Harrison’s Marine Chronometer and the Longitude Problem

For most of the history of ocean navigation, sailors out of sight of land could find their latitude, their distance north or south of the equator, with reasonable accuracy, but had no reliable way of finding their longitude, their position east or west. The consequences were measured in lost ships, lost cargoes and lost lives. In 1714 the British Parliament offered a reward of up to £20,000 for a practicable method of determining longitude at sea. The two methods that eventually succeeded both depended on knowing the time at a reference meridian while at sea: one found it by observing the motion of the Moon against the stars, and the other carried it in a clock. The clock was the work of John Harrison, a self-taught carpenter and clockmaker from Lincolnshire, who spent more than forty years building a series of timekeepers of unprecedented accuracy and much of his old age in a dispute with the authorities over the reward. This article describes the longitude problem, the approaches tried before Harrison, the development of his four timekeepers, the trials and the controversy, and the spread of the marine chronometer that followed.

Latitude, Longitude and Time

Latitude can be found from the sky. The altitude of the Pole Star above the horizon is roughly equal to the observer’s latitude in the northern hemisphere, and at any place the Sun’s altitude at noon, combined with tables of its declination for the date, gives the latitude directly. By the sixteenth century sailors measured these altitudes with the astrolabe, the cross-staff and later the backstaff, and from the 1730s with the reflecting octant and sextant, which allowed an accuracy of a minute of arc or better. Navigators commonly practised latitude sailing: they sailed to the latitude of their destination and then ran east or west along it until they arrived.

Longitude is a different matter, because the Earth turns. All places on the same meridian see the Sun cross the sky at the same moment, and places to the east see it earlier. The Earth rotates through 360 degrees in twenty-four hours, or fifteen degrees an hour, so the difference in longitude between two places is equivalent to the difference in their local times. Local time could be found at sea by observing the Sun or stars. If a navigator also knew the time at the same instant at a reference place, such as the home port, the difference would give the longitude. Each minute of time error corresponds to a quarter of a degree of longitude, which at the equator is about fifteen nautical miles. To find longitude within half a degree, the standard eventually set by Parliament, after a voyage of six weeks, a clock would have to keep time to within about three seconds a day on a ship rolling, pitching and passing through extremes of heat, cold and humidity. The best pendulum clocks on land in the early eighteenth century could do this, but a pendulum is useless on a moving ship.

Without a means of finding longitude, navigators relied on dead reckoning, estimating the ship’s position from its course by compass, its speed measured by the log line, and the time elapsed. Errors in speed, steering, currents and leeway accumulated, and after a long voyage the estimated position might be wrong by hundreds of miles. Ships missed islands where they had intended to take on water, ran aground on coasts they believed to be far away, and took longer routes to avoid uncertainty. The most famous disaster occurred on the night of 22 October 1707, when a British fleet returning from the Mediterranean under Admiral Sir Cloudesley Shovell misjudged its position on approaching the English Channel and struck the rocks of the Isles of Scilly. Four ships were lost, among them the flagship Association, and some fourteen hundred men died. The Scilly naval disaster is usually attributed to errors in latitude and to the poor charts and compasses of the time as much as to longitude, but it made navigation a matter of public concern.

Astronomical Methods

Several astronomical methods of finding the time at a reference place had been proposed. In 1610 Galileo discovered the four large moons of Jupiter, whose eclipses as they pass into the planet’s shadow occur at predictable moments that could serve as a clock visible from anywhere on Earth. Giovanni Domenico Cassini at the Paris Observatory compiled tables of the eclipses in 1668, and the method was used with great success on land to map France and later other countries, revealing that the coastline of France had been drawn too far west. But it required a long telescope held steady, which was impossible on the deck of a ship.

The other celestial clock was the Moon, which moves about its own diameter against the background stars every hour. If its position could be predicted accurately for a reference meridian, a navigator could measure its angular distance from a bright star or the Sun, compare it with the tables and so find the time at the reference meridian. This was the method of lunar distances, first proposed by Johannes Werner in 1514. Its difficulty lay in the complexity of the Moon’s motion, which is disturbed by the Sun and the planets, and in the lack of an accurate catalogue of star positions. To solve these problems Charles II founded the Royal Observatory at Greenwich in 1675, with John Flamsteed as the first Astronomer Royal, charged with “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 the perfecting the art of navigation”. Isaac Newton’s theory of gravitation, published in 1687, provided a framework for calculating lunar motion, but Newton found the problem of the Moon the hardest he attempted, and accurate tables were still decades away.

The idea of a timekeeper had also been considered. In 1530 the Flemish mathematician Gemma Frisius suggested carrying a clock, but no clock of the time came close to the required accuracy. Christiaan Huygens invented the pendulum clock in 1656 and later the balance spring for watches, and in the 1660s marine pendulum clocks made to his designs were tried at sea on several voyages, with some promising results in calm weather but failures in storms. Robert Hooke also worked on spring-regulated timekeepers for longitude and disputed priority for the balance spring with Huygens. Newton, giving evidence to Parliament in 1714, said that a watch to keep time exactly had not yet been made, and doubted that one could be, because of the motion of the ship, the variation of heat and cold, wet and dry, and the difference of gravity in different latitudes.

Earlier Prizes

Britain was not the first state to offer a reward for the solution. In 1567 Philip II of Spain offered a prize, and in 1598 his son Philip III promised a substantial pension to anyone who could find longitude at sea. Among the applicants was Galileo, who in 1616 proposed his method of Jupiter’s satellites to the Spanish court and continued to correspond about it for many years without result. The States General of the Netherlands offered a reward in the early seventeenth century and also considered Galileo’s proposal. In France the founding of the Académie Royale des Sciences in 1666 and of the Paris Observatory in 1667 was closely connected with the problem, and from 1720 a bequest from Rouillé de Meslay funded prizes of the Académie for work on navigation and longitude. None of these rewards produced a method that worked at sea, but together they show how important the problem was thought to be by every maritime power in an age of expanding ocean trade, and how widely it was assumed that the solution, when it came, would be astronomical.

The Longitude Act of 1714

In 1714, after a petition from a group of sea captains and London merchants, the House of Commons appointed a committee to consider the longitude problem. It heard evidence from Newton and Edmond Halley and recommended a public reward. The Longitude Act, passed in July 1714, offered £10,000 for a method that would determine longitude to within one degree, £15,000 for two-thirds of a degree and £20,000 for half a degree, equivalent to about thirty nautical miles at the equator, on a voyage from Great Britain to a port in the West Indies, chosen by the commissioners. A body of commissioners, later known as the Board of Longitude, was established to judge proposals and could make smaller awards to encourage promising work. Its members included the Astronomer Royal, the President of the Royal Society, the First Lord of the Admiralty, the Speaker of the House of Commons and the professors of mathematics at Oxford and Cambridge. The prize attracted many impractical schemes, and “finding the longitude” became a byword for an impossible project, satirised by Hogarth in the madhouse scene of A Rake’s Progress.

A Carpenter from Barrow

John Harrison was born on 24 March 1693 at Foulby, near Wakefield in Yorkshire, the eldest son of a carpenter, and grew up at Barrow upon Humber in Lincolnshire, where he followed his father’s trade. He had little formal schooling, but he was given a manuscript copy of lectures on natural philosophy by the Cambridge mathematician Nicholas Saunderson and taught himself mechanics. Between 1713 and 1717 he made three pendulum clocks with movements almost entirely of wood, oak for the frames and lignum vitae, a tropical hardwood with a natural oil, for wheels and bearings, which needed no lubrication. In the early 1720s he built a turret clock for the stable block at Brocklesby Park, the estate of Sir Charles Pelham, which still runs. With his younger brother James he then made a series of wooden longcase clocks incorporating two inventions that removed the main causes of error in pendulum clocks.

The first was the gridiron pendulum. The rod of a pendulum expands in warm weather and contracts in cold, lengthening and shortening the period of the swing. Harrison made the rod from alternating parallel rods of brass and steel, linked so that the greater expansion of the brass raised the bob while the expansion of the steel lowered it, and by choosing the lengths correctly the two effects cancelled. The second was the grasshopper escapement, a light, almost frictionless mechanism in which two hinged pallets released the escape wheel one tooth at a time with very little sliding, and so needed no oil. Oil in the eighteenth century thickened and decayed, and was a principal source of error in clocks. The Brocklesby clock and the longcase clocks of the 1720s are reported to have kept time to within a second a month, a performance far better than that of any other clock of the period.

The First Sea Clock

Harrison’s land clocks convinced him that a timekeeper could be made accurate enough to find longitude, provided its motion could be freed from the effects of the ship. In 1730 he travelled to London with drawings for a sea clock and called on Edmond Halley, then Astronomer Royal and a commissioner of longitude. Halley, judging that the Board would not support a scheme that existed only on paper, sent him to George Graham, the leading clock and instrument maker in London, inventor of the deadbeat escapement and the mercury pendulum. Graham spent a day with Harrison, was impressed, and lent him money without security or interest to build the machine.

Harrison returned to Barrow and spent five years building it. The timekeeper now called H1, completed in 1735, is a large machine of brass in a glazed case, about sixty centimetres high and weighing some thirty-four kilograms. In place of a pendulum, it is controlled by two large dumb-bell-shaped balances, linked by crossed wires so that they swing in opposite directions, and governed by helical springs. Any motion of the ship that tended to speed one balance would slow the other, so that the effects cancelled. Temperature compensation was provided by a gridiron of brass and steel rods acting on the springs. Most of the wheels were of brass but had pinions of lignum vitae rollers, and the whole movement, like his wooden clocks, ran without oil. It was the first serious attempt to build a precision timekeeper that would work at sea.

H1 was shown to members of the Royal Society, who gave Harrison a certificate of approval, and in 1736 the Admiralty sent it on a trial voyage to Lisbon aboard HMS Centurion, returning on HMS Orford. Harrison went with it. On the return voyage, as the ship approached the English Channel, the master of the Orford believed from his dead reckoning that they were near Start Point in Devon; Harrison, using H1, said they were about ninety miles further west, off the Lizard in Cornwall. Harrison proved to be right. In June 1737 the Board of Longitude met for the first time, more than twenty years after it was created, to consider his machine. Harrison himself was critical of it, saying that it had defects he wished to correct, and asked for funds to build an improved, smaller version. The Board granted him £500, half at once and half on completion.

Twenty Years of Development

H2, completed around 1739, was similar in principle to H1 but heavier and more robust, with the two balances linked by a pair of segments rather than wires, and a remontoire, a small spring rewound at regular intervals by the mainspring, which delivered a nearly constant force to the escapement regardless of the state of the mainspring. It was tested on land but never sent to sea, partly because Britain was at war with Spain, and Harrison found during testing that the bar balances were affected by the centrifugal effects of the ship’s yawing motion. He set it aside and began a third machine.

H3 occupied Harrison for nearly nineteen years, from 1740 until 1759. It was more compact than its predecessors, with two large circular balances linked by a metal ribbon, and it contained two inventions still widely used. The first was a bimetallic strip, a strip of brass and steel riveted together, which bends as the temperature changes because the two metals expand at different rates; Harrison used it to alter the effective length of the balance spring and so compensate for temperature. The second was the caged roller bearing, in which the rollers are held apart by a cage so that they do not rub against one another, the ancestor of modern ball and roller bearings. Yet H3 never achieved the accuracy Harrison sought. He came to believe that large, slow balances were the wrong approach. In 1749 the Royal Society awarded him the Copley Medal, its highest honour, for his work.

The change of direction came from a watch. In 1753 Harrison had a pocket watch made to his own design by the London watchmaker John Jefferys. It was small, with a fast-moving balance, and to his surprise it kept time remarkably well. He concluded that a small, high-frequency balance, given enough energy and properly compensated, would be less disturbed by the ship’s motion than a large slow one.

H4

The timekeeper now called H4, completed in 1759, looks like an outsize pocket watch: a silver case about thirteen centimetres in diameter, weighing about 1.45 kilograms, with a white enamel dial decorated with black floral patterns. Inside, it was the product of all Harrison’s experience. The balance was large for a watch and oscillated five times a second. A bimetallic curb, adjusting the effective length of the balance spring, compensated for temperature. A remontoire, rewound eight times a minute, delivered constant force to the escapement, which was a modified verge with pallets of diamond, and other bearing surfaces were jewelled with rubies and diamonds to reduce friction. The movement was finished to an extraordinarily high standard. Harrison wrote that he thought there was neither any other mechanical or mathematical thing in the world that is more beautiful or curious in texture than this my watch or timekeeper for the longitude.

In November 1761 Harrison’s son William sailed with H4 aboard HMS Deptford from Portsmouth to Jamaica; John Harrison, now sixty-eight, stayed at home. Longitude was to be determined at Portsmouth and at Port Royal in Jamaica by astronomical observations, and the watch’s indication compared with the difference. After eighty-one days at sea, H4 was found to be only 5.1 seconds slow, corresponding to an error in longitude of about a mile and a quarter. Along the way, William used it to predict the arrival at Madeira correctly when the ship’s officers believed they had passed it. The Board, however, was not satisfied. It doubted the accuracy of the longitudes of Portsmouth and Jamaica, pointed out that Harrison had not stated the watch’s rate of gain or loss before the voyage, and argued that a single success might be due to chance. It awarded Harrison £1,500 on account and called for a second trial.

The second trial took place in 1764 aboard HMS Tartar to Barbados. This time the rate was declared in advance, and astronomers were sent ahead to fix the longitude of Bridgetown. One of them was Nevil Maskelyne, a young astronomer who had tested the method of lunar distances on a voyage to St Helena in 1761 and was its leading advocate. After forty-seven days at sea H4 showed an error of 39.2 seconds, equivalent to about ten nautical miles at that latitude, more than three times better than the half degree required for the full reward. Maskelyne’s lunar observations at Barbados, by contrast, were accurate to about thirty miles.

The Dispute over the Reward

Under the terms of the Act, Harrison had now met the conditions for the prize of £20,000. The Board did not see it that way. It argued that the Act required a method that was “practicable and useful”, and that a single handmade watch, whose principles had not been disclosed and which might never be reproduced, did not meet that test. In 1765 a new Act of Parliament set out the terms under which Harrison would receive his reward. He was required to explain the construction of H4 to a committee of experts, including the watchmakers Thomas Mudge and Larcum Kendall, to hand over all four of his timekeepers to the Board, and to make, or have made, two further copies to show that the design could be reproduced. In return he would receive £10,000, less what he had already been paid, with the remaining £10,000 to follow when the copies had been made and tested.

Harrison complied with great reluctance. He took H4 apart before the committee in August 1765, and his explanation was published in 1767 as The Principles of Mr Harrison’s Time-Keeper, with engravings. In 1766, the year after Maskelyne became Astronomer Royal, H4 was taken to Greenwich and subjected to a ten-month trial at the observatory, in which it performed poorly, gaining irregularly. Harrison complained that the trial was conducted unfairly, that the watch had been tested in positions and conditions for which it was not adjusted, and that Maskelyne, who had a personal interest in the lunar method, could not be impartial. Historians remain divided about how far the Board’s treatment of Harrison was unjust and how far it reflected reasonable concern about whether a single machine of such complexity could be turned into a practical instrument for the navy.

In the meantime the lunar distance method had become practical. In 1755 the German astronomer Tobias Mayer of Göttingen sent the Board lunar tables of unprecedented accuracy, and Maskelyne, as Astronomer Royal, began publishing the Nautical Almanac for 1767, which gave predicted distances of the Moon from the Sun and selected stars at three-hourly intervals for the meridian of Greenwich. With the Almanac and a sextant, a skilled navigator could find longitude to within about half a degree after some hours of calculation. Mayer’s widow received £3,000 from the Board, and the Swiss mathematician Leonhard Euler, whose theory Mayer had used, £300. Because the Almanac referred all its data to Greenwich, it established the habit of reckoning longitude from the Greenwich meridian that was confirmed internationally in 1884.

The copy of H4 was made by Larcum Kendall, who completed it in 1769 at a cost of £450. Known as K1, it was taken by James Cook on his second voyage to the Pacific in HMS Resolution, from 1772 to 1775. Cook, who had used lunar distances on his first voyage, found the watch excellent, calling it “our trusty friend the Watch” and “our faithful guide through all the vicissitudes of climates”. Its daily rate never exceeded eight seconds. K1 went on to sail with Cook on his third voyage and later with the First Fleet to Australia in 1787.

Harrison, meanwhile, was refused the second half of the prize. He and William built a fifth timekeeper, H5, between 1770 and 1772, and through the intervention of the astronomer Stephen Demainbray, they arranged for it to be tested by King George III at his private observatory at Kew. Over ten weeks in 1772 it was found to be accurate to within a third of a second a day. The King is reported to have said, “By God, Harrison, I will see you righted.” With his support, and after a petition to Parliament, Harrison was awarded £8,750 in June 1773 by a separate Act of Parliament, as a bounty rather than as the longitude prize, which was never formally awarded to anyone. In all, he received some £23,000 from the government over forty years. He died in London on 24 March 1776, his eighty-third birthday, and was buried at Hampstead.

Harrison’s Character and Later Claims

Harrison was a difficult man to deal with. He was suspicious of the scientists and gentlemen who sat on the Board, many of whom regarded him as an artisan without learning, and his written explanations of his work were notoriously obscure. Having taught himself, he distrusted mathematical theory and placed his confidence in experiment, and he believed, with some justice, that the astronomers on the Board favoured the lunar method because it was theirs. His son William, who conducted both sea trials, managed much of the family’s correspondence and campaign in the later years and became a Fellow of the Royal Society in 1765. Harrison’s final work, published in 1775, the year before his death, was a long and rambling book titled A Description Concerning Such Mechanism as Will Afford a Nice, or True Mensuration of Time. It mixed an account of his grievances against the Board with technical description and with a theory of the musical scale, on which he had views of his own, and with the claim that a pendulum clock built to his principles could keep time to within a second in a hundred days.

The claim was widely dismissed as fanciful, since the best observatory clocks of the time were far less accurate. In the 1970s the English clockmaker Martin Burgess began to build clocks to Harrison’s late design, using his grasshopper escapement, gridiron pendulum and other features, and one of them, completed by Charles Frodsham and Company and known as Clock B, was tested at the Royal Observatory over a hundred days in 2014 and 2015. At the end of the trial it was found to be only five-eighths of a second in error, and it was recognised by Guinness World Records as the most accurate mechanical clock with a pendulum swinging in free air. The result vindicated, nearly two and a half centuries later, a boast that most of Harrison’s contemporaries had considered absurd.

Harrison’s reputation grew slowly after his death. For much of the nineteenth century the credit for the practical chronometer went to Arnold and Earnshaw, whose designs were the ones in use, and to the astronomers whose methods had dominated navigation for half a century. Gould’s restoration and his book revived interest in the timekeepers, and Harrison’s standing was further raised in 1995 by Dava Sobel’s popular account Longitude and by a television adaptation in 2000. Some historians have since argued that the popular story exaggerates Harrison’s isolation and the hostility of the Board, which in fact supported his work with grants for more than thirty years, and underestimates the contribution of the lunar method, which most navigators continued to use well into the nineteenth century. In 2006 a memorial to Harrison was unveiled in Westminster Abbey, close to the grave of Newton, who had doubted that such a timekeeper could ever be made.

The Chronometer Becomes Practical

H4 and K1 showed that a timekeeper could find longitude at sea, but they were too complex and expensive for general use; K1 had cost almost as much as a small ship. The task of turning Harrison’s achievement into an instrument that could be made in quantity at a reasonable price fell to other makers. Pierre Le Roy in France, who had developed a detached escapement and a temperature-compensated balance by 1766, and Ferdinand Berthoud, who supplied the French navy, both made successful marine timekeepers. In England, John Arnold and Thomas Earnshaw developed the spring detent escapement, in which the balance swings freely for most of its arc, and the compensation balance, whose rim was made of bimetallic strips that changed its effective diameter with temperature. These designs, simpler and more robust than Harrison’s, became the standard form of the marine chronometer, the name Arnold popularised for his timekeepers, by about 1800, and were made in their basic form until the second half of the twentieth century.

In practice, finding longitude with a chronometer was much simpler than with lunar distances. The chronometer was set to Greenwich time before departure and its daily rate of gain or loss was established by observation over several days in port. At sea, the navigator measured the altitude of the Sun with a sextant in the morning or afternoon, when it was rising or falling quickly, and noted the chronometer reading at the same moment. From the altitude, the ship’s latitude and the Sun’s declination, a short calculation with spherical trigonometry, known as a time sight, gave the local time. The difference between local time and Greenwich time, corrected for the chronometer’s accumulated error, gave the longitude directly. The whole procedure took perhaps a quarter of an hour, compared with several hours for a lunar distance, and needed no exceptional skill. Lunars remained useful as a check, especially on long voyages, until the second half of the nineteenth century, when cheaper and more reliable chronometers made them largely unnecessary.

The adoption of chronometers at sea was gradual. In 1802 a chronometer by Earnshaw could cost about £80, and many naval officers bought their own. The Royal Navy began to issue them to its ships in the early nineteenth century, and by the 1820s most of its ships carried at least one. Ships generally carried two or three so that the chronometers could be checked against one another. The surveying voyages of the nineteenth century, such as that of HMS Beagle under Robert FitzRoy from 1831 to 1836, which carried twenty-two chronometers, used them to fix the longitudes of points around the world and to produce accurate charts. Ships needed to check their chronometers at the start of a voyage, and time balls, which dropped at a fixed hour, were erected at ports; the one at the Royal Observatory has dropped at one o’clock every day since 1833. From the middle of the nineteenth century time signals were transmitted by electric telegraph, and from the early twentieth century by radio, which eventually made it possible to check the time at sea anywhere.

Restoration and Legacy

After Harrison’s death his timekeepers were stored at Greenwich and neglected. In 1920 Rupert Gould, a retired naval officer, obtained permission to restore them, and over the next seventeen years, unpaid, he cleaned and repaired all four, publishing The Marine Chronometer: Its History and Development in 1923. H1, H2, H3 and H4 are now displayed at the Royal Observatory, Greenwich, where H1, H2 and H3 are still kept running, while K1 is held by the National Maritime Museum. Harrison’s papers, together with those of the Board of Longitude, have been digitised by Cambridge University Library.

Harrison’s work belongs to a broader eighteenth-century effort to measure the Earth and to standardise the quantities on which navigation and commerce depended, an effort that also produced the metric system, as described in the account of the metre and the meridian. The principle he exploited, that position can be found from accurate time, has never been abandoned. Atomic clocks, whose development is described in the history of the lab that measured time, now keep time to within a billionth of a second a day. The Global Positioning System uses atomic clocks on satellites to transmit time signals; a receiver calculates its position from the differences in the time at which the signals arrive from several satellites, each nanosecond of error corresponding to about thirty centimetres. It is the same problem Harrison set out to solve, in which an error of one second meant a quarter of a mile at the equator, solved with clocks of a precision that would have been unimaginable to him.

References

1. Harrison’s clocks and the longitude problem - Royal Museums Greenwich
2. Harrison’s first marine timekeeper, H1 - Royal Museums Greenwich collections
3. Harrison’s second marine timekeeper, H2 - Royal Museums Greenwich collections
4. Harrison’s third marine timekeeper, H3 - Royal Museums Greenwich collections
5. Harrison’s marine timekeeper, H4 - Royal Museums Greenwich collections
6. Larcum Kendall’s marine timekeeper, K1 - Royal Museums Greenwich collections
7. Papers of the Board of Longitude - Cambridge Digital Library, Cambridge University Library
8. John Harrison - Grokipedia, life and timekeepers
9. Longitude Act - Grokipedia, the Act of 1714 and later legislation
10. Marine chronometer - Grokipedia, from Harrison to Arnold and Earnshaw
11. Lunar distance (navigation) - Grokipedia, the astronomical method of finding longitude
12. Nevil Maskelyne - Grokipedia, Astronomer Royal and the Nautical Almanac
13. Royal Observatory, Greenwich - Grokipedia, foundation and history
14. Larcum Kendall - Grokipedia, K1 and Cook’s voyages