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    Re: Altitudes, close to 90
    From: Alexandre Eremenko
    Date: 2004 Nov 24, 14:21 -0500

    The formula I gave in my previous message is correct
    but my conclusions from it are totally wrong:
    On Wed, 24 Nov 2004, Alexandre Eremenko wrote:
    > The source of error is that you cannot determine precisely
    > the point on the horizon which is exactly "below" the body.
    and also wrote:
    > Maskelyne (Phil. Trans., May 28 1772) does not give this
    > formula, but discusses its practical consequences at length.
    > "Observers are commonly told, that in making the fore
    > observation they should move the index to bring the Sun
    > down to the part of the horizon directly beneath him, and turn
    > the quadrant about upon the axis of vision...
    > "I allow that this rule would be true, if a person could by sight
    > certainly know the part of the horizon beneath the Sun; but,
    > as this is impossible, the precept is incomplete.
    > Moreover, in taking the Sun's altitude in or near the zenith, this
    > rule entirely fails, and the best observers advise to
    > hold the quadrant vertical, and turn one's SELF ABOUT UPON THE HEEL,
    > stopping when the Sun glides along the horizon without cutting it:
    > and it is certain that this is a good rule in this case, and
    > capable with care of answering the intended purpose."
    > Finally, a very short explanation for those
    > "mathematically inclined":
    > the distance, as a function on the sphere has one
    > singularity (fails to be smooth), at 180 degrees;
    > the altitude, as a function on the sphere has two
    > singularities (fails to be smooth), at 90 and -90 degrees.
    > Alex.

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