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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
almanac.

True position of Rocky Mnt. House
 52?21'20"N
114?58'50"W

Latitude
Date
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"

Longitude
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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