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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