Dear Frank,
the problem of equal or unequal hours, I left it out of the article
but commented it only in my book on the Greek sundials. The reason is
that the winter side of the Oropos dial looks as if made for equal hours
and the summer side as if made for unequal hours. Strange thing!
You have shown by the dotted lines in your drawing which gives
the situation rather
exactly that equal nd unequal hour lines do not differ very much.
Sometimes we want to see things that are not intended, sometimes we do not want
to see things because they cannot be. Who knows?
Therefore my opinion is: they hour lines on the winter side could be equal hour
lines.
Hope, this answer your questions,
best wishes
Karlheinz
-----Ursprüngliche Mitteilung-----
Von: Frank King <[EMAIL PROTECTED]>
An: [EMAIL PROTECTED]
Cc: [EMAIL PROTECTED]
Verschickt: So., 24. Aug. 2008, 13:45
Thema: Re: Fwd: equal and unequal hours
Dear Karlheinz,
I have now read your article more carefully.
It is excellent, one of the most interesting
rticles 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
ut the WAY it is divided is not as it
hould be for unequal hours. Is that right?
I attach a PDF showing the winter side of
n equatorial sundial at latitude 40 degrees.0DThe two circles are for
declinations of -24 degrees
the value you used for the winter solstice) and
or -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
ittle black circle which (on the winter side) is
BOVE the horizon line. It is, of course, where
he polar axis through the nodus intersects the
lane of the dial. It corresponds to your point
W in Fig. 6.
The temporary hour lines do not really *radiate* from
point but they do *converge* to a point, your FW in
ig. 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
ial are *temporary* hour lines. I don't understand :-(
The lines in your Fig. 3 look very much like the dashe
d
ines in my PDF. They appear to radiate from a point
BOVE the horizon line. Surely, these lines are *equal*
our lines?
Have I misinterpreted your sentence that begins: "This
eing so..."?
I am sorry to be so slow at understanding!!
Best wishes
Frank
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