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Alex 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.


Try making a drawing of it, Alex. I think you will find that that
confirms my version.

Bruce has made the point in a less equivocal way: Imagine a prism placed
in the light ray to cause the extra, anomalous refraction. That prism
will displace the light through an angle which depends of the geometry
of the system (and the optical density of the glass) but an angle which
is constant. Now view the light emerging from the prism from a point
close to the prism: The angle between the light reaching your eye and a
straight line to the source of that light will be large. But if you back
off from the prism, that angle will be far smaller -- not because the
prism is bending the light any the less but because the distance from
the prism to the light source subtends a smaller angle at your eye as
you back away from both of them.


> 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:-)

It proves nothing of the kind.

For anomalous dip to decrease with height of eye, we have to assume that
the amount of anomalous refraction decreases with height above the sea
surface. The observer on the bridge of a large ship thus sees a ray of
light which bent unexpectedly sharply (or the reverse) when rising from
the horizon to a height of about 6 feet (i.e. to beside George's head)
but which then conformed more closely to the expectations of the dip
tables as it rose to 24 or 60 feet up. That reduction in non-standard
refraction, within what is otherwise a single near-surface air mass, is
clearly normal (though not universal) in the real world.

A hypothetical observer aboard the International Space Station, however,
would observe the Earth's horizon through a deep ocean of air, with many
layers of different refractive index, the surfaces of which would not be
normal to his view. That many-layered system involves a potential for
anomalous refraction after the light ray passes George's head and before
it reaches the Space Station which greatly exceeds the potential for
anomalies over the tiny distance between the horizon and George's eye,
let alone that between the back of George's head and the sextant of the
(now very annoyed) ship's captain who is trying to get a Sun sight while
that ****ing little sailing boat keeps blocking his view of the horizon!


Trevor Kenchington



--
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

                     Science Serving the Fisheries
                      http://home.istar.ca/~gadus

   

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