to win the prize themselves.

James Bradley, who had succeeded Halley as Astronomer Royal in 1742, and Tobias Mayer were convinced that the lunar distance method would lead to the solution of the longitude problem. Mayer had sent his lunar tables to the Board of Longitude in 1756 but the Seven Years War with France had prevented proper trials. In 1761 Maskelyne, another strong believer in the lunar distance method, was sent to St Helena on Prince Henry to test the lunar distance method for the Board of Longitude and in particular to test Mayer's tables. In [7] Howse describes Maskelyne's work on the lunar distance method on this voyage:-

He felt that he had proved the utility of Mayer's tables and of the method generally on the outward voyage. Homeward bound, therefore, he took few observations himself... What he did do, though, was to encourage the ship's officers to take such observations and to show them how to do the laborious calculations...
Maskelyne claimed:-
Longitude can always be found within a degree, or very little more, which answers to about 40 geographical miles in the latitude of the English Channel.
Bradley claimed that he and Tobias Mayer would have shared the £10000 longitude prize but for Harrison's blasted watch. It was not only Harrison who was feeling hard done by.

James Bradley and Mayer both died in 1762 but Mayer's widow later received £3000 from the Board of Longitude. It remained for Harrison to continue his battle but he began to fear that Mayer's report on his success with Mayer's tables might be seen as worthy of the prize since his own success had been ignored. A second trial for H4 was arranged and H M S Tartar sailed from Portsmouth on 28 March 1764 with William Harrison and H4 on board. On arrival at Barbados William Harrison discovered that Maskelyne had been sent on ahead to judge the success of the trial.

William Harrison complained that Maskelyne was not an impartial judge and Maskelyne had the good grace to ask that the necessary observations be made by someone else as he was ill. H4 lost only 54 seconds in the 5 months of the journey and after correction for errors, which Harrison had set out before the journey, the error was reduced to 15 seconds.

The scientific case for H4 winning the £20000 prize was indisputable. A copy of H4 made by Kendall, called K1, was also found to come well within the conditions of the prize and John Harrison, at the age of 78, made another clock H5 in his attempts to satisfy further conditions set out by the Board of Longitude. However it took a petition of John Harrison to the King George III before he received his prize for solving the longitude problem.

In [6] the development of the marine chronometer after Harrison is described:-

It was left to [Harrison's] younger colleagues to design chronometers ... cheap enough to be within reach of ordinary navigators. ... The British East India Company was early in insisting that all their ships carry chronometers. The Royal Navy was somewhat slower in following suit: it was 1840 or later before ships carried chronometers in home waters... annual chronometer trials took place at Greenwich from 1821, with prizes for the best chronometers submitted.

Article by: J J O'Connor and E F Robertson

April 1997

MacTutor History of Mathematics