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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 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.

-FER
42.0N 87.7W, or 41.4N  72.1W.
www.HistoricalAtlas.com/lunars

   

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