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    Re: Swinging the Arc
    From: Joel Jacobs
    Date: 2005 Oct 20, 12:50 +0000
    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.
     
     
    Thanks,
     
    Joel Jacobs
     
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    -------------- Original message from Frank Reed <FrankReedCT@AOL.COM>: --------------


    > SWINGING THE ARC
    >
    > 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 li! ne 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 met! hod 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 i! n 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.
    >
    > -FER
    > 42.0N 87.7W, or 41.4N 72.1W.
    > www.HistoricalAtlas.com/l! unars
       
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