Arthur, The first dial you described was invented in the first half of the 17th century by Samuel Foster in London. It was subsequently rediscovered by J.H. Lambert, and has had a number of subsequent rediscoveries since. See my article:
Fred Sawyer, "A Self-Orienting Equiangular Sundial", Bulletin of the British Sundial Society, Oct 1991, 91(3):24-25. For details on design of bifilar dials and the general theory, see: Fred Sawyer, "Bifilar Gnomonics", Journal of the British Astronomical Association, Jun 1978, 88(4):334-351. Reprinted in Bulletin of the British Sundial Society, Feb 1993, 93(1):36-44, also Feb 1995, 95(1):18-27. To help you along, I will send these articles to you attached to a separate email - zipped MS Word documents. I hope you are able to view them. Fred Sawyer
