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A Comparison of Declination Tables
copyright Bob Graham 2002

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.

Martin Cortes
Compiled in 1551 as Breve Compendio de la Sphera y de la Arte, de Navigar and translated and published in English by Richard Eden as The Arte of Navigation in 1561.

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


William Bourne

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'.
That's all there is to it--done!
Bourne did all the work for you.


"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).
But, of course, not knowing his longitude, and having no way to capture and preserve Time, he could not make that adjustment.

"...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

By retro calculation, the solar declination at meridian transit on that day in 1579 at longitude W123 was 20° 36'.

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?
Because when having sailed 360° west and returned to Plymouth, he found his reckoning of the date to be off by one whole day.
According to the last paragraph of The World Encompassed, the day of his return was "...Monday in the iuft and ordinary reckoning of thofe that had ftayed at home in one place or countrie, but in our côputation was the Lord's Day, or Sonday."

Related pages:
go AN EXPERIMENT IN THE DETERMINATION OF LATITUDE: This is a followup to the proceeding article, in which the conclusions made therein are put to practical test that may be repeated by anyone wishing to go to the trouble.
go A DAY AT THE COVE: An actual on-site demonstration of the determination of latitude with an astrolabe at Campbell Cove before a group of interested spectators >>>>>
How Polaris has moved 2 degrees closer to the celestial pole during recorded California history, and why John C. Frémont got up at 3:00 a.m. to sight Polaris in 1844--wasn't it there all night long?
go March, 2013. A look at longitude determined on Drake's Circumnavigation of September 15, 1578 (old calander date)

A Short Bibliography of Essential Reading:

Bourne, William, A Regiment For the Sea (1574), Cambridge, 1963.
Bowditch, Nathanial, The New American Practical Navigator: Any 19th Century Edition is most usefull.
Sir Francis Drake (Bart.), The World Encompassed, 1628: Any edition, but especially The Argonaut Press, London, 1926.
Hanna, Warren L., Lost Harbor, University of California, 1979.
Kelleher, Brian T., Drake's Bay, Day Publishing, San Jose, 1997.
Taylor, E. G. R., An Elizabethan in 1582; the Diary of Richard Madox, Fellow of All Souls, The Hakluyt Society, London, 1967.
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.

©1999, 2007
Bob Graham