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George,

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



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Trevor J. Kenchington PhD                         Gadus@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

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