Finding the Longitude

 Latitudes are the (imaginary) lines running parallel to the equator. As Neil Armstrong wrote in his introduction to Dava Sobel’s book, Longitude:

“(Early sea captains could measure latitude) by the elevation of the North Star above the horizon.”

But knowing one’s longitude is a lot harder. Because longitudes don’t run parallel to each other, the distance between two longitudes isn’t the same everywhere.

 

In theory, the solution was simple, as Sobel explains:

-       The earth takes 24 hours to rotate; or 24 hours maps to 360 degrees; and thus 1 hour maps to 15 degrees;

-       In principle, here’s how one could then know one’s longitude:

“Every day at sea, when the navigator sets his ship’s clock to local noon when the sun reaches its highest point in the sky, and then consults the homeport clock, every hour’s discrepancy between them translates into another fifteen degrees of longitude.”

In practice, however, nobody knew how to build a clock that was reliable:

-       Remember, those were the days of pendulum-based clocks. But a pendulum expanded and contracted with temperature. And since the period of oscillation of a pendulum is linked to its length, it would vary with temperature at sea;

-       The swaying of a ship with waves added to a pendulum’s woes.

 

Given the importance to maritime navigation, the British government announced a £20,000 prize, with specific terms:

-       It had to find accuracy within half a degree. For a clock based solution, this meant it couldn’t lose/gain more than 3 seconds in 24 hours. Why that particular precision? It was just maths:

“Half a degree of longitude equals two minutes of time – the maximum allowable mistake over the course of a six-week voyage from England to the Caribbean.”

-       The solution should be mass-produce’able, cheap and easy to use. After all, it was to be used sea captains, not scientists and engineers alone.

 

Given its importance to all maritime navigation, multiple approaches were pursued by different people in parallel, not just a clock-based solution.

 

One approach considered “appealing to the clockwork universe”, like tracking the movement of the moon against the stars. Or using the periodicity of the eclipse of Jupiter’s moons. This approach was the domain of stalwarts like Galileo, Cassini, Huygens, Newton and Halley. Unfortunately, any such astronomy based approach required clear skies, compensation for the shaking of the ship, and lots of maths. Despite all the practical issues, this approach was pursued for long because, hey, it was a science-y solution.

 

A third approach was to use the difference between true north and magnetic north to gauge one’s longitude. This didn’t go too far because, as they later discovered, the earth’s magnetic field varies across regions.

 

A multi-country solution of anchoring ships at fixed points in the ocean was considered. The idea was that those ships would signal their position on an hourly basis. Observe the signal and you knew the time. But this was found to be impractical, costly and liable to attack by pirates.

 

No wonder then that “discovering the longitude” became a synonym for the impossible. Finally though, the solution to the longitude problem was a precise enough clock built by John Harrison. No wonder then that Sobel ends her book with an Einsteinian reference:

“With his marine clocks, John Harrison tested the waters of space-time. He succeeded, against all odds, in using the fourth – temporal – dimension to link points on the three-dimensional globe.”