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Dear all,
for some of you it might be of interest that there will be an article published
in Archäologischer Anzeiger on the development of equal hours in Greece in the
4th and 3rd cent.BC (I know it because I am a coauthor). The sundial of which
Fabio sent a picture is not in Berlin, but in Cairo.
Regards,
Karlheinz Schaldach
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Von: Fabio nonvedolora <fabio.sav...@nonvedolora.it>
An: sundial <sundial@uni-koeln.de>
Verschickt: Mi, 29 Jul 2015 11:02 am
Betreff: Re: Temporal Hours
Hi all,
I think the temporal hours some time are not temporal hours.
For example, when they converge in the center of a scaphen, or when they are
straight lines that radiate from the base of the style in a plane dial.
The sundials of the past with temporal hours sometime show these kind of
lines.
These psedo-temporal hours have different justifications. They were designed
so for ignorance in the Middle Age; to semplify their construction with a
neglectable and aware error in the Greek and Roman Age (these plane dials are
insensitive of latitude); probabily as the first system hours, not temporal,
in the most ancient time, when the first sundials were born, revolving the
meridian plane around an horizontal style N-S.
The horizontal lines, dawn and sunset, and the vertical one, the noon,
identify correctly their time, the other lines may be a first simply attempt,
instinctive and not calculated, to divide the day, not only with the start, the
middle and the end of the day.
I think this was an original time system, the first time system, not
temporal, worthy of a definition. Some years ago I proposed ‘vertical hours’
(on the italian magazine Gnomonica Italiana) from the name of the angles
between the meridian plane and the same plane revolved around the horizontal
N-S axes, the vertical angle defined by Ptolemy.
For example, you can see the recent finding of this Egyptian sundial (more
than 3000 years ago) www.sundialatlas.eu/atlas.php?so=EG9
or this reconstruction of an ancient portable Egyptian sundial, similar to a
temple (if I well remember the original is located in a museum of Berlin),
where the hour lines are the edge of the steps, simulating the scent and the
descent of the Sun
ciao Fabio
Fabio Savian
fabio.sav...@nonvedolora.it
www.nonvedolora.eu
Paderno Dugnano, Milano, Italy
45° 34' 10'' N, 9° 10' 9'' E, GMT+1 (DST +2)
From: Roger Bailey
Sent: Wednesday, July 29, 2015 5:58 AM
To: Michael Ossipoff
Cc: sundial list
Subject: Temporal Hours
Hi Michael and all,
Temporal or Antique hours co-existed with equal hours from way back,
thousands of years. It didn't take a technological device like a clock to
cause a change. A more interesting point is the portrayal of temporal hours,
12 unequal hours in the day on a flat sundial. It is easy on Greek/Roman
hemispheres but what about flat planar sundials. Is it sufficient to calculate
the points for the solstices and draw a straight line between them? This works
but is it right mathematically? To answer this question, Fred Sawyer gave an
excellent presentation on Antique Hours at the NASS Conference in 2010 in
Burlington. Was it really five years ago! Here is a clip of the abstract from
the NASS website.
"Antique Hour Lines: Fred Sawyer gave another excellent example of his
reviews of the history of complex mathematical concepts for sundials. In the
case of Antique Hour Lines, the question was “Are they straight lines?” For
millennia they were assumed to be, but the assumption was questioned by many
mathematicians. Proofs were offered by Ibrahim Ibn Sinan in the 10th century,
Christopher Clavius in the 16th, Hellingweth in the 18th and many including
Montucla, Delambre and Cadell in the 19th, offering proofs that the lines were
in fact curved. The various proofs tended to be empirical based on plotting the
results of individual calculation. Biot offered an analysis in 1841 and Davies
in 1843, but the problem was not fully solved until 1914 when Hugo Michnik
studied the curves for the equatorial sundial, providing a method to come up
with non-parametric equations for the curve for each hour. Fred then presented
the graphs of various hour lines at different latitudes and inclinations. The
curves were amazingly complex looking but the specific area of interest, where
a shadow would be projected was very close to the straight lines of the
traditional method."
This is why I belong to NASS, to read the Compendium and to go to the
conferences. Here we see solutions to problems we didn't even know existed.
Regards, Roger Bailey
From: Michael Ossipoff
Sent: Tuesday, July 28, 2015 4:47 PM
To: Dan Uza
Cc: sundial list
Subject: Re: Precision: the measure of all things
(I should clarify again that, for clarity, I like to capitalize _kinds_ of
whatever sort of thing I'm talking about...such as kinds of sundials or
hour-systems, though I realize that that capitalization is probably not
officially correct.)
Another closely-related interesting question is the matter of what _kind_ of
hours are used. Of course every book or article on sundials points out that,
before mechanical clocks became widespread, civil time was measured in
"Temporary Hours", which divided the day, from sunrise to sunset, into 12 equal
parts, and likewise divided the night, from sunset to sunrise, into 12 equal
parts.
Those books and articles nearly always imply or say that equal hours was a new
invention when it was adopted--that someone invented a new way to designate
time, and so it was adopted. Another frequent, and related, statement or
implication is that the Horizontal Dial was an innovation that was came into
use upon its invention because, before that, its possibility was there, but
just hadn't occurred to anyone.
But I read different. I read that Equal Hours were in use by astronomers and
astrologers long before they were adopted for civil time, and so they were
hardly a new invention at the time of their adoption for civil time.
In fact, look at a Hemispherium or Hemicyclium. Designed to read in Temporary
Hours, its hour-line, for a particular hour, crosses a different Equal-Hours
line, according to the declination. Whether those Temporary Hours were drawn
by calculation, or by empirical observation, it's plain that it would have
been obvious to the dial-maker that he was making the 3 p.m. hour-line cross
different Equal-Hours lines at different solar declinations.
One thing that I'm objecting to is that many of those books imply that
Temporary Hours are more primitive, and Equal Hours are something more
advanced that therefore, when invented, immediately replaced Temporary Hours.
Primitive? Rather, a lot more complicated and laborious to make. For sundials,
and likewise for water-clocks.
People should be impressed by the ingenuity and determination of early makers
of sundials and water-clocks, who devised Temporary Hours markings and
mechanisms for them.
As for the Horizontal Dial, of course it's for Equal Hours. That's what it's
convenient for. Sure, Flat Dials, including Horizontal Dials, and Polar Dials,
and Equatorial Dials, and others, could have likewise been made for Temporary
Hours, but they wouldn't have been easier to mark than a Hemicyclium. So it
isn't surprising if the Horizontal Dial came into use around the same time as
Equal Hours.
What I read was that, though Equal Hours were well known and used by
astronomers and astrologers, no one wanted them for civil timekeeping. Hence
the effort and ingenuity used to devise Temporary Hours sundials and
water-clocks.
But, when the mechanical clock was invented, and came into relatively wide use
(as tower-clocks, and in some homes), it was so much simpler to make clocks
for Equal Hours, that, as a result, Equal Hours replaced Temporary Hours, for
that reason of pure manufacturing-practicality.
(By the way, were the early mechanical clocks, the Folliet Balance
intertially-slowed clocks, without the fusee compensation, any more accurate
than water-clocks, which were much cheaper and easier to build?)
Temporary Hours surely made a lot of sense in agricultural societies, where it
must have been very important and practical for farmers to know what
percentage of the day remained. I don't advocate a return to Temporary Hours,
because, speaking for myself, it seems to me that finding what percentage of
the day is over, and how much or how little remains, seems a bit pessimistic,
and maybe not a good way to name the time of day. ...but I realize that it
had practical importance in agricultural societies.
Michael Ossipoff
On Mon, Jul 27, 2015 at 5:59 PM, Dan Uza <cerculdest...@gmail.com> wrote:
Hi everyone,
If you haven't already, you might want to check out the first part of the
documentary "Precision: the measure of all things". It's about the
measurement of time and length, featuring the topic of sundials. There's an
interesting theory about how the day got split into 12 hours because this
number is highly divisible (but why not 60?). I just watched it on Da Vinci
Learning.
Dan Uza
Romania
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