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    Re: Swinging the Arc
    From: George Huxtable
    Date: 2005 Oct 20, 16:44 +0100

    Joel Jacobs wrote-
    > Before we start hunkering down down for Hurricane Wilma, I want to thank
    > Frank for his scholarly explanation.
    > One question remains since I find this statement from the 1918 Bowditch
    > ambiguous.
    > 1918: "the observer should move the instrument to the right and left of
    > the vertical, swinging it about the line of sight as an axis, taking care
    > to keep  the object in the middle of the field of view. The object will
    > appear to  describe the arc of a circle, and the lowest point of this arc
    > marks the true  vertical."
    > Which object is it talking about. If its the celestial body, i.e., the
    > sun, then what I visualize would be the same as shown in the diagrams used
    > to illustrate Method 2.
    Reply from George.
    It's simple, really. Yes, the object (the Sun, say) stays in the centre of
    the field of view, as near as an observer can manage it, as he swings his
    sextant about an axis which is a line pointing to the Sun. But as the
    sextant swings, so does that field of view (with the Sun at the middle)
    appear to swing, superimposed as it is on the view of a part of the horizon
    in the horizon mirror.
    So as the sextant swings, it's the horizon view that's racing past the
    horizon mirror, not the Sun view racing past the index mirror. If you do the
    job properly, that is. One bit of the horizon looks very much like another,
    so you don't notice that happening. You would, if there was another vessel,
    on the horizon, to show it up.
    Say there was a lighthouse, on the horizon exactly below your view line to
    the Sun. Assume that the Sun is rather high in the sky. If you swing your
    sextant about the line to the Sun (Frank's method 1), then the Sun would
    stay still in your view frame, and the lighthouse would shoot from side to
    side in the horizon mirror as you rocked the sextant to home in. And in the
    end the measurement would be when the Sun limb grazed the horizon line just
    at the lighthouse. If you used method 2, you could swing the sextant about
    the line to the lighthouse, in which case the lighthouse would stay still at
    the centre of the horizon mirror, and the Sun would shoot about across the
    field of view, through the index mirror, as you momed in on it. That way
    would work, but only if you happened to know in advance that the lighthouse
    was indeed directly below the Sun. In practice, you're never provided with
    such a convenient marker, and it's impossible to guess which point on the
    horizon is the one that's directly below a high Sun.
    That's why method 2 doesn't work, in practice, for a high Sun. You might
    start off rocking that way, but once the Sun has been captured in the index
    mirror, then the Sun has to stay in view, and it's the horizon that gets
    rocked about, using method 1. That's always how the rocking procedure has to
    end up though perhaps unconsciously.
    Remember, what started this discussion was Joel's contention, which ran as
    "The procedure of rotating the sextant is to have the celestial body subtend
    an arc in which its lowest point just kisses the horizon. At that moment,
    the sextant is perpendicular, and the reading is taken. To do that
    correctly, the object will sweep across the field of view as an arc, and not
    be centered "at all times" as he suggests."
    I hope Joel can now accept the combined opinions of Bowditch (1918),
    Letcher, and Bauer, who all agree with Frank and with me that the object in
    the sky should remain in the centre of the field of view as the sextant is
    rocked, and does not "sweep across the field of view as an arc".
    All this comes about because with a horizon observation, you are trying to
    find the smallest angle between a point (the observed object) and a line
    (the horizon). For lunar distances, it's a different matter. Then, you are
    looking for the angle between two points in the sky. With a lunar, you can
    capture either object in either view, "horizon" or index, and then swing the
    sextant about either axis until the other appears in view, and the two brush

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