Before the invention of accurate clocks, it was nearly impossible for sailors to find their longitude. This did not stop them from trying, however. Columbus made two attempts in his lifetime to measure his longitude. Both results were pretty bad, even by the standards of his day.

The only practical method for determining longitude in the fifteenth century was the well-known method of timing lunar eclipses. This method had been in use since ancient times, but since eclipses are rare, it is of limited use. A recent suggestion (Molander 1992) that Columbus used planetary conjunctions to determine his longitude on the first voyage has been shown to be incorrect (Pickering 1996). [See the bibliography.]

The eclipse timing method is simple: first, you determine the local time that the lunar eclipse starts or ends by direct observation. Then you compare your local time for that event against the local time at some distant place. The difference in the two times is the difference in longitude. For example, if the eclipse starts at 8:00 p.m. where you are (say, in Virginia), and the same eclipse starts at 1:00 a.m. in London, you find that there is five hours difference between Virginia and London; or you might say five time zones, which is the same thing. This works out to 75 degrees of longitude.

We now know that observers can tell the moment a lunar eclipse starts or ends to within a few minutes. That means that the biggest source of error for Columbus would have been finding the correct local time. But this is also easy: in the tropics, the sun rises at nearly 6:00 a.m. and sets nearly 6:00 p.m. every day. Also, sailors used a device called a nocturnal which was used to determine the time of midnight from the positions of the circumpolar stars.

Using these clues and a sandglass, Columbus should have been able to determine the correct local time of an eclipse to within about ten minutes, if he was careful. The problem is that both of Columbus's eclipse timing longitudes are off by much, much greater amounts than this. His 1494 longitude was recorded as 5 hours 23 minutes west of Cadiz; at the time, he was 4 hours 10 minutes west of Cadiz, so his error is an hour and 20 minutes. Columbus's error in 1504 is even worse: from Jamaica, he claimed a longitude of 7 hours 15 minutes west of Cadiz, while his actual longitude was 4 hours 45 minutes west of there -- an error of two and a half hours!

The best way to explain the errors is to assume that Columbus didn't really use the lunar eclipses at all. We know that Columbus believed that one degree of the Earth's surface was 56 and two-thirds miles long. Using this formula, it's possible to convert Columbus's transatlantic distance (1142.25 leagues -- see the first voyage summary) into a longitude. When we make this conversion, the transatlantic distance measured by Columbus on his first voyage comes out to 5 hours and 23 minutes -- the exact figure he reported on the second voyage as his longitude.

The 1504 longitude can be explained in a similar manner. On his fourth voyage, Columbus reported that the distance from Puerto Rico to a place in western Cuba was 400 leagues. This is the longest east-west distance within the Indies that Columbus ever recorded in his lifetime. If we add this 400 leagues to the transatlantic distance from the first voyage (the longest transatlantic distance that he recorded in his lifetime), we get 1542.25 leagues. Converting this to a longitude using Columbus's own formula yields 7 hours and 15 minutes, exactly the figure that Columbus reported.

So Columbus didn't really use these lunar eclipses to find his longitude. He really used his dead-reckoning distances, and claimed that they were celestially determined. This was probably done to make his results look scientifically respectable.

In 1997 I delivered a lecture about this hypothesis, which you can read by clicking here.

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