Columbus Found Longitude?
In our computer age, one
may acquire some programming skills; learn some rudimentary
astronomy and celestial navigation; and with a regressive
ephemeris reconstruct the celestial tapestry of the past and focus
on great historical events.
Let us revisit
Columbus’s first voyage. The eminent Columbus scholar Samuel Morison always
characterized Columbus as a dead reckoning (DR) sailor who muffed
his opportunity to determine his longitude on two occasions when
observing eclipses. Another
view holds that Columbus may have relied upon celestial
observations for his navigation.
This view contends that certain eclipses, conjunctions, and
culminations could aid Columbus in determining his latitude and/or
had no sailing instructions to steer to a specific set of
quest was to find a western route to Cipangu (Japan) and Cathay
and he had a perception of a smaller world which encouraged him to
believe that Cipangu was 2,760 miles away as opposed to
roughly 12,200 miles away.
He sailed with crude instruments and experienced the
changes in magnetic variation as noted by comparing the direction
of the pole star to his magnetic compass.
The magnetic variation was dominantly westerly.
Columbus’ charts showed that he held the latitude of 28°N
for close to 1,400 nmi after departing the Canaries without
altering course. He
was not concerned that his track would be deflected to the left as
a result of the westerly magnetic variation.
The return voyage would experience the same deflection to
the left of course in the dominantly westerly variation that
prevailed. His charts
showed constant course segments with no evidence of changes (other
than to avoid weather) leading one Columbus researcher, Admiral
Robert McNitt USN (ret.), to conclude that Columbus relied
exclusively on dead reckoning in his navigation.
Implicit in this conclusion was that if a celestial
observation was made and it showed a difference in latitude over
the DR position one would expect a course change to be made.
Columbus’ age, dead reckoning was the dominant method used for
required knowing one’s course as determined from the magnetic
compass and speed by timing the movement of a chip log thrown over
the side with reference to external markers on the side of the
ship (although Morison believed that Columbus just estimated his
speed). The distance
made good per hour was noted by placing a peg in a hole along a
radiating line marked on a peg-board representing the course of
the ship hourly. The
results of this peg-board tracking were then transferred to the
map at the end of the day. The
DR position could be updated by celestial observations obtained by
observing Polaris, low grazing stars, and conjunctions according
to the recent paper by Arne Molander who noted correlation of
Columbus’ fixes with certain celestial events.
The problem was that the astrolabe and the quadrant both
capable for use to measure the elevation angle of the celestial
body to yield latitude were sensitive to gravity owing to their
pendulous element for establishing the vertical.
In a ship subject to the vagaries of the ocean motions, the
pendulous element was almost constantly in motion.
These instruments were primarily used for observing
celestial bodies from the land or the quiet waters of a harbor.
The cross staff would have improved the sighting accuracy,
but it was not in use until the next century.
is the diagram for obtaining latitude when a celestial body
is on your meridian. It
is a cross section of the celestial sphere when the celestial
triangle degenerates into the arc of a circle when a celestial
body is observed on
Low Grazing Star at Culmination on Your Meridian
can be calculated by the addition or subtraction of measured
angles with known values. The elevation of the star or Sun is measured and the
declination of the body is obtained from a table.
Columbus’ first voyage, his chart indicated adherence to 28°N
after departing the Canaries.
If he were relying upon celestial observations to maintain
this latitude line, he could verify his adherence to the course by
observing the pole star with his quadrant or astrolabe (despite
their susceptibility to error at sea).
Molander believes that Columbus may have used low grazing
circumpolar stars when they appeared above the northern horizon at
their culmination (on his meridian as they were at their lowest
elevation) to determine his latitude to maintain adherence to his
course. He may have
used a kamal in his measurements, a simple instrument held by both
hands and held taught by string whose one end was clenched in the
observer’s teeth and the other end bridled to the instrument.
Determining one’s latitude by observing the culmination
of a low grazing star is not susceptible to verticality errors as
the tangent to the arc of the measured star remains close to
parallel to the horizon over a wide range (1-cosine effect for
small angles) as viewed in
. We cite Schedar
(Cassiopeia) as the star Columbus could have used on his return
trip at the latitude of the Azores.
It is an example of a low grazing circumpolar star to aid
in establishing latitude adherence.
, we see how one obtains latitude by observing Polaris.
The pole star is at P with the horizon at (HH’).
Since its declination (angle between the celestial body and
the equatorial plane QQ’)
the polar distance to the horizon arc PH’ is equal to the
latitude of the observer arc QZ.
Determining Latitude by Observing Polaris
and/or a Low Grazing Star
this example, the
elevation angle of Polaris is 37°,
therefore Columbus’s latitude is 37°N
latitude. We ignore
the effects of refraction and dip.
The question will be what elevation angle should Schedar be
at culmination to establish that the observer is at 37°N
latitude? We assume
that Schedar’s declination is 56°
in the Columbus era.
longitude was accomplished on land by observing lunar eclipses.
Columbus had access to Ephemerides for lunar and solar
eclipses. Both the
Regiomontanus’s Ephemerides and Zacuto’s Almanach Perpetuum
contained the predicted times of total eclipses at Nuremberg and
Salamanca. A total
lunar eclipse occurs when the Moon enters the umbra sector and
ends when the Moon exits the umbra sector and enters the penumbra
sector as seen in Figure
A Lunar Eclipse
when a full moon enters the shadow of the Earth and the Moon is
near or at one of its nodes (intersection of its plane of orbit
and the plane of the ecliptic) (not to scale).
On February 29, 1504,
Columbus observed a lunar eclipse from the middle of the north
coast of the island of Jamaica. A lunar eclipse can be observed by anyone within a hemisphere
if the full Moon is observed.
One need only note the local time of the event and compare
it to the local time at the reference location in the ephemeris.
This is an observation of simultaneity.
He concluded that the difference in time between the Isle
of Cadiz in Spain and the center of Jamaica was 7 hours 15 minutes.
As the eclipse began before sunset, he based his
calculation on observing the end of the eclipse when the
illumination of the Moon returned.
He knew the elapsed time between the end of sunset and the
end of the eclipse which was two-and-a-half hours as timed by the
half-hour glass (five half-hour glasses in duration).
He obtained the altitude of Polaris as 18 degrees using his
quadrant. This was
close to the correct latitude of his location presumed to be Santa
Gloria (today’s St. Anne’s Bay) at 18° 27'N,
The difference of longitude between Cadiz and his location
was actually 70°56' or 4 hours 44 minutes.
He incurred an error of 2 hours 31 minutes.
It appears that Columbus knew the difference in longitude
between Salamanca and Cadiz.
(~ 39 arcminutes of longitude) since
his ephemeris was based on observations made at Salamanca and
There are various reasons
that could explain Columbus’ colossal errors in determining
longitude by timing the lunar eclipse.
The one half-hour glass introduced an error.
If he backed into his estimate for the beginning of the
eclipse by using the elapsed time from sunset to the end of the
eclipse to establish the beginning of the eclipse was another
source. He could have
exaggerated the longitude difference to establish a vaster domain
under discovery. Clearly
this dependence on a half-hour glass as a basis for time reference
was an error source and extrapolating the time of the beginning of
the eclipse was another error source.
Let us assume for this
Brain Game that our Columbus had a clearer awareness of the
beginning of the lunar eclipse and concluded that the difference
in time between the island of Cadiz and Santa Gloria for the
beginning of the eclipse was 4 hours 30 minutes.
He also knew that the reading of the half-hour glass
reference introduced an error of 1 percent of the time on the
slow side. Assume
that 5.5 hours elapsed from local noon (last setting of the
half-hour glass) to the time of the eclipse.
Columbus knew that his time master was slow.
We will presume that he also read the time of the eclipse
using his nocturnal (an instrument used to determine time at night
and not available until the next century).
It had an index error of ‑0.1 hour.
Based on his uncorrected nocturnal reading, he concluded
that the longitude difference between the two sites was 4 hours
30 minutes. He
then corrected the readings of his time sources for their errors
and averaged them. What
was his measurement of the difference of longitude between Cadiz
and St. Anne’s Bay?
The elevation angle of
Schedar and the longitude difference between Cadiz and St.
Anne’s Bay was:
longitude difference 4 hours 35 minutes
longitude difference 4 hours 30 minutes
longitude difference 4 hours 32 minutes
longitude difference 4 hours 26 minutes
The answer is:
Referring to the
elevation angle of Schedar to yield a latitude of 37°N
The half-hour glass
error after 5.5 hours was -0.01 x 330 minutes = -3.3 minutes.
Correction is +3
minutes to be added to 4 hours 30 minutes
= 4 hours 33 minutes.
The nocturnal error
was -0.1 hour or -6 minutes.
Correction is +6
minutes to be added to 4 hours 30 minutes
= 4 hours 36 minutes
Then the average
difference in longitude is:
This corresponds to
4.58 hour x 15°/hour = 68.7°
west of Cadiz. His
actual longitude difference was 4 hours 44 minutes or 4.73 x 15°/hour = 70.95°
west of Cadiz. What
we find with the ascribed nominal errors to the instruments that
Columbus in this simulation would be within 2.25°
of his actual longitude. We would then conclude that the balance of the error was due
to his perception of the beginning of the eclipse and other
errors. It is known
that he measured his altitude of the pole star as 18°
at St. Anne’s Bay which was close to the actual latitude of
Columbus typically had a history of determining his
latitude with significant error. He blamed this on his quadrant.
Some scholars believe he was reading his instrument high to
record higher latitudes initially to keep his discovery within the
bounds ascribed to the Spanish sovereignty in accordance with an