On Saturday, August 11 (old calendar), 1582, at
Sierra Leone on the coast of Africa, Richard
went to take the sone a shore, and the declination
being 12 degrees 18 mynuts I took the sone on a
perfe[c]t instrument at 3 degrees 26 mynuts
fro[m] the zenith so that I
pronow[n]sed the place to be 9 degrees
lacking 8 mynuts.
Because there had been almost no change in
longitude between Plymouth England and Sierra
Leone, this latitude determination is very correct
at 8° 52'.
Note that in the above observation of the sun at
noon (meridian transit, or, the noon shot),
Madox states the complement of the angle of
the observed altitude of the sun above the horizon.
He consistantly states the distance of the sun from
the zenith, not horizon, so this was how the scale
of his instrument ran. The mathmatical reduction of
that observation was subtractive from the published
solar declination for the calendar date and season
of the year.
Elsewhere in his diary Madox rounds this off
when he says that "Serra Liona [sic for Sierra
Leone] standeth in 8 [degrees] 2
terces"--8 2/3 degrees, which would be 8°
of Madox' purchases before the start of the voyage
was "for an ephemerides...3s
6p" on January 31, 1582. From a later
reference on April 8, we might infer that the
ephemerides were those in A Regiment for the
Sea, by William Bourne2, which Madox
says he had "read over." However, Madox' stated
declination of "12 degrees 18 mynuts" for August
11, 1582 varies by 1 arc minute from the tables in
Bourne's 1574 publication for the second year after
bissixtilis (leap year).
What the "perfect instrument" was we are not
told, but it was either a mariner's astrolabe (as
above) or a portable quadrant, because the sun
observed at a near vertical 86° 34' above the
horizon was far outside the 50° useful range
of the cross staff (Jacob's staff; balla
For a more detailed look at this science of
celestial navigation in the 16c, see:
of Latitude on the Coast of California in
1579, January 1999, Bob Graham Library of
Congress TX 5-606-271
And for a look at the published ephemerides at
the time, see this comparison of the tables
published in Richard Edin's The
Art of Navigation, his 1561 translation of
Martin Cortes' 1551 Breve Compendio de la Sphera
y de la Arte, de Navigar, contrasted with the
tables published by William Bourne.
here, an example of the noon observation from
October 6, 1999 on the coast of California.
On this day, due to the equation of time, the
sun was approximately 16 minutes before the clock.
Campbell Cove (123 W) is also 3 degrees west of the
120th meridian Pacific Standard Time 12:00, making
it 12 minutes late by the clock. Therefore, the
actual meridian transit of the sun (see my watch in
photo) occurred at about 12:56 PDT (11:56 PST).
Note the shadow of the foresight on the
backsight, and the concentric halo of light
surrounding the aperture in the backsight.
On this particular day at this place the
determined latitude was N38° 19'--the actual
latitude by GPS was N38° 18' 19". More
It is this very excellent sighting method that
makes the astrolabe a useful instrument--a 9"
diameter astrolabe is, after all, a quadrant of
only 4 1/2" semi diameter! And because of its
double articulated suspension, it is always
perpendicular to the center of the earth, so there
is no necessary correction for dip of the
here my article on how longitude was
established on September 15, 1578 in the Mar del
Zur south of the western entrance of the
Magellan Stait on Drake's voyage of
circumnavigation. This has never been written of
before March 13, 2013.