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    Re: Carry on, Mr. Bowditch
    From: Fred Hebard
    Date: 2003 Jan 16, 13:42 -0500

    David Weilacher  wrote:
    >I keep hoping that someone will start over with truly basic description of the
    >process. I'm missing it badly.
    It might be OK for me to go over the basics of lunars, since that's
    pretty much the level I'm at.  There are numerous people on this list
    who are much more knowledgeable on this than I; I hope they'll jump
    in if I hash something up.  This piece is highly simplified, covering
    only the extreme basics.  For instance, it does not even refer to
    refraction and parallax.  George Huxtable's contributions should be
    consulted if you wish to learn more details (see
    http://www.i-DEADLINK-com/lists/navigation/0201/0177.html for the first one
    and look in the archives for the rest; a revised Part 4 was just
    published this month, January, 2003).
    The basic problem being solved by lunars was to tell what time it
    was.  This was necessary to establishing one's longitude, which might
    help one avoid running onto the rocks.
    The moon rotates around the earth once every 28 days or so, moving
    from west to east across the sky.  This week of January 13, 2003, as
    we approach the full moon, it's rising in the east right about the
    time the sun is setting in the west.  Next week, it will be rising
    about 6 hours after sunset.  Two weeks from now, at the new moon, it
    will be rising with the sun, and three weeks from now, about 6 hours
    after sunrise.  It finally will complete one revolution a month from
    now, again rising as the sun sets.
    The stars on the other hand, take pretty much exactly one year to
    appear to rotate around the earth, as we circle the sun, and they
    move in the opposite direction from the moon.  For example, in
    mid-November, Orion was more or less rising in the east at sunset.
    Now, 2 months later in January, it's about 2/12ths of a full circle
    up in the sky at sunset.   In mid-March, 4 months later is will be
    4/12ths of a circle up in the sky at sunset, and in mid-May it will
    have circled around the half circle of sky visible to us at any one
    moment and be right where the sun is at sunset.  The stars only move
    about 1/365th of a circle in one day, or one degree per day.  The
    moon on the other hand, is moving about 1/28th of a circle in one
    day, or 12 or 13 degrees per day.
    The very fast motion of the moon across the sky enables one to
    determine the time of day by measuring the distance between the moon
    and stars along its path, and comparing that measurement to distances
    predicted for various times of day, at least in principle.  However,
    there were several difficulties with implementing this method.  One
    was to predict the motion of the moon across the sky in detail.
    Although the moon makes one revolution in around 28 days, it also
    jogs up and down quite a bit.  Even once the motion of the moon could
    be predicted, it was still very difficult to predict the distance
    between the moon and nearby stars, as well as planets and the sun, so
    that the predictions could be compared to observations.  The
    calculations of these predictions were first completed with the
    publication of the Nautical Almanac in the 1760s.  The Almanac was
    authored by Nevil Maskelyne, although his efforts benefited strongly
    from work by non-English astronomers.
    The mariner was still left with a difficult calculation in reducing
    (clearing) his measurement of moon-star or moon-planet or moon-sun
    distance to that tabulated in the Almanac.  One factor in this
    difficulty was that the measurements had to be very precise.  The
    moon is moving 12 or 13 degrees per day, or about half a degree, 30
    minutes of arc, per hour.  Dividing by sixty yields 30 seconds of arc
    per minute of time.  Unfortunately, in determining longitude, an
    error of 1 minute in time gives an error of 15 nautical miles at the
    equator.  But this was close to the best that could be done.  In
    contrast, an error of 30 seconds of arc when determining latitude
    only leads to an error of half a nautical mile of distance.
    Thus for clearing of observed lunar distances it was necessary that
    the calculations be carried to more places than was needed for
    latitude.  Five or six-place tables of logarithms and sines were
    required, and these had to be consulted repeatedly during the
    clearing.  It wasn't easy and took a long time.  Slight errors during
    some parts could lead to wildly erroneous results
    After the publication of the first Nautical Almanac, various authors
    published manuals of tables for use with it and descriptions of how
    to use them.  A popular manual on navigation in the late 18th century
    was written by the Englishman, John Hamilton Moore, entitled "The
    Practical Navigator."  Bowditch's contribution was to correct errors
    in some of Moore's tables and to develop a markedly easier method for
    clearing a measurement of lunar distance to where it could be
    compared to predictions in the Nautical Almanac.  Bowditch's
    revisions were published as "The New Practical Navigator."  Note that
    he did not correct errors in the Nautical Almanac, to my knowledge.
    Bowditch's book was marketed by emphasizing what was new and
    different in it; what made it better than its competitors.  Thus
    there was a natural tendency to elevate his contributions above those
    of others.  I don't believe his book was translated into foreign
    languages.  His fame persisted because his book was good enough that
    the U.S. Navy bought the rights to it, for use by Navy sailors.  The
    Navy still publishes it today under his name, but bears almost no
    resemblance to the original.
    Occultation of a star or planet by the moon occurs only infrequently.
    When the moon does happen to occult a star, it is possible to predict
    the time when this occurs.  So when one observes an occultation, one
    can determine the time.  But in navigation it is helpful to determine
    the time every day.  Occultations do not occur frequently enough to
    allow one to do that.  Hence the Nautical Almanac.  Bowditch did not
    change the basic procedure of using the Nautical Almanac to tell time
    by observation of lunar distances.  He did not substitute the method
    of lunar distances for that of observing occultations, as
    occultations were not used on a daily basis.
    Frederick V. Hebard, PhD                      Email: mailto:Fred{at}acf.org
    Staff Pathologist, Meadowview Research Farms  Web: http://www.acf.org
    American Chestnut Foundation                  Phone: (276) 944-4631
    14005 Glenbrook Ave.                          Fax: (276) 944-0934
    Meadowview, VA 24361

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