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George,

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
often.

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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