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At 08:46 06/08/2005, you wrote:
>Thank you George for your contribution.
>
>May I just add some further comments
>
>>Marcel's question puzzled me considerably, until it emerged that was
>>referring to bubble-sextant observations, with respect to the true
>>horizontal, not altitudes measured up from the observed horizon with an
>>ordinary sextant.
>
>This comment reminds me of something I forgot to think of. Yes, the observed
>(apparent) horizon is not the physical (true) horizon. Due to the
>terrestrial refraction the apparent horizon is already something below the
>physical one.

There are really three different "horizontals" being discussed here. First,
there is the true horizontal, at 90 degrees from the zenith and from the
direction of gravity, which a bubble-sextant would show if it were accurate
enough. That's the horizon to which we correct our observations, so that we
get the true altitude above it.

Then there's the horizon we see from a boat or a plane, at a dip angle from
the true horizon of a few minute (from a boat) up to a few degrees (from a
plane). The dip is mostly caused by simple geometry; that the observer
raised above the surface of a sphere sees its boundary as a flattened cone
(a coolie-hat) rather than as a disc. Geometrical dip is precisely
predictable, if the height of eye is known.

But about one-twelfth of the dip comes from another effect: the curvature
of light, in its path from the horizon to the eye, caused by refraction in
the lower few feet of the atmosphere. So the horizon that you see is not in
quite the same direction as the sea surface actually is. This is the effect
that Marcel was referring to.

Refraction works in the opposite direction to geometrical dip, reducing it
by about 8% when seen from a boat. It can be roughly predicted, for
standardised atmospheric conditions. However, the lower few feet of the
air, being strongly influenced by the temperature of the sea surface just
below it, can suffer from unpredictable temperature gradients, which can
upset the predicted dip by several arc-minutes, on a bad day. This can be
the biggest source of error in marine sextant observations.



>>>R(-2?)  =  R(0?)  +  (  R(0?) - R(+2?)  )
>
>The idea behind this approximation is that in the case of negative altitudes
>the light has to pass the lower air masses twice, once incoming until e.g.
>the tangent point at the earth surface and a second time outgoing from the
>tangent point to the observer at the elevated position.

To me, that argument doesn't hold water. If Marcel wishes to maintain it, I
would like to see a more detailed justification. Agreed, in the case of
negative altitudes, there's a curved light path on both sides of the
tangent point. The curvature of this second light path is in the same
direction as the first, so their refractions add. But how does his
conclusion follow?

>Marcel
>
>P.S. Greetings to Abingdon, where I lived something over twenty years ago...

And from Abingdon to you, Marcel.

George.



===============================================================
Contact George at george@huxtable.u-net.com ,or by phone +44 1865 820222,
or from within UK 01865 820222.
Or by post- George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13
5HX, UK.

   

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