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    Re: Jack Aubrey's fixing of longitude
    From: Frank Reed
    Date: 2011 Jun 26, 17:27 -0700

    Geoffrey, you wrote:
    "The Nautical Almanac of the period gave the
    positions of the moon and also the positions of
    Venus. The declination of the moon and Venus at
    any given time would have been known. It would
    have been possible to calculate the time of an
    occultation of Venus using the data in the
    Nautical Almanac."

    But there is an interesting problem. The Nautical Almanac circa 1805 only listed certain data at the required precision. Maybe a year and a half ago, I noted on NavList that the normal navigation manuals did not include the method of longitude by lunar altitudes despite the fact that it's easier to understand for most navigators, frequently easier to observe, and can often be quite accurate (though unlikely to be as accurate as actual lunars in the hands of a skilled navigator). One reason that these methods were not included is simply that they did not have easy access to the required astronomical data at high enough accuracy. This data was not included in the Nautical Almanac until the big overhaul in 1834 (I should check: some of it may have been included a few years before that).

    Here's what you will find for each month in 1805:

    I. Phases of the moon, holidays, other phenomena. This is where one might have found a note indicating an occultation of Venus, for example. This is only a list. No numerical details are provided except the date and time at Greenwich calculated to the nearest minute of time.
    II. For every day at 0h Greenwich Apparent Time (not mean time), the Sun's longitude (meaning ecliptic longitude, largely irrelevant to practical navigators), right ascension, declination, and also the equation of time. These are all given to the nearest second of arc or time (and tenth of a second for the RA). This is the highest precision data in the almanac pages reflecting the overwhelming importance of the Sun in 19th century navigation. Note that the ecliptic longitude is given in units of "S.D.M.S." which means sign, degrees, minutes, seconds.
    III. The time of the Sun's semi-diameter's meridian passage (and since they always used GAT in these early almanacs, this is always a little over one minute), the Sun's semi-diameter in angular minutes, seconds and tenths of seconds, also a few less important items.
    Also on this page, dates and times of eclipses of the satellites of Jupiter to the nearest second of time (GAT as always).
    IV. Planetary data given every two or three days for Mercury, every six days for Venus, Mars, Jupiter, and Saturn, and every ten days for the Georgian (Uranus). But these data are insufficient in precision for most problems like longitude by occultations. The tables include the heliocentric and geocentrtic ecliptic latitude and longitude (again, largely irrelevant to practical navigators) and also the planet's declination. All of these data are listed to the nearest minute of arc only, not accurate enough for any navigational longitude problem like the ones we've discussed in this thread. This table also gives the time of meridian passage at Greenwich for each planet to the nearest minute of time.
    V. The Moon's ecliptic longitude and latitude to the nearest second of arc for noon and midnight GAT. Note that these again are ecliptic coordinates which have no real place in practical navigation though a very determined calculator could convert them to RA and Dec. The precision is good here but since the coordinates are only given every twelve hours, standard linear interpolation would not be good enough.
    VI. More Moon data: age of the Moon to the nearest day, meridian passage at Greenwich, RA and Dec of the Moon at noon and midnight. Unfortunately for this navigation puzzle, these data are given to the nearest minute of arc only. And again, linear interpolation would not work.
    VII. The Moon's semi-diameter and horizontal parallax at noon and midnight given in minutes and seconds of arc for noon and midnight of every day. These data are required for standard lunars which explains why they are provided at higher precision than other data for the Moon.
    VIII, IX, X, XI. Lunar distances every three hours of GAT in degrees, minutes and seconds. This was the officially sanctioned astronomical method for determining longitude and therefore the only method where the data were provided at high enough precision.
    XII. A graphic table of the configurations of the satellites of Jupiter. Note that the moons we know today as Io, Europa, Ganymede, and Callisto were always known as 1,2,3,4 until the end of the 19th century.

    This was the pattern for every month


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