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    Re: HO 249 Vol 1, epoch 2010, Typo
    From: George Huxtable
    Date: 2010 Aug 1, 22:56 +0100

    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 90� 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 32�, then for various declinations at 2� intervals from 0� to 
    24�, 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 0.1�. Indeed, one of the 
    quantities appears to have been taken directly from fig 27, where it's 
    given to the nearest 0.1�. So each term in the subtraction has a "random" 
    fluctuation of +/- 0.05�. It's no surprise, then, to see the result 
    wobbling about, itself rounded to the nearest 0.1�, 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: 
    To: 
    Cc: 
    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 
    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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