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    Re: Swinging the Arc
    From: Frank Reed CT
    Date: 2004 Dec 5, 18:23 EST
    Alex wrote:
    "How can you possibly do this in practice??
    Except by invereting your sextant and looking at the Sun through
    the horizon mirror?"
     
    Try it. Use a light on your ceiling and a window sill as surrogates for Sun and horizon. Suppose the angle is 45 degrees. Can you see that you can rotate the sextant all the way around a complete circle starting at the horizon (window sill), rolling left to horizontal, right through straight overhead, back through horizontal on the right, and finally back to the horizon from the other side? In order to do this, the sextant has to be rotated about an axis that points to the Sun (celing light). In the real case, the axis of rotation can be well outside the sextant, but in this model case, the axis will have to pass nearly through the index mirror because the object is so close (parallax from shifting a few inches).
    And:
    "Maskelyne also asks the same question and concludes that one
    has to rotate the sextant about BOTH horizontal and vertical axes."
     
    I don't think that makes any sense. The rotation is about a single axis. I'm pretty sure that the mathematical and physical analysis of solid-body rotation was worked out after Maskelyne's time. The wording he used may have reflected looser terminology from that earlier era.
     
    And:
    "When the altitude is small it is enough to rotate about horizontal axis, when it is large, the main part of the motion is about the vertical axis."
     
    And try this with the real Sun: Place the reflected image of the Sun on some horizontal line (assuming you don't have a sea horizon handy). Rotate the sextant so that the Sun's image stays centered in the field of view. How is the sextant turning? I think you'll find that it's rotating about the axis that points to the Sun. Wouldn't you agree that this is the rotation required to find the vertical angle?
     
    You have Bruce Bauer's book, right? Read his section on this topic. He's clearly describing something very different. And that description is similar to what you'll find in some other navigation textbooks. It must work to some extent under some conditions. That's why I was proposing that three method comparison earlier.
     
    By the way, the other method works perfectly if the sextant is used upside-down. Were some of the early sextant designs meant to be used with the object in the fixed mirror (our "horizon" glass) and the horizon brought to it via rotation of the index mirror? If so, that might explain some of the confusion.
     
    Frank R
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois
       
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