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From: Frank Reed (no email)
Date: Sun Sep 05 2004 - 23:46:15 EDT
Henry H wrote:
" Taken as a whole, Arnold's book is more descriptive of the Lunar Distance
method than are either Bowditch or Norie, although the theory on which the
actual solution is based remains rather secretive - it is unfortunate that this
book seems rather rare and that the author has received little or no recognition
for his apparently unique and perhaps purely American contribution to the
art."
Can you describe a little further how Arnold's book is more descriptive than
Bowditch or Norie? What does he describe?
As for the tables, although Arnold may not get into the details, they would
have been relatively familiar to any navigator who read Bowditch carefully.
From your description, it appears that Arnold's technique lies half-way between
two standard methods in Bowditch. The method listed for most of the 19th
century as "Bowditch's Third Method" is essentially identical to the method of Don
Jose de Mendoza y Rios. Whether Bowditch somehow acquired it from the
(unquestionably) earlier publications of Mendoza Rios or not is something that I'm
investigating. Meanwhile, the method listed for most of the century as "Bowditch's
First Method" is a close cousin of the method of Mendoza Rios and
incorporates the same procedural and tabular simplifications that you've discovered in
Arnold's work. Like Arnold, Bowditch has three tables (numbered XVII, XVIII,
XIX) which are nearly identical to the tables I, II, III you've described in
Arnold. For example, the values in Bowditch's table XVII are calculated from
9.6990 + logcos(altitude) + PL(altitude correction).
As you can see, this is identical to the Arnold's table II. I wonder why
Arnold wrote out "log sin 30 deg" for the constant log 9.6690 (log of 1/2). Any
ideas? Tables of this type save one lookup and two additions. That's a distinct
time savings. As a guess, a navigator would save maybe 10% of the total
calculational process, but the method is really still Mendoza Rios.
I should note that Bowditch's version includes several other modifications
which enhance efficiency beyond the tables in Arnold. These enhancements were
certainly already in place by 1820, so unless Arnold had an earlier version, he
was simply beaten to the punch by the navigator from Salem.
You noted that it strikes you as "unfortunate" that Arnold's book is rare and
the method unsung. I know what you mean, but I think it's important to
remember that this type of navigation manual was not science --not discovery-- but
rather economics and education. The theory of navigation, including lunars, was
well-established and had been for decades by the time these books by Bowditch
and Arnold came on the market. Bowditch's American Practical Navigator became
a publishing success and the "bible" of American mariners because it promised
something new. It promised that lunars would be "easy". And they were (and
are!), but few navigators in that era believed this. The stories surrounding
Bowditch and the tales of whole crews taught to work lunars made his work a "must
have". Since Arnold's work offered no particular improvement (that I can see)
over Bowditch's methods, it would have had to find its way in the market on
some other selling point. Maybe the only thing Arnold lacked was an aggressive
and talented publisher and publicist like Bowditch's publisher, Edmund Blunt.
And there's an irony about rare books. I would speculate that Arnold's book
is rare today in no small measure *because* it was less successful than
Bowditch's similar book. But that rarity now makes Arnold's book a collector's item.
It now shares the aura of collectibility that srrounds those early editions of
Bowditch.
I would be very interested to hear more about the ways in which Arnold's book
was "more descriptive" of lunars than Bowditch. Anything you can think of on
that score would be appreciated.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
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