A Comparison of
Declination Tables
Martin Cortes First the month and day are found in table 1, and 27° 57' is taken out. In table 2 the year is found, and 00° 44' is taken out and added to the previous giving 28° 41'. Because it is not a leap year (year of bissextilis), 1° is subtracted. The result 27° 41' in Cancer is the true place of the sun in the zodiac. Next we find the column with the sign for Cancer in table 3 and find the 27° in the right column; the declination given is 20° 49', but this figure does not include the additional 41' which must be added to the 27° of the sun's true place in the zodiac. Interpolation between 27° and 28° is required. Because of the great difficulty of multiplication and division by the 16th Century galley method, Cortes would give the following instruction to interpolate. I paraphrase to fit this particular day. "In the year 1579 the eleventh day of Iuly, the Sunne shalbe in 27D, 41M. of Cancer: and to the27D. presyse [precise--exactly] shall corresponde 20D.49M. of declination. And to veryfye the declination that cometh to 41 minutes, whiche is more than the 27D. (which is 20D. 49M.[the declination]) to the declination of 27D. whiche is 20D. 37M. The difference is 12D. Of these you must take such part as is 41 of 60, which are almost twoo terces [thirds]. Then twoo terces of 12 are 8 which must be taken of 20D. 49.M whiche correspond to the 27D. of cancer: because the declinations go decreasinge, and remayneth 20D. 41M. And if the declinations increase, you must add thereto, as you take away when they decrease." That is the result; 20° 41' 27° 57' month and day table 20° 49' declination not exact (3rd
table) 41' (1st col.) is about 2/3 of one degree. 00° 44' year table 20° 37'
declination following day 2/3 of 12' (2nd col.) is 8' 28° 41' sum 00° 12' difference 20° 49' 01° 00'
because not leap year 00° 08' 27° 41 position of sun in Cancer 20° 41' declination
Contrast the above mental exercise with the table at right published by William Bourne in London in 1574 and 1576. Because they were current, and much improved in accuracy and ease of use, these would have been the tables most likely used by Drake on his voyage in 1579. Note the declination for the same calendar date is
20° 42'. Because.... "I do knowe that euery person that goes vnto the Sea as maister of a shippe, hath not capacitie to calculate the Sunnes declination by the place of the Sunne [in the zodiak] although they have the tables of declination, as the Ephemerides, or Martin Curtyse [Cortes]." William Bourne In either of these cases, the solar declination should then be moved forward in the day by interpolating for the Longitude / Time west of the prime meridian. Otherwise, except on two days of the year, the wester one travels, the wronger one gets. In Francis Drake's case on the coast of California in
1579, he would have had to interpolate for 123° (about
8 hours). "...calculated for England, and will serue all Europe without much error, or any other country, or place that hath our Longitude, and the most part of Africa, as Ginnie, and those parts to the South wards , as farre as the Antartick pole...will do for most nauigations as farre as the VVest Indies." William Bourne
On that day at Campbell Cove under Bodega Head (N38° 18' 18"), the sun at meridian transit was at an altitude of 72° 13' 28", which would be read as 72 1/4° if resolved to the nearest 1/4 degree, or 72° even if resolved to the nearest 1/2 degree. Mathematical reduction of the observation for that particular day in the solar season would have yielded latitude determinations of 38° 42', and N38° 26' respectively. The mean is 38° 34'. Because at the resolution of instruments of the period, there is a window of some eleven minutes in time at meridian transit, so quite a number of observations can be made. This is the only place where a determination of latitude could have been recorded as "38. deg. 30. min." on the Pacific Coast of North America on that particular day in 1579. How do we know Drake did not make the adjustment
for longitude in his declinations? Related pages: A Short Bibliography of Essential Reading: Bourne, William, A Regiment For the
Sea (1574), Cambridge, 1963.
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The
date we will use is July 11, 1579 (old calendar)--one
of the 37 days when Francis Drake was on the coast of
California.
William
Bourne
By
retro calculation, the solar declination at meridian transit
on that day in 1579 at longitude W123 was 20°
36'.
WATCHING THE HEAVENS CHANGE.
