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    Old Style Lunar
    From: Ken Muldrew
    Date: 2005 Jan 10, 11:01 -0700

    Before Christmas we were discussing some lunars shot by the Fur Trader
    David Thompson about 200 years ago and the accuracy that he was capable of
    obtaining. The discussion ended awaiting further analysis of the old
    almanacs to see if the poor lunar theory of those days was responsible for
    the large variation in Thompson's data. Bruce Stark kindly sent me the
    pages out of the old almanacs so that I could check. I have completed
    checking just the lunar distance to time part of his calculations, relying
    on Thompson's written longitudes as a check on my transcription (this is
    the toughest part of checking his lunars: I've assumed that if I can
    recapitulate Thompson's longitude by using his cleared distance and local
    time, with the old almanac, then I've properly read his text). Below is a
    list of Thompson's data from Rocky Mountain House. The column marked
    "Thompson" contains his original calculated longitudes and the column
    marked "corrected" has been recalculated using Frank Reed's online
    True position of Rocky Mnt. House
    Apr 09,1800  52?21'29"
    Feb 20,1801  52?21'27"
    Feb 21,1801  52?21'35"
    Mar 05,1801  52?21'32"
    Average      52?21'30"
    Date         Thompson    Corrected
    Apr 17,1800  115?12'00"  115?18'20"
    Apr 18,1800  114?57'45"  115?01'58"
    Dec 22,1800  115?11'00"  115?29'44"
    Feb 17,1801  114?51'15"  115?14'02"
    Feb 17,1801  114?39'00"  115?04'17"
    Feb 24,1801  114?36'00"  114?57'01"
    Feb 24,1801  114?13'00"  114?38'09"
    Feb 25,1801  114?28'45"  114?52'06"
    Feb 25,1801  114?26'45"  114?48'33"
    Feb 28,1801  114?52'15"  115?04'48"
    Feb 28,1801  114?59'45"  114?57'54"
    Mar 01,1801  115?11'00"  115?14'32"
    Mar 18,1801  114?44'15"  114?59'10"
                 ---------   ---------
    Average      114?47'38"  115?02'50"
    The corrected values reduce the spread somewhat, bringing his standard
    deviation down from about 20' to about 14', but he's not in the class of
    lunarians like Augustus Gregory. I'm still going through the process of
    checking all of Thompson's calculations to see if any errors like the one
    we found in his Nov. 26, 1800 lunar (discussed in the Old Style Lunar
    thread in December) figure in Thompson's results. This is slow going but
    perhaps I'll put all the calculations up on a web page when I'm finished
    in case anyone is interested.
    Ken Muldrew.

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