The “Ai Khanum” dial that Rohr studied was on tour a few years ago along with various artifacts from Afghanistan and made a stop in Washington DC, the area where I live.
Perhaps the most interesting thing about the dial is not so much that it is cylindrical, but that it uses a polar orientation while being designed to tell unequal, or temporal. hour lines. I believe the polar orientation is virtually unique for ancient dials. Normally a polar orientation would generate equal hours, but the Ai Khanum sundial is inscribed with temporal hours, presumably because temporal hours were what people actually used and wanted. The other interesting thing about the dial is that it appears to be designed and built and oriented for the location where it was found, Ai Khanum in Afghanistan, but the inscribed temporal hour lines were calculated for a different latitude of approximately 23 degrees. This poses something of a mystery. I did a study of this dial, which was published in the NASS compendium, and is also at http://chezaubert.net/AiKhanum/AiKhanum.pdf. My own study drew heavily on Rohr’s paper, along with measurements taken from the original archeological report. I came to the admittedly very speculative conclusion that the 23 degree hour line layout was the result of a construction error stemming from confusing the two triangles that could have been used to specify all the angles needed to construct the dial. This led to further speculation that, absent standardized units of measure, Hellenic sundial calculation and construction techniques were probably specified by using triangles and ratios. Jack Aubert From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of nicolasever...@libero.it Sent: Wednesday, October 23, 2013 3:48 PM To: sundial@uni-koeln.de Subject: R: Re: Re: Shape of Greek and Roman sundials Dear Sasson, I think the accuracy to plot the hour lines on a cylindrical surface is more easy that a conical surface, but I not think that in the Roman era there was no need of the minutes of precision! In any case, sorry for your sentence " not a single cylindrical dial has been found.", because Sharon Gibbs described 6 or 7 cylindrical roman sundials and René J-R- Rohn written a famous paper about this topic in the 1980. His article you can read here: http://adsabs.harvard.edu/full/1980JRASC..74..271R The best wishes, Nicola ----Messaggio originale---- Da: saskauf...@gmail.com Data: 23/10/2013 18.57 A: "nicolasever...@libero.it"<nicolasever...@libero.it>, <sundial@uni-koeln.de> Ogg: Re: Re: Shape of Greek and Roman sundials Thanks, Nicola. Obviously, one can achieve accuracy if so desired on any surface, yet at least to my reckoning it would be more difficult. Am I mistaken about my assumption that with a cylindrical surface it's far easier to plot the lines and achieve accuracy? Because if I'm correct, I would have expected at least some cylindrical dials to surface, yet to the best of my knowledge (and from your comprehensive knowledge you'd surely be able to affirm or contradict this statement), not a single cylindrical dial has been found. I somehow dislike the notion that I'm smarter than all of the dial makers of the ancient world, especially, since some of them did manage to plot accurate lines on spheres and cones, proving that they were in fact quite smart. On Tue, Oct 22, 2013 at 11:47 PM, nicolasever...@libero.it <nicolasever...@libero.it> wrote: Dear Sasson, I think the precisione in the roman sundials depend from the ability of the marble workers. The greco-roman sundial in the attached images, from the Vatican Museum, probably shows that it is able to point out a precision approximately of the minute. Nicola ----Messaggio originale---- Da: saskauf...@gmail.com Data: 22/10/2013 21.52 A: "Schechner, Sara"<sche...@fas.harvard.edu>, <sundial@uni-koeln.de> Ogg: Re: Shape of Greek and Roman sundials Thanks for your reply, Sara. Although the dial in my previous message doesn't seem cylindrical, I can assure to you that it is. See the attached side-view of the dial taken from the TinkerCad file. If I understand correctly, you confirm my suspicion that the concave dials were not accurate to the minute, and furthermore, you claim they weren't meant to be. Some of the dials however show quite a high level of craftsmanship, and I therefore find it a bit surprising that those who invested painstaking efforts into their dials didn't strive towards accuracy, unless like you say, from their perspective it was more important to have the dials shaped like the heavens. Sasson On Tue, Oct 22, 2013 at 7:02 PM, Schechner, Sara <sche...@fas.harvard.edu> wrote: Dear Sasson, Your sundial looks pretty, but it does not seem cylindrical to me in the photo. As for your questions concerning the preference of the Greeks and Romans to concave spherical sundials, there are several answers: 1. The bowl mirrored the spherical shape of the heavens, and this was satisfying from a cosmological and philosophical standpoint. 2. Finding time to the hour was accurate enough for public lives, and indeed, many thought it was more of a bother to divide the day into twelve parts. Other cultural divisions of the day were also in use, and had names like, the time of the cock crowing. 3. It is a misconception to think that the Greeks and Romans strongly preferred concave sundials. Perhaps the most famous of Greek sundials is the Tower of the Winds in Athens. It has eight vertical sundials with pin gnomons. The most famous Roman sundial was likely the large horizontal azimuth dial in Rome which used an Egyptian obelisk for a gnomon. Romans also used altitude dials, including the pillar dial. Cheers, Sara Sara J. Schechner, Ph.D. David P. Wheatland Curator of the Collection of Historical Scientific Instruments Department of the History of Science, Harvard University Science Center 251c, 1 Oxford Street, Cambridge, MA 02138 Tel: 617-496-9542 | Fax: 617-496-5932 | sche...@fas.harvard.edu http://www.fas.harvard.edu/~hsdept/chsi.html From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Sasson Kaufman Sent: Tuesday, October 22, 2013 6:40 AM To: sundial@uni-koeln.de Subject: Shape of Greek and Roman sundials Hi. Greek and Roman sundials measured temporal time. They were generally spherical or conical, and, if I understand correctly, their surface was designed to provide a mirror image of the sun's paths in the sky throughout the different seasons. These paths, whether short or long, were then divided into twelve ostensibly equal parts. Yet this seems rather odd, since the sun's orbit remains at the same tilt (depending on altitude) throughout the year, only going back and forth, thus creating the shape of a tilted tunnel or cylinder. If the objective of the dial was to divide the day into equal hours, wouldn't it have been more appropriate for the surface of the dial to be that of the inner part of a cylinder? Shaping the surface as a sphere or cone would seemingly distort the shape of the sun's path projected on the surface and complicate the calculations for line plotting. This leads me to suspect that the ancient dials were of limited accuracy. With this question in mind, I recently created a portable dial (see the attached image) with a cylindrical surface tilted according to latitude, and so far, to the best of my reckoning, it's precise to about a minute. The dial was created using TinkerCad, and printed in 3d. Plotting the lines for my dial was fairly simple using paper. I created a 2d insert equal in shape to that of the cylinder surface, divided it into 12 equal-width parts, and glued it to the dial. I haven't found though the formula to do this in 3d. My questions- - Why did the Greeks and Romans prefer spheres and cones over cylinders which presumably would have been more accurate and simpler to plot the lines on? - Would anyone here have an idea how to plot the lines for my dial using a CAD program? Thanks in advance, Sasson Kaufman --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial -- This message has been scanned for viruses and dangerous content by <http://www.mailscanner.info/> MailScanner, and is believed to be clean. -- This message has been scanned for viruses and dangerous content by MailScanner, and is believed to be clean.
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