There have been at least six published attempts to trace Columbus's track across the Atlantic to Island I, and all of them are fraught with unmeasured (and usually unmentioned) errors.
Charles A. Schott of the US Coast and Geodetic Survey was the first to trace the track in 1880. Schott started with a guess at magnetic variation in the North Atlantic in 1492. Then he simply took all of the daily courses and distances in the log of the first voyage, and computed the daily positions Columbus should have been at, if the courses and distances were correct. He applied a correction for magnetic variation to arrive at the true course sailed on a given day.
Since Schott assumed that Columbus used the Portuguese Maritime League of 3.2 nautical miles, the initial position he arrived at was far west of the Bahamas. So he applied an arbitrary 'fudge factor' of 11% to his computations to ensure that his mathematical Columbus would not run aground before sighting land.
Schott's final position was near Mayaguana Island. But since he knew that the magnetic declination he used was quite speculative, he also suggested that any island between Samana Cay and Grand Turk was also possible.
U.S. Navy lieutenant John McElroy, apparently unaware of Schott's work, traced the track in 1940. McElroy followed the same procedure as Schott, and applied a similar fudge factor to the distances.
McElroy applied daily corrections from an isogonic chart drawn up by Willem Van Bemmelen in 1899. Van Bemmelen had done extensive research on old sailing ship records to reconstruct the isogonic field (that is, the pattern of magnetic declinations) during past centuries, going back as far as 1500.
But McElroy apparently did not realize that Vam Bemmelen's chart used Columbus's first voyage data as a primary source -- and Van Bemmelen had assumed that the landfall was at Watlings Island. Therefore, using Van Bemmelen's chart, McElroy's reconstructed track ended right at Watlings Island, in a classic piece of unintentionally circular reasoning. Samuel Eliot Morison then used McElroy's transatlantic track as a cornerstone for his contention that the Watlings Island landfall had been proven.
In 1986, Luis Marden traced the track again as part of the National Geographic's attempt to prove the Samana Cay landfall. Although he still used Van Bemmelen's isogons, and still used a fudge factor for distance overruns, Marden correctly noted that McElroy had not accounted for currents or leeway in his reconstruction. Marden attempted to fill this gap.
Using a pilot chart of the North Atlantic, Marden applied prevailing currents from the chart to each day of the track -- but only for the first half of the trip. Marden excused the last half of the trip by claiming (incorrectly) that the currents on the last half of the trip were always westerly, therefore would have had no effect on Columbus's westerly course. In truth, currents are a little southerly in the eastern Atlantic and a little northerly in the western Atlantic, so Marden's procedure applied the southerly drift but not the northerly.
But leeway (in this region of prevailing northeast trades) would always push a little southward, so Marden applied an arbitrary leeway factor to the whole trip, again pushing Columbus southward. His track ended predictably off Samana Cay, south of Watlings.
Marden's lame effort did not go uncriticized in the scientific community. At the Wood's Hole Oceanographic Institution, Roger A. Goldsmith and Philip L. Richardson pointed out that Marden's use of prevailing currents from pilot charts was incorrect: he should have been using vector averages, which can be computed from data collected by the U.S. Navy since the mid-nineteenth century. Vector averages give overall lower speeds, and are appropriate when the length of time studied is greater than a day or two. Goldsmith and Richardson properly applied current drift to the entire voyage, and also applied a different type of leeway to their track. Again using Van Bemmelen's isogons, and again using a fudge factor for distance, their track returned to the vicinity of Watlings Island. A copy of their report can be found in the WHOI library.
First, following Peck's lead, they dropped the Portuguese Maritime League and adopted the more sensible Geometric League of 2.67 nautical miles. This allowed their track to reach the Bahamas without the usual fudge factor for distance overruns. Second, they dropped the use of Van Bemmelen's isogonic chart. Instead, they derived their own isogons which depended primarily on analysis of the transatlantic tracks sailed by Columbus's eastbound first voyage, and westbound second voyage. These changes resulted in a more southerly and shorter track, ending between Grand Turk Island and East Caicos Island. Goldsmith and Richardson also verified their magnetic declinations by simulating the eastbound first voyage and the westbound second voyage, to insure that those tracks also ended in the correct places.
In 2004 I completed a new study of the transatlantic track based on the most detailed model of the earth's magnetic field yet produced for the epoch of Columbus. I presented these results to the 2004 annual meeting of the Society for the History of Discoveries.
These results support the Plana Cays and Mayguana landfalls best, although Samana Cay also looks reasonably good.
You can read about it here.
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