16C Latitude determinations; how accurate?

On Saturday, August 11 (old calendar), 1582, at Sierra Leone on the coast of Africa, Richard Madox1 wrote:
[We] 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° 40'.

One 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 stella)

For a more detailed look at this science of celestial navigation in the 16c, see:
Determination 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.

And 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 about this day.

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 horizon.

See 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.

Notes and a short bibliography:

1 Donno, Elizabeth Story, An Elizabethan in 1582: The Diary of Richard Madox, The Hakluyt SocietyLondon, 1976.

2 Bourne, William (E. G. R. Taylor, ed.), A Regiment For the Sea (1574), Cambridge, 1963.

Nuttall, Zelia, New Light on Drake, Hakluyt Society, London, 1914.

Taylor, E. G. R., Tudor Geography 1485-1583, Methuen & Co. Ltd., London, 1930.

Wagner, Henry R., Sir Francis Drake's Voyage Around the World, John Howell, San Francisco, 1926.

Waters, D. W., The Art of Navigation, Yale University Press, 1958.

Wright, Edward, Certaine Errors in Navigation (1599), Walter Johnson, Norwood, N.J., 1974.

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