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    Re: Lunar Distance in Wikipedia
    From: Fred Hebard
    Date: 2007 Aug 4, 10:50 -0400

    I'm most certainly not asking for an exhaustive coverage of methods
    of clearing, but rather a general discussion, such as Mendoza's over
    100 methods.  The need for high precision falls out of the 30-
    arcminute-per-hour speed of the Moon's passage, plus the 30-arcsecond
    uncertainty in its calculated position and the 30-arcsecond error in
    distances observed with a sextant or quadrant, as is already
    mentioned in the article.  The necessity for using 5-figure logs of
    trig functions then leads to laborious calculations.  Any improvement
    in method that reduced errors, usually by simplifying calculation and
    reducing table lookups and reducing table size, was then very welcome
    to mariners during that time, and the large market for clearing
    tables ensured an abundant variety of same.  Because of the
    prominence of the US Navy's editions of "The American Practical
    Navigator" and the mention of his lunars in its preface, I believe
    Americans especially will be interested in the role of Bowditch in
    the development of lunars, which was to provide a reprint of English
    clearing tables, with some correction of errors and simplification of
    calculation.  Likewise, I believe many readers will be interested in
    an explanation of Bruce Stark's tables.  This will necessitate
    presentation of the basic formula for clearing, which would be a good
    thing in the article, in my opinion.  After that, one might as well
    present the basic Taylor expansion, which was the method used most
    The above is a short outline, very poorly written, of such a discussion.
    Fred Hebard
    On Aug 4, 2007, at 5:52 AM, George Huxtable wrote:
    > I'm not sure what Fred is asking for, but I think he wishes to
    > include a
    > discussion of the various procedures for clearing a lunar. I would
    > resist
    > that, as it would unbalance the article. I think it was Mendoza who
    > claimed
    > to identify over 100 such methods, and that was in the early 1800s!
    > It may
    > however be useful, when we get round to the corrections,  to simply
    > say that
    > many such methods have been developed, and possibly provide a
    > reference.
    > Even though it has many shortcomings, I would suggest Charles H
    > Cotter, A
    > History of Nautical Astronomy, London 1968, chapter 6.
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