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    Swinging the Arc
    From: Frank Reed CT
    Date: 2005 Oct 18, 16:36 EDT

    There are two methods  for "swinging the arc". The method that I prefer and
    that is really more useful  I will call Method 1. The method that a majority of
    navigators learned in the  second half of the twentieth century I will call
    Method 2.
    Method  1:
    This is the method that you will find described in most older works of
    navigation including The American Practical Navigator (Bowditch) through the  first
    half of the 20th century. You'll also find it in some more recent works  such
    as John Letcher's Self-Contained Celestial Navigation. The procedure here  is
    to bring the Sun (other object) down to the horizon and then rotate the
    sextant about the line of sight to the object so that the horizon moves back and
    forth "behind" the image of the Sun in the horizon glass. The Sun remains more
     or less centered in the field of view the entire time. Quoting Bowditch from
     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." Letcher in his book has a nice diagram demonstrating that the object
     stays in the middle of the field of view throughout the rocking  process.
    Method 2:
    Starting sometime around the middle of the 20th  century, navigators began
    using a different method for swinging the arc, and  many navigation textbooks
    repeated it. I believe that this method originally  evolved from confusion over
    Method 1, but this method does work --up to a point.  This method seems to be
    described in post-war editions of Bowditch. Though the  language is ambiguous,
    the diagram is clear. In the diagram illustrating  swinging the arc in the
    1962 Bowditch, the Sun is moving across the field of  view while the horizon
    remains level. This is basically what you see when the  instrument is rotated
    about an axis pointing straight to the  horizon.
    When you're looking at an object that is, let's say, 35 degrees  high in the
    sky, both Method 1 and Method 2 will find the vertical, and thus the
    shortest, correct distance between the horizon and the object in the sky. They  both
    work because the sextant is essentially a device that lets you look in two
    directions at once. So rotating the instrument about the line of sight to the
    object in the sky (Method 1) and rotating the instrument about the line of sight
     to the horizon (Method 2) should be symmetrical operations. And that's true.
    You  can use a sextant upside-down, and it works just fine. But there is in
    fact an  asymmetry here --it's in the objects we're viewing. While the star or
    other  celestial object is basically a point in the sky, the horizon is, of
    course, an  extended object. We're trying to locate a particular point along the
    horizon,  the point that is directly beneath the star in the sky. Finding
    that point on  the horizon is the whole point of swinging the arc. By the way,
    when the object  is very low in the sky, it should be obvious that Method 1 and
    Method 2 become  identical.
    Where's the problem then? The trouble is that, while Method 1  always works,
    unfortunately Method 2 will work only when we have already more or  less found
    the point on the horizon directly beneath the celestial body. If it's
    outside the field of view, as it often is at very high altitude, you will have  to
    find that point by trial and error. Furthermore, when you use Method 2 with
    objects at high altitudes, the curvature of the arc becomes harder to see. This
    had led many sextant users to the incorrect conclusion that they cannot
    accurately measure altitudes above about 70 degrees. Bruce Bauer in his book
    concludes from his experience with Method 2 that one should limit observations  to
    stars in middle altitudes only. And this is simply a mistake. It's an
    unfortunate outcome of using this method of swinging the arc.
    Since  Method 1 came first, always works, and seems no harder to learn than
    the more  popular Method 2, I highly recommend that students of celestial
    navigation stick  to this method. Swing the arc by rotating the instrument about
    the line of sight  to the object in the sky. The Sun or other celestial body
    should remain more or  less centered in the field of view throughout this
    operation. The goal of the  operation is to find the point on the horizon where the
    image of the Sun just  touches the horizon (without dipping below it).
    Finally, I would add that  swinging the arc is unnecessary when the altitude
    is very low, and it's only  necessary for basic setup when the altitude is
    very high. There is an exception  to this and that occurs when the high altitude
    object's azimuth is changing very  rapidly as it does when it reaches the
    meridian. In that case, you're better off  facing south or north as the case may
    be. This is a separate issue from the  question of swinging the arc.
    42.0N 87.7W, or 41.4N  72.1W.

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