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    Re: declinations equal to observer's latitude...
    From: Chuck Taylor
    Date: 1997 Oct 31, 3:54 PM

    Dave observed that at low altitudes it is easy to get the sun to
    rock on the horizon, but very difficult when the sun is directly
    overhead.
    
    This is as it should be. Think of swinging a pendulum, say a
    fishing weight at the end of 12 inches of string. Hold it so it
    just grazes a table. Swing it two inches to one side and measure
    how far it comes off the table. I did the math and the answer is
    about 2 inches. Now make the string 24 inches and repeat,
    swinging the pendulum two inches to the side and again measure
    how far it comes up off the table. This time it will be about 1
    inch. How far the pendulum comes up is a function of the length
    of the string, and how far it is to the table at a given
    deflection.
    
    Similarly, when you swing your sextant, the higher the altitude,
    the less the body comes up when deflected a given distance to the
    side. The reason we want to get it exactly vertical is that the
    distance between the body and the horizon is longer if we are off
    a bit from the vertical.
    
    The longer the string, the less difference there is in the
    distance to the table if the deflection is off a bit. Similarly,
    the higher the sun is in the sky, the less difference there is
    between a measurement that is exactly vertical and one that is
    off a bit. In other words, yes, it is harder to tell when you are
    exactly vertical for a higher altitude sight, and, yes, it is
    hard to get it just right.
    
    In the case of the sun directly overhead, the angular distance to
    the horizon in any direction is essentially the same (at least
    from the center of the sun). Therefore, you *shouldn't* see any
    appreciable deflection when you swing your sextant.
    
    Altitudes greater than 90 degrees are called back sights, or
    "over the shoulder" sights. One reason for taking such sights is
    that the horizon may be obscured in actual direction of the body.
    
    For an ordinary sight, when you swing the sextant, the body
    appears to follow an arc upward as you move from side to
    side, and you mark the lowest point.
    
    For a back sight, when you swing the sextant, the body will
    appear to arc *downward* as you get away from the vertical. A
    backsight should be marked at the *highest* point of the arc,
    just the opposite of what you see for an ordinary sight.
    
    A body directly overhead is at the inflection point, where the
    "arc" curves neither up nor down.
    
    Chuck Taylor
    Everett, WA, USA
    ctaylor{at}premier1.net
    
    On Thu, 30 Oct 1997, Dave Boatman wrote:
    
    > I had been shooting noon sights to the South for about 10 days and set up to
    > face South again but couldn't get the sun to rock on the horizon.   It turns
    > out that swinging the sextant on a low altitude sight causes the sun to rock
    > right up off the horizon......but at extreme high altitudes (and most books
    > don't recommend relying on such sights) the sun just won't come up off the
    > horizon when you rock the sextant.
    >
    > In fact, you keep losing the sun off the mirror as you move the sextant more
    > and more extremely and find the sun running along the horizon.
    >
    > Finally, I turned around and faced true North and had the sun sort of
    > rocking off the horizon out to the West and East.
    >
    > I guess the point is (other than the difficulty) is that if the sun were at
    > 95degrees altitude facing South then it must be North of you and you'd turn
    > around, face North and find it at 85degrees altitude.
    
    
    
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