I assume that you are referring to the Arachne of the Amphiareion. I have a photocopy of your article on that dial, which was reconstructed from fragments, describing a (very old) horizontal dial with equal hours.
Another atypical dial: The Ai Khanum dial found in the ruins of Alexandria on the Oxus (in modern Afghanistan) that dates from approximately 145 BC is an example of a polar-oriented gnomon with unequal hours. This dial is interesting for several reasons, in particular the fact that while it “naturally” told equal hours using the line-shadow of the gnomon, the constructor carefully incised lines to read unequal hours using the gnomon tip. (It was done incorrectly for its latitude, but that’s another story.) However, both these dials are quite exceptional. My general impression from what I have been able to read is that equal hours were used by astronomers and astrologers. While there is at least one example of a horizontal dial that uses equal hours and at least one example of a polar gnomon using temporal hours, people generally wanted their time in temporal hours so the vast majority of surviving dials prior to the Ibn al-Shatir dial used temporal hours. Jack Aubert From: schalda...@aol.com [mailto:schalda...@aol.com] Sent: Thursday, July 30, 2015 1:55 AM To: rtbai...@telus.net; email9648...@gmail.com; sundial@uni-koeln.de Subject: Re: Temporal Hours Greek and Roman dials were not horizontal or vertical flat planar dials, but hemispheres, scafes or other projections of the sky onto a spherical or conical surface. Planar dials came with the Islamic dials. Only a short note:This is not true. The first Greek dials were plane equatorial dials with equal hours. Karlheinz The first planar dial with a polar gnomon was by Ibn al-Shatir in Damascus in 1371. This dial had temporal hours, equal hours based on noon, sunrise and sunset, and Islamic prayer times, including reference lines to prayer times when the sun was well below the horizon. For me this dial is the epitome of sundials. It includes all the time systems in vogue at that time and for hundreds of years before and after. They all existed and were in common usage suited for different purposes. The question remains "Who is bringing the duck" for dinner. Time is important. Don't overcook it. Regards, Roger Bailey Michael <mailto:email9648...@gmail.com> Ossipoff Sent: Wednesday, July 29, 2015 11:57 AM To: Roger Bailey <mailto:rtbai...@telus.net> ; sundial list <mailto:sundial@uni-koeln.de> Subject: Re: Temporal Hours Roger, thanks for the answer. Ok, I shouldn't say that as a fact without having more information than I do. This is what I was implying or saying, without really having much support for it: "In Europe and the fertile-crescent region, in ancient, classical and medieval times, before mechanical clocks (starting with Folliet-balance clocks) came into wide use, Equal Hours were of interest, for the most part, only to astronomers and astrologers. For ordinary civil timekeeping, for arranging meetings, keeping schedules or other civil/social purposes, Temporary Hours were preferred by pretty much everyone." Were a fair percentage of people making their appointments and schedules by Equal Hours in the times and places named in the above paragraph? I'm not being argumentative--I really don't know. ---------------------------------- Thanks for reminding me about Temporary Hours lines on Flat Dials being satisfactorily approximated by straight lines. I'd temporarily (no pun intended) forgotten that. It was a question that I'd asked, and received an answer to, when I first wrote to NASS. Were Flat-Dials (for Temporary or Equal Hours) in use before mechanical clocks were getting popular? What about _wide_ use? How early? ------------------------------------- Can anyone explain why the early, inaccurate inertia-controlled Folliet-Balance clocks replaced the cheaper, more easily-made water-clocks? Were those earliest, most inaccurate mechanical clocks significantly, or any, more accurate than water-clocks? Michael Ossipoff On Tue, Jul 28, 2015 at 11:58 PM, Roger Bailey <rtbai...@telus.net> wrote: 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 <mailto:email9648...@gmail.com> Ossipoff Sent: Tuesday, July 28, 2015 4:47 PM To: Dan Uza <mailto:cerculdest...@gmail.com> Cc: sundial list <mailto:sundial@uni-koeln.de> 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 No virus found in this message. Checked by AVG - www.avg.com Version: 2015.0.6081 / Virus Database: 4392/10332 - Release Date: 07/29/15 --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial -- This message has been scanned for viruses and dangerous content by MailScanner, and is believed to be clean.
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