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Latitude is easy to find at sea: measure how high the Sun or the pole star stands. Longitude is not, and ships were lost because of it. The fix turned out to be a clock, and the man who built it was a carpenter from Yorkshire with no formal training in clockmaking. This post explains why longitude is a timing problem, what John Harrison built, a worked example converting clock error into distance, and what his way of working can teach you.
Who was John Harrison?
Westminster Abbey's memorial page records that he was baptised at Foulby in Yorkshire on 31 March 1693, worked as a carpenter before turning to clocks, and died in London on 24 March 1776. Royal Museums Greenwich describes him as self-taught; in the mid-1720s his wooden longcase clocks kept time to about one second a month.
Why is longitude a problem about time?
Royal Museums Greenwich explains the principle: Earth rotates through 360° in 24 hours, so one hour of time difference equals 15° of longitude, or one degree every four minutes. If you know your local time from the Sun and also the time at a reference place, the difference gives your longitude.
The hard part was carrying the reference time on a ship. Westminster Abbey's page sums up what a sea clock had to overcome: motion, and variations in gravity and temperature.
The stakes were high. Royal Museums Greenwich records that on 22 October 1707, navigational errors sent ships onto rocks off the Isles of Scilly and more than 1,400 men died. On 9 July 1714 the Longitude Act offered a reward of £20,000 for a practical method.
What did Harrison build?
Harrison made four marine timekeepers, now called H1 to H4, according to Royal Museums Greenwich:
H1 was tested on a voyage to Lisbon in 1736. On the way home Harrison said a headland the officers took for the Start was the Lizard. He was right; the ship was 60 miles off course.
H2 never went to trial because Harrison found a basic flaw in it.
H3 took him 19 years, from 1740, and still struggled to reach the accuracy he wanted.
H4 looked like a large pocket watch. It ticks five times a second, with a large balance that swings faster and wider than a normal watch's.
The museum's catalogue entry for H4 says it was completed in 1759 and measures 165 mm by 124 mm. Harrison aimed for a timekeeper accurate to within three seconds a day. After a 1761 trial to Jamaica and a 1764 trial to Barbados, the Board of Longitude confirmed in 1765 that H4 had kept time within the strictest limits of the 1714 Act. It paid Harrison in stages and demanded proof that others could copy the design, which led to a long dispute.
Westminster Abbey's memorial includes a bimetallic strip, which it names as one of Harrison's inventions. Two metals that expand by different amounts bend when heated, and that bending can correct for temperature. Our post on thermal expansion problems shows the physics.
Worked example: what does clock error cost you?
Take Harrison's target of three seconds a day and a sample voyage of 42 days.
Total clock error. 3 s/day × 42 days = 126 s.
Into degrees. One degree of longitude is 4 minutes = 240 s. So 126 / 240 = 0.525°.
Into distance at the equator. One degree of latitude is 111.1 km, according to Royal Museums Greenwich. On the equator a degree of longitude is almost the same, so 0.525 × 111 ≈ 58 km.
Away from the equator. Lines of longitude get closer together towards the poles, so multiply by the cosine of the latitude. At 20° N, 58 × cos 20° = 58 × 0.94 ≈ 55 km.
A clock that loses a little time every day still leaves you tens of kilometres out after six weeks. The museum notes that even the best watches of the time were far less accurate, which is why Harrison's target mattered.
What mistakes do students make with time and longitude?
Using 24° per hour. It is 360° / 24 h = 15° per hour.
Getting east and west backwards. Places to the east see the Sun earlier, so their local time is ahead.
Forgetting the cosine. A degree of longitude shrinks with latitude; a degree of latitude does not.
If converting between time, angle and distance feels slippery, Fermi's AI tutor can work out what you already know and build a plan for the session, so you practise the step that is actually holding you back.
What can you take from how Harrison worked?
Test in the real setting. H1 went to sea in 1736, not just onto a workbench.
Drop a design when the evidence says so. He abandoned H2 when he found its flaw, and moved from big clocks to a watch when the small balance worked better.
Fix the hidden variable. Temperature changes the length of metal parts, so he built correction into his clocks.
Practice routine: two ports are 30° apart in longitude; find their difference in local time. Then find the longitude error, in degrees and in kilometres at the equator, for a clock that loses 5 seconds a day on a 30-day voyage.
Next step: open a map, pick two cities on roughly the same latitude, and convert their longitude difference into hours and minutes.
