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    Re: Lunar distances - short clearance methods
    From: Frank Reed CT
    Date: 2004 Sep 5, 23:46 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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