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    Swinging the Arc
    From: Frank Reed CT
    Date: 2006 May 25, 16:22 -0500

    "Can you possibly  differentiate those 2  methods a little better? From
    reading your description, I  take it as being  pretty much the same procedure (i.e.
    treat the view through the  sextant as  if the celestial body were at the
    bottom of a pendulum, and swing the   sextant back and forth on the horizontal
    axis that points to the horizon  until  you find the lowest point, which means
    the sextant is perpendicular  to the  horizon). Hope *I've* described that so
    it makes sense.    ;-)"

    They do sound similar. A sextant is an instrument that lets you look  in two
    directions at once. Those two directions define two axes about which the 
    instrument can be rotated. Imagine you're measuring the altitude of the Sun and 
    just by chance a seagull is resting on the water off in the distance directly 
    below the Sun. Let's suppose the Sun is about 45 degrees high. Suppose I swing
    the arc by method 1 (the original method). That means that I rotate the 
    instrument around an axis that points directly to the Sun. When I look through 
    the sextant, I will see the Sun always centered in the field of view. That 
    seagull off close to the horizon will pass across the field of view, and the 
    horizon will slide away from the Sun's image as I swing left and right. The 
    observer adjusts the instrument until the horizon just touches the Sun at one 
    point without overlapping it. Next suppose I swing the arc by method 2 (the 
    later 20th century method). This means that I rotate the sextant about an axis 
    that points to that spot on the horizon in front of me where the seagull is 
    sitting. In this case, the seagull stays centered in the field of view while the 
    Sun's image sweeps back and forth. The image of the Sun swings along a curved
    arc, and the observer's goal is to get that arc to touch the horizon without
    overlapping it. The curvature of that little arc decreases rapidly as I go
    to  higher altitudes which has occasionally led to the mistaken impression that
    very  high altitudes can't be measured correctly with a sextant.

    You can  experiment with this indoors. Find a ceiling light with a window
    sill beneath  it. The light is your Sun and the sill is the horizon. You might
    want to  estimate the spot directly beneath the light on the window sill and put
    some  small marker there, like a piece of tape. Stand in a location where the
    "Sun" is  about 45 degrees above the "horizon" and try swinging the arc by
    the two  methods. You don't actually have to think about axes of rotation and
    all that.  Just look through the instrument and swing the instrument from side
    to side in  such a way that the "Sun" remains exactly centered in the field of
    view at all  times (method 1). Next rock the instrument from side to side so
    that your marker  on the window sill remains exactly centered at all times
    (method 2). You should  find that both methods work and yield the same angle for
    altitudes from zero up  to maybe 50 or 60 degrees. So far so good. Now try it
    all again when you're  standing almost directly underneath your stand-in Sun.
    That is, stand in a  location where the "Sun" is, say, 80 degrees high. Under
    these circumstances,  method 1 (where the Sun is centered) still works, but
    method 2 (where the marker  on the window sill is centered) doesn't work at all.
    While you're keeping the  Sun centered in the field of view with the Sun
    almost straight up, you should  find that you are rotating your sextant almost
    about a vertical axis [note that  since the real Sun and other celestial objects
    are extremely far away, it's  easier to do this than it may appear to be at
    first when you're using a ceiling  light as a pseudo-Sun]. So method 1, the
    original method, always works, and once  you've seen it done, it's easy.

    If this doesn't do it, I'm gonna have to  make a video!

    42.0N 87.7W, or 41.4N  72.1W.

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