On this page, observations of various kinds will appear that are related to big history teaching, as well as to big history
A few years ago, as part of teaching big history for small groups I started developing a series of observations that can
be done by students in class. To my surprise, some of these observations turned out not only to be very helpful for teaching
big history, but they also led to a few intriguing discoveries. This report is the second of a series of such observations with unexpected,
DID COLUMBUS FALSIFY HIS LATITUDE MEASUREMENTS DURING HIS FIRST VOYAGE TO THE AMERICAS?
2, 2015 (with later additions)
To improve students’ understanding of navigation in the period of early globalization, most
notably the scientific and technological knowledge underpinning it, they measure in class the altitude of the sun using both a homemade
These instruments were formerly used to determine one’s latitude,
which is a measure of one’s distance between the equator (which is defined as zero degrees), and one of the poles (located at ninety
degrees either north or south). One degree along a line connecting the north and south pole equals 60 nautical miles, 69 (statute)
miles, or 111 km.
The city of Amsterdam, for instance, is situated at 52 degrees north of the equator. The concepts of latitude
(and also longitude, the distance along the equator measured from a certain point) had already been used by Claudius Ptolemy of Alexandria
(c.100-170 CE), whose geography was firmly based on the idea that the world was a globe. And Ptolemy had also been familiar with the
quadrant for determining celestial and geographic altitudes.
The quadrant and the astrolabe are both used
by holding them and
lining up two holes on the instrument while aiming at a celestial object, the sun or a star, and then read the resulting angle on
the scale. Doing so provides the celestial object’s altitude in degrees with respect to the local horizon.
For observing the
sun’s altitude, this lining up of the holes is done by letting the sun shine through one hole and projecting its resulting small but
bright image right onto the next hole, and then read the scale.
In contrast to what is stated on many web sites, there is no
need at all to look at the sun through the holes, which would damage one’s eyes. At night, however, one would directly observe Polaris,
the pole star, by looking through these holes.
Because the sun’s altitude changes throughout the year between +23.5 degrees north
and -23.5 degrees south, accurate data about its daily positions are required to calculate one’s latitude.
rather stable altitude above the North Pole, by contrast, will immediately yield one’s latitude with a precision of about one degree.
No greater direct precision is possible because the pole star wobbles a little with respect to the true north. In practice, both sun
and star observations were used whenever possible, sometimes as a check on each other.
The technology of using quadrants and
astrolabes for measuring latitudes was further developed by the Portuguese after they started sailing southwards on the Atlantic Ocean
to reach the African gold coast and later also Asia, both famous for their wealth.
Navigating the Mediterranean had not necessitated
using such instruments because of its largely east-west orientation. Sailing it meant moving through changing longitudes, but never
experiencing a significant change in latitude.
By sailing southward, however, the Portuguese did encounter a significant change
in latitude. They also found that Polaris, situated almost exactly above the North Pole, disappeared below the horizon as soon as
they crossed the equator. And in the southern hemisphere there proved to be no suitable stars situated above the South Pole that could
be used for determining latitude.
The Portuguese solved this problem by developing more accurate methods to measure the sun’s
altitude, preferably at noon when the sun appears the highest in the sky. But because the altitude of the sun changes during the year
from +23.5 degrees north to -23.5 degrees south and back, the Portuguese needed to construct tables based on accurate measurements
that would provide those data from day to day.
Such documents are known as sun declination tables. The oldest extant Portuguese
sun declination table, called Regimento do estrolabio e do quadrante
, probably dates from 1509 CE, and was likely a printed version
of earlier editions. A copy of the Regimento can be downloaded here as a PDF
Such tables may have been constructed with
careful observations made at the peninsula of Sagres, where the first Portuguese navigational school
was founded in 1420 CE by Prince
Henry the Navigator (1394-1460 CE).
Although old documents that could have shed a light on what happened at Sagres were lost,
it is remarkable that this peninsula is oriented to the south, and thus very suitable for observing the noon sun and stars.
Point still offers the widest unobstructed view of the horizon over the ocean available in Portugal, and, in consequence, the largest
possible reference line for determining celestial altitudes during both day and night over the broadest possible range.
Sagres was perfectly situated for making sun declination tables. This would have allowed the Portuguese to take the remarkably accurate
measurements that appeared in the Regimento.
Such measurements could not possibly have been taken with the small hand-held quadrants
and astrolabes used by mariners. Much larger instruments were needed to achieve such a high precision. Traces of such possible
instruments can still be seen at Sagres Point.
The rule for determining latitude, explained here
, is: 90 degrees, minus the measured
noon sun altitude, plus the noon sun declination of that particular day.
This way of determining latitude at sea remained in use until
the 1990s CE while using sextants, which are much more precise than quadrants and astrolabes. And even after NavSat and GPS replaced
sextants for everyday use, these instruments still remain in use as an emergency back-up option in case GPS fails.
a fix on the horizon or an artificial horizon are required to determine celestial altitudes. This is not needed while using quadrants
and astrolabes, because gravity’s action on the instrument provides the required frame of reference.
In Columbus’ time, the sun’s
altitude was preferably measured using a quadrant, because it was deemed more precise than the mariner’s astrolabe, mostly because
the plumb line can be very thin, and can therefore be read more precisely than the astrolabe’s pointer (usually called alidade), which
is a little more complicated to make, and therefore more likely to have a systematic error.
It can be very hard, however, to
keep the quadrant’s plumb line sufficiently steady on a rolling ship. The mariner’s astrolabe is more stable, and therefore provides
more accurate measurements at sea, which explains why that instrument became the preferred choice on board.
The mariner’s astrolabe
was a simplified version of the much more complicated medieval astrolabe, which has been called the world’s first portable computer
Based on earlier Sumerian and Babylonian designs, astrolabes were already known in antiquity, and had reached Western Europe through
the Arabs, who had developed them further.
The simplification of the mariner’s astrolabe consisted of retaining only the alidade
and the scale in grades, while making it so heavy so that it would be sufficiently stable on board of a rolling ship. Holes in the
instrument provided as much room as possible for wind to blow through it to prevent it from swaying. In short, the mariner’s astrolabe
was a very rationally-designed and convenient solution based on the best available technology.
In class, students are asked to
measure the sun’s altitude with both instruments. They must also estimate the margin of error of their results, most notably by answering
the following questions: what is the estimated average error of their measurements? And how large is the estimated systematic error
due to the instrument’s lack of perfection? And how would you deal with that to improve your measurements? In doing so, students become
familiar with these concepts, which are most important aspects of all systematic observations.
The students’ results tend to
coincide with my measurements and estimates: 0.5 to 1 degree of maximum average error of measurement, and 1 to 2 degrees of maximum
systematic error. Much like the mariners of old, also the students consider the quadrant more precise than the mariner’s astrolabe,
and for the same reason.
If students were able to measure the noon sun altitude –the sun does not always shine in Amsterdam–
, they are requested to determine their latitude using sun declination data from the Regimento do estrolabia e do quadrante
particular day, while comparing these data with modern data
obtained from the Internet.
This introduces another problem, namely
that the sun declination data provided by the Regimento are off by ten days. The reason for that is that in the meantime there has
been a calendar change, from the Julian to the Gregorian calendar.
In 1582 CE, the Catholic church led by pope Gregory XIII struck
ten days off the calendar, because it was no longer in phase with the observed solar positions, while a different arrangement with
the leap years was made to ensure that this would not happen again for a long time to come.
Going back ten days in the Regimento,
students will find data for the solar declination that rather closely conform to the modern predictions. So the Portuguese had done
an excellent job!
This small remaining difference can be explained by several factors. First of all, the Gregorian calendar reform
took place about 80 years after the sun declination tables were published, which means that the calendar error had increased about
half a day by the time the ten days were removed from October of 1582 CE. This difference needs to be subtracted from the table.
the second place, the noon sun declination for a certain date changes from year to year, because the solar calendar, which is determined
by Earth’s orbit around the sun, does not exactly fit day length, which is determined by Earth’s rotation around its axis.
annually increasing difference is mostly, but not entirely, corrected every four years by adding an extra day to the calendar. As
a result, these tables had to be adjusted from year to year. If not, over a period of four years these tables would go out of
whack to a maximum of about 20 minutes, which would add an error of about 35 km (21 miles) distance.
a result of the decreasing tilt of Earth’s axis over the past centuries, about 1 minute needs to be subtracted from these data. This must
have been known to the scientists who constructed the Regimento tables.
And last but not least, all of this does not yet take
into account that the sun declination keeps changing during the day. Around the equinox (around March 20 and September 23), for instance,
the sun declination changes as much as 20 minutes in 24 hours.
This means that these data also depend on the place where
they were measured, or for which they were calculated to happen. In fact, the precision in stating the daily noon sun declination
in degrees and minutes would allow us, in principle, to calculate all of that.
Such an assumption seems reasonable, because the
differences per day mentioned in the Regimento very much agree with modern observations and predictions. Checking these old tables
and interpreting them in such ways could become a fascinating research project.
While using these data, most students will usually
arrive at a latitude of about 52 degrees for Amsterdam. They have, on average, at most an error of about 30 miles (45 km) with respect
to their real position. Not a bad result at all with this ancient technology.
Thanks to the fact that my long-standing
research interest into the history of Peru had included its initial conquest, and that I had defended my Ph.D. thesis about Peru on
October 12, 1992 CE, in name exactly 500 years after Columbus had stepped ashore for the first time on the other side of the Atlantic
Ocean, I had begun studying the accounts of some of these early explorers.
Because the commemoration in 1992 CE had led to a
wave of publications about Columbus and his exploits, I had become aware of some very smart recent Spanish scholarship, mentioned
below. As a result, I was familiar, among other things, with Columbus’ diaries as well as with some of the scholarly discussions about
All of that explains how I got onto the track of trying to find out which specific instruments Columbus had used on his
first voyage and what measurements he had reported. This turned out to be a fascinating trail.
After students have determined
their latitude using this ancient maritime technology, they are confronted with Columbus’ measurements that he made during his first
voyage in 1492-93 CE to what later would become known as the Americas.
According to Columbus’ diary, of which only a partial
transcription of a transcription survives, he measured his latitude several times: first on the island of Hispaniola on October
30, 1492 CE, with a quadrant. Columbus' result was 42 degrees, "if my transcription of his letters is not corrupted," wrote
Fray Bartolomé de las Casas (1484-1566 CE), who transcribed and edited Columbus' diary (p.85). In reality, however, it was
only about 20 degrees.
(All the pages mentioned in this context are from: Consuelo Varela, editor, Cristóbal Colón: Los cuatro
viajes; Testamento. Madrid, Alianza Editorial, 1986.)
On November 2, 1492 CE, Columbus used the quadrant at night in the same
place (apparently to get a fix on Polaris) and obtained the same result (p.88). On November 21, 1492 CE, along the coast of Cuba,
Columbus found the same latitude of 42 degrees with his quadrant (p.102), while reporting very high temperatures.
At this point
in the diary, Fray Bartolomé de las Casas expressed further doubt, because he thought, among other things, that at 42 degrees
north (about the latitude of modern Boston, MA) it had to be a lot colder in November (even though no Europeans were known to have
gone there yet). On December 13, 1492 CE, Columbus measured his latitude on the island of Hispaniola with the quadrant and obtained
34 degrees, while his correct latitude was closer to 19 degrees (p.128).
On February 3, 1493 CE, on the Atlantic Ocean on his
way back to Spain, he used both the quadrant and the mariner’s astrolabe to determine latitude, but was unsuccessful because of the
high waves. Yet Columbus did note then that Polaris was high in the sky, much like “cabo de Sant Viceinte” (p.183).
Cabo de São Vicente, the most southwesterly cape of Portugal, is situated at 37 degrees latitude, so still 5 degrees lower than three
of the four measured latitudes in the Carribean just mentioned. Apparently, during that earlier portion of his trip the pole star
had been a lot lower in the sky, which indicates that by that time Columbus must have been aware of the fact that the values that
he had reported earlier were erroneous.
How could the so very experienced sailor Columbus get this so very wrong, one wonders,
while his instruments would have caused an error of at most 1-2 degrees? What would students think about that? Was Columbus incompetent,
or was something else going on?
Spanish scholar Consuelo Varela (1945 CE - ), mentioned above, thought that Columbus probably
falsified his data, because Cipangu, Japan, was also at 42 degrees on his map, and Columbus thought that he had reached that island
(note 31, p.85). This may be a partial explanation for this situation.
But there may be more to this than that. The Spanish nautical
expert and sea captain Luis Miguel Coín Cuenca (1953 CE - ) has argued for decades that Columbus systematically falsified the diary
of his first voyage for one single specific reason: namely to make it appear that he had stayed out of territory that the Portuguese
Dr. Coín Cuenca’s thesis
is best documented in his brilliant but virtually unknown book Una travesía de 20 dias
a dos rumbos que cambió el mundo
, Universidad de Cádiz, 2003.
When Columbus started his first voyage, Coín Cuenca argues, there
was a treaty between Spain and Portugal known as the Alcáçovas Treaty, signed in 1479 CE, and confirmed in 1481 CE by the papal bull
Æterni regis. This treaty granted all lands south of the Canary Islands to Portugal, and thus allowed the Spanish to go only as far
south as the Canary Islands (about 25 degrees north).
According to Coín Cuenca, this is why Columbus reported in his diary that
he sailed straight west from the Canary Islands, even though his descriptions of what he witnessed actually fit a more southernly
course, while they do not agree with his stated course.
This also explains why, on all his subsequent voyages, Columbus did sail
further south. He could do so legitimately, because the earlier treaty had been replaced by papal bulls issued in 1493 CE, and by
the Treaty of Tordesillas of 1494 CE, which had redefined this situation in legal terms.
In his book, Coín Cuenca provides ample,
very carefully assembled, evidence for his thesis, including his first-hand experience of having sailed this more southernly trajectory
in 1990 CE as captain on a carefully-constructed replica of one of Columbus’ ships.
But because Coín Cuenca’s analysis ends when
Columbus first reached land in the Americas, he did not discuss Columbus’ later quadrant and astrolabe measurements, which very much
support his thesis.
As a result of the Alcáçovas Treaty, Columbus had every reason to make sure that his measurements showed
latitudes well north of 25 degrees, so that not only those lands could not be claimed by the Portuguese, but that also a considerable
stretch of possible land situated to the south of where he had gone could be claimed by the Spanish. That is why, I think, all his
measurements show these large systematic errors.
This may also explain why, in the fragments of his diary that survive, Columbus
never reported latitude measurements on his way to the Americas, simply because he knew he was sailing in Portuguese territory.
if Columbus indeed sailed west after leaving the Canary Islands, as he reported in his diary, he would have been right on the borderline
between Spanish and Portuguese territories, which could easily have led to Portuguese suspicions and claims. So from a political point
of view it was a smart move not to report any latitude measurements on his outbound voyage.
This lack of celestial measurements
on his way to the Americas has led to the impression that Columbus almost exclusively relied on dead reckoning: determining his position
with the aid of measuring his direction by compass and his velocity by other means, which were rather unreliable.
did use dead reckoning all the time, as all mariners before and after him have done until the advent of GPS. Yet on his way home,
Columbus did try to measure his latitude, as we saw above. So he was not averse to doing so if he felt the need.
If Dr. Coín
Cuenca is right, how would Columbus have determined his (lower) latitude while sailing to the New World? I think that the observation
mentioned above of Columbus estimating the altitude of Polaris may indicate that he also did so on his outbound voyage. This would
explain how Columbus estimated his latitudes during that portion of his trip without making observations with an astrolabe or a quadrant.
such guesses inevitably contained a considerable margin of error, this may also explain why Colombus missed the first Carribean islands,
simply because he was a little more to the north than he thought he was. By using an astrolabe, he might have hit them right
More in general: in addition to successfully navigating around the globe, carefully measuring latitude and longitude has
had great many other profound consequences in human history over the past 500 years, most notably in North America, Australia, and
Africa, where many borders have been drawn along such geographically-determined lines (cf. Mark Monmonier: Drawing the Line, 1995,
New York, Henry Holt, p.107-8). The Alcáçovas Treaty may have been the first instance in which such lines were drawn.
the problem of knowing where exactly the Tordesillas line should be drawn on the ground on the northern coast of South America
may have motivated the Spanish and Portuguese to stay away from each other there in order to avoid conflicts. If so, this may have
provided room for other Northern European powers (who did not respect the Tordesillas treaty) to colonize the Guyanas and, in doing
so, deeply influence the history of those areas.
What students learn from these observations, apart from doing the measurements
themselves, is that one may only be able to judge historical documents well if one tries to place oneself into the other persons’
positions, and that this may be surprisingly easy to do. They also learn that very interesting questions can be raised as a result
of very simple and basic observations.
Finally, the change into the Gregorian calendar in 1582 CE may have led to new commercial
opportunities. During the sixteenth century, the Dutch overtook the Portuguese and the Spanish by producing mariner’s handbooks that
were printed and sold in different languages. The Dutch first copied these manuals and subsequently improved them. This turned out
to be an excellent business.
Remarkably, the seafaring Dutch provinces of Holland and Zeeland accepted the Catholic Gregorian
calender almost immediately, even though the Dutch were rejecting papal authority by turning Protestant while fighting the Catholic
The British, by contrast, only adopted the Gregorian calendar as late as 1752 CE, apparently because of their dislike
of papal power. Could this coincide with the fact that in the 17th century and beyond, British mariner’s handbooks appear to have
sold not nearly as well as those of their more pragmatic Dutch competitors? And were these different attitudes perhaps connected to
the Dutch running a republic in which mercantile interests dominated, while Britain was a mix between royalty and parliament?
these intriguing questions, to which I do not have clear answers yet, as well as Columbus likely having falsified his latitude measurements,
came as a result of the decision to ask students to observe the sun's altitude with ancient instruments and determine their latitude,
while comparing those data with information from old documents.