NavList:

On Nav-L back in June there was much discussion on the mathematics of
advancing a position circle. At the time I was too busy to read the
postings closely, so I don't know if anyone mentioned a paper
by George H. Kaplan of the U.S. Naval Observatory, available in PDF via
a link at the USNO site:
http://aa.usno.navy.mil/research/celnav.html

The second link ("The Motion of the Observer in Celestial Navigation")
deals directly with the topic: "First, a celestial LOP is actually a
circle, and if it is advanced so that each point on it follows a rhumb
line defined by the vessel's course and speed, it will not precisely
retain its shape."

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