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    Re: Dip uncertainty
    From: Trevor Kenchington
    Date: 2004 Dec 6, 19:58 -0400

    Perhaps the key point here is in your:
    > If he looks through a prism, the prism deviates light through a constant
    > angle. It doesn't matter a damn where he puts it in the light path, close
    > up or far away. That constant angular deviation can indeed alter the
    > apparent position of the pencil line, depending on how far away it is, and
    > how far away the prism is. But the only thing that matters to a sextant  is
    > the ANGULAR DIRECTION of the incoming light. Bruce's example doesn't quite
    > correspond to the situation we are considering, because his pencil line is
    > on the wall, not at "infinity", as is the horizon.
    If we were talking about anomalous refraction of the light from a star,
    or even from the Moon, you would be right: Parallel rays of light could
    be refracted through almost any complex path and all that would matter
    would be the angle between the ray which reached the observer's eye, as
    it reached that eye, and the initial path of that ray outside the
    atmosphere -- which would be the same as the angle between the ray at
    the observer's eye and some parallel ray which would have reached the
    observer if there had been no refraction at all.
    But that is NOT what we are discussing here because the horizon is NOT
    effectively an infinite distance from the observer. In your case, or
    mine when standing by the shore or sitting on the centreplate case of my
    little boat, it is really very close.
    In all of the thought experiments that we have been sharing, the two
    hypothetical observers are on the same anomalously-refracted light ray
    extending from the horizon. It is therefore impossible for them to also
    be on either the same straight line or, of more relevance, the same ray
    of light that is curved by standard refraction between the horizon and
    the observers. Because the horizon is not at an infinite distance from
    the two observers, the different standard-refracted rays from the
    horizon to their eyes will not be parallel to one another. Hence the
    angles that they make with the single anomalously-refracted ray on which
    both observers' eyes lie will not be the same.
    If the degree of anomalous curvature between the two observers is less
    than that between the horizon and the first observer (as it usually will
    be), then the extent of anomaly in the observed dip will be less for the
    second observer, on his high bridge, than for the first one standing at
    about sea level.
    In my view, Bruce's prism analogy is relevant and your theorizing based
    on parallel rays of light is not.
    Trevor Kenchington
    Trevor J. Kenchington PhD                         Gadus{at}iStar.ca
    Gadus Associates,                                 Office(902) 889-9250
    R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
    Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555
                         Science Serving the Fisheries

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