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    Re: Sadler
    From: Frank Reed
    Date: 2008 Dec 25, 20:20 -0800

    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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