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LONGCAMP.COM'S NOVA ALBION ANNEX

DETERMINATION OF LATITUDE BY
FRANCIS DRAKE ON THE COAST OF
CALIFORNIA IN 1579
Copyright © January 1999 by Bob Graham
Library of Congress TX 5-606-271

The World Encompassed, page 64

 

Due to its comprehensiveness, what follows is quite a lot of information. If you are curious enough to proceed, it will cover the following:

  • The navigational instruments available to Drake at the time of his circumnavigation.
  • The published epemerides available, and how they are used in reducing a celestial observation to a position.
  • The use of the rule for the obliquity of the ecliptic to calculate the height of the sun at meridian transit for each of the 37 days in 1579 at the potential ports near 38° North latitude.
  • How to take the altitude of a meridian transit and to make the mathematical reduction of the observation of that observed transit at the resolution of the instruments of the time.
  • The identification of the one port on the Pacific Coast of North America at Drake's reported "38 deg.30.min."
goRead the preface to this article

Nuno da Silva, a Portuguese captain and pilot whose merchant ship was captured by Francis Drake during his epic circumnavigation of the globe in 1577 - 80, made the following comments on Drake's skill as a navigator: "The first thing he did when he had captured a vessel was to seize the charts, astrolabes, and mariner's compasses . . . He carries three books of navigation, one in French, one in English, and another, the account of Magellan's voyage, in a language I do not know . . . He is a very skillful mariner . . ." The book in English that Drake was very likely carrying aboard the Golden Hind when he departed Plymouth, England, in 1577, was either the first or second edition of William Bourne's A Regiment for the Sea, published in London in 1574 and 1576, respectively. Bourne's Regiment was far and away the most current and important English book on navigation available at the time of Drake's departure. As such, it is hard to conceive that Drake, the foremost English navigator of the age, would not have been carrying it.

"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, of Martin Curtyse [Cortes]." William Bourne

go See a comparison of the Tables of Solar Declination by Martin Cortes with those of William Bourne.

Though its seems to have escaped the notice of past researchers, the fact that Drake was likely using Bourne's Regiment (or at least its tables) to instruct him in his navigational techniques and to make his computations of latitude, gives us a useful means of identifying the location of some of his disputed landfalls. Drake's "Nova Albion" landfall on the coast of present day California is among them. The World Encompassed by Sir Francis Drake (the 2nd, bart.) (1626), the most detailed extant account of Drake's circumnavigation, includes two latitude readings for Nova Albion: the latitude given for the "Port of New Albion" is "38 deg. 30 min."; the latitude given for the furthest point Drake explored to the south along the coast of Nova Albion is "38 deg." With the instruments of the time, how would Drake have made these determinations of latitude, and how accurate would they be? By reference to the Regiment, we can answer these questions with a considerable degree of confidence.

Note: For comprehensive histories of the publications of Drake's The World Encompassed and Hakluyt's The Famous Voyage, see: Kelleher, Brian T., Drake's Bay, Unravelling California's Great Maritime Mystery, Day Publishing, 1997, and Thrower, Norman J. W., (editor) Sir Francis Drake and the Famous Voyage, 1577-1580, University of California Press, 1984

go The World Encompassed covering the days addressed in this article with Hakluyt's The Famous Voyage in parallel.

DRAKE'S INSTRUMENTS OF NAVIGATION

In Drake's day there were three instruments that mariners used to make celestial sightings for use in computing their latitude: the quadrant, the cross staff, and the astrolabe. The sixteenth-century mariner had no means for measuring longitude. The ability to measure longitude practically and accurately, particularly at sea, was150 years in the future with Harrison's invention of the sea chronometer.

The quadrant was the first instrument developed for use in celestial navigation, dating back to the fifteenth century. It was a very simple devise constructed of wood or metal in the form of a quarter circle with degree graduations along the arc. It had sights along one of the radial arms and a plumb-bob suspended from the right angle. The observer held the quadrant with the arc straight down and looked up through the sights at the sun or star. When his sights were aligned, he simply held the plumb-line fast against the face of the quadrant between his finger and thumb and read off the altitude from the scale. In Drake's day, the quadrant was probably most commonly employed on land to make Pole-Star observations.

The cross-staff in use in 1579 was a simple device that worked reasonably well for measuring the angle of the sun above the horizon at noon. It was fitted with one movable vane (transversary) that, with the end of the staff placed at the eye of the observer, was positioned so that it appeared to touch both the horizon and the sun. The angle was then read from a scale on the staff. In his Regiment, Bourne admonishes the navigator against using the cross-staff for measuring an altitude of over 50°, the maximum angle that the sun and the horizon could be taken in together with one glance. The cross-staff was the method of resort on a rocking ship since its use did not rely on gravity. Illustrated at right is a polaris shot. It also illustrates the problem with polaris (see below).

go Edward Wright's comments--warnings and reservations


The mariner's astrolabe in common use by English seamen at the time was a wheel-shaped, cast-brass instrument of perhaps 7 or 8 inches in diameter with a thumb ring at the top. The ring mount was designed to allow the instrument to hang vertically plumb and to provide for precise rotational control by the user. The disk was divided into four quadrants, two or more of which had scales divided into 90 degrees each. The astrolabe had a rotating sighting arm (alhidada), mounted through the center. Though the astrolabe offered a reliable and accurate method of measuring altitude, the mariner's ability to read the degree scales along the rim was a limiting factor on the precision of the observation. Since each degree division for a 7-inch diameter instrument was only about one-sixteenth of an inch, the mariner could read the angle only to the nearest half degree. As with the quadrant, the mariner's ability to make an astrolabe sighting at sea could be completely frustrated by movement of the ship.

go More about what constitutes a Mariner's Astrolabe.

The astrolabe was best suited for use on land where it could be held steady in hand or suspended from a tripod. For his land-based readings, however, Drake, may have been using a simple astronomical ring or a larger astrolabe such as a 2-foot diameter instrument known to have been produced in England by Humphrey Cole in 1575. Due to their size and weight, these larger instruments were not practical for use at sea. With the stable foundation and larger scale (almost 1/4 inch per degree for a 2-foot ring), the mariner could easily make his altitude readings to the nearest quarter of a degree and could at least attempt readings to the nearest 10 minutes of arc.

DRAKE'S METHODS OF NAVIGATION

There were two common methods by which Elizabethan navigators made celestial determinations of latitude in the Northern Hemisphere: they made sightings of the sun at noon; and they made sightings of the Pole Star (Polaris, the North Star) during any hour of darkness. From the following passages in The World Encompassed, it appears that Drake, weather permitting, may have employed both techniques during his California sojourn: "neither could we [during their stay in California] at any time in whole fourteen days together [presumably toward the beginning of their stay], find the air so clear as to be able to take the height of sun or star."

In the evaluations to follow, it will be assumed that when he actually recorded a latitude in his log, Drake, given the choice, would always have used his noon observations of the sun rather than his pole-star observations. This is because for sixteenth-century navigators like Drake, the noon sighting was, in modern-day terminology, the reference method. Though it involved more complicated calculations than the Pole-Star method, it was the tried and true method for obtaining latitude by which the accuracy of other techniques such as dead reckoning and Pole-Star readings were measured. In addition, Drake, as a practical astronomer and practiced navigator, would have had much experience with both Pole Star and solar sightings. He would have made many comparisons of his results at known positions, and would surely have come to realize what was formally brought to light by Edward Wright when he published Certain Errors in Navigation at the very end of the sixteenth century: "I must for the present only give the mariner warning that he not trust to it [the Pole-Star reading], being very erroneous, and grounded on two false positions."

Thus, to accurately measure the latitude of his Port of Nova Albion Drake would have measured the sun's height above the horizon at noon (meridian altitude). Being near the summer solstice, the sun was too high in the sky to allow him to measure the angle with a cross-staff. Drake would use his astrolabe.

Whatever sized astrolabe he used, as the sun approached noon, Drake would begin to track its final east to west ascent by simultaneously rotating the disk itself along its vertical axis while adjusting the alhidada to keep the rays of the sun passing parallel through the two small holes on the front and rear sights. At noon, the sun would finally stop climbing, seem to stand still for a few moments, and then begin to descend. With the tip of the alhidada pointing to the position on the quadrant scale where the day's maximum rise had occurred, Drake would record the instrument altitude.

go Averaging a number of observations at noon. Huh?
go See this being done.
go Read William Bourne's instructions for the noon shot.

To convert the instrument altitude into a position of latitude, Drake first needed to correct for any instrument error (index error) to obtain what is called the observed altitude. The astrolabe was easily checked for index error by rotating the instrument 180 degrees, taking sightings from opposite directions, halving any difference detected, and then adding or subtracting this value from the reading.

There were then no corrections for parallax or dip of the horizon (dip is not applicable with the astrolabe). There is also no correction for semi-diameter of the sun, because it is the center of the sun which is projected onto the back vane. Drake would next turn to his astronomical almanac (ephemeris). This would contain the tables of changing but predictable astronomical events (ephemerides) useful to the mariner that were then called a regiment. Bourne's 1574 Regiment contains tables of ephemerides, including those for the declination of the sun north or south of the equator for four-year cycles including leap year (year of bissextilis) and covers the years 1573 through 1592.

The year 1579 in Bourne's table falls in the third year of the cycle. The summer solstice occurred on June 11 (June 21 by the modern calendar) when the sun's position in its apparent annual orbit about the earth (ecliptic) reached the northern limit of its drift away from the equator (Tropic of Cancer at 23° 27' North Latitude). Drake landed at his port of Nova Albion seven days after the solstice on June 17 when the solar declination (amount of drift from the equator), by Bourne's tables, was 23° 24' at noon in London, and departed on July 23 when the solar declination was 18° 00'. These declinations are to be subtracted from the true altitude, which gives the altitude of the celestial equator at the point where it crosses the meridian.

EVALUATION OF THE LATITUDE EVIDENCE FOR NOVA ALBION

There is no safe harbor at the exact "38 deg. 30 min." position The World Encompassed records for Drake's California harbor. The closest candidate anchorage site to the reported position is Campbell Cove at the mouth of Bodega Harbor in Sonoma County. Its actual latitude is 38° 18' 19". The site in Marin County's Drakes Bay where most historians currently believe Drake made port is located at 38° 02' 04". How well do these candidate anchorage sites correlate with the latitudes reported in the account?


From Drake's Bay, Unravelling California's Great Maritime Mystery with additions.


Campbell Cove/Bodega Harbor. At left is the Cove as it appeared in the 1960s before alteration by PG&E. - If Drake had been at Campbell Cove (actual latitude 38° 18' 19") and made a noon sighting on, for example, June 30, 1579 (old calendar), modern-day reckoning tells us that the sun would have risen to an elevation of 73° 56' above the horizon at noon. Thus, if Drake could have read his astrolabe to the nearest minute after corrections for index error, he would have recorded 73° 56' as his observed altitude. From Bourne's table, he would have found the declination for June 30th to be 22° 24'. Drake would subtract the 22° 24' declination of the sun from his observed altitude of 73° 56'; the result, 51° 32'. The altitude of the equator where it crosses the meridian is the complement of the altitude of the pole--a latitude reading of 38° 28'. We see that if Drake could have read the astrolabe to the nearest minute, his measurement by reference to Bourne's tables would have been 9 minutes high. The reasons for this positive bias are discussed later on.

go 1797 Bodega y Quadra clarifies the confusion of "three distinct harbors."
go Capt. James Colnett's 1790 plan of his "Port Sir Francis Drake on the Coast of New Albion," which shows the springs in the cove as above left, and the location of the Indian Village.
go See at Google Maps
go See Drake's the course in the Pacific from Guatulco.

Drake, however, could not read instrument altitude to the nearest minute of arc. If we assume he used either the standard 7-inch astrolabe or Cole's 2-foot astrolabe, did not make a sighting error, and corrected for any index error, his best estimate of the observed altitude in reading the astrolabe's scale to either the nearest half or quarter degree, would have been 74°. After subtracting the solar declination 22° 24' from 74° and subtracting the result from 90°, he would have arrived at a latitude of 38° 24'.

To determine the latitude of his landfall to the best of his ability, Drake, as weather permitted, would have made additional sightings during the course of his stay to refine his determination. As a skilled navigator, Drake would have recognized that his calculated atitude readings would change somewhat daily due to his inability to read the ever-changing meridian altitude of the sun to any closer than half or quarter degree. Repeating the sightings would have allowed him to average not only these daily variations, but also any non-biased sighting error. To assess the variability of Drake's readings, we must know the sun's altitude for each of the thirty-seven days of Drake's California sojourn.

This can be determined by creating a table of solor declinations for 1579. Current tables must be adjusted backwards by the rule for the obliquity of the ecliptic--a factor of 468.15 seconds of arc per thousand years. Adding those declinations, and a small amount of solar parallax and refraction to the complement of the latitude being examined, establishes just where the sun would have been seen in the sky in that place at noon on the day in question.

tracking a virtual sun
Yes, I was still using that HP-67 card-reading calculattor in 1999 :-)

In Tables 1 and 2 (appended below) the true altitudes of the sun at Campbell Cove and Drakes Estero have been calculated for each of the days between June 17 and July 23, 1579. Though we do not know on what days Drake actually made his sightings, by reference to these tables we can make some useful observations. For example, if Drake took sightings at Campbell Cove (38° 18' 19") with the 7-inch mariner's astrolabe on the day he landed (June 21), and repeated the observations weekly (on June 28, July 5, 12, 19), the results for Campbell Cove would have looked like this:

38° 13', 38° 37', 38° 13', 38° 30', and 38° 30'; the average is 38° 26'.

If Drake had used a larger instrument and recorded the altitude to the nearest quarter degree, the result for the same five days would be:

38° 28', 38° 22', 38° 28', 38° 30', and 38° 30'; the average is 38° 28'.

For the entire thirty-seven days of Drake's California sojourn, the average of all Campbell Cove readings made to the nearest half degree is 38° 26', and for the nearest quarter degree is 38° 28'. If we assume that the two-week period the Elizabethans could not make a sighting due to fog was at the beginning of the sojourn, the averages are a little higher: 38° 33' and 38° 30'. Though the averages for the smaller and larger instruments are close, the advantage of the larger instrument in reducing the range of the extremes is apparent.

Because of the difficulty of doing division by the galley, or scratch method of dividing numbers in the sixteenth century, Drake would have estimated an average from his results, which in this example, he very likely would have called "38 deg. 30 min." for either the larger or smaller instrument. Thus, based on the results of this evaluation, there is certainly very good reason to believe that Campbell Cove is indeed the location where Drake logged the "38 deg. 30 min." reported in The World Encompassed.

go reading the scale.


Drake's Cove/Drakes Bay - The estero at Drake's Bay has long been the favored candidate anchorage site, as evidenced by its name on modern maps. The mouth of the estero (Drake's Cove) is at a latitude of 38° 02' 04". If Drake had been there during his thirty-seven day California sojourn, the weekly series of readings described above would look like this for readings made to the nearest half degree:

38° 13', 38° 07', 38° 13', 38° 00', 38° 00'; the average is 38° 07'.

for readings made to the nearest quarter degree 38° 13',

37° 58', 38° 07', 38° 13', 38° 15', 38° 15'; the average is 38° 09'.

The average for all the thirty-seven days for the estero when read to either half or quarter degrees would probably have recorded the latitude either as "38 deg." or "38 deg. 10 min.", depending on the size of the instrument. He certainly would not have logged the "38 deg. 30 min." reading reported in The World Encompassed.


The Farallons - According toThe World Encompassed after departing the port of Nova Albion on July 23, 1579, Drake arrived at certain islands the next day out, July 24. From there he set sail on July 25 en route across the Pacific for the Mollucas. Assuming Drake did indeed harbor in the San Francisco area, these certain islands had to have been today's Farallon Islands, the largest of which stands at about 37° 42'. The Farallons thus mark the southern extent of Drake's exploration of the California Coast which The World Encompassed reports to have been "38 deg." By modern calculation the altitude of the sun at noon July 24, 1579 was 68° 50'. If Drake had taken an astrolabe sighting for the Farallons that day, he probably would have measured the altitude of the sun as 70° even and, after reduction, recorded the latitude as "38 deg." Given the relatively short distance from port, Drake may also have approximated the reported "38 deg." latitude by dead reckoning. If so, this would be consistent with a July 23 departure from Campbell Cove which is roughly a half degree north of the Farallons. Such is not the case for Drakes Estero, however, which is only about 1/4 degree north of the Farallons.

go Is "nipping cold" weather in June/July 1579 evidence for a much higher latitude than N38°30'? "Every hill (whereof we saw many, but none verie high) though it were in Iune, and the Sunne in his neereft approch vnto them being covered with snow...During all which time, notwithftanding it was the height of Summer, and fo neere the Sunne; yet were wee continually visited with like nipping colds."

SOURCES OF ERROR IN DRAKES MEASUREMENTS

Pole-Star Readings - The false positions to which Wright refers to with respect to Pole-Star readings concern the corrections that must be applied to account for its angular distance from the pole. Polaris, in our century, rotates within about plus or minus 1 degree of arc about the pole every 24 hours. Thus, the observed altitude of Polaris today is within about a degree of the latitude. In the sixteenth century, however, the distance of Polaris from the pole was significantly greater (about 3 degrees), and not accurately determined until the very end of the century. Various authorities placed the distance at from 4° 9' (Johann Werner in 1541) to 3° 30' (Martin Cortes in 1551). Bourne in 1574 also put the angle at 3° 30' minutes, which seems to have been the most accepted figure until 1599, when Edward Wright corrected this to 2° 52'. Thus, assuming Drake was using Bourne's value of 3° 30', his Pole-Star readings, depending on the time of day of the observation and the relative positions of the stars, were subject to an error from this source alone that ranged from zero to plus or minus just over a half degree.

There were other sources of error. After taking a sighting of the altitude of Polaris for purposes of latitude determination, it was necessary to correct for the distance of the star above or below the pole at the time of time of the observation. To do this Drake may have been using Bourne's Regiment of the North Star which gave the approximate degrees of correction to apply based on the relative position of Polaris to the Guard Stars of Ursa Minor (Little Bear or Little Dipper) which rotates about the pole approximately once each day. To obtain a more refined value for the angle of correction, Drake could have employed a simple astrolabe-derived device similar to a nocturnal in conjunction with an associated table. Either way, however, the correction for altitude was an approximation that was apt to increase the error of the Pole-Star latitude measurement. Sighting error was another problem due to the small size of the star and the lack of optical instruments. Additional errors associated with cross-staff observations are discussed below.

go Sighting problem.

go Read about changes in polaris since Drake's time

Solar Readings - It was fortunate for our purposes that Drake was compelled to use the astrolabe to make solar observations during his California sojourn, because the astrolabe provided several advantages over the cross-staff that navigators were not aware of at the time.

The problems with the cross staff were first comprehensively addressed by Edward Wright in Certain Errors in Navigation in 1599. The principle problem was instrument parallax. If the end of the staff was not placed so that the top surface was in the exact center of the eye, and the scale (because of the length of the staff) was not an exact distance from the focal plane of the eye, the angle would not be determined correctly. Bourne noted this problem, but offered no practical solution. Because there is no solution. The error can be quite large, a whole degree of arc or more.

go Improvements in the cross staff.

Unlike the cross staff, the astrolabe or quadrant were not subject to errors of instrument parallax. Because it is referenced by gravity to the center of the earth, a visible horizon was not needed (a distinct advantage on the foggy California coast) and the sighting needed no correction for dip of the horizon. The error due to dip (not addressable in 1579) would have amounted to 3 to 4 minutes of arc from a sighting made from the deck of a ship of the time, or from that same elevation on land. Furthermore, because the rays of the sun passing through a hole in the front sight of the alhidada pass through another hole in the back sight, both limbs of the sun are the reference, and there is no necessary correction for semi-diameter of the sun. The errors of solar refraction and solar parallax for altitude correction that would apply to the time and location of Drake's Nova Albion sighting amount to only 17 seconds of arc, and while not addressed here, are too small to be considered in sighting with the relatively course instruments of the time.

Notwithstanding the advantages of the astrolabe over the cross staff, Drake's latitude determinations for the thirty-seven days in California would have been high by 4 to 11 minutes of arc with the error increasing with time. There are two causes for this increasing positive bias in the readings during those particular days.

First, Bourne's declination tables published in 1574 contained errors which are due in part to the apparent slow and swift motions of the sun between the solstices and equinoxes.

go Edward Wright's comments

These slow and swift motions were not fully explained until Kepler's laws of planetary motion.

go Copernicus

Bourne's declination table puts the sun on the June 11th solstice as 23° 28' (for the longitude of London). The correct figure is two minutes lower at 23° 26'. As the days progress forward, however, away from the solstice, the error in Bourne's tables increases, so that by the time Drake left the coast, the error resulting from Bourne's tables would have been about 6 minutes of arc.

Secondly, Bourne's declination tables, which were derived for London, had to be corrected for longitude when used anywhere significantly east or west of London. Bourne notes in Regiment that his solar declinations "will serve for all Europe, without much error, or any other country or place that has our longitude, as the most parts of Africa, as Ginnie..." Mariners in 1579, however, with no way to measure their longitude presumably ignored the problem .

We know for certain that Drake did not correct his solar declinations for longitude.
Because after having sailed 360° west and returned to Plymouth, he found his own 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 just and ordinary reckoning of those that had stayed at home in one place or country, but in our computation was the Lord's Day, or Sunday."

Circumnavigation, H.M.S. Beagle, Captain Robert FitzRoy.
Charles Darwin, Tahiti, November, 1835:
16th:
"This was our Sunday, but the Monday of Tahiti: if the case had been reversed, we should not have received a single visit, for the injunction [of the missionaries] not to launch a single canoe on the Sabbath is rigidly obeyed.
17th: "This day is reckoned in the log-book as Tuesday the 17th, instead of Monday the 16th, owing to our, so far, successful chase of the sun."

By the time Drake had reached the coast of California, he had traveled one third of the way around the world from London (W120° or eight hours, although Drake would have called it east 240°). At noon in London on the 17th of June, the north declination of the sun by Bourne's tables, was 23° 24'. Adjusted eight hours from London, however, Drake, had he known, should have corrected 23° 24' to 23° 22' for June 17, a difference of 2 minutes of arc. When he departed California, longitudinal error had increased to 5 minutes of arc as the rate of change in declination increased. By July 23, 1579, the combined errors from the use of Bourne's tables, and the fact that he did not correct for longitude, resulted in a total positive bias of about 11 minutes of arc.

Latitude: Interpolation between dates.
In the example at right, on the 25th the declination is 4° 30'.
Twenty-four hours later, on the 26th, it is 4° 52'.
To be able to determine the correct latitude at a place at 123 West longitude, about 8 hours of time must be added to the declination of the 25th by interpolation.

Even if one understood the necessity, and had a good approximation of their longitude, interpolation between days was difficult.
go Here an example of interpolation as taught by Eden in his translation of Martin Cortes.

D. W. Waters, The Art of Navigation in England in Elizabethan and Early Stuart Times, Yale University Press, 1958: Accuracy [of determinations] depended in great part upon the correct calculation of declination. This in turn depended upon the conversion into time of the difference in longitude between the position and the meridian for which the declination tables were calculated, a problem skated over so far [1594] by all the manuals.

As late as 1705, Pére Labat would write, "I only report the longitude [of Hispaniola] to warn the reader that nothing is more uncertain, and that no method used up to the present to find longitude has produced anything fixed and certain."

After Drake's circumnavigation:

Richard Madox, Diary, 1582. I considered that all ephemerides which are calculated according to the latitude of any place have certainty of truth no wher but in the same longitude wher the observation was taken, which is a note ether not heeded or not as I knoe by any yet published.

Edward Wright, Certaine Errors in Navigation, 1599: Seamen do take the sun's declination out of their regiments without any equation by addition or subtraction of the part proportional agreeable to the difference of longitude of the place where they are . . . so may be deceived sometimes 10 or 12 minutes in taking the sun's declination.
go Edward Wright further illustrates the problem and presents the solution in Certain Errors in Navigation, 1599.

go Longitude determined on Drake's Circumnavigation

Longitude=Time: how easy it is today to carry the correct time about.

The bias in Drake's latitude determinations resulting from his use of Bourne's declination tables was not always positive. The error for a given longitude is dependent on the season relative to the solstices and equinoxes. For example, for the longitude of Drake's Nova Albion landfall, for the plus or minus 91 days from the summer solstice to the fall and spring equinoxes, the error would range from plus 15 minutes to minus 13 minutes of arc.

CONCLUSIONS

The error in Drake's reported determinations come from three components: reading error (+/-), his longitude west of London (+), and errors in Bourne's tables of solar declination (+/-). The first and last of these will be either additive or subtractive depending on the day and the season of the year. It is possible for some errors to compensate for others. Therefore,

there is no constant error; every determination must be looked at on an individual basis.

Though the 4 to 11 minutes of positive bias in Drake's astrolabe readings for this particular range of days in the 1579 calendar is relatively small, it appears to have considerable significance with regard to the long-standing debate about the location of Drake's port of Nova Albion. The results of this analyses demonstrate that if Drake had harbored at Sonoma County's Campbell Cove (true latitude 38° 18' 19") in June 1579 and made a competent measurement of the latitude using the instruments and methods available at the time, the value he most likely would have recorded would have been "38 deg. 30 min.," just as reported in the most detailed account of the voyage. The results of this analysis further show that the "38 deg." latitude The World Encompassed reports for Drake's furthest exploration south is consistent with what Drake would have recorded at the Farallon Islands (actual latitude 37° 42'). The reported latitude of the Farallons is also consistent with a July 23 departure from Campbell Cove since the Farallons are located roughly a day's sail and a half degree south of this port. Conversely, the latitude evidence in The World Encompassed does not support a sojourn at today's Drakes Bay or points south.


NOTE: The dates in these Excel® tables below are adjusted for the difference in the Julian and Gregorian calendars. Many thanks to Dr. Andrew T. Young, Astronomy Department of San Diego State University who visited this website and straightened out some of my terminology and provided me with the rule for the obliquity of the ecliptic.

TABLE 1
Reconstruction of Drakes Readings for Campbell Cove (38°: 18' 19") Landfall

Key to Table Columns:
Date
is by the old (Julian) calendar.
Dec. Actual is the solar declination for noon at London calculated for the year 1579 from rule for the obliquity of the ecliptic.
Alt Sun (at noon) is calculated for solar declination and longitude west of London.
Dec. Bourne is the solar declination table for London as published by William Bourne in 1574.
Read 1/2° is the altitude Drake would have recorded with an instrument of this resolution, followed by the column showing his reduction of that observation to latitude.
Read 1/4° is the altitude Drake would have recorded with an instrument of this resolution, followed by the column showing his reduction of that observation to latitude.

TABLE 2
Reconstruction of Drake's Readings for Drake's Estero (38° 02' 04")Landfall

 

Sonoma County Press Democrat, October 17, 2012. The Interior Department announced a 5,965-acre Drakes Bay landmark area as the site of the "earliest documented" contact between Europeans and California Indians and the earliest recorded shipwreck on the West Coast, referring to the San Agustin, a Spanish galleon that sank in 1595.

A Park Service report calls it "the most likely site" of Drake's California landing during his circumnavigation of the globe. The landmark designation is "an important aspect of the ongoing debate" over Drake's landing point, Park Service spokesman Mike Litterst said.

But the landmark nomination form "does not address the controversy regarding [Drake's] landing site" and the designation "should not be interpreted as providing a definitive resolution of the discussion," he said in an email.

Does anybody read this stuff?
Some do.


April 19, 2009

Dear Bob,
I looked for some followup to your announcement at http://www.longcamp.com/news.html that you and Brian Kelleher would be addressing the Bodega Historical Society on 9/20/08. Did that happen (I couldn't find anything on the web to confirm it). And has anything else come to light since?

Your careful calculations indicating that Campbell Cove is a much better match for Drake's cited 38 degrees 30 minutes for his Nova Albion landing than the alternative candidates are very impressive.

Vaughan Pratt
Professor Emeritus
Stanford University


January 16, 2012

Hi Bob,

I liked your work on your website, which was well done.

Best regards,
Kathy Haramundanis

Note: Dr. Katherine Haramundanis is an astronomer and science historian, the daughter of astronomers Sergei Gaposchkin and Cecilia Payne-Gaposchkin (the sun is hydrogen). Two of her papers I look forward to seeing are:

--An Elizabethan Survey and Possible Astronomical Observations on the Oregon Coast
Katherine Haramundanis, Edward Gaposchkin

--Sixteenth Century Lunar and Solar Ephemeris Accuracy and the Lunar-distance Method for Longitude Determination
Edward Gaposchkin, Katherine Haramundanis

 
January 9, 1012

Dear Bob Graham

Your adventure with Drake's methods proves that anywhere one grabs hold of a meridian, a portal opens to the past.

Dava Sobel
Longitude: The Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, Walker Publishing Co., Inc., 1995.


For a look at an experiment to test the conclusions of the above, click the astrolabe.

go See a comparison of the 16th Century Tables of Solar Declination by Martin Cortes with those of William Bourne.
go Peter Bailey, retired United States Coast Guard and area resident comments.
go What does the Drake Navigators Guild (the DNG) say about this article, and about the latitude of Drake's landing site? This page includes my analysis of the Guild's accepted latitude.
go Read an email to this site by a descendant of Drake's crew.
go Simon Barclay publishes FrancisDrakeInfo, a collection of information and links relating to Francis Drake.
go The Sir Francis Drake related websites index.
email interest, comments, or questions
A Short Bibliography
  • Aker, Raymond, Identification of Sir Francis Drake's Encampment At Point Reyes National Seashore; Report of Findings Relating to Identification of Sir Francis Drake's Encampment At Point Reyes National Seashore; A Research Report of the Drake Navigators Guild, Drake Navigators Guild, California, 1970.
  • Bourne, William, A Regiment For the Sea (1574), Hakluyt Society Reprint, Cambridge, 1963.
  • Bowditch, Nathanial, The New American Practical Navigator: Any 19th Century Edition is most useful.
  • Colnett, James, The Journals of Captain James Colnett aboard the Argonaut from April 26, 1789 to Nov. 3, 1791, Toranto, The Champlain Society, 1940.
  • Davidson, George, Identification of Sir Francis Drake's Anchorage on the Coast of California in the Year 1579, Calif. Historical Society, 1890.
  • Davidson, George, Francis Drake on the Northwest Coast of America in the Year 1579, Transactions and Proceedings of the Geographical Society of the Pacific, Vol. V, Series II, 1908.
  • Donno, Elizabeth Story, An Elizabethan in 1582: The Diary of Richard Madox, The Hakluyt SocietyLondon, 1976.
  • Drake, Sir Francis (Bart.), The World Encompassed, 1628: Any edition, but especially The Argonaut Press, London, 1926.
  • Hanna, Warren L., Lost Harbor, University of California, 1979.
  • Heizer, Robert F., Elizabethan California, Ballena Press, 1974.
  • Holliday, J. S., The Francis Drake Controversy, California Historical Quarterly, Fall, 1974.
  • Kelleher, Brian T., Drake's Bay, Unravelling California's Great Maritime Mystery, Day Publishing, San Jose, 1997.
  • Robertson, J. W., The Harbor of St. Francis, San Francisco, 1926.
    Robertson, J. W., The Harbor of Saint Francis, Private distribution, San Francisco, 1926.
  • Sobel, Dava, Longitude: The Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, Walker Publishing Co., Inc., 1995.
  • 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.
  • Thrower, Norman J. W., (editor) Sir Francis Drake and the Famous Voyage, 1577-1580, University of California Press, Berkely, 1984.
  • 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.
  • Waters, D. W., Chapter 2 in Elizabethan Navigation, in Sir Francis Drake and the Famous Voyage, 1577-1580, edited Norman J. W. Thrower, University of California Press, Berkeley, 1984.
  • Wright, Edward, Certaine Errors in Navigation (1599), Walter Johnson, Norwood, N.J., 1974.
Some web sites that have links to this page:

  • The National University of Singapore
  • The University of Bonn
  • Celestial Navigation in the Classroom
  • World Book online
  • Lehrstuhl für Didaktik der Physik Würzburg
  • Columbia University
  • Southern Polytechnic (Georgia)
  • United States Corps of Topgraphical Engineers
  • University of California San Diego
  • Education on the World Wide Web
  • Wirtualna Polska
  • Absolute Astronomy
  • The Hakluyt Society
  • Education America Network
  • The University of Kansas
  • Four Directions Institute
  • Plebius - Architecture of the Mind
  • BigTome.com
  • Lassen County California: History and Culture
  • Minnesota Public Radio: The Writer's Almanac
  • ENFIA -- The Eldorado National Forest Interpretive Association
  • Mill Valley Schools
  • El Dorado County--History
  • Wikipedia.com


©1999, 2007
Bob Graham