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    Re: Refraction at the horizon.
    From: George Huxtable
    Date: 2008 Mar 18, 17:17 -0000

    Marcel has let us watch his reasoning develop, which was interesting.
    
    But to explain a total refraction of only 16.3', as observed on one occasion
    from Mauna Kea, Hawaii, at 4205 m. altitude, in terms of the over-island
    refraction, is difficult, and it really needs no calculation to show that.
    
    Assume that the refraction over the ocean, on the way down to the horizon,
    is close to34', corresponding to the standard atmosphere  And then add on
    another lesser, amount, to corresponding to the 100 miles or so path length
    over oceanic waters. I don't know how much to add for that, but those that
    are familiar with refraction integrals might offer some values for a
    standard atmosphere, where the integration up from the horizon has been
    truncated at certain heights, at say 1000 metre intervals.
    
    Anyway, an expected oceanic refraction to that altitude would be in the
    range of 40' to 50', at a guess.
    
    Then, after an over-island path of only 30 miles or so, the light arrives at
    Mauna Kea, by which point the total refraction was only 16.3'. If so, that
    would have to be explained by a highly NEGATIVE refraction over that 30
    miles! That means the light would have to be bending concave-upwards, the
    opposite way to the usual, and by an enormous amount. That implies that the
    air density has to be INCREASING, and considerably so, as the altitude
    increases. The laws of physics tell us that air pressure can only decrease
    as the altitude increases, because there is less weight of air above
    pressing it down. And for the density to increase with altitude, requires a
    decreasing temperature, and by much more than the amount required to
    compensate for the pressure change. An unfeasibly unstable state of affairs!
    
    So something is wrong. What might that be? One possibility is a simple
    cock-up, in the sunset timing or in its calculation. Another might be that
    the over-ocean part of the refraction, on that evening, differed greatly
    from the expected value, to an extent that some pundits on this list would
    find hard to accept.
    
    ==========================
    
    In an earlier message (4717) Marcel wrote-
    
    "I investigated some time ago how the refraction at large zenith distance
    depend on changes in temperature and pressure at the observer and found  at
    that time that those dependencies are quite exponential."
    
    Marcel, I have searched for some meaning in that sentence, but remain
    baffled by it. What on earth does "quite exponential" imply? A naive view is
    that the quantity (refractive index - 1), which defines refractive bend, is
    almost exactly proportional to air density. That is, to pressure, to the
    power +1, and to temperature, to the power -1. Is Marcel saying that isn't
    so? What does "quite exponential" mean in this context?
    
    George
    contact George Huxtable at george---.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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