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    Re: Easy Lunars in 1790
    From: Alexandre Eremenko
    Date: 2006 Apr 27, 21:04 -0400

    Ken,
    
    > errors. He used a Dolland brass sextant of 10" radius with a vernier
    > divided to 15". His DR position can be back calculated using the almanac
    > data below but I haven't done it for this case.
    >
    > >From Thompson's notebook:
    >
    > Feb 17, 1801 - Aldebaran
    > Sun RA  22?01'17"
    > Moon RA  29?01'50"
    > Dec  15?05'03"N
    > SD  15'10"
    > HP  56'10"
    > Sun TA  51?56'10"
    > Sun AA  51?56'10"
    > Moon TA  33?56'48"
    > Moon AA  33?11'26"
    > D  35?53'06"
    > Temperature -6?F
    > Longitude 114?39'00"W
    >
    > Witchell's method corrections:
    > Corect'n 1      -12"
    > Corect'n 2   -51'42"
    > Corect'n 3       12"
    >
    > time of sight   moon FL to aldebaran
    > hr| min| sec| deg | min| sec
    > 7 | 35 | 25 |  37 | 03 | 00
    > ....36 | 25 |.......02 | 30
    > ....37 | 22 |.......01 | 25
    > ....38 | 16 |.......01 | 15
    > ....39 | 11 |..........| 45
    > ....40 | 12 |..........| 15
    > 7 | 37 | 48 |  37 | 01 | 35  | avg
    > ...-19 |-44 |....| -21 |-19  | watch & index errors
    > 7 | 18 | 4  | 36 |  40 | 16
    >
    > time of sight   procyon
    > hr| min| sec| deg | min| sec
    > 7 | 45 | 01 |  75 | 08 | 15
    > ....46 | 06 |.......20 | 15
    > ....47 | 03 |.......31 | 15
    > 7 | 46 | 04 |  75 | 19 | 55  | avg
    > ...-19 |-44 |....| -21 |-19  | watch & index errors
    > 7 | 26 | 20 | 74 |  58 | 36
    >
    > The watch error is calculated from the time sight and then put back into
    > the tabular results (so he calculates the local apparent time when the
    > altitude of Procyon is 7?26'20", compares that to the watch time that he
    > wrote down and then gets a correction). That correction is then put back
    > into the lunar data to get the proper time for his lunar shot.
    >
    > d  36?24'55" at 7h18m04s LAT
    >
    > 1801 Almanac lunar distance (GAT)
    > 12:00  37?22'31"....15:00  35?51'25"
    > JPL lunar distance
    > 12:00  37?23'19"....15:00  35?52'16"
    > D 35?53'06"
    > GAT from 1801 almanac: 14h56m40s
    > GAT from JPL data: 14h58m21s
    > LAT   7h18m04s
    > Longitude from almanac: 114?39'06"W
    > Longitude from JPL data: 115?04'17"W
    >
    > If we clear the distance using a calculator, then we get:
    > D  35?53'16"
    > resulting in:
    > GAT from 1801 almanac: 14h56m18s
    > GAT from JPL data: 14h57m59s
    > LAT   7h18m04s
    > Longitude from almanac: 114?33'44"W
    > Longitude from JPL data: 114?58'54"W
    >
    > True longitude (modern survey): 114?58'50"
    >
    > So if Thompson had an almanac based on a better theory of the moon as well
    > as a calculator to clear his lunar more precisely, his longitude would
    > only have been off by 4"  ;-)
    >
    > But seriously, when we looked at a bunch of Thompson's lunars last year
    > (the posts are in the archives) we found that his standard deviation was
    > 20' (in longitude) using the old almanacs and would have been 14' if he
    > had the JPL data, so not bad but not great. But we do have to consider
    > that he got this sextant in 1792 and there was much rough travel in the
    > interim (perhaps 30,000 miles by canoe, horseback, dogsled, and foot).
    > There are instances in his journals where his canoe is overturned in
    > whitewater and the sextant has to be fished out downstream. Sometimes he
    > has to rely on other fur traders to carry his sextant (a practice so
    > abhorent that he notes it in his journals). He had no opportunity to have
    > the instrument serviced so one has to be impressed with the performance he
    > coaxed from the instrument.
    >
    > Note: I haven't corrected the data for temperature or pressure (his
    > altitude above sea level was about 3250 ft.).
    >
    > Ken Muldrew.
    >
    
    
    

       
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