In October 1707 a British fleet, sailing home from the Mediterranean, struck the rocks off the Isles of Scilly. Its admiral, Sir Cloudesley Shovell, and well over a thousand sailors died. The navigators weren't careless. They simply could not tell how far east or west they were. Latitude was easy: measure the Sun's height at noon. Longitude, the east–west position, had no instrument at all.

Seven years later Parliament offered a fortune for a fix: £20,000 to anyone who could find longitude at sea to within half a degree, about 30 nautical miles. The answer turned out to be a clock.

The Sun is a clock face

The Earth turns 360° in 24 hours, so the Sun appears to sweep 15° of longitude every hour, or 1° every 4 minutes. Travel east and your local noon comes earlier. If you know the time back home, and you can see when it is noon where you are, the gap between the two tells you how far you have come.

Drag the ship below. Each time, the Sun is at its highest for the ship (local noon), and the readout shows what a chronometer still keeping Greenwich time would say.

Say the ship's chronometer reads 14:00 at the moment the Sun is highest. Local noon is two hours behind Greenwich's clock, so you are 2 × 15° = 30° west. The astronomy is simple. The hard part was the clock: it had to keep Greenwich time through months of storms, heat, cold and a pitching deck.

How good does the clock have to be?

One minute of clock error is 15 minutes of arc of longitude, which at the equator is about 15 nautical miles. So the half-degree prize limit allows just 2 minutes of total error at the end of the voyage. Over a six-week trip to the West Indies, that works out to roughly three seconds a day. A good pendulum clock on land could manage it. On a rolling ship the pendulum stalled or swung wildly.

Try it: choose how many seconds a day your clock drifts and how long you have been at sea.

The carpenter who won

John Harrison, a self-taught clockmaker from Yorkshire, spent decades building sea clocks that ignored the swell: paired balances, bimetallic strips against temperature, bearings that needed no oil. His fourth design, H4, looked like a big pocket watch. In 1761 it sailed to Jamaica and arrived about five seconds slow, an error of only a mile or two. Five seconds over two months is a drift of well under a tenth of a second a day, far better than the three the prize demanded.

The Board of Longitude never formally awarded him the full prize. Haggling, new tests and a second watch dragged on for years, and Parliament eventually paid Harrison a final sum in 1773 after he appealed to King George III. He died in 1776, aged 83. Within a few decades, chronometers descended from his ideas were standard on navy ships, and the 1707 kind of wreck became far rarer.

Why it still matters

Every time your phone fixes its position, the same trick is at work: GPS satellites carry atomic clocks, and your phone works out where it is from tiny differences in the time signals' arrival. Navigation, then and now, is timekeeping in disguise. A clock off by a millionth of a second puts you hundreds of metres out; off by a few seconds a day, in 1760, it could put you on the rocks.

So the next time you glance at a watch, remember what a second of its error was once worth: about a quarter of a nautical mile, and sometimes a whole ship.