Uddrag af Kelley:
In the Wake of Columbus on a Portolan Chart, 1983
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Uddrag af James E. Kelley, Jr.:
In the Wake of Columbus on a Portolan Chart.
Terrae Incognitae, The annals of the Society for the History of Discoveries, 15,
Appendix D: Columbus and the Quadrant
It has bothered me that Columbus had
such apparent difficulty in measuring latitude using a quadrant. On November 2,
1492, while in the harbor of Mares (21.1° N) his quadrant reading was 42° N. he
got the same reading at sea on November 21. Later, on December 13, while in the
harbor of Conception (19.1° N) his quadrant reading was 34°. How could Columbus
make such gross errors of som twenty degrees? He knew the readings were wrong
and thought the quadrant was broken. A quadrant is so easy to use that even
Morison does not suggest Columbus mishandled the instrument. Rather he suggests
Columbus shot the wrong star. Morison’s explanation does not seem valid to me.
Columbus had been looking at Polaris and the “guards” all during the trip in
order to tell time at night. Polaris’s general position in the rigging and
relative position on the horizon would be well known by the time he used the
quadrant on November 2. To misselect Polaris at the latitude of Cuba would be
like selecting a twety-five-story building to survey instead of a twelve-story
building while standing three hundred feet away.
I remember reading the suggestion that
Columbus may have used a quadrant which, for som reason, had twice the number of
degree graduations it should have had. The idea that the scales on Columbus’s
quadrant may have been out of the ordinary could have merit. The standard
quadrant often had other scales besides the equal interval degree scale along
the circumference. The large variety of scales in surviving instruments, even
long before Columbus’s time, must be seen to be believed. Included were standard
scales for the elementary trigonometric ratios: tangent (umbra recta),
cotangent (umbra versa), sine (corda recta), cosine (corda
versa). There were many ways to represent these functions, which found their
way into everyday use by builders, military men, surveyors, pilots, and the
like. It is not unlikely that Columbus’s quadrant had a tangent/ cotangent scale
running parallel, and just inside, the degree scale, and along the
circumference. Such a scale is shown in Apian’s quadrant. This scale gives one
hundred times the trigonometric tangent of angles under forty-five degrees, and
one hundred times the cotangent of angles over forty-five degrees.
Suppose then when Columbus took his
quadrant readings – in the dark, of course – his thumb, which held in place the
weighted thread which measures the angle, covered the numbers on the degree
scales. In the light of a lantern or at the binnacle he might mistakenly read
the nearby numbers on the tangent scale. If this was the case the inverse
tangent (arc tangent) of his reading should approximate his true position. Let’s
do the arithmetic.
Arc Tangent of
These are pretty good results and
conform to the reasonable assumption that one could easily measure angles to
within a couple of degrees with a quadrant.
On February 3, 1493, Columbus records
observing Polaris to be very high, as at Cape Saint Vincent (37° N). This
observation sans quadrant or astrolabe is pretty close to the latitude
calculated by McElroy to be the fleet’s position that day, namely 35° N.
I suppose that Columbus never resolved
his difficulty with the quadrant during the course of the voyage. For in his
letter of February 15, 1493, he notes that the new lands are twenty-six degrees
from the equinoctial line. This position corresponds closely with the plotted
location on a portolan chart of his landfall relative to the Canaries. Hierro is
in 27.7° N.