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    Re: refraction
    From: Alexandre Eremenko
    Date: 2007 Jan 5, 18:54 -0500

    Let me give a VERY simplified example,
    for illustration purposes.
    Suppose that the Sun rises exactly in the E
    goes up to Z (90d) and then down to W.
    (This is a VERY idealized situation which never happens,
    but something close to it does happen sometimes).
    When the Sun is at Z, there is no refraction,
    and you can pinpoint the moment when it is at Z.
    Now in this situation, the altitude of the Sun should
    change uniformly. So you can predict the moment when
    it will be on a given altitude, say 45d.
    You look at the Sun at this moment, and of course
    you do not see it exactly at 45d, because of refraction.
    The difference is the refraction, roughly speaking.
    It was all much more complicated in reality, because,
    the Greeks could not measure time precisely...
    neither could they measure angles as well as we do
    with our modern sextants:-)
    The main observation which permitted to develop
    a very exact theory of the motion of the Sun was
    that the motion is very uniform and regular,
    and that small errors in determining the parameters
    of this regular motion would
    accumulate with time to large errors.
    So by doing observations over VERY large periods of time,
    one can determine the parameters of the Sun motion very
    Then you compare the Sun motion with observations and
    derive refraction.
    As we know now, Ptolemy still could not do this,
    though he understood how to do it.
    It was only Tycho
    who could make instruments of sufficient precision
    (using generous royal grants and his own money:-)
    to make the tables of refraction.
    But the theory of the Sun motion was already nearly perfect
    at that time.
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