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Nicolas, you wrote:
"On board of a vessel the whole issue is indeed academic, but let us not 
forget that Sadler's original idea was "...to observe the dip, accurately by 
theodolite, from fixed locations on the seashore ... using the height of the 
tide to give varying heights above sea-level.". Tidal ranges of more than 10 
metres are not uncommon and can be very useful in such an experiment, as this 
will produce a difference in dip of more than 3 arc minutes (assuming the 
observer stands at 3m above high water and thus 13m above low water)."

There's nothing wrong with that idea, of course. And when practicing celestial 
navigation from shore, it's important to remember that you need your height 
of eye above the water at that time, and not a height taken from a chart, 
e.g., which would give the height relative to some fixed datum, like low tide 
level or MLLW or something else. But that's obvious enough.

And:
"Sadler only pointed out that it was difficult to determine the relation 
between the tide measured near the shore with the one measured at the 
horizon, an unknown perhaps not measurable with a sextant, but surely with a 
theodolite."

I really think that Sadler was inventing a pseudo-explanation for variability 
which he could not otherwise explain. We know today that the variability in 
dip is caused by significant variations in terrestrial refraction due 
primarily to the temperature structure of the air near the sea surface. He 
mentions that he had access to air and sea temperature data from a lightship 
on the horizon and apparently he believed that this would show some 
correlation with the variability of dip. With observations taken from shore 
like this, the variations in dip can be quite substantial --several minutes 
of arc easily. Air and water temperatures at the horizon are simply 
insufficient to explain those variations (you need much more detail on the 
air temperature profile). 

Now what about the tides? Let's consider the case that you mentioned 
previously: that area near the amphidromic point in the North Sea between 
England and the Netherlands. The tilt is on the order of 2 feet in 20 
nautical miles (I believe that's about right). The sea surface is tilted, 
very much like a tilted tabletop, with the direction of tilt depending on the 
tide phase. A normal vector to the mean sea surface over a broad area in this 
part of the North Sea is tilted by about 3.5 seconds of arc in a direction 
which rotates around the zenith with the period of the tides. So if we 
measure altitudes relative to the sea horizon, they will be too low by about 
one twentieth of a minute of arc when we are looking "uphill" and too high by 
the same amount when we are looking "downhill". That would be the variation 
of dip due to the tidal tilt of the sea surface, and this is an area with 
among the highest tilts on the oceans. This is very small and "academic," as 
Jeremy put it, and it would be considerably smaller than the expected 
variation due to variability of terrestrial refraction (I would say roughly 
ten times smaller). I agree that you could, with care, measure an angle that 
small with a theodolite, but I really cannot believe that this was any 
serious issue for those dip observations made by Sadler and his group. It's 
also interesting, and somewhat "telling," that Sadler says he couldn't find 
anyone who could tell him the shape of the sea surface for a given state of 
the tide. Even in the 1950s, this information was well-known at a sufficient 
level of accuracy to do this sort of analysis. Maybe he simply asked the 
wrong people, astronomers rather than oceanographers?? Or, did their answers 
not explain what he thought he was seeing. I think that's a real possibility.

-FER




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