The art of navigation is rich in numbers, which is both a blessing and a curse. A blessing, because if those numbers are carefully measured and faithfully transmitted through the years, they allow us to confirm an explorer's location with unparalleled confidence. And a curse, because if those numbers are sloppily measured, badly conserved, or even fraudulent, we are left with the task not only of resolving any discrepancy but also of explaining its very existence. The many navigational records left by Christopher Columbus, the Admiral of the Ocean Sea, are frequently cursed. Today we will examine several outstanding discrepancies in those records, and we will suggest a new hypothesis that will unlock these mysteries and show how they came about.
As you may know, Columbus kept a detailed log of his first voyage, which has been lost. But we do have an abstraction of the log, made by Bartolome de Las Casas, and known as the Diario. This document contains the courses and distances sailed by the fleet every day of the voyage, in the transatlantic sections. In addition to the Diario, we also have a biography of Columbus by his son Fernando that contains some additional material from the lost log.
On the westbound passage many of the daily distances in the Diario are given twice, one figure being Columbus's own true figure, and a smaller number which was (according to Las Casas) a falsified number given publicly to allay fears of the crew that they had sailed too far from Spain[1]. But this story has been doubted by many, because most of the crew were experienced mariners in their own right, and they were certainly just as able to determine the distance sailed as was Columbus. In 1983, James E. Kelley Jr. proposed an elegant solution[2] to this problem. Kelley noticed that the true and false numbers tend to cluster around a ratio of 6 to 5. This is quite close to the ratio between the Italian or Geometric league of 2.67 nautical miles, and the Portuguese Maritime league of 3.2 nautical miles. Kelley proposed that Columbus was using the Italian league, while the Spanish sailors were using the Portuguese Maritime League; the double bookkeeping was then simply an artifact of Columbus converting between the two units of measure, although these conversions were sometimes haphazard, and were misunderstood by Las Casas.
With this as background, let us proceed to a small, but unsolved, mystery in the Diario of the first voyage. On October 1st, 1492, Columbus gives us a summary total of the voyage so far:
"The Admiral's pilot held at dawn today that they had made up to this point 578 leagues west from the island of Hierro. The smaller account that the Admiral showed to the men was 584. But the true account that the Admiral figured and kept to himself was 707."[3]
The problem here is that when we do our own subtotals, adding the daily distances given up through dawn on October 1st, we don't get 707 leagues. We get only 657 leagues, a full 50 leagues short of the total given by Columbus. Now if we read the quote carefully, it does not specifically say that Columbus's own subtotal was taken at dawn, as was the other pilot's; so we could legitimately include the day's run of October 1st itself in our reckoning. But the fleet only made 25 leagues that day, which still leaves us well short of Columbus's total. So it would appear that there are between 25 and 50 leagues missing from the figures given in the Diario between September 8th, when the fleet left Hierro in the Canary Islands, and October 1st. This amounts to a good day's run, and it seems unlikely that a whole day could have been lost; further, it is more than one league per day, so no accumulation of rounding errors can explain the difference.
Even stranger is the problem with the 'false' subtotal. During this same period there are ten days (or partial days) in which Las Casas does not record the number of 'false' leagues; and considering the total of 584, those ten lost days must account for 224 leagues. But the number of 'true' leagues on these same ten days is only 212, less than the number of missing false leagues. Yet we know that the true figures must be greater than the false ones. David Henige[4] was the first to note this conundrum in 1991.
The key that unlocks both of these mysteries is found not in the Diario, but in the other major historical record of Columbus's lost log: the biography of the Admiral by his son, Fernando. This biography also notes the double bookkeeping, but there is a key discrepancy between the two accounts. According to Fernando, the double bookkeeping starts on September 9th. On that day, Columbus sails 18 'true' leagues (or Italian leagues), and reports to the crew 15 leagues[5]. But Las Casas records only the publicly announced 15 league figure; he does not start the double figures until the following day, September 10th[6].
So, by reading the Diario alone, we have assumed that the 15 league figure is the number of 'true' leagues, even though it is not explicitly labeled as such by Las Casas. In reading Fernando, we realize that our assumption was wrong; the unlabeled figure is actually the public figure, in Portuguese Maritime Leagues. By correcting this mistake, we add three leagues to the voyage. But can this same mistake also have occurred elsewhere in the Diario? I believe that it can. Besides the case that we have just discussed, there are seven other[7] cases in the first two weeks of the voyage where Las Casas gives only one figure for the day's run, not explicitly labeled as being either a 'true' or 'public' figure. Up until now, all historians have assumed that these unlabeled singletons are the 'true' figures in Italian Leagues. But suppose, as in the case of September 9th, that we have been wrong? Suppose that the unlabeled numbers are really Portuguese Maritime Leagues? In that case, we could reconstruct the correct figures in Italian Leagues by applying the 6-to-5 ratio, and rounding to the nearest whole number. If we do this, as shown here, we will add 33 or 34 leagues to the voyage between September 9th and October 1st. This is enough to account for the 25 to 50 leagues known to be missing from the Diario on that date. And it also explains David Henige's conundrum, since most of the missing numbers are now shown to be true figures and not false ones.
| Date | Las Casas | As Corrected | Difference |
|---|---|---|---|
| September 9 day | 15 | 18 | 3 |
| September 9 night | 30 | 36 | 6 |
| September 11 | 20 | 24 | 4 |
| September 15 | 27 | 32 | 5 |
| September 20 | 7 or 8 | 9 | 1 or 2 |
| September 21 | 13 | 16 | 3 |
| September 22 | 30 | 36 | 6 |
| September 23 | 27 | 32 | 5 |
| Total | 33 or 34 |
Our next mystery is recorded in the Diario on November 2nd, 1492, while Columbus is off the coast of Cuba:
"And he says that by his account that he had gone 1,142 leagues from the island of Hierro."[8]
Once again we seem to have a problem with addition, since up to this point Columbus has sailed over 1230 leagues on the whole voyage. Most scholars assume that Columbus derived this number by measuring a chart, but if he had been measuring correctly, he should have found that his true distance from Hierro was only about 1100 leagues. Note particularly that Columbus does not say to where from Hierro the 1142 leagues is measured. Once again, we have an unspoken assumption that his current position off Cuba is being measured. But this assumption may also be wrong.
Because of some ambiguities in the daily records, there is no absolutely correct way to add up the total transatlantic distance on the first voyage. But suppose we make reasonable decisions in the ambiguous cases, and suppose we include the 33 or 34 missing leagues that we have reconstructed. In that case, the total transatlantic distance from Hierro to the ever-elusive first landfall in the Bahamas becomes exactly 1142 1/4 leagues, or 1142 leagues when rounded to the nearest whole number. It stands to reason that this transatlantic distance would be of fundamental importance to Columbus as a navigator; and I believe that it was just this transatlantic distance that Columbus was recording in his log on November 2nd. (Remember that number: we're having a quiz later.)
But for now, hold on to these thoughts as we take a great leap in space and time. On September 20th in the year 331 BC, the army of Alexander the Great was encamped near Arbela in Mesopotamia. The full Moon rose at sunset, and two hours later an eclipse of the Moon began. At that same instant, the start of the eclipse was also seen in Carthage; but in Carthage, the local time was sunset, not two hours later as at Arbela. Ancient astronomers realized that this was because of a longitude difference of two hours, or thirty degrees, between Carthage and Arbela. This early eclipse longitude was widely known in the ancient world, and was reported both by Pliny the Elder and by Claudius Ptolemy. Prior to the invention of the telescope, timing a lunar eclipse was the only[9] reliable way to find a longitude difference between two points.
Columbus had read Ptolemy, so it is not especially surprising that he would try to use this method of determining longitude. In 1474, the astronomer Johann Müller published an almanac that predicted the times of lunar eclipses for thirty years in advance. Columbus owned a copy of this ephemeris, and he carried it with him on his first voyage and probably on his other voyages too. Several sources report that on his second voyage, the Admiral observed the lunar eclipse of September 14th 1494, and determined his longitude from that eclipse.
In a fragmentary biography of Columbus, written perhaps around 1497, the Genoese Antonio Gallo reported:
"He declared also from the observation of his people that when in the year of our Lord 1494 there appeared an eclipse in the month of September, it was seen in Española four hours before that it was visible in Spain."[10]
In his biography, Fernando Colon gave this report, which may have been taken from the missing log of the second voyage:
"On September 15th by the mercy of God they sighted an island which lies off the eastern end of Española . . . in the middle of a great storm he anchored behind this island . . . That night he observed an eclipse of the moon and was able to determine a difference in time of about five hours and twenty-three minutes between that place and Cádiz."[11]
In his Libro de las Profecías, or Book of Profecies, Columbus himself reported:
"In the year 1494, when I was at the island of Saona, which is at the eastern end of the island of Hispaniola, there was an eclipse of the moon on the 14th of September, and it was found that there was a difference from there to the Cape of St. Vincent in Portugal of five hours and more than one half."[12]
In a letter to King Ferdinand and Queen Isabela of July 7, 1503, Columbus himself again reported:
"In the year ninety-four I navigated in twenty-four degrees to the westward to the end of nine hours, and I cannot be in error because there was an eclipse."[13]
(In this quote, the twenty-four degrees refers to his latitude.)
Las Casas' great work, the Historia de las Indias, quotes Columbus as follows:
"From the end of Cuba (that is seen in Hispaniola), which was called the End of the East, and by another name Alpha and Omega, he sailed westward from the southern part, until he passed the end of ten hours on the sphere, in such a way that when the sun set to him, it was two hours before rising to those that lived in Cádiz, in Spain; and he says that there couldn't be any error, because there was an eclipse of the moon on the 14th of September, and he was well prepared with instruments and the sky was very clear that night."[14]
Now if that weren't enough, in a later chapter Las Casas repeats the eclipse story, only the second time around the longitude is five hours and 23 minutes west of Cádiz [15], the same as reported in Fernando's biography.
As you can see, we have a problem here. In five primary sources by four authors, we have six reports of the longitude giving five different results. And these results differ from each other by as much as 6 hours, or 90 degrees of longitude. Even worse, as it turns out, if Columbus had found his longitude by comparing the time of the eclipse to the prediction in the almanac, not one of these reports would be correct.
On that night, Columbus's correct longitude at Saona was four hours and ten minutes west of Cádiz[16]. As it happens, Müller's prediction of the eclipse was 24 minutes[17] late, so Columbus should have found his longitude to be four hours 34 minutes west of Cádiz. We know from modern experiments that an eclipse can be timed in this way to within five minutes or less; and the correct local time should be measurable to within ten or fifteen minutes using a sandglass or a nocturnal. So the total error should be no more than fifteen or twenty minutes. But all of the longitude reports are off by thirty-four minutes or more, and in the worst case, by more than five hours. Indeed, it seems impossible to reconcile any of these longitudes to actual celestial observation, unless we resort to a series of mistakes or improbable procedures; and to account for all of the erroneous longitudes, the repertoire of such mistakes must be both huge and self-contradictory.
Our suspicions are raised even further when we read that Columbus anchored at Saona that night to take shelter from an approaching storm. Fernando even reports that the storm had already broken at the time of the anchorage. So how is it that celestial observations were made during a storm? Why does Columbus later report that the sky was clear that night? Why are there no actual observations in any of these reports? No time of the start or end of the eclipse, only computational results? And how is it that according to both Fernando and Las Casas, Columbus was apparently able to time his observations to the nearest minute using a sandglass?
Indeed, the ten-hour longitude is so clearly at odds with reality that it, at least, has been viewed suspiciously for decades[18]. But why would Columbus falsify such a result? A critical clue can be found in Columbus's Book of Privileges. Prior to both his second and third voyages, Columbus requested that the Spanish Sovereigns confirm his appointments as Admiral of the Ocean Sea and Viceroy of the newly discovered lands. The documents confirming these privileges confine the Admiral's realm only to "the Ocean Sea in the region of the Indies"[19]. Therefore, if the newly discovered lands were not really in the region of the Indies - that is, in Asia - Columbus's entire fortune may have been at risk. Indeed it may have been just such a thought that led the Admiral to demand that the crew of his second voyage sign a document swearing that Cuba was the mainland of Asia[20].
In his letter of 1503, Columbus reminds the Sovereigns that according to the ancient geographer Marinus of Tyre, the combined landmass of Europe and Asia made up fifteen hours of longitude,[21] or twelve hours according to Ptolemy. If true, the remaining longitude difference - in Columbus's mind, the width of the Ocean Sea from Europe westward to Asia - must have been between nine and twelve hours. In this context, it is easy to see is why Columbus claimed longitudes so clearly fraudulent as nine or ten hours between Spain and the West Indies: if the Ocean Sea were nine or ten hours wide, then according to Marinus his discoveries were firmly within Asia and his privileges were secure. Since he needed the Ocean Sea to be nine hours wide, he simply claimed it as a fact, and then added in the part about the eclipse to give his statements a figleaf of scientific respectability.
But even if this is true, what about the other reported longitudes from the same eclipse? Where did they come from? And why are they less than nine hours? Such differences are commonly seen in cases of fraud. When a story is true, it is drawn from a real memory of actual events; but when a story is fabricated, the fabrication often changes over time, as the hoaxer seeks to make his story ever more unimpeachable. Ironically, these very changes are one of the best ways to detect a hoax.
In the case at hand, an argument between Columbus and the cosmographers of his day provides clues to the mechanism that the Admiral used to fabricate his longitudes. The size of the earth had been measured fairly well in ancient times by both Eratosthenes and Poseidonios, but due to errors in translation of various units of measure, the uncertainty in the Earth's size had grown larger by Columbus's day. Many believed that a degree of the Earth's surface measured 66 2/3 miles; Columbus himself held for a smaller degree of only 56 2/3 miles[22]. One consequence of knowing the size of the earth is that it allows you to convert between linear measurements, like miles or leagues, into angular measurements, like degrees of latitude, or hours of longitude. As it turns out, all of the remaining longitude results from 1494 can be derived in just this way. It is possible that Columbus wanted to view the eclipse, planned to view it, perhaps even promised to view it. But on the night itself, bad weather intervened. In his frustration, it must have occurred to Columbus that there was another method for determining longitude right at his fingertips: a method that had nothing to do with eclipses or celestial observation at all.
Las Casas records that on his second voyage, Columbus measured the transatlantic distance from Gomera to Dominica to be 850 leagues[23]. If we take this 850 league measurement and convert it into a longitude using Columbus's own size-of-the-Earth formula, it becomes exactly[24] four hours of longitude: the same longitude reported by Gallo in his biography. Cartographers here will have noticed that in making this computation, we neglected to account for the fact that these distances were not measured along the equator, but at a somewhat higher latitude. Indeed, we will ignore this nicety throughout the rest of this lecture. There is some evidence[25] that Columbus had little or no knowledge of trigonometry, necessary to make this correction; and the conclusions that we eventually reach will provide additional justification for this position. If Columbus actually figured in this way, he probably would have rejected the four hour result rather quickly, because it is not close enough to the desired nine hours that he needed to secure his position. He may have confided this result to his brother Diego, or one of the Genoese merchants on the voyage, from whence the story was picked up by Gallo.
It probably occurred to Columbus that he had measured a longer transatlantic distance on his first voyage than on his second. You recall that earlier we determined this distance to be (I warned you there would be a quiz) 1142 1/4 leagues, including the missing 33 leagues. If we convert this into a longitude, it becomes exactly five hours and 23 minutes, the same as the longitude reported in Fernando's biography and by Las Casas in the Historia.
But apparently, as the years passed, Columbus still wasn't satisfied. At some point, he must have realized that the transatlantic distance, taken by itself, was still too low. To increase the total, he added in the distance sailed westward within the Indies. In referring to the Diario of the first voyage, we find that the westerly distances along the north coast of Cuba have been omitted. But the westerly distance from the Bahamas landfall to the landfall in Cuba must have been at least 31 leagues[26]. Adding this to the transatlantic total and converting to a longitude gives us at least 5 hours 31 minutes. This matches the longitude in the Profecías, given as more than five and a half hours. Interestingly, the lack of precision expressed by Columbus in this longitude may indicate that the omitted Cuban distances in the Diario are attributable to Columbus himself, and not to the abridgment of Las Casas.
The impact of Columbus's fraud may have been felt most keenly by Amerigo Vespucci, his friend and correspondent. Ironically Vespucci, unaware of Columbus's fraud, very likely plagiarized this five and a half hour result when he constructed his own longitude fraud[27] in 1499. But that's a story for another lecture.
As icing on the cake, let us consider our final mystery. The eclipse of 1494 was not the only eclipse from which Columbus claimed to have derived a longitude. On his fourth voyage, the Admiral observed the eclipse of February 29th, 1504, while he was marooned at St. Anne's Bay, Jamaica[28]. Columbus wrote in the Profecías that he determined from the eclipse that his longitude was 7 hours and 15 minutes west of Cádiz[29]. Columbus's actual longitude was four hours and 44 minutes west of Cádiz, so again there is a huge error that demands explanation. In 1992, astronomer Donald W. Olson proposed[30] a series of mistakes that would explain most of the discrepancy. If Columbus made the mistakes Olson attributed to him, he would have computed a longitude of 7 hours 13 minutes west of Cádiz, which is tolerably close to the 7 hours 15 minutes he actually recorded.
However, knowing that the 1494 eclipse longitudes are fraudulent, and knowing how they were constructed, leads us to suspect another explanation entirely. In his letter to the Sovereigns of July 7, 1503, Columbus writes the following description of his return from Central America:
"When I set out thence to come to Española, the pilots believed that we were going to reach the island of San Juan, and it was the land of Mango, four hundred leagues more to the west than they said."[31]
The island of San Juan is the modern Puerto Rico, and Mango is a part of western Cuba. The significance of this passage is that this is the longest distance, east-to-west within the Indies, that Columbus ever recorded in any of his writings. So let's take this, and add to it the longest transatlantic distance that Columbus sailed in his lifetime -- the 1142 1/4 leagues from the first voyage. This gives us 1542 1/4 leagues, the maximum westerly distance that Columbus could reasonably claim to have ever sailed from Spain. When we convert this maximum distance into a longitude, we get exactly 7 hours and 15 minutes: the same longitude that Columbus reported as being derived from the eclipse of 1504.
So, starting with the little mystery of the subtotal that wouldn't add up, we proposed a mechanism for resolving the discrepancy; and in so doing, we added about 33 leagues to the westward passage on the first voyage. For those who may have lost count, those 33 leagues can now explain, in whole or in part, no less than six previously unexplained navigational results in the annals of Columbus. These are:
As satisfying as it may be to kill six birds with one stone, perhaps more important is what we learn about Columbus the man. For Columbus, his theory about the size and contents of the Ocean Sea was more important than any evidence that might cast doubt on that theory. Truth for Columbus was not to be found so much in observation or experiment, as it was in the voice of ancient and authoritative texts from which there could be no appeal. Living in an age before the scientific revolution, this attitude is understandable even if the outcome is not completely forgivable.
Those who have studied Columbus closely will not be surprised that he was capable of deception when the occasion arose, for this is not the first such instance recorded or suggested. But those who have viewed Columbus as a leader in the scientific thinking of his day would do well to re-evaluate his reliability as an objective observer.
1 Dunn, Oliver, and James E. Kelley, Jr. (1989). The Diario of Christopher Columbus's First Voyage to America, 1492-1493. Norman and London: University of Oklahoma Press. 28, 29.
2 Kelley, James E. Jr. In the Wake of Columbus on a Portolan Chart. Terrae Incognitae 15, 77-111.
3 Dunn & Kelley (1989) 48, 49.
4 Henige, David (1991). In Search of Columbus: Sources for the First Voyage. Tuscon: The University of Arizona Press. 130.
5 Keen, Benjamin, trans. (1992). The Life of the Admiral Christopher Columbus by His Son Ferdinand. New Brunswick: Rutgers University Press. 48.
6 Dunn & Kelley (1989) 28, 29.
7 There are nine unlabeled distances in the first two weeks of the voyage, followed by two weeks in which there are no such cases. Distances recorded in the last three days of the voyage are again unlabeled. Here we make the conventional assumption regarding the final three days, i.e., that they are 'true' figures in Italian Leagues.
8 Dunn & Kelley (1989) 130, 131.
9 A recent alternative suggestion [Molander, Arne B. (1992) Columbus and the Method of Lunar Distance, Terrae Incognitae 24, 77-103] has been shown to be flawed [Pickering, Keith A. (1996) Columbus's Method of Determining Longitude: An Analytical View, The Journal of Navigation 49:1, 99-113. See also ensuing discussion in The Journal of Navigation 49:3, 444 and 50:1, 144-147.]
10 Thacher, John Boyd (1903). Christopher Columbus: His Life, His Work, His Remains. New York and London: G. P. Putnam's Sons. I, 192, 195.
11 Keen (1992) 145.
12 West, Delno C. and August Kling (1991). The Libro de las profecías of Christopher Columbus. Gainesville: University of Florida Press. 226, 227.
13 Jane, Cecil, ed. (1988). The Four Voyages of Columbus. New York: Dover. II, 82.
14 Las Casas, Bartolome de (1951). Historia de las Indias. Mexico: Fondo de Cultura Economica. I, 390. Author's translation.
15 Las Casas (1951) I, 395-396.
16 Actual longitudes of cited places: Nuremberg, 11° 5' E; Cádiz, 6° 16' W; Cape S. Vicente, 9° 0' W; Saona, 68° 39' W; St. Anne's Bay, 77° 12' W. Longitude differences are converted from degrees to hours by dividing by 15.
17 Müller, Johann (1489). Kalendar Maister Johannes Kunisperger. Augsperg: Erhart Radolt, unpaged. Müller's predicted time of mid-eclipse (19h 45m past noon) is converted to UT by correcting for convention (12h), longitude (44m), and equation of time (10m), so 19h 45m + 12h - 44m - 10m = 06:51 UT on the 15th. Actual mid-eclipse was 06:31 ET; applying 4m dynamical time correction gives 06:27 UT according to Meeus, Jean & Hermann Mucke (1979) Canon of Lunar Eclipses -2002 to +2526. Vienna: Astronomisches Buro Wein. Müller's prediction of semi-duration (1h 48m) is 5m too great, but this is far too small to explain Columbus's discrepancies.
18 Morison, Samuel Eliot (1942). Admiral of the Ocean Sea. Boston: Little, Brown & Co. II, 147.
19 Nader, Helen, and Luciano Formisano (1996). The Book of Privileges Issued to Christopher Columbus by King Fernando and Queen Isabel, Volume 2 of the Repertorium Columbianum. Berkeley: University of California Press. 73, 74, 87, 151, 153.
20 Morison (1942). II, 140-141.
21 Jane (1988) II, 84.
22 Jane (1988) II, 84.
23 Las Casas (1951), I, 497.
24 All longitude computations here are rounded to the nearest minute. There are four miles to a league and fifteen degrees to an hour of longitude, so: Leagues x 4 ÷ 56 2/3 ÷ 15 = hours. Or combining terms, L ÷ 212.5 = h, with remainders expressed sexigesimally.
25 Columbus timed the length of the daylight on December 13, 1492, the day after the winter solstice. This was clearly an attempt to determine his klimata, which was often used as a substitute latitude by Ptolemy and Marinus of Tyre. But Columbus did not then convert this measurement into an actual latitude, which he easily could have done by trigonometric or geometric means. See Wilson, Curtis (1997) "Hipparchus and Spherical Trigonometry," Dio 7.1 (February), 14-15.
26 Eight leagues (assumed westerly) from the landfall island to Isabela (Dunn & Kelley 1989, 160-163), plus 23 leagues westerly from Isabela to the Islas de Arena (ibid, 112-115). From there to the Cuba landfall, Columbus sailed 17 leagues SSW; the 6.5 league westerly component of this leg is ignored here, but this does not affect the conclusion.
27 Randles, W. G. L. (1995). Portuguese and Spanish Attempts to Measure Longitude in the Sixteenth Century. The Mariner's Mirror, 81:4 (November), 403.
28 Keen (1992) 272-273.
29 West & Kling (1991) 226, 227.
30 Olson, Donald W. (1992). Columbus and an Eclipse of the Moon. Sky & Telescope 82 (October), 437-440.
31 Jane (1988) II, 98.