Dear Karlheinz, I have now read your article more carefully.
It is excellent, one of the most interesting
articles I have read for a long time!
I think now understand your comment...
> ...you see that the winter circle is not
> divided in 12 parts as it should be for
> unequal hours.
I misinterpreted this when I first read it.
The winter circle IS divided into 12 parts
but the WAY it is divided is not as it
should be for unequal hours. Is that right?
I attach a PDF showing the winter side of
an equatorial sundial at latitude 40 degrees.
The two circles are for declinations of -24 degrees
(the value you used for the winter solstice) and
for -2.5 degrees which has no special significance.
I have drawn two sets of hour lines:
1. The solid lines are temporary hour lines
which I have taken all the way to the
horizon line by letting the declination
run down to -50 degrees.
This cannot really happen of course but it
emphasises your point: "Strictly, the lines
are curves..."
2. The dashed lines are (modern) equal hour lines
which are at 15-degree intervals.
Importantly, the equal hour lines radiate from the
little black circle which (on the winter side) is
ABOVE the horizon line. It is, of course, where
the polar axis through the nodus intersects the
plane of the dial. It corresponds to your point
MW in Fig. 6.
The temporary hour lines do not really *radiate* from
a point but they do *converge* to a point, your FW in
Fig. 6.
There is one remaining puzzle. You say:
Strictly, the lines are curves, but they diverge
only slightly from the rectilinear, and so we may
take them as straight lines...
[Here you are talking about temporary hour lines
and, of course, I agree.]
... This being so, the hour lines on our dial show
a high degree of precision.
This last sentence suggests that the hour lines on the
dial are *temporary* hour lines. I don't understand :-(
The lines in your Fig. 3 look very much like the dashed
lines in my PDF. They appear to radiate from a point
ABOVE the horizon line. Surely, these lines are *equal*
hour lines?
Have I misinterpreted your sentence that begins: "This
being so..."?
I am sorry to be so slow at understanding!!
Best wishes
Frank
winter.pdf
Description: winter.pdf
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