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    Re: dip, dip short, distance off with buildings, etc.
    From: Frank Reed CT
    Date: 2006 Jan 7, 07:14 EST

    Bill, you wrote:
    "I let go of your Chicago  observations"
    They're not dead yet!
    Just today, I finally got  around to measuring the heights of the towers in
    question above lake level --the  results are suprising. Damn near froze my
    fingers off --I parked too far away  and forgot my gloves. But it's all coming
    together quite nicely. The  observations on that day in late September from the
    beach in Indiana are  consistent with the refraction from a moderate
    temperature inversion and  distinctly *IN*consistent with Bowditch Table XV. I'll get
    into the details as  time permits.
    Before I forget (again), I wanted to mention that the "lean  back" of the
    buildings from the curvature of the Earth, which was something you  were
    concerned about, should be entirely insignificant. If a flagpole is 20  nautical miles
    away from me, then it is tipped away from my vertical by 20  minutes of arc
    almost exactly. The difference in angular apparent height from  that tilt is
    going to be proportional to the cosine of 20 arcminutes which  differs from
    unity by about one part in 60,000, so a one degree high skyscraper  20 miles in
    the distance is shorter in apparent angular height by a thousandth  of a minute
    of arc because of that "lean back". The standard calculations can,  and do,
    account for this effect (implicitly), but even if they didn't, it  wouldn't
    And yet another "before I forget", Lake Michigan is not  sinking. The level
    fluctuates a lot, and yes very recently there have been some  down-trending
    years, but those boaters you mentioned who are convinced that it  is draining
    away because the piers are inconveniently high are wrong --it's  urban legend.
    The harbor builders built the piers years ago well above the  fluctuations
    *intentionally*. When you live on a body of water with natural  level fluctuations,
    it's much easier to deal with harbor infrastructure that  ends up too high
    for convenient use than it is to deal with infrastructure that  is underwater!
    42.0N 87.7W, or 41.4N  72.1W.

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