Warren, I wrote a fairly detailed analysis of Bifilar Dials in 1978, complete with day curves, etc. - most recently it was reprinted in the Bulletin of the British Sundial Society (95.1:18-27) for Feb 1995.
A conic section treatment of the day curve for a traditional dial can be found as Problem #84 in Heinrich Dorrie's "100 Great Problems of Elementary Mathematics" published by Dover Publications. Fred Sawyer
