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Dear George,
Thank you for your interesting letter.
Indeed the sign and magnitude of the error I observed
look like an error produced by "positive dip".

But I suppose that the physical conditions you are
talking about were not present in Kielerforde on that day.
The water was very cool (and always is) here.
I mean most people do not dare to swim in Kiel till the beginning of
August:-)
But the air was hot, at least that was what I felt:-)

So I suppose the gradient of temperature could not be "inverted"
on that day, that is the air was cooler near the water and
hotter above. As I understand from your message
this is the "normal gradient", not inverted.

The dip correction was taken from the almanach tables,
and it was -2.2, -2.8 and -3.5 at the three places of various elevation
where the observations were made.
The observations on the highest place were such as if there was
no dip.

So I am looking for another explanation.

I thought of filters prismaticity (which I cannot estimate
at this moment) but it is unlikely that a manufacturer of
good reputation would have 3.5' of filter prismaticity:-)

The index glass might be not perpendicular by a large amount and
I don't know how to test this.

Or the teeth on the arc can be dirty, and I cannot clean them,
because the pocket sextant has to be disassembled for this,
and I do not have a proper screwdriver for this.

Anyway, I hope that the weather will permit me to do further testing
on my sailing trip.

Alex

On Fri, 16 Jun 2006, George Huxtable wrote:

>
> Alex mentioned the paper I recommended-
>
>  > "I've just received an offprint of a new article by Andrew T Young,
> of
> | > the Astronomy Deparment, San Diego State University,
> "Understanding
> | > Astronomical Refraction", which has recently appeared in the
> journal
> | > "The Observatory"(Vol. 126, no. 1191, pp. 82-115, 2006 April.)"
>
> and asked-
> | Have you seen the paper? Is it available on the web?
>
> Yes, I've kindly been sent a reprint. I must be on his refraction
> mailing-list, having discussed a lot of details about refraction with
> him in the past. I don't know whether it's on the web. I can no longer
> find Andy Young's email address at SDSU, but you could try asking
> them. I have always found him to be a most helpful character.
>
> In my opinion, his paper is the sort of thing you might want to keep
> in printed form, rather than as web ephemera, but I take a somewhat
> old-fashioned attitude toward such things. I get the picture that to
> some (here I exclude Alex) if it isn't available online then it
> doesn't truly exist.
>
> Anyway, now I consider myself somewhat better informed by Andy's lucid
> exposition, and can try to comment further about Alex's problems with
> dip; if dip really is the underlying reason for his sextant
> discrepancies.
>
> Imagine that in the Kielefjord, on the day Alex was observing, there
> was a temperature inversion in the air over the surface of the water.
> Here we are considering just the lower few feet, between the level of
> the water surface and Alex's height of eye; probably just the lower
> couple of metres, depending on Alex's height and how far up the beach
> he was standing. If in that region the temperature gradient, with
> increasing height, was as great as -0.115 degrees C per metre, that is
> sufficient to bend light downwards, towards the water surface, so that
> it's curvature exactly matches the curvature of the surface. In that
> case, light would be "trapped" into following the water surface. In
> that case the visible horizon, the boundary between sea and sky, would
> appear to be exactly horizontal, no matter what your height of eye. So
> the actual dip under thise conditions would not be the text-book value
> that Alex took corresponding to his height of eye, but zero instead.
> Wouldn't that, on its own, account for most of Alex's observed
> discrepancy? If the gradient were higher still, that would give rise
> to a reversed dip.
>
> Note that we are talking here about the temperature at the water
> surface being only a quarter-degree or so cooler that it is at eye
> level, which doesn't seem to be a great deal. However, that gradient
> is a lot greater ( and in the opposite direction) than the value taken
> for the Standard Atmosphere, which is only +.0065 degrees C per metre.
> But there's nothing unphysical or unfeasible about a gradient of -
> 0.115 degrees C per metre. If the air is cooler below, as it is in
> such an inversion, then that is a stable state of affairs, and air
> convection doesn't act to stir things up. So, according to Young,
> there's no limit to the gradient in such inversions, and "... rates
> exceeding a degree a meter are common. An inversion gradient of 20
> degrees per metre has been measured directly ..."
>
> So how can such a temperature inversion near sea-level come about?
> Consider a land-mass near the water, such as happens in the Red Sea
> (and the Keilefjord). The worst situation is apparently caused over
> desert sand, and you can sea why. When  the Sun shines directly on
> sand, it can get so hot that it's painful to walk on, the reason being
> that all those grains separated by air, just making point contact with
> grains below, act as a good insulator, so heat can't conduct down into
> the earth. The high local temperature, close to the surface, causes
> the air layer in contct with it to be efficiently heated. Conversely,
> at night, the surface of sand cools down very quickly. Black volcanic
> sands would presumably absorb Sun energy even more effectively and
> heat the air above them more.
>
> But it's not necessary to invoke desert sands. Any land surface will
> heat more quickly in daytime, and cool more quickly at night, than the
> local sea. In the sea, turbulence causes mixing between the upper
> layers, making any water-mass an effective heat-sink, with a
> temperature that changes little, and slowly.
>
> Now we have a picture, of air being warmed in the daytime over
> adjacent land, then a light breeze carrying it or drifting it over the
> surface of the cooler water, so that lower layers of the air, in
> contact with that water, are somewhat cooler than the rest, and the
> resulting temperature gradient gives rise to anomalous dip. Alex
> reports his measurements as being in fine weather, daytime, taken over
> a sea-body that's surrounded by land. That seems like perfect
> conditions for upsetting the dip. The moral might be that sextant
> observations should be taken, not near land, but out at sea, where
> there's no local source of warm air.
>
> Does any of that seem plausible? Please note that I am no
> atmospheric-scientist, but just doing my best to make a few logical
> deductions from the evidence that Young has provided.
>
> George
>
> contact George Huxtable at george@huxtable.u-net.com
> or at +44 1865 820222 (from UK, 01865 820222)
> or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
>

   

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