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    Re: Dip uncertainty
    From: Alexandre Eremenko
    Date: 2004 Dec 6, 13:52 -0500

    On Mon, 6 Dec 2004, Trevor J. Kenchington wrote:
    
    > further anomalous curvature between George's head and the man behind
    > were minimal, the angular anomaly corresponding to that vertical
    > displacement would be reduced by the greater distance.
    
    I think this argument is wrong.
    The dip is the angle between the ray from the horizon that enters
    your eye and the horizontal direction.
    Refraction distorts the angle, not the "height of the ray".
    The error due to refraction of the taller observer in our example
    is the SUM of the error due to refraction of the shorter observer
    and the additional error caused by refrraction on the interval
    between the shorter and taller observer.
    
    > Which raises the issue of why Alex can recall a Russian textbook arguing
    > for lower heights of eye to address dip. Could that perhaps be for the
    > rather special conditions of Arctic navigation?
    
    Unfortunately this precious book is lost. So I can only rely on my memory
    of 30 years ago. The recommendation was to do observations from lower
    decks if the waves are small. I don't remember any Arctic conditions
    mentioned in this connection.
    
    Let me give another, somewhat indirect argument supporting Georges and my
    point of view. We know that the errors in altitudes due to refraction are
    very large on low altitudes. So large that low altitude observations are
    not recommended. (This was recently discussed on the list).
    The errors in the dip due to refraction are much smaller (they affext
    all altitudes, big and small).
    
    Now suppose you do your observations from VERY high place, say from
    a space ship orbiting the Earth.
    Then the error in the dip due to refraction is one half of the
    total error due to refraction (just by symmetry: the ray travels
    the same distance in the atmosphere before and after it touches the
    horizon). So the error in the dip in this experiment is clearly greater
    than the error of the dip when the observation is made from a ship.
    
    Which proves that this dip error cannot decrease with height:-)
    
    Alex.
    
    
    

       
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