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