Re: Temporal hours to modern hours
That sounds like just a conversion between two ways of naming the equal-hours. ...converting between the.modern 12-hour naming, and a numbering that calls the hour from 6 a.m. to 7 a.m. the 1st hour. It doesn't take into account the different lengths of the hours, which depend on the varying length of the day, because the sunrise-sunset day is divided into 12 equal parts (as is the sunset-sunrise night). I don't agree with the term "temporal hours". The first book that I found that mentioned seasonal-hours called them "*temporary hours*". That name makes sense, because the length of an hour is temporary instead of constant, because it varies with the season. "Temporal hours" doesn't make sense, because all hours are temporal. "Temporal" just means "of, about or pertaining to time". Maybe a good term would be "seasonal-hours", because their length varies seasonally. One way to get temporary-hours is from Babylonian and co-Italian hours. Divide the Babylonian hour from the sum of the Babylonian hour and the co-Italian hour. Michael Ossipoff 19 Th (Thursday of the 19th week of the calendar-year that started with the Monday that started closest to the South-Solstice. ...or closest to the approximation to the South-Solstice, based on the assumption that a South-Solstice occurs exactly every 365.2422 days, starting from the actual South-Solstice of 2017). (The South-Sostice of 2017 occurred at December 21.686...where the time of day is expressed as a fraction of the day from midnight of that day.) ... On Thu, May 2, 2019 at 5:05 PM Dan-George Uza wrote: > Hello, > > In a note quoted below from the "Dictionary of Greek and Roman > Antiquities, John Murray, London, 1875" I found the following advice to > convert temporal hours to modern hours. > > *"A very quick and easy rule of thumb, when we read "the third hour, the > sixth hour", etc., is to add 3, 6, etc. to 5:00 A.M.: The first hour, for > example, runs from roughly 6 to roughly 7 A.M.; and the ninth hour from > roughly 2 to roughly 3 P.M."* > > Source: > http://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Hora.html > > Of course back then there was no summer time either... > > But is there a closer aproximation for this, perhaps using a simple > mathematical formula? Are there apps that can convert temporal hours > directly to modern equivalents, perhaps as a spreadsheet? > > Dan Uza > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Temporal hours to modern hours
Hello, In a note quoted below from the "Dictionary of Greek and Roman Antiquities, John Murray, London, 1875" I found the following advice to convert temporal hours to modern hours. *"A very quick and easy rule of thumb, when we read "the third hour, the sixth hour", etc., is to add 3, 6, etc. to 5:00 A.M.: The first hour, for example, runs from roughly 6 to roughly 7 A.M.; and the ninth hour from roughly 2 to roughly 3 P.M."* Source: http://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Hora.html Of course back then there was no summer time either... But is there a closer aproximation for this, perhaps using a simple mathematical formula? Are there apps that can convert temporal hours directly to modern equivalents, perhaps as a spreadsheet? Dan Uza --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Temporal Hours
Sasch, in the repository you may find an article on the database “sundials”. Via http://www.ancient-astronomy.org/en/2013/05/03/antike-sonnenuhren/ and “documents” you may get to other articles concerning the project. If you are looking for an article on the history of the early equinoctial dilas you will have to wait two months till it is published. K.--- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Temporal Hours
In the meanwhile there are at least 6 equatorial dials known from antiquity, some were made for temporal hours, some for equinoctial hours, some were done with a polar, some with a horizontal gnomon, all happened in the 4th or the 3rd cent. BC. You may have a look at the not yet completed digital archive of Greco-Roman sundials http://repository.edition-topoi.org/projektinfo.php?project=BSDP Karlheinz (hope my posting works now with the new email address) --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Temporal Hours
HI Roger, Thank you for sending the René Rohr reference. I wish I had had it when I was writing my article for the compendium, which on re-reading I find to be pretty incoherent. René Rohr’s version is more or less what I should have written up to the point where he explains the latitude mismatch. I think René Rohr (and others) are wrong about the dial having been correctly made for somewhere else and then moved. I have a copy of volume XXX of the archeological report on the excavation which covers the two sundials found at the site. The report also includes the speculation, repeated by others, that it was designed for India or Syene, even though the report notes that the dial is made from limestone similar to other carved items, such as pillars, found at the site. My own contribution to the Ai Khanum discussion is an admittedly speculative theory that the latitude mismatch could have resulted from a simple construction mistake. I start with the assumption that the astronomer or mathematician who designed the dial specifications would not be the person who would do the physical construction including stone cutting. I tried to imagine how one might go from a theoretical specification to actually marking lines out on a piece of stone at a time when most of the measuring tools and methods we might use did not exist or were not widely available. I concluded that the specification of the angles would likely have been stated in terms of ratios which would then have been realized by making right triangle templates to do the physical layout. All the measurements needed for the physical construction of this dial could have been specified by two triangles: one representing the earth’s obliquity and the other the local latitude. My hypothesis is that the obliquity triangle was mistakenly used in place of the latitude triangle. It is therefore not a random coincidence that the temporal lines which would be correct for a latitude of about 23.7 degrees is also the same as the earth’s obliquity at the time. But since my knowledge of paleo-mathematics is even weaker than my knowledge of stone-cutting techniques, I would be interested in the opinions of those who know more about the period whether my “right triangle theory” is plausible. As Karlheinz has already pointed out, the Arachne of the Amphiareion is, of course, equatorial and not horizontal as I originally said. Jack Aubert From: Roger Bailey [mailto:rtbai...@telus.net] Sent: Monday, August 03, 2015 8:13 PM To: Jack Aubert; sundial@uni-koeln.de; Sasch Stephens Subject: Re: Temporal Hours Hi Jack, While following a lead based on Sasch Stevens display at the conference, I came across an interesting article on the Al Khanum dial by Googling "Alexander the Great sundial". This search found this article: "A Unique Greek Sundial Recently Discovered in Central Asia" by Rene Rohr in 1980 in the JRASC. The article describes the work at Al Khanum by Paul Bernard. See http://adsabs.harvard.edu/full/1980JRASC..74..271R Their conclusion is the same as yours, the dial is a an equatorial with a polar gnomon but the lines show temporal hours rather that straightforward equal hours. Regards, Roger From: Jack Aubert <mailto:j...@chezaubert.net> Sent: Sunday, August 02, 2015 6:55 PM To: schalda...@aol.com ; rtbai...@telus.net ; email9648...@gmail.com ; sundial@uni-koeln.de Subject: RE: Temporal Hours 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 -- 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 s
Re: Temporal Hours
Hi Jack, While following a lead based on Sasch Stevens display at the conference, I came across an interesting article on the Al Khanum dial by Googling "Alexander the Great sundial". This search found this article: "A Unique Greek Sundial Recently Discovered in Central Asia" by Rene Rohr in 1980 in the JRASC. The article describes the work at Al Khanum by Paul Bernard. See http://adsabs.harvard.edu/full/1980JRASC..74..271R Their conclusion is the same as yours, the dial is a an equatorial with a polar gnomon but the lines show temporal hours rather that straightforward equal hours. Regards, Roger From: Jack Aubert Sent: Sunday, August 02, 2015 6:55 PM To: schalda...@aol.com ; rtbai...@telus.net ; email9648...@gmail.com ; sundial@uni-koeln.de Subject: RE: Temporal Hours 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 --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Temporal Hours
Interesting riff Kevin. It reminds me of an old B.C. cartoon where one caveman is showing the other the sundial he has made and asks, "Guess what I have invented here?" Then the other answers, "A race of neurotics." --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Temporal Hours
ing 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> > [mailto:schalda...@aol.com <mailto:schalda...@aol.com>] > Sent: Thursday, July 30, 2015 1:55 AM > To: rtbai...@telus.net <mailto:rtbai...@telus.net>; email9648...@gmail.com > <mailto:email9648...@gmail.com>; sundial@uni-koeln.de > <mailto: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 Ossipoff <mailto:email9648...@gmail.com> > 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 <mailto: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 l
RE: Temporal Hours
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 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 re
Re: Temporal Hours
Hi Roger-- Thanks for the info. You answered my question about the first known Horizontal, Polar-Gnomon Dial. On Thu, Jul 30, 2015 at 12:26 AM, Roger Bailey wrote: > . Meeting for lunch was no problem. > ...unless you're using a portable Altitude Dial. I've long felt that that's a big disadvantage of Altitude Dials--their inaccuracy around noon, just the time when people would make lunch appointments. Michael Ossipoff --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Temporal Hours
Hi Michael and all, I don't know the dominance of temporal hours or equal hours before mechanical or water clocks were in common usage. It is clear they co-existed. It is a significant research endeavor to determine the dominance and the reasons. Meeting for lunch was no problem. Dinner was more chancy; remember the verse of Cattulis, "Cenabis bene, mi Fabulle". Once the time and location were set, the important question remained "Who is bringing the duck". 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. 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 Ossipoff Sent: Wednesday, July 29, 2015 11:57 AM To: Roger Bailey ; sundial list 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 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 p
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 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 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. Ano
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
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, thou
RE: Temporal Hours and Refraction
Hello Noam, This is an appropriate question for this list. You would be amazed by the range of questions we consider in the name of sundials. Ask and you will receive a variety of answers from diverse and knowledgeable respondents. I can only offer opinions as I could not open your _javascript_. At least I was courageous enough to download the executable file from an "unknown" source. Here are my opinions based more on concepts than calculations. For normal sundials and uniform hours, refraction is minor effect. At most refraction is about 34' or half a degree as the sun sets. As one degree of time angle is 4 minutes of time. this may cause an error of a couple of minutes, no big deal for sundials. This is based on the the normal case when the gnomon is parallel to the polar axis and time is uniform. In your case of temporal (unequal or antique hours) and a vertical gnomon, the refraction error can be significantly greater. Increasing latitude and declination amplify the problem. This is because the angle of the setting sun (Phi) varies with latitude and declination. The math is Cos Phi = Sin Lat / Cos Dec. This explains why sunsets at fast in the tropics and go on forever at higher latitudes in the summer. The saying that time passes when you are having fun is a reality during tropical vacations. I gave a presentation on "Sunset Phenomenon" at the NASS conference in Hartford in 1999 and would be happy to provide the slides as a 425 kb pdf file. The presentation covers the equations for the time, location, path and rate of sunset. It does not specifically cover refraction but does discuss the "Green Flash". Temporal hours are unequal. The time from sunrise to sunset is always divided into 12 hours, no matter how long the day is. At higher latitudes and declinations the length of a temporal hour in the summer can be twice that of the winter. I am used to less than 8 equal hours in the summer and over 16 equal hours in the winter. We will not even consider the endless days and nights above the polar circles. The small difference for refraction has much more of an effect on unequal or temporal hours as the sun is just skimming the horizon at higher latitudes and declinations. Try some sample calculations using Fer De Vries ZW 2000 program* for local time and antique hours for different latitudes. The non linear nature of temporal hours is quite apparent. Regards, Roger Bailey Walking Shadow Designs N 48.6 W 123.4 *http://www.de-zonnewijzerkring.nl/eng/index-links.htm and click on downloads for ZW 200 -Original Message-From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]On Behalf Of Noam KaplanSent: September 23, 2004 3:30 PMTo: sundial@rrz.uni-koeln.deSubject: Can anyone answer this? If this is the wrong forum, I apologize. I have a calculation to figure out the atmospheric refraction from Fred Sawyer's article in the NASS Compendium. It is based on calculations that Meeus brings in his book. Refraction changes the apparent altitude of the sun, thereby changing both the apparent declination and apparent hour angle of the sun. Am I making a mistake when I use the apparent declination and apparent hour angle for the temporal hour calculation? The effect of a few seconds difference for atmospheric refraction on the hour angle seems to have a much bigger effect on the temporal hours. Thanks for any help you can offer, Noam My calculations can be seen on the web at http://www.riets.edu/stuff/suncalc/zman.js in the function temporal(localTime)
Re: temporal hours
The Roman hemispherical sundial indicated temporal hours using a set of curves. So does a vertical shepherd's dial, which is rotated to the current date. See Eric Bruton's "History of Clocks and Watches." Gordon You wrote: >Now, if the sundial was used to determine the length of the hour, how were >they marked? If the sundial was used as the midday marker only (a noon >dial) as you suggest, then perhaps they used some form of computed tables? > >Curious, > >A r t h u r V a l a i s > >[EMAIL PROTECTED] > >phone 02 9360 1729 >PO BOX 729 >Kensington NSW 2033 >Sydney Australia -- | XII | Gordon T. Uber, 3790 El Camino Real, Suite 142 |XI| Palo Alto, CA 94306-3314, email: [EMAIL PROTECTED] | X \ /| CLOCKS and TIME: http://www.ubr.com/clocks/ | IX \ / | Reynen & Uber WebDesign: http://www.ubr.com/rey&ubr
Re: temporal hours
>Shouldn't this be accurate enough for the people so many centuries ago? >Indeed the people could read the sundial if they needed the time more >precize, but I think they didn't care about minutes or seconds as we do. > >Fer de Vries >Netherlands. Hi! Thanks for replying. You're probably right about the vast majority of people at the time, however I was thinking more about the early clocks and time-keepers. I was under the impression that early clockwork which rapidly became fast or slow were synchronized with a sundial (the standard measure of time). And I've also heard that temporal hours being the norm, medieval clocks were periodically (weekly?) adjusted through the foliot and verge mechanism to beat faster or slower to give twelve hours to the available daylight. Since this was a hassle, canonical hours became popular and the amount of hours in the day began to vary. Now, if the sundial was used to determine the length of the hour, how were they marked? If the sundial was used as the midday marker only (a noon dial) as you suggest, then perhaps they used some form of computed tables? Curious, AV -- scribere qui nescit nullam putat esse laborem whoso knows not how to write thinks it to be no trouble -- A r t h u r V a l a i s [EMAIL PROTECTED] phone 02 9360 1729 PO BOX 729 Kensington NSW 2033 Sydney Australia --
Re: temporal hours
Valais wrote: > > Hi all! > > I've just recently joined the list. Probably just a simple question: In > times past, people measured the time through temporal hours, ie. the amount > of daylight was divided into twelve equal parts, and so the hour varied > throughout the year. Now, how was this hour-length measured? If a sundial > was used, was each hour marked on each "day-line" and found with the nodus > (assuming a horizontal dial)? As far as I can see the main problem is that > the first hour for each day begins slightly earlier or later and so shifts > the hour lines out again (ie. a zero-error _and_ an expansion error if you > like). > > Thanks in advance, > > AV > > -- > > scribere qui nescit nullam putat esse laborem > > whoso knows not how to write thinks it to be no trouble > > -- > > A r t h u r V a l a i s > > [EMAIL PROTECTED] > > phone 02 9360 1729 > PO BOX 729 > Kensington NSW 2033 > Sydney Australia > > -- Hi Arthur, Some thoughts about the antique hours or temporal hours. Every day the sun rises and at that time the first hour begins and the "clock" automaticly is set to the right time. And if the sun sets the 12th hour ends. Just simple. And at the time the sun reaches its highest point, due south ( or north) the 6th hour ends and the 7th starts. Shouldn't this be accurate enough for the people so many centuries ago? Indeed the people could read the sundial if they needed the time more precize, but I think they didn't care about minutes or seconds as we do. Fer de Vries Netherlands.
temporal hours
Hi all! I've just recently joined the list. Probably just a simple question: In times past, people measured the time through temporal hours, ie. the amount of daylight was divided into twelve equal parts, and so the hour varied throughout the year. Now, how was this hour-length measured? If a sundial was used, was each hour marked on each "day-line" and found with the nodus (assuming a horizontal dial)? As far as I can see the main problem is that the first hour for each day begins slightly earlier or later and so shifts the hour lines out again (ie. a zero-error _and_ an expansion error if you like). Thanks in advance, AV -- scribere qui nescit nullam putat esse laborem whoso knows not how to write thinks it to be no trouble -- A r t h u r V a l a i s [EMAIL PROTECTED] phone 02 9360 1729 PO BOX 729 Kensington NSW 2033 Sydney Australia --
