“The principle underpinning using time differences to chart longitudinal distance is based on the idea that if you know the time in one place, relative to the time where you are, you can use the difference to work out the longitudinal distance you have travelled,” A.B says. This is based on the understanding that the earth takes 24 hours to spin 360 degrees on its axis. So, if your clock reads 8 o’clock and it is daytime, it is safe to assume it is 8pm on the other side of the planet. That time is exactly 180 degrees, and just under 11,000 miles away at the equator, from where you are at that time.
A.B goes on to point out that the spherical shape of the planet means longitudinal distance is greatest at the equator and negligible at the poles. “So, while half a degree of longitude at the poles does not mean much in terms of distance travelled, at the equator this means around 35 miles,” she says.
The calculations assume that it would take an hour to for the earth to rotate 15 longitudinally. By that maths, 1 degree of longitudinal rotation would take four minutes of time. “The £20,000 prize was for a method capable of finding longitude to within half a degree, which in terms of elapsed time works out to be two minutes, or an accuracy of within 35 miles at the equator,” explains A.B. A useful navigational clock would therefore have to be accurate to within two minutes over the course of weeks-long voyages, meaning a daily deviation of no more than a second or two. At the time, this level of precision was almost unheard of even in clocks based on land.
Based on the longitudinal calculation noted above, 'if you could find the local time of wherever you were at sea, which was possible with an instrument like a sextant, and you were also carrying an accurate clock which you'd set to the local time of the port you'd departed from, and say the clock was exactly an hour ahead of the local time, then you'd know that you were 15 degrees east of where you started,” says A.B.
It was a self-taught English carpenter and watchmaker, John Harrison, whose final design (there were four iterations) would win the £20,000 prize. His successful marine timekeeper, the H4, “featured a large balance which beat at 18,000 bph and an amplitude of about 240 degrees. It had a remontoire which operated every seven-and-a-half seconds and a verge escapement designed to have very little recoil,” says A.B. “It had a form of temperature compensation that helped the balance maintain a constant rate. Crucially, the watch could continue running while being wound up.”