The Longitude Problem: How a Clock Taught Ships Where They Were

For several days in October 1707 the navigators of a Royal Navy fleet could not take a sight of the Sun. Admiral Sir Cloudesley Shovell was bringing his ships home from the Mediterranean, and without sights the fleet's position was an estimate built from compass headings and guessed speeds. Most of the navigators believed the ships were still west of Ushant, an island off the French coast. On the night of October 22 the flagship Association and three other ships struck rocks off the Isles of Scilly, off the south-west coast of England.

Royal Museums Greenwich says more than 1,300 men were lost, Shovell among them, with only about 26 survivors reported in its print record (a Greenwich blog on the disaster counts a few fewer, about two dozen). Other accounts put the dead at 1,400 or as high as 2,000, so the toll is uncertain. That date is Old Style: Britain still used the Julian calendar, which ran 11 days behind ours in 1707, so it was November 2 by today's calendar (our calculation).

This is part three of our series on the history of time. Bells, Gears and Pendulums: How the Mechanical Clock Changed Daily Life ended with pendulum clocks that kept good time on land and failed on a rolling ship. This part follows the problem the Scilly wreck has come to stand for: how a ship far from land could know how far east or west it was.

The wreck everyone points to#

The Scilly disaster is often said to have led to the Longitude Act of 1714. The evidence is thinner: in its record of a print of the wreck, Royal Museums Greenwich says the claim is often made but there is no hard evidence for it. The National Archives lists public outcry as one influence, next to a petition of 1714 that we come to below. A fair reading: a famous tragedy that made the problem vivid, whose weight in Parliament's decision cannot be shown.

Even the cause is argued. The usual account blames a longitude error. But a blog summary of the scholarship mentions a study of the fleet's surviving logbooks arguing that latitude errors mattered more, and notes that the Scilly Isles were themselves not accurately placed on charts. Royal Museums Greenwich has a blog series testing how much the wreck contributed to the Act. What nobody disputes is the larger point: far from land, in bad weather, officers could not be sure where they were.

Latitude is easy, longitude is not#

Finding how far north or south you are is a problem the sky solves for you. At noon the Sun is at its highest, and its angle above the horizon, combined with a table of its declination (how far north or south of the equator it stands that day), gives your latitude. At night the Pole Star does the job in the Northern Hemisphere. The Australian National Maritime Museum sums up the contrast: latitude had obvious reference points in the sky that were easy enough to measure, while longitude needed very accurate tools and tables.

East and west have no such anchor. Nothing overhead tells you where you are along a line of latitude, and even the starting line for counting longitude is a human choice. Without a fix, ships relied on dead reckoning: heading from the compass, speed from a log thrown over the side, time from a sandglass. Each is an estimate, and a hidden current or a sideways wind adds error that builds over weeks. Navigators often knew how far north they were and had to guess the rest.

The arithmetic that turns a clock into a map#

The principle was understood long before anyone could use it. The Earth turns through 360 degrees in about 24 hours: 15 degrees every hour, or one degree every four minutes. Two clocks that disagree by an hour stand 15 degrees of longitude apart.

A navigator needs two times. Local time comes from the sky, because the Sun is at its highest at local noon. The other is the time at a place of known longitude, such as the Greenwich observatory, and that must come from a clock that kept Greenwich time all the way from home. Take a made-up ship whose navigator marks the instant the Sun peaks, which is noon on board, when the Greenwich clock reads 15:20.

1. The Greenwich clock is 3 hours 20 minutes ahead: 200 minutes.
2. At four minutes per degree, 200 ÷ 4 = 50 degrees.
3. Greenwich has already passed noon, so the ship, where noon comes later, is west of it: 50 degrees west.

The Sun runs a little ahead of or behind an evenly ticking clock through the year, and navigators corrected for that. The even-ticking version is mean time, the "mean" in Greenwich Mean Time.

• 15 degreeshow far the Earth turns in one hour, so one hour of clock difference equals 15 degrees of longitude
• 2 minutesthe clock error that equals the half degree allowed for the Act's £20,000 prize, or 30 geographical miles (nautical miles)
• 5.1 secondshow far behind H4 was reported to be on reaching Jamaica, once its rate was allowed for, about 1.3 nautical miles of longitude at the equator (our calculation)
• 22chronometers FitzRoy carried on the Beagle's voyage of 1831 to 1836

How good did the clock have to be? The Act's top tier was half a degree, which is two minutes of time. Royal Museums Greenwich says Harrison aimed for a portable clock good to within three seconds a day, which over a six-week voyage adds up to 126 seconds (our calculation; six weeks is how the test is usually described). Part two found early pendulum clocks quoted anywhere from a few minutes to about 15 seconds a day on steady ground. Even the best-case 15 seconds is five times the target before a ship's motion is added.

Prizes, Jupiter's moons and the Act of 1714#

Offering a reward was not a British invention. Spain had a prize from the 16th century, confirmed in 1598, according to a scholarly history of the European longitude prizes. Galileo's proposal to Spain, around 1616 or 1617, was clever: the moons of Jupiter slip into the planet's shadow at predictable times, so each eclipse is a signal that anyone with a telescope can see. On land it worked, and by the late 1600s it was used for surveying and mapping, according to a Royal Museums Greenwich blog. At sea, holding a telescope on a tiny moon from a pitching deck was very difficult, and the same blog records that a "marine chair" built to steady observers gave no real advantage when Nevil Maskelyne tried it in the early 1760s (sources date the test to his 1761 St Helena voyage or to the 1763 Barbados voyage).

Clocks had the opposite problem. Huygens and his Scottish partner Alexander Bruce had pendulum sea clocks made in the early 1660s, and National Museums Scotland, which owns one of the two survivors, describes them as not the hoped-for solution. A pendulum keeps time only when gravity is the one force pushing it, and a ship supplies shoves of its own.

By 1714 the problem had a campaign behind it. William Whiston and Humphry Ditton petitioned Parliament for a reward, a parliamentary committee including Isaac Newton and Edmond Halley supported them, and the Act became law that July. Cambridge University Library's catalogue gives July 20, and other references give July 8 or 9, so sources differ on the exact day. The Act set a sliding scale:

• £10,000 for a method within 60 geographical miles, or one degree
• £15,000 within 40 miles, or two-thirds of a degree
• £20,000 within 30 miles, or half a degree

In clock terms those are 4 minutes, 2 minutes 40 seconds and 2 minutes (our calculation). The Act also set up commissioners to judge claims, a body usually called the Board of Longitude.

The Moon as a clock#

The sky offered a clock of its own. The Moon moves against the background stars by about 13.2 degrees a day, roughly 33 minutes of arc an hour, so its angle from the Sun or a bright star changes steadily. If a table gives that angle for every third hour of Greenwich time, a navigator who measures it with a sextant, an instrument for measuring angles, can look up the matching Greenwich time. After that the arithmetic is the one above. The Royal Observatory at Greenwich, founded in 1675, was set up with navigation in mind.

The catch was labor. The measured angle had to be corrected for refraction and parallax, then interpolated between table entries, as a history of the method describes. The Moon's pace also sets a hard limit. At its average pace of about 33 arcminutes an hour (it varies, and is slower relative to the Sun), a one-minute error in the angle shifts the computed time by roughly 1.8 to 2 minutes and the longitude by about 27 to 30 minutes of arc, nearly half a degree (our calculation).

The practical breakthrough came from Maskelyne. After the astronomer Tobias Mayer produced lunar tables, Maskelyne tested the method on a voyage to St Helena in 1761, then published it in The British Mariner's Guide in 1763. At the Board's meeting of February 9, 1765 he argued that the method could find longitude within a degree. He proposed a printed almanac that would take the heaviest calculations ashore, and the first Nautical Almanac, for 1767, tabulated lunar distances at three-hour intervals, computed from Mayer's tables and given in Greenwich time.

John Harrison's four machines#

The other answer had been under construction for decades. John Harrison, born in Yorkshire in 1693, was a self-taught clockmaker already known for precision longcase clocks. His first sea clock, H1, had no pendulum. Two linked, weighted bars swung against each other instead, a design meant to cope with a ship's motion. Harrison brought H1 to London in 1735, and it was shown to the capital's scientific community in the workshop of the clockmaker George Graham.

In May 1736 Harrison and H1 sailed for Lisbon on HMS Centurion. The outward leg went badly, but the return, on HMS Orford, went well. The best-known moment comes as the ship neared England: popular accounts say Harrison told the officers they were about 60 miles west of where their reckoning put them, and that he was right. The retelling usually names the Lizard and the Start as the two headlands, though we could not confirm those names in the records we found. That is the traditional version, and it is contested: a History Today article argues from newly examined documents that H1 reached Lisbon with a very substantial error. Harrison asked the Board not for a second trial but for money to build another machine.

H2, made from 1737 to 1739, never went to sea. He worked on H3 from 1740 for 19 years. Royal Museums Greenwich's record of H3 credits it with two inventions that outlived it: the bimetallic strip, still used in thermostats, and the caged roller bearing. Other accounts are more cautious about who first made the bimetallic strip, so read the credit as the museum's.

H4 changed the shape of the answer. The museum's record says Harrison came to see that the solution lay not in H3 but in a smaller watch. Work began in 1755 and the watch was finished in 1759. Its dial is 102 millimeters across and the whole piece weighs 1.45 kilograms, a large pocket watch rather than a machine. Watch-trade writing on the watch gives its balance as running at 18,000 beats an hour, which is five beats a second (our arithmetic), against the one beat a second of the seconds pendulum in part two.

Trials, rules and a long dispute#

Harrison was about 68 when H4 was ready for the sea, and his son William made the voyage. In November 1761 William sailed for Jamaica aboard HMS Deptford with H4, and the ship reached Port Royal on January 19, 1762 (the date as one account gives it). The Linda Hall Library says H4 was only about five seconds slow on arrival, which it puts at about two miles of longitude, a rounder conversion than ours. The figure usually quoted is 5.1 seconds, and by our calculation that is about 1.3 nautical miles at the equator. Two cautions apply. The 5.1 seconds is the error after allowing for the rate Harrison declared for the watch, so it is not a raw reading, and it depends on the longitude assumed for Port Royal, a point some historians of navigation have questioned. The Board of Longitude was not satisfied and called for a second trial.

The second trial was to Barbados in 1764, again with William, aboard HMS Tartar. Maskelyne went to Barbados to take the astronomical observations that fixed the island's position. Sources give H4's error as 38.4 seconds (the Naval Historical Society of Australia, about 9.6 nautical miles) or 43 seconds (a Christie's catalogue entry, an auction description and so a weaker source). A figure of about 39 seconds also circulates in popular accounts, so treat the exact number as uncertain. All of them come to roughly 10 nautical miles at the equator, and the Linda Hall Library simply gives the result as an error of 10 miles. That is about a third of the 30-mile limit and well inside the most stringent tier of the 1714 Act.

The quarrel started there. The Board proposed that Parliament pay Harrison £10,000 once he had explained how H4 worked, with the rest to follow once other makers had produced timekeepers that passed trial. A new Act of May 10, 1765 set those terms. The effect of the condition was that the prize would go to a method others could build, not to a single watch. The Harrisons saw it differently: they argued that the full reward was already due under the 1714 Act and that the Commissioners had changed the rules, as Royal Museums Greenwich describes their view.

From May 1766, H4 was tested for ten months at the Royal Observatory under Maskelyne, by then Astronomer Royal. Royal Museums Greenwich says it did not perform well there; Maskelyne published the results, Harrison challenged them, and the dispute reignited. After an appeal to King George III, Parliament voted Harrison a further £8,750 in 1773. The ONS records that sum and the £10,000 of 1765, £18,750 in all, and notes he never received the reward specified under the 1714 Act. The Linda Hall Library adds £4,315 in advances he had already received, which brings his total receipts to roughly £23,000 (our addition), more than the headline £20,000. So the point is not that he was paid less than £20,000; it is that none of it was the prize as the 1714 Act defined it. He died in 1776.

1. October 22, 1707Four Royal Navy ships are lost off the Isles of Scilly (November 2 by today's calendar).
2. July 1714Parliament passes the Longitude Act, with rewards of up to £20,000.
3. 1736H1 sails to Lisbon aboard HMS Centurion and returns aboard HMS Orford.
4. 1759H4 is completed.
5. November 1761 to January 1762H4 crosses to Jamaica and is reported as 5.1 seconds slow on arrival, once its rate is allowed for.
6. 1764The second trial, to Barbados.
7. May 10, 1765A new Act sets the terms for Harrison's payment.
8. 1767The first Nautical Almanac, for that year, carries lunar distance tables.
9. 1773Parliament votes Harrison £8,750.
10. 1884The International Meridian Conference recommends Greenwich.

Cook, Kendall and a chronometer at sea#

The Board commissioned a copy of H4 from the London watchmaker Larcum Kendall. It is known as K1, and it went to sea with Captain James Cook.

Cook's first voyage, from 1768 to 1771, carried no chronometer. Cook and his astronomer Charles Green used the 1768 and 1769 editions of the new Nautical Almanac instead. On the second voyage, from 1772 to 1775, K1 sailed aboard the Resolution, with the astronomer William Wales testing it. The Oxfordshire Blue Plaques scheme reports that Cook called K1 his trusty friend and never-failing guide, and the Royal Museums Greenwich record of K1 gives the same wording in shortened form. We did not find the original log text, and the other accounts we found repeat the same wording from secondary sources, so treat the phrases as reported rather than checked against the log.

A copy that worked suggested that H4's result had not been a one-off.

From one watch to Greenwich time and time zones#

The roll-out of marine chronometers was gradual. Later makers such as John Arnold and Thomas Earnshaw, rivals over who invented what, are credited with simplifying the designs and making them in larger numbers, according to a collectors' site (a popular source, used here only for the names). In 1821 the Royal Observatory under the Astronomer Royal John Pond took over testing, rating and issuing the Navy's chronometers, according to its chronometer records.

The Beagle's voyage of 1831 to 1836 shows how far things had moved. Captain Robert FitzRoy carried 22 chronometers and wanted a chain of longitudes right around the world. According to Royal Museums Greenwich, the chain closed with an error of only 33 seconds of time (the amount by which the sum of the world-wide chain exceeded 24 hours), though only 11 of the chronometers were still working fully on the return. Other accounts count the well-behaved instruments differently, so read the 11 as the museum's figure. That is about 8 miles of longitude at the equator (33 ÷ 4 = 8.25, our calculation). Cook had one trusted watch. FitzRoy had a fleet to check against each other.

Greenwich was always part of the story. The 1767 Nautical Almanac was built on Greenwich observations, and Royal Museums Greenwich says a ship's chronometer was kept on Greenwich Mean Time so the navigator could compare it with local solar time. By 1884 most of the world's shipping used charts built on the Greenwich meridian. That October delegates from 25 nations (one account counts 26) met in Washington for the International Meridian Conference and voted 22 to 1, with two abstentions, to recommend Greenwich as the common zero line for longitude. A shipping table in the proceedings shows 72 percent using Greenwich charts; other accounts give figures from two thirds to three quarters. How Time Zones Were Born: Railways, Telegraphs and the Day of Two Noons tells the rest of that meeting, including what it did not decide. GMT then served as the international standard of civil time until 1972, when Coordinated Universal Time took over; our guide to UTC vs GMT: What Is the Difference and Which Should You Use? explains the difference.

Ashore, the same arithmetic became the time zone map. One hour is 15 degrees, so zones were drawn as bands about 15 degrees wide, each an hour from the next. Real boundaries follow borders and laws, and some countries choose offsets that are not whole hours; India, at UTC+5:30, is the best-known case, covered in Why India Is UTC+5:30: Half-Hour and 45-Minute Time Zones. What pushed whole countries to agree on one clock on land was the railway, the subject of the next part. Whenever you use the time zone converter, you are doing the navigator's sum in reverse: the places are known, and the clock gap is the answer.

Frequently asked questions

Sources and further reading

1. H4 (collection record) — Royal Museums Greenwich
2. Who was John Harrison? — Royal Museums Greenwich
3. K1 (collection record) — Royal Museums Greenwich
4. Sir Cloudesly Shovel in the Association with the Eagle, Rumney and the Firebrand, Lost on the Rocks of Scilly, October 22, 1707 (print record) — Royal Museums Greenwich
5. Papers of the Board of Longitude, 1605 - 1830 — Cambridge University Library
6. How did astronomers including Nevil Maskelyne help solve the longitude problem? — Royal Museums Greenwich
7. Nevil Maskelyne — MacTutor History of Mathematics, University of St Andrews
8. What is Greenwich Mean Time (GMT) and why is it so important? — Royal Museums Greenwich
9. Look to the horizon: why latitude was easier to find than longitude — Australian National Maritime Museum
10. John Harrison (Scientist of the Day) — Linda Hall Library
11. Valuing John Harrison's work: how much is that £20,000 longitude reward worth today? — Office for National Statistics
12. The Barrington Papers and the Board of Longitude — Royal Museums Greenwich
13. 1884 International Meridian Conference (scans of the proceedings) — Lick Observatory, University of California
14. Longitude: The Hidden Evidence — History Today