I followed your whole letter with great interest, and understand it all,
except for one thing. Is it possible to determine the wall's declination
once I have drawn the equinoctial line and the substyle line using this
method?
At first I thought that if I drew a horizontal line on the paper and
determined the angle of the sloping equinoctial line, that this angle would
equal the wall's declination, but it doesn't in all the examples I've
tested.
For examples, I played around with a sundial drawing program and entered
different wall declinations (0, 45 and 90 degrees East of South) for my
latitude 32.3 deg N. and then I measured the sloping angle of the
equinoctial lines. Here are the results:
1. If the wall is due south, then the equinoctial line is horizontal which
means the declination is 0. so far so good.
2. But if the wall declines say 45 degrees to the East of South, and I draw
a sundial face using Shadows or Zonwvlak, then I thought it's angle is
should be 45 also, but it's not. It's 48.2 degrees.
3. If I draw a dial the declines 90 degrees East of South, then the angle of
the equinoctial line should be 90, but it's not. It's 57.7 degrees.
So obviously my supposition is wrong. The angle of the equinoctial line is
NOT equal to the wall declination.
How can I get the wall declination using your Indian Circle method?
Thanks
John
----- Original Message -----
From: "Roger Bailey" <[EMAIL PROTECTED]>
To: "Sundial Mail List" <sundial@rrz.uni-koeln.de>
Sent: Friday, December 03, 2004 9:42 PM
Subject: Zarbula's Method for Wall Declination
Hello Colleagues,
The Piedmontese painter and sundial maker, Giovanni Francesco Zarbula left
an amazing legacy in the villages of the French alps. Between 1832 and
1870
he crafted over 60 sundials in the area from Grenoble to Gap, near the
Italian border. Over half of these flamboyant folk art masterpieces still
survive; recently many have been expertly restored. I often wondered how
Zarbula laid out these designs on vertical declining walls. As an
itinerant
craftsman, carrying all the tools of his trade on the back of a mule, he
would not be able to utilize the methods summarized in Frank King's note
following John Carmichael's good question. How did he do it?
I am pleased to report that Google found the answer for me. Follow the
link
to: http://www.meridianeitaliane.it/Rivista%20Gnomonica/gnomonica6.pdf
On
pages 8- 10 of this 61 page edition of "Gnomonica", there is a letter by
Alessandro Gunella outlining Zarbula's method: "L'orolgio Francese e il
metodo DI ZARBULA per trovare la declinazione del muro". Thanks,
Alessandro
for answering the question. I guess that I am not the first to be
impressed
by Zarbula's dials and wonder about his techniques.
As Alessandro reported, Zarbula didn't actually measure the declination of
the wall. He didn't need to. Zarbula seems to have applied a variation of
the "Indian Circle" technique (Cassini's Method on Frank King's list) to
establish the equinoctial and sub-style line on the wall. From these he
could lay out the hour lines using well known graphical gnomonic
techniques.
The "Indian Circle" method ("cerchio indu" in Italian) is a simple
technique
for finding north. All you need is a stick, a string and sunshine. Put the
stick vertically into the flat level ground. Use the string to describe
some
circular arcs, using the stick as the center. Watch the shadow of the tip
of
the stick and note where the path of the shadow tip crosses the arc in the
morning and then again in the afternoon on the other side of the circle.
The
line between the crossing points is due east - west. North - south is
perpendicular to the east - west line. Zarbula's method is based on the
fact
that every vertical declining sundial has an analogous horizontal sundial
somewhere else in the world. To apply this variation to a declining wall,
all you have to do is mount a stick perpendicular to the wall, draw one or
more concentric arcs, mark the shadow tip crossings on the wall, and draw
a
straight line through them. This line is the equinoctial line,
(equinoziale
in Italian), the intersection of the equatorial plane with the plane of
the
vertical declining wall. This important construction line is highlighted
in
most of Zarbula's dials. A perpendicular line from the equinoctial is the
sub-style line (sostilare in Italian) for the polar axis parallel. QED
I hope that I got this right as I used Babblefish to transliterate
Alessandro's note and some points may have been lost in translation. The
web
link brings up the whole pdf file, 3.6 MB. If any one wants to have a copy
of the extracted pages, a 60 kb file and/or my interpreted translation
based
on Babblefish, I would be pleased to send them on as email attachments. I
assume Alessandro Gunella or Nicola Severino of Gnomonica will allow such
single copies to colleagues within the copyright laws.
I am continuing my research on Zarbula, his methods and his dials. If any
one has information to share on these topics that doesn't come up among
the
~200 Google hits on "Zarbula", I would appreciate a note.
Regards,
Roger Bailey
Walking Shadow Designs
Now back at N 48.6 W 123.4
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