The problem of determining one's position around the world in longitude.

This was regarded as one of the major technological challenges in the 18th century, and many of the world's great minds were focussed on it, including Leonhard Euler and Isaac Newton. Many suggestions were made for solving the Longitude Problem, but in the end it was solved by John Harrison's clock, the H4.

By knowing both local time and the time on the Prime Meridian, the difference gives the longitude. Since the Earth rotates once every 24 hours, 24 hours must equate to 360 degrees of longitude. Therefore 1 hour is 15 degrees, and 4 minutes is one degree of longitude. Thus 1 minute of time difference equates to 15 arc-minutes of longitude.

To put this in context, 4 seconds difference in time equates to one arc-minute, which at the equator is 1 Nautical Mile. To keep time to better than 4 seconds total in a journey of perhaps three months, in varying temperature, pressure, and in potentially very rough seas, was thought impossible by many. It was for this reason that using the stars was considered to be the only practical solution.

They were wrong.

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