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    Re: HO 249 Vol 1, epoch 2010, Typo
    From: Stan K
    Date: 2010 Aug 04, 10:38 -0400
    Thanks, George.  This is exactly the same conclusion my students and I were settling on, right down to the fact that there are two quantities involved.  It is nice to get agreement from an independent source.

    Stan



    -----Original Message-----
    From: George Huxtable <george@hux.me.uk>
    To: NavList@fer3.com
    Sent: Sun, Aug 1, 2010 5:56 pm
    Subject: [NavList] Re: HO 249 Vol 1, epoch 2010, Typo

    Stan wrote, on July 27-

    "In Bowditch Table 23 (28), Correction of Amplitude as Observed on the
    Visible Horizon, the correction values do not always increase monotonically
    from left to right (increasing declination) for a given latitude. (For
    example, look the lines for latitudes of 25, 30, 32, 36, and 44 degrees.)
    How can this be explained?

    FYI, those lines are from "recent" editions of Bowditch. The table in the
    1938 edition does not have the same correction values. I do not have it in
    front of me right now, but, as I recall, even though the values are
    different, they do increase monotonically."

    ====================

    I think those small discrepancies can be simply explained. Mine is the
    2-volume edition of Bowditch, in which the relevant table is Table 28, in
    volume 2, which dates from1981.

    The table lists the small difference between amplitude observed when a
    body's centre is on the true celestial horizon (that is, exactly 90º from
    the observer's zenith), which is itself tabulated in Table 27, and the
    amplitude you would get if the body was on the apparent horizon, affected
    by refraction and dip, at a true altitude of -42'. The table shows that
    difference for various latitudes and declinations. For example with a
    latitude of 32º, then for various declinations at 2º intervals from 0º to
    24º, the tabulated difference in degrees is as follows-
    0.4, 0.4, 0.4, 0.4, 0.5, 0.4, 0.4, 0.4, 0.4, 0.4, 0.5, 0.5, 0.5
    Is this the non-monotonic behaviour that worries Stan?

    At low values of latitude, the real correction changes hardly at all with
    declination, but it's the difference between two quantities which do change
    significantly with declination. And presumably, those two quantities have
    each been calculated only to the nearest 0.1º. Indeed, one of the
    quantities appears to have been taken directly from fig 27, where it's
    given to the nearest 0.1º. So each term in the subtraction has a "random"
    fluctuation of +/- 0.05º. It's no surprise, then, to see the result
    wobbling about, itself rounded to the nearest 0.1º, just as Stan observed.
    It's entirely the result of the accumulation of rounding errors.

    Remember, those basic tables were produced years ago. Done today, each term
    would be calculated by computer to umpteen decimal places, and then the
    rounding-off would occur only as a final step after the subtraction. That
    would produce the monotonic behaviour that Sten expects.

    George.

    contact George Huxtable, at george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message -----
    From: <slk1000@aol.com>
    To: <NavList@fer3.com>
    Cc: <slk1000@aol.com>
    Sent: Tuesday, July 27, 2010 5:50 PM
    Subject: [NavList] Re: HO 249 Vol 1, epoch 2010, Typo





    Dave,

    I agree, but how the heck did you ever notice this? Working on old
    problems?

    Here's another one for you: In Bowditch Table 23 (28), Correction of
    Amplitude as Observed on the Visible Horizon, the correction values do not
    always increase monotonically from left to right (increasing declination)
    for a given latitude. (For example, look the lines for latitudes of 25,
    30, 32, 36, and 44 degrees.) How can this be explained?

    FYI, those lines are from "recent" editions of Bowditch. The table in the
    1938 edition does not have the same correction values. I do not have it in
    front of me right now, but, as I recall, even though the values are
    different, they do increase monotonically.

    Stan








    -----Original Message-----
    From: Dave Walden <waldendand@yahoo.com>
    To: NavList@fer3.com
    Sent: Tue, Jul 27, 2010 8:10 am
    Subject: [NavList] HO 249 Vol 1, epoch 2010, Typo


    Seems to be a little typo in Table 4, GHA Aries FOR THE YEARS 2006-2014, at
    the back of Vol 1. Part a. for May 1, 2010 reads 219-49. Perhaps it
    should be 218-49?
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