Dear Geoff,
You get full marks and go to the top of the class!!
Your analysis almost exactly parallels what I
had in mind and your description is delightfully
eloquent!
SOLUTION TO THE PUZZLE
The S-shaped curves in your attachments are
very convincing. It seems not to be well
known that
Sunny friends,
For various reasons, I'm wanting to build a rather different dial. The
plan is for a south-facing vertical dial, but I want to design it with a
horizontal gnomon.
Waugh states that a vertical south-facing dial has the same hour lines
as a horizontal dial at the colatitude.