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    Re: Lunar distances - short clearance methods
    From: Frank Reed CT
    Date: 2004 Sep 6, 00:05 EDT
    George H wrote:
    "What Arnold has done is to shrink the remaining 3 terms of Mendoza's method
    into a single term."

    Yes, and this is exactly the same approach as in the principal 19th century method in Bowditch, and it was published well before Arnold's book.

    George wrote:
    "If a lunar was taken to Venus or Mars, which require non-standard parallax corrections, that parallax, if known, could readily be applied. (Does anyone know when lunar distances to planets started to appear in the Almanac?)"

    In the British Nautical Almanac and the American almanacs derived from them, the planets were included starting in 1834. In the logbooks that I have examined in the past few years, roughly 85% of lunars were Moon-Sun lunars, and the rest were lunars off the brighter of the nine lunars stars. I have not encountered a lunar taken using one of the planets (I'm sure they were done occasionally... I'm only suggesting that they were rare and perhaps rare enough to be no great loss). As for handling the parallax of the planets, Bowditch includes separate tables calculated for every 5 seconds of parallax from 0 to 35. Problem solved. Each of these occupies a single page, so they don't cost much in terms of weight.

    George H adds:
    "As I see it, however, Arnold's method, including standard refraction and parallax in his tables I, II, and III, was inflexible in that it would have been unable to adapt to such requirements."

    And yet, it was almost identical to the main method in Bowditch for seven decades. Inflexible though these methods may have been in a theoretical sense, they were very easy to follow.

    And:
    "The final steps in the clearing process, using table XXXV in Mendoza's case, or Arnold's Table VII, appear to be identical, from Henry's account."

    Yes. The quadratic correction was small enough and simple enough that it did not seem to generate much variation in method. But Bowditch did change things a little bit in later years. Instead of using the double look-up procedure that you're familiar with from Norie's table XXXV, Bowditch printed tables that simply listed all possible values for each minute of the Moon's HP. To avoid dealing with negative numbers, he added 18 arcseconds to all these values and subtracted 18 arcseconds from the Moon's correction table.

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