Dear Gianni, Your analysis has silenced the Lista Inglese!
I will summarise what you said so that new readers may start here... You have: D = length of day (sunrise to sunset) Whenever D is an integer number of hours, the associated constant-declination curve passes through a hyperbolic arc of points at which Babylonian and Italian hour-lines intersect. Whenever D is an EVEN integer number of hours, the associated constant-declination curve passes through a hyperbolic arc of points at which Babylonian, Italian AND French hour-lines intersect. Whenever D is 6, 12 or 18 hours, the associated constant-declination curve passes through a hyperbolic arc of points at which Babylonian, Italian, French AND Temporary hour-lines intersect. This makes 58.49 degrees North an interesting latitude to set up a dial because: At the winter solstice D = 6 hours At the equinoxes D = 12 hours At the summer solstice D = 18 hours I attach a PDF which shows a dial marked out for a direct south-facing wall at this latitude. The Babylonian, French and Italian hour-lines are obvious and I have drawn the Temporary hours in blue to distinguish them. Design exercise for the reader: Number all the lines in an elegant way! The equinoctial line has quadruple crossing points all along it. The winter and summer solstice curves have these quadruple crossing points at noon and at: B=6, F=9, I=12, T=4 and B=12, F=15, I=18, T=8 There are, of course, triple crossing points along the D=6, 8, 10, 12, 14, 16 and 18 hyperbolae where Babylonian, French and Italian hour-lines intersect. There are a few "surprise" triple crossing points too such as those at: B=5 I=14, T=4 and B=10, I=19, T=8 The French hours at these points are half-integers. One more thing: Babylonian, French and Italian hour-lines are STRAIGHT on a plane dial. Temporary hour-lines are narrow S-shapes. Print out my attachment and squint along the blue lines. You will see that they are gentle curves. It is very cold here at 52 degrees north so I shall not be moving to 58.49 degrees north myself :-) Best wishes Frank
GF.pdf
Description: GF.pdf
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