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    Star sights on reciprocal bearings
    From: Paul Hirose
    Date: 2006 Dec 10, 13:33 -0800

    Geoffrey Kolbe wrote:
    >
    > "Hints for Travellers", published by the Royal Geographical Society,
    > (about which there was some discussion recently when Frank Reed
    > pointed out that the 1906 edition was up for auction on ebay and I
    > successfully bid on it), details the methods by which a surveyor may
    > fix his (or her) position to within a few seconds of arc. The
    > underlaying principle is to take sightings of bodies in opposition
    > (North-South for latitude, East-West for longitude) in order to
    > reduce systematic error - principally in how level the theodolite is.
    
    How would these paired observations reduce the effect of leveling error?
    It seems to me that if the theodolite vertical axis is inclined say 1
    minute to the north, then a star to the north will measure 1′ too high
    and a star to the south will measure 1′ too low. The leveling error has
    not been eliminated: both observations agree that you're 1′ north of the
    true location.
    
    On the other hand, reciprocal sights would reduce the effect of
    refraction error. I've read that precise latitudes were obtained on land
    from precomputed pairs of stars which crossed the meridian at nearly the
    same time, high in the sky, at almost identical distances north and
    south of the zenith.
    
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