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    Re: Lunar distances - short clearance methods
    From: Frank Reed CT
    Date: 2004 Sep 6, 00:18 EDT
    Henry H wrote:
    "After all, were not the short methods developed to avoid the rigorous spherical trigonometrical approach."

    Series solutions, variously called "approximate" (though they weren't necessarily) and "short" (though they might not be) were developed for a variety of reasons, not all of them entirely rational! But their principal benefit from a calculational stand-point was that they required shorter log tables (typically four-place logs instead of six-place logs).

    And wrote:
    "There is no intent to enter into a discussion of who came first, but it is of interest that two men working at opposite sides of the ocean at roughly the same time should come up with such similar methods - but then again, as they say, there can be only so many ways to skin a cat."

    Though it's barely possible that this was a case of independent invention, the overwhelming similarity of the Arnold method to the method of Mendoza Rios at the basic level and to Bowditch's First Method at the table level suggests that Arnold was quite familiar with those methods. Mendoza Rios published first, in Spanish in 1795 (date?) and in French in early 1797 (in the Transactions of the Royal Society of London). But consider that ocean you mentioned... Bowditch and Arnold on one side, Mendoza Rios on the other side. Obviously it was an era before electronic communication, an era when major news from Europe would take weeks to cross the Atlantic and scientific work might take more than a year. But then consider Bowditch. He sailed to Manila in 1796. Speculating wildly, perhaps it was on the opposite side of the globe that the navigator from Salem was exposed to the clever new method developed by Don Jose in Europe... That's a long way to go for an equation. I think they would have appreciated the Internet!

    Frank R
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois
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