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    Re: Old style lunar
    From: Fred Hebard
    Date: 2004 Dec 11, 13:18 -0500

    On Dec 10, 2004, at 5:44 PM, Ken Muldrew wrote:
    
    > On 10 Dec 2004 at 15:45, Fred Hebard wrote:
    >
    >> On Dec 10, 2004, at 3:36 PM, Frank Reed wrote:
    >>
    >>> Fred H wrote:
    >>> "At this point, it does not appear that they account for much of the
    >>> variation."
    >>>
    >>> But how did you reach this conclusion, Fred? Have you looked at the
    >>> almanac inaccuracies for 1800?
    >>
    >> Fair point Frank.  Most of your samples were in error in the range of
    >> 0.1' of arc.  I was extrapolating from that.  But it's speculation.
    >
    > Below are the errors in the almanac lunar distances for October 1800 at
    > noon (astronomical time). The table gives the date, the error for stars
    > East of the moon (the value from the nautical almanac is subtracted
    > from
    > the value in Frank's online almanac, given in seconds), and the error
    > for
    > stars West of the moon. I haven't done this for the other 7 values
    > given
    > for each date.
    >
    > 1   37
    > 2   38  -55
    > 3   40  -58
    > 4   39  -45
    > 5   41  -39
    > 6   12  -53
    > 7   15  -48
    > 8   34  -49
    > 9   34  -49
    > 10  33  -45
    > 11  40  -45
    > 12  35  -41
    > 13  32  -37
    > 14  24    7
    > 15  15   14
    > 16       -6
    > 17
    > 18
    > 19
    > 20  44
    > 21  48  -33
    > 22  45  -30
    > 23  40  -23
    > 24  40  -19
    > 25  28  -21
    > 26  34  -27
    > 27  39  -33
    > 28  42  -39
    > 29  42  -56
    > 30  40  543
    > 31  39  -43
    >
    > The large error on the 30th is real. The almanac gives 71?20'16" while
    > the
    > modern value is 71?29'19". The "0" was probably meant to be an "8".
    >
    > Presumably the error bounces around a bit more over the year (or else
    > they
    > would have noticed pretty quickly), but the magnitude is enough to
    > explain
    > longitudes with +/- 1/2 a degree.
    >
    > Ken Muldrew.
    
    Ken,
    
    Errors for stars east and west of the moon often cancel each other out.
      Would not paired observations such as those made by Thompson similarly
    cancel the error in longitude?
    
    Below are the sums for those two values from your table.  Out of 25
    pairs, 11 sums are under 12" of arc,  9 more are are under 24" of arc,
    and 5 are larger, including the egregious mistake on the 30th.  That
    would correspond to 11 days of errors of less than 6' of longitude, and
    9 additional days of errors of less than 12' of longitude, due to the
    almanac.  The remaining are errors of 21', 16.5', 15', 15' of
    longitude, then that huge one.  The huge error would have been picked
    up since there would have been a tremendous discrepancy between the
    east and west shots.  Tacking on an additional measurement error of
    0.3' of arc would add 9' of error for the case where the errors were
    all in the same direction.  It would appear that an expectation of an
    error of +/- 30' of longitude is a bit on the high side.  Perhaps Alex
    could further massage these data for us.
    
    Fred
    
    .
    -17
    -18
    -6
    2
    -41
    -33
    -15
    -15
    -12
    -5
    -6
    -5
    31
    29
    .
    .
    .
    .
    .
    15
    15
    17
    21
    7
    7
    6
    3
    -14
    583
    -4
    
    
    

       
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