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From: Alexandre Eremenko (no email)
Date: Wed Nov 24 2004 - 14:21:09 EST
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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