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    Re: Easy Lunars in 1790
    From: Ken Muldrew
    Date: 2006 Apr 27, 13:38 -0600

    On 27 Apr 2006 at 11:34, Alexandre E Eremenko wrote:
    
    > Could you post the data of your lunars?
    > GMt, DR position, sextant reading, and IC
    > and the brand of sextant used?
    >
    > How your error in longitude compares with Thompson's?
    > Can you tell what part of the error comes from Thompson's
    > almanac and reduction and what part comes from observation?
    
    I don't have those particular calculations handy as they are at home (and
    I just did the clearing; I haven't compared Thompson's error with the
    almanac error for those sights). However, I pulled up one that I looked at
    last year from an excel file as it will provide an example of Thompson's
    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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