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 --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial -------------------------------------------------------------------------------- --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial -------------------------------------------------------------------------------- No virus found in this message. Checked by AVG - www.avg.com Version: 2015.0.6081 / Virus Database: 4392/10325 - Release Date: 07/28/15 -------------------------------------------------------------------------------- --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
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