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George,

Rephrase or rewrite as you see appropriate.  The main point was was
that the need for high precision-calculation stemmed from the
slowness of the Moon's motion, the imprecision of its predicted
position, and the practical limit of 30 arcsecond observation
precision, maybe going to 10" on excellent days.  A sidelight is why
a sextant was preferred to an octant: lunars are why octants became
sextants (although perhaps sextants also became preferred because of
the need for three-point determinations of distance from shore).

I additionally was suggesting that the need for high precision in the
calculations is a natural leadin to a later, unwritten section on the
various clearing methods and some overview of what they were, such as
Frank Reed's Taylor series-like numeric approximation method versus
brute force methods --and didn't the approximation methods start with
Maskelyne?-- and Bowditch's role in that, which is famous to every
American navigator, if not to those from other countries.  This stems
from the necessity to use five-figure log tables, which can be very
difficult to use, especially when you are tired, etc. Finally, it can
lead in to Bruce Stark's new brute-force method for clearing lunars
which accomplishes the subtraction within the logs rather than taking
antilogs and going back into logs.

Another area of contention is to discuss Maskelyne versus Harrison in
the broader picture of which method worked first for the larger
number of mariners. Examples can come from Frank Reed's forays into
the logs of American whaling vessels.

Fred

On Aug 2, 2007, at 10:10 AM, George Huxtable wrote:

>
>
>
> Thanks to Fred for his comments.
>
> He wrote-
>
> | Move the sentence on calculation precision to the end of this
> | paragraph, to dovetail with the discussion of overall error.  This
> | also sets up a discussion of the various methods of clearing, which
> | all aimed to simplify the clearing process, hence Bowditch's
> claim to
> | fame.
>
>  I had intended to steer clear of any detail about various methods of
> clearing, because that could be never-ending. Was I right?
>
> And Fred has suggested the following insertion, the sentence starting
> "Because"-
>
> "...it
> | > became a
> | > severe test of a navigator's skill.  Because of the half-arc-
> minute
> | > errors in both the moon's position predicted by almanacs and in
> the
> | > measurement, great precision was required in the calculation of
> | > Greenwich time.  The calculations, which were complex, called for
> | > five-figure log tables of trig functions."
>
> I disagree in detail with those words, Fred. It wasn't really the
> imprecision of the observation or prediction that gave rise to that
> need for
> precise calculation. More, it was due to that factor of 30, because
> of the
> Moon's slow motion. The precision was needed in the clearing
> process, of
> course.
>
> George.
>
> contact George Huxtable at george@huxtable.u-net.com
> or at +44 1865 820222 (from UK, 01865 820222)
> or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
>
>
>
> >



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