At sea Columbus measured distances in leagues, each of which was four miles long. But in the fifteenth century, there were many "mile" units of various lengths in use, both in Europe and in the Arabic world. This has given rise to disagreements over just how long Columbus's league and mile were in modern terms.
Samuel Eliot Morison assumed that Columbus used the "Roman" mile of 4860 feet (1.48 km). This would make his league 3.2 nautical miles long, which is the accepted length of the so-called Portuguese Maritime League (PML). The PML was known to be in common use among Spanish as well as Portuguese sailors.
The PML has serious problems, however. First, when we compare the distances Columbus reported sailing along the north coast of Cuba (between known points), we find these distances are much less than what Columbus reported. Also, if we accept Morison's landfall at Watlings Island, there are several other coastline lengths that would have been vastly overstated by Columbus. To solve these problems, Morison suggested that Columbus measured coastlines with a different length league (about 1.5 nautical miles) than he used for distances in the open sea. But there are no historical records that support such a league length; Morison's guess was entirely empirical.
Also, when tracing Columbus's transatlantic voyages (both eastbound and westbound), it is impossible to make the distances come out correctly when using the PML. Most of those who have traced the transatlatic tracks of Columbus have had to rely on fudge factors to make the distances come out correctly.
And finally, Columbus was Genoese, not Spanish. A shorter mile, the Italian or Geometric Mile of 4060 feet (1.24 km) was in common use in 15th century Italy. If Columbus used the Geometric Mile, his league would be 2.67 nautical miles, which is the Italian League, or Geometric League (GL). There are a number of 15th century documents on metrology that support this league length.
James E. Kelley, Jr. was the first to propose that Columbus used this league, in his 1983 paper (See bibliography). Kelley supported his thesis with an analysis showing how the shorter Geometric League, combined with an accounting of currents along the north coast of Cuba, could explain Columbus's overstated length of the island. In 1992, Douglas Peck showed that this league length could also reconstruct Columbus's transatlantic track without the usual fudge factors for distances.
For these reasons the 2.67 nautical mile Geometric League has gained wide support among historians as the league used by Columbus.
There were a number of ancient and medieval measurements of the Earth's size available in Columbus's day, but the one he preferred was made by the Persian astronomer Al-Fargani (or Alfraganus, when Latinized), who in the 9th century had determined that one degree of latitude spanned 56 2/3 miles. That implies that the whole earth is 20,400 miles in circumference. Since an Arabic mile of that day was between 1.9 and 2 km, this measurement was about right. (The equatorial circumference of the Earth is 40,075 km).
The problem was that Al-Fargani was measuring in Arabic miles, while Columbus himself used Italian miles, and Columbus didn't realize the difference. And since an Italian mile was only 1.24 km, Columbus was underestimating the size of the earth by 37%.
This underestimate directly contributed to his belief that reaching the east coast of Asia was doable from western Europe with the ships of his time.
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