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    Re: Swinging the arc: two methods, one preferred
    From: Hewitt Schlereth
    Date: 2011 Jan 6, 11:55 -0400

    Frank -
    
    Is there a picture of this anywhere on line? Being self-taught (or
    more accurately having learned from 20th century books) I had never
    heard of this way of swinging the arc.
    
    To take the sun as an example: when you have it at the right altitude,
    does the horizon appear to slide around the edge of the sun's disk,
    just touchng it; as it were, stroking it?
    
    Thanks.  Hewitt
    
    
    
    On 1/5/11, Frank Reed  wrote:
    > Greg Rudzinski, regarding your Jupiter sights, you wrote:
    > "I did use Byron's vertical sextant technique of rocking the body from
    > horizon to horizon through the dark back ground of the sea then splitting
    > the difference to get the mid point."
    >
    > Note that what you are describing here is essentially the original (and
    > preferred) method of "swinging the arc".
    >
    > Sometime in the middle of the 20th century, probably involving the big
    > changes of navigation education during the Second World War, navigators
    > started swinging the arc by rocking the instrument about the axis of the
    > telescope that points to the horizon. This makes the Sun or star shoot from
    > side to side across the field of view and, while it does make an arc, it's
    > not much of an arc and especially for high altitude objects it can be hard
    > to say whether that arc is really hitting the horizon at its low point. This
    > is definitely the most widely taught method of rocking the sextant, and it's
    > not literally wrong, of course. It works very well for low altitudes.
    >
    > The original method for swinging the arc is described with some cumbersome
    > words in most older books on navigation going at least as far back as
    > Maskelyne in the 18th century. It involves rocking the sextant by rotating
    > it about an axis pointing to the body in the sky, and necessarily that means
    > that the observer has to rotate from side to side while the instrument is
    > being rocked. By doing so, the Sun or star remains centered in the field of
    > view while the horizon shifts up and down beneath it (that's what you see
    > looking through the instrument). If you're having trouble picturing this,
    > try holding a sextant horizontally, face up, with it set to the approximate
    > altitude of the Sun. Point the direct "horizon" view through the instrument
    > to a point in the sky left of the Sun at about the angle from the Sun that
    > you have pre-set. Scan about until you see the Sun (reflected image,
    > properly shaded! don't point the horizon side at the Sun). Get the Sun
    > reasonably close to the field of view. The horizon side should show nothing
    > but sky. Now slowly rotate the instrument down to a vertical orientation
    > keeping the Sun centered in the field of view. Then continue rotating until
    > the sextant is horizontal again but face down on the other side. This is an
    > exaggerated 180-degree sweep through the motion of the original method of
    > swinging the arc. In practice, you would normally only sweep through a small
    > fraction, say 30 degrees, of this motion. When you use this method of
    > swinging the arc, if you start with an altitude that is a bit too large, the
    > Sun will cut the horizon on one side descending, then pass a low point in
    > the middle where its image is partly superimposed over the sea (and that low
    > point naturally is vertical position), and then the Sun will cut the horizon
    > again rising on the other side. The vertical orientation is, of course, in
    > the direction halfway between the two azimuths where the Sun crossed the
    > horizon during the rocking motion.
    >
    > The mid/late-20th century method of rocking the arc is the one described in
    > nearly all modern textbooks, and if you see animations, they almost always
    > show the horizon remaining fixed with the Sun swinging back and forth across
    > the field of view (there's an animation just like this on the Wikipedia
    > "Sextant" article). There are some exceptions. For example, in John
    > Letcher's "Self-contained Celestial Navigation with H.O. 208" there's a very
    > fine diagram illustrating the original (correct) method where the Sun stays
    > centered in the field of view for the whole operation (Letcher's book is
    > filled with interesting little gems and I always recommend it. It's still
    > available from used book dealers. John Letcher is yet another former
    > physicist who found great pleasure in celestial navigation. Yes, we are a
    > pox on the subject, aren't we?).
    >
    > A number of people, including, so it would seem, Byron Franklin, have
    > re-discovered the original method of swinging the arc at some point in the
    > past few decades and done their best to recommend its virtues. I'm in the
    > same boat. Unfortunately, navigators tend to be "mildly confident" in the
    > veracity of those things which they learned at their first navigation
    > instructor's knee, and there's tremendous resistance against doing things
    > the "right way". How, after all, could it be wrong if so many navigators
    > have used it successfully for so many decades?? And that's the thing, it's
    > not "wrong" --it's just less effective and definitely worse, to the point of
    > being useless, for higher altitudes. BOTH methods of swinging the arc work
    > very well for low altitudes, and both work well enough for middle altitudes
    > (though the original method has a real advantage here), but ONLY the
    > original method works at all altitudes, including those times when the Sun
    > or star are very high in the sky. The original method is universal --there
    > are no cases where it fails-- and it's no more difficult to learn than the
    > more popular late-20th century method of swinging the arc.
    >
    > -FER
    >
    >
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