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    Re: Old style lunar
    From: Ken Muldrew
    Date: 2004 Dec 14, 16:31 -0700

    On 13 Dec 2004, Alexandre Eremenko wrote:
    
    >For the discussion of Thompson's observations
    >it would be desirable to compare the data on the specific
    >dates of his observations. These are in 1800 and 1801 almanacs.
    >I am not sure who has them, but my impression that someone
    >from this list has 1800 almanac.
    
    Here is some more information from Thompson's two lunars of November 26,
    1800 (I posted his times and measured distances for Altair and Aldebaran
    previously). I believe (but am not positive) that his position on this day
    was 50?47'N 114?16'W (give or take a minute). This position comes from
    following his course on a topographic map. Thompson's latitude comes from
    a meridian altitude of Rigel from the same night.
    
    (s)=sun, (*)=star, ))=moon
    
    Thompson's notes contain the following information so that (presumably) he
    can recalculate his lunar at a later time if necessary.
    
    Nov. 26, 1800 - Aquilae (Altair)
            ?  ?  "
    (s)RA  16h11 13
    (*)RA  19h41  3 dec 8 20 40
      Dec   8 22 25 N
    ))RA   17h36 25
     Dec    7  3 45 N
     SD       15  5
     HP       55 24
    (*)TA  10 54 19
       AA  10 59 58
     ))TA  46 44  9
       AA  46  6 44
    D      81 11 20
    +3'48", -4', +2"
    
    8:53:05  81?17'45"
    8:53:55  81?17'45"
    8:54:38  81?18'00"
    8:55:20  81?18'30"
    8:56:00  81?18'45"
    8:56:52  81?19'30"
    8:57:38  81?19'15"
    8:58:29  81?19'30"
    ------------------
    8:55:45  81?18'37"
    +  8:00   - 22'22"
    ------------------
    9:03:45  80?56'15"
    
    [the time correction above comes from an average of his two time sights
    given further below]
    
    long  113 49 15 W
    lat    50 47 24 N
    
    Nov. 26, 1800 - Aldebaran
            ?  ?  "
    (*)RA   4h24 29 dec 16 5 46
      Dec  16  5 46 N
    ))RA   17h27 48
     Dec    7 32 30 N
     SD       15  5
     HP       55 22
    (*)TA  40  6 16
       AA  40  7 29
     ))TA  46 39  8
       AA  46  1 35
    D      48 15 35
    +37", -12'3", +9"
    
    9:01:43  49?5'45"
    9:02:52  49?5'15"
    9:03:20  49?5'00"
    9:04:15  49?4'45"
    9:05:12  49?4'15"
    9:06:10  49?4'00"
    9:07:08  49?3'45"
    9:07:58  49?3'15"
    ------------------
    9:04:47  49?04'30"
    +  8:00   - 22'22"
    ------------------
    9:12:47  48?42'08"
    
    long  114 33  0 W
    lat    50 47 24 N
    
    Average longitude 114?11'7"W
    
    Double altitudes (reflected altitudes) time sight:
    Capella
    8:32:20  98?58' 0"
    8:33:10  99?13' 0"
    8:34:00  99?26'45"
    -----------------
    8:33:10  99?12'35"
       7:54    -22'22"
    -----------------
    8:41:04  98?50'13"
    
    Lyra
    8:41:45  49?46'30
    8:42:30  49?33'46
    8:43:10  49?22' 0
    -----------------
    8:42:28  49?34' 5
       8:07    -22'22
    -----------------
    8:50:35  49?11'43
    
    From a 1796 star chart:
    Capella: RA 5h51 58 dec 45 46 50
    lyra: RA 18h30 10 dec 38 36  9
    
    From the 1800 almanac:
    sun
    Nov 26 RA 16h8 14.3 dec 20 58 58 S EOT 12 24.6
    Nov 27 RA 16h12 30.6 dec 21 10 06 S EOT 12 5.0
    SD 16'16" hourly motion 2'32"
    
    moon
    Nov 26 midnight RA 15h15 dec 6 24 N SD 15'7" HP 55'30"
    Nov 27 noon RA 20h47 dec 9 15 N SD 15'3" HP 55'15"
    
    moon-altair distance
    Nov 26 15:00 80:29:28, 18:00 81?45'33" (1800 almanac)
    True values: 80?28'26"       81?44'31" (Frank Reed's online almanac)
    New longitude: 114?26' 9"
    
    moon-aldebaran distance
    Nov 26 15:00 49 11 22, 18:00 47?40'54" (1800 almanac)
    True values: 49?12'08"       47?41'40" (Frank Reed's online almanac)
    New longitude: 114?55'59"
    
    Thompson was pretty lucky with the poor almanac data of 1800 as it put him
    within 5 minutes of his true location whereas the better data from Frank's
    almanac puts him 25 minutes too far West. It's odd that his Aldebaran shot
    puts him so far off since that appeared to be the better sight (Fred
    Hebard posted a graph containing these two lunars a few days ago--the
    Altair data had a few bad points but the Aldebaran data was nice and
    smooth).
    
    I wonder if his DR put him out? Comparing his calculated altitudes to
    those given by the USNO celestial navigation data site, Thompson has
    Aldebaran too high by 2 degrees and Altair too low by 2 degrees. That
    seems like an awfully large error. Unfortunately his account has been
    updated by all his celestial sights so we don't get to see the original DR
    position (although now that I think about it, perhaps one could work
    backward from his calculated altitudes to get the DR position). His lunar
    altitudes are much better (within a few minutes of the USNO data), but
    then we expect them to be worse due to the error in the old almanac.
    
    Ken Muldrew.
    
    
    

       
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