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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.

Fred
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Frederick V. Hebard, PhD                      Email: mailto:Fred@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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