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    Re: dip, dip short, distance off with buildings, etc.
    From: Bill B
    Date: 2006 Jan 14, 21:36 -0500

    On a serious note, I do appreciate your help and insights.  It can be a
    stretch exercise for a layman to keep pace the insights of a keen mind
    educated in the area.
    On a less serious note:
    Frank wrote:
    > With a sextant we
    > are  measuring the altitude of point  B from point A so that means that  we
    > know the angle in the triangle at point A,  let's call that  gamma.
    Bill asked:
    "Which triangle?  The small oblique or large oblique?"
    Frank responded:
    "The only triangle I defined . You have point C at the center of the
    Earth, point A at height h above the Earth's surface, and point B some
    You dog. Having sport with a liberal-arts major because you can.  I may not
    be able to count, but I can read (not spell or keyboard). 
    When you wrote, "Now apply the law of sines to the big triangle..." I
    somehow made a logical leap that there may be another, perhaps smaller,
    triangle.  An assumption, perhaps formed by the angle measured at A from B
    to the horizon?
    Frank continued:
    "Clearly that's just 90 degrees  plus the measured altitude.
    Ok so  far?? If you haven't drawn a picture of this yet, you can't possibly
    be here  so please make sure you've got a picture of this."
    Drew a sketch, but not a full blown picture.  Which may account for my
    sketchy thinking (and he's here all week).  Plus the whole pastels, Crayola,
    conte crayon, charcoal, pencil (which lead?) decision making process.
    Airbrush, or is that not a drawing tool? Or go magic marker--solvent based
    or water based? (Love the solvent-based in a small room, great buzz ;-)  All
    those lovely drawings starting to mimic the lead character in "Close
    Clearly? I tried to avoid the pitfalls of assumptions that already caused me
    problems above.  OK with treating ABCA as a right triangle given the ratio
    of R to H and h, but semi-clearly an oblique triangle in almost all cases
    once the horizon "dips" due to height of eye/curvature/refraction and B is
    raised above the horizon.
    And added:
    "Now what do we measure with our sextant or theodolite? Well, we're at point
    A, and we measure altitudes above the horizontal which is, by definition,
    the plane perpendicular to side AC of the triangle."
    Bear with me for a minute.  If the horizon is perpendicular to a line
    segment from A to C, then there would be no need for dip adjustments as
    height of eye rises from 0 in other uses.  But Bowditch does not adjust
    observes angle for dip directly in the T15 formula, but rather keeps the
    line site parallel (perpendicular) using H-h--as you propose (keeping it a
    right triangle.)  My major fault assigning new constants to T15 and other
    formulas is that I started with the formula as a given without question, and
    adjusted to new values for refraction.  Exactly what Richard Feynman would
    dub "Cargo Cult Science.  One must question what came before, as we are
    doing with refraction values but not with the formula itself--until your
    recent post.
    Based on your earlier posts, I leaned over forwards to treat it as a right
    triangle (s), but remembered your statement that the equations compensated
    for back leaning, so opted for oblique triangle(s). That said, again I see
    no significant problem treating the triangle(s) as right, but needed to
    confirm that with you before following your train of thought further.
    "I don't know if anyone will get a kick out of it or not, but if  you like
    this kind of math/physics, I've photographed some of my notes."
    Steven right in a map shop. "Are those aerial drawings?  Is the blue sky or
    water? He threw me out."  I recall some of his earlier material.  "I went to
    Alaska for the 4th of July.  Very disappointing, they had to hold the
    fireworks display indoors. So I spent the rest of my summer trying to do
    close-up photographs of the horizon."  Thanks to the list et al, I now know
    if I get my eye level close to water level, I can do close-up pictures of
    the horizon.  Now it's just a matter of refining refraction so I can define
    "close-up" ;-)
    As to your drawings, I thought you stated size as over 5MB, a bit chunky for
    dial up.
    On a serious note again, the above is not at all meant as a criticism of
    your post.  I hit a brick wall until I could understand your underlying
    assumptions and possible simplifications.

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