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    Lunars: Thomson's Tables
    From: Frank Reed CT
    Date: 2006 Apr 2, 03:23 EDT

    A few years back, Jan Kalivoda wrote a couple of posts to this list about
    Thomson's Tables for clearing lunar distances (which were adopted as Bowditch's
    Second Method in 1837). He noted that the calculation of the "third
    correction"  table was considered mysterious in the 19th century. For anyone who read
    this  account back then, I just wanted to note here that the table is not at
    all  mysterious, and it can be calculated directly. It's a lot of work because
    there  are thousands of entries, but the steps involved are simple, and the
    majority of  cases had already been tabulated before Thomson's time. Most similar
    works  tabulated the linear refraction plus the Moon's quadratic term.
    Thomson adds in  the quadratic cross-term. This additional calculation rarely
    changes the result  by even a tenth of a minute of arc (equivalent to three minutes
    of longitude in  the result) except when the lunar distance is less than 30
    degrees and even then  only when the Moon's altitude is rather low [Jan
    Kalivoda's earlier post noted a  difference of a full minute of arc however this was
    only correct for methods  which ignored the quadratic corrections entirely]. To
    a navigator, this was  simply a number to be extracted, never mind the
    details, and it was a very  popular method, involving about 30% less work than other
    similar  methods.
    By the way, I believe it was Baron von Zach who started the  urban legend
    that they're was something extraordinary in the calculation of  Thomson's table,
    although Thomson himself may have had a hand in it. There's a  paper about the
    tables by the Baron briefly described in the Monthly Notices of  the Royal
    Astronomical Society in 1829 which can be found on the web via  adsabs:
    (if you've never used this service,  when you do a search and it says 'zero
    records found', give it about thirty  seconds. It's working on it...)
    42.0N 87.7W, or 41.4N  72.1W.

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