Re: equal and unequal hours
Dear Frank, > Mixed in with the discussion ... was a question > ... about when the use of equal hours by the > Romans began. You are quite right that, in astronomical matters, equal hours were used in antiquity. As you say: > Little doubt that the refined values quoted by > these ancient fellows refer to equal hours. Equal hours were not, though, used for governing ordinary life. As Gianni Ferrari says: For what I know the equal hours were never used in western classical antiquity by the common people and they were used only from astronomers and scholars in their calculations of the durations of periods of time (Ptolemy, etc.) The only system of hours used was that of the temporary or seasonal hours: 12 hours from dawn to sunset (period of light) and 12 hours from sunset to dawn (night). This system of temporary hours persisted for a considerable time but my historical knowledge is very limited. No doubt the transition to equal hours (whether starting at noon, midnight, sunrise or sunset) was gradual but I feel it long predates mechanical clocks. Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Frank (King), Frank King wrote: > No doubt the transition to equal hours (whether > starting at noon, midnight, sunrise or sunset) > was gradual but I feel it long predates mechanical > clocks. Do you have any evidence supporting your feeling? I have studied the question when the pole-style sundial, reading equal hours, appeared in the Western world. Zinner appeared to be the most important reviewer of the few written primary sources. My conclusion was that the pole-style dial appeared around 1400, hence a century or so AFTER the introduction of mechanical clocks. I have written an article about this (in Dutch ;-) for the Dutch and Flemish bulletins in 2004. It has been suggested that the pole-style dial (and hence equal hours) was brought to the West by returning crusaders. Karlheinz Schaldach gave convincing arguments against this in BSS Bulletin 96.3. Best regards, Frans Maes --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Frans, You ask a very perceptive question: > > No doubt the transition to equal hours (whether > > starting at noon, midnight, sunrise or sunset) > > was gradual but I feel it long predates mechanical > > clocks. > Do you have any evidence supporting your feeling? No! I had heard (from you and others) that the polar-oriented gnomon was a much later development than one might guess, sometime around or after 1400 as you say. Also... I knew there were mechanical clocks at that time but I had frogotten that clocks had been around for a century or so by then. You are almost suggesting (perhaps you are actually suggesting) that the development of the polar-oriented gnomon was a consequence of the development of mechanical clocks. A polar-oriented gnomon is not, of course, essential for indicating equal hours. Indeed, Italian Hours are (almost) equal hours but you do not indicate Italian Hours with a polar-oriented gnomon. My thought (my feeling!) was that Gianni or someone else could suggest that sundials showing Italian Hours were around before clocks. His answer is clear: > The equal hours started to be used after the advent > of the tower clocks... This suggests that the advent of tower clocks was seminal to the popular use of equal hours and, I assume, this applies to ANY kind of equal hours system, whether the day started at sunset, sunrise, noon or midnight. Given the late development of the polar-oriented gnomon I had assumed that equal hours sundials starting at noon or midnight were around before the introduction of the polar-oriented gnomon. Is this a false assumption? You say: > It has been suggested that the pole-style dial > (and hence equal hours)... I wonder about the use of the word "hence"? You don't need a polar-oriented gnomon to indicate equal hours (starting at noon or midnight) although it certainly helps. I am in danger of going wildly astray! Maybe you could confirm (or refute) the suggestion that there were sundials that showed equal hours starting at noon or midnight before the advent of the polar-oriented gnonom? I promise not to challenge your answer :-) Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Frank, Frank King wrote: > You don't need a polar-oriented gnomon to > indicate equal hours (starting at noon or > midnight) although it certainly helps. > The way I view the transition from temporary to equal hours follows Zinner's reasoning. The usual medieval sundial was vertical and semi-circular, with 12 (equally spaced) temporal hour lines. A perpendicular gnomon was inserted into the center, where all lines intersect. How to adapt this lay-out to the equal hours of clocks? Zinner imagines that people have been experimenting with bending the gnomon and/or slightly rotating the hour lines to or away from the meridian, until success. One could have attained the same result by moving the gnomon down (until its tip would fall on the imaginary pole-style arising from the center), but that would have required a more difficult mental step. Of course this reasoning applies only to 'anchored' equal hours, which start from a fixed time point in the day, such as noon or midnight. I would not dare to speculate on how sundials for Italian (or Babylonian) hours evolved. When did such dials emerge? Do you know, Gianni? Best regards, Frans Maes --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Frank King scripsit: Equal hours were not, though, used for governing ordinary life. As Gianni Ferrari says: For what I know the equal hours were never used in western classical antiquity by the common people and they were used only from astronomers and scholars in their calculations of the durations of periods of time (Ptolemy, etc.) The only system of hours used was that of the temporary or seasonal hours: 12 hours from dawn to sunset (period of light) and 12 hours from sunset to dawn (night). Do you have a reference (source) for this quote? (not doubting you, but I may want to reference it in some articles I'm writing) Keith -- Col Keith E. Brandt, MD, MPH USAF-NASA Aerospace Medicine Liaison Officer Johnson Space Center, Houston, Texas [EMAIL PROTECTED] Goodbye cruel world that was my home- there's cleaner space out here to roam Put my feet up on the moons of Mars- sit back, relax, and count the stars *This message transmitted with 100% recycled electrons --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Let's go back to Damascus for a less euro-centric perspective on this question. In a previous discussion Gianni reported his research and conclusions on the introduction of the polar gnomon. He attributed it to Ibn Al-Shatir and the sundial at the Great Umayyad Mosque in Damascus in 1371. Ibn Al-Shatir also introduced a sundial compendium, a small universal polar sundial that incorporated a magnetic compass for orientation. Al-Shatir was a genius in math and astronomy who made many contributions to science but what was his day job. He was the timekeeper "muwaqqits" at the Mosque responsible for setting the times to pray. In that role he was responsible for the other amazing timepiece at the mosque, the mechanical clock. This ancient water clock kept equal hours striking at each hour. The sundial and clock complemented each other to give accurate time with equal hours. See http://www.muslimheritage.com/topics/default.cfm?ArticleID=685 for one reference to the clock. See http://en.wikipedia.org/wiki/Ibn_al-Shatir for references to Ibn Al-Shatir. Regards, Roger Bailey - Original Message - From: "Frans W. Maes" <[EMAIL PROTECTED]> To: "Frank King" <[EMAIL PROTECTED]> Cc: "Sundial" <[EMAIL PROTECTED]> Sent: Friday, August 22, 2008 12:46 AM Subject: Re: equal and unequal hours > > Dear Frank (King), > > Frank King wrote: > >> No doubt the transition to equal hours (whether >> starting at noon, midnight, sunrise or sunset) >> was gradual but I feel it long predates mechanical >> clocks. > > Do you have any evidence supporting your feeling? > > I have studied the question when the pole-style sundial, reading equal > hours, appeared in the Western world. Zinner appeared to be the most > important reviewer of the few written primary sources. My conclusion was > that the pole-style dial appeared around 1400, hence a century or so > AFTER the introduction of mechanical clocks. > I have written an article about this (in Dutch ;-) for the Dutch and > Flemish bulletins in 2004. > > It has been suggested that the pole-style dial (and hence equal hours) > was brought to the West by returning crusaders. Karlheinz Schaldach gave > convincing arguments against this in BSS Bulletin 96.3. > > Best regards, > Frans Maes > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > > No virus found in this incoming message. > Checked by AVG - http://www.avg.com > Version: 8.0.138 / Virus Database: 270.6.6/1627 - Release Date: 22/08/2008 > 6:48 AM > > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Frans, Like Gianni, you produce splendid scholarly input to this list! I promised not to challenge your answer so I will constrain this reply accordingly! You have made me think about Zinner's imagination... If you have a medieval sundial such as you describe [a vertical dial, assumed direct south-facing, and a horizontal gnomon] AND a clock (no matter how bad) there will be a natural temptation to compare the clock and the sundial. If you choose noon as your start-of-day, then you can set the clock each day at the moment of transit (vertical shadow) and then mark the position of the tip of the shadow of your gnomon at hourly intervals (as timed by the clock) from noon. If you keep this up for six months, then you will see that the marks for a given hour join up in a straight line. Moreover, the set of straight lines all intersect at a point some way above the foot of the gnomon. Then one night, someone looks up at the dial and notices that the line from the tip of the gnomon to the magic point is at an angle to the horizontal that corresponds to the altitude of Polaris. Wow! This way you get to invent the polar-oriented gnomon. :-) Now, if you choose sunRISE as your start of day, you set the clock at sunrise and you can again mark the position of the tip of the shadow at hourly intervals. Again you get straight lines but they don't intersect at a common point. You don't get to invent the polar-oriented gnomon but you do get to invent a Babylonian hours sundial. If you choose sunSET as your start of day then you can do the same thing but you will have to wait until daylight before you can mark the positions. The early clocks would have drifted during the night so it would be more difficult to notice the straight lines but not impossible. For completeness I could note that (accurately laid out) temporary hour lines are not (quite) straight (because they are not projections of great circles). They DO intersect at the sub-nodus point but only because they curve towards that point. The straight sections of temporary hour lines approximately intersect at a point a little above the sub-nodus point. I assume that it is this higher point that was used for the medieval gnomon? This is already suggesting a reason for bending the gnomon downwards. Zinner could be right! As you can tell, I am very weak on the history side of this business :-( Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Sundial List, Just for completeness, there is a discussion of the possible use of equal hours in Egypt in about 1300 BCE in Marshall Clagett's source book "Ancient Egyptian Science" Volume II, "Calendars, Clocks, and Astronomy" 1995, pp. 98-106, in the section "Traces of a 24-hour day with Equal Hours." He concludes that the values came from a "poorly computed and badly copied text." I doubt that many on this list will find it worth pursuing. Back then hours were determined either from star/constellation/decan risings or transits, from water clocks, or from early sundials and shadow clocks. Gordon Uber San Diego --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Hello Keith, perhaps you may find some news here http://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Dies.html Best wishes Gianni 2008/8/22 Keith E. Brandt, WD9GET <[EMAIL PROTECTED]> > Frank King scripsit: > > Equal hours were not, though, used for governing > ordinary life. As Gianni Ferrari says: > > For what I know the equal hours were never used > in western classical antiquity by the common > people and they were used only from astronomers > and scholars in their calculations of the > durations of periods of time (Ptolemy, etc.) > > The only system of hours used was that of the > temporary or seasonal hours: 12 hours from dawn > to sunset (period of light) and 12 hours from > sunset to dawn (night). > > > > Do you have a reference (source) for this quote? (not doubting you, but I > may want to reference it in some articles I'm writing) > > Keith > > -- > > Col Keith E. Brandt, MD, MPH > USAF-NASA Aerospace Medicine Liaison Officer > Johnson Space Center, Houston, Texas > [EMAIL PROTECTED] > > Goodbye cruel world that was my home- > there's cleaner space out here to roam > Put my feet up on the moons of Mars- > sit back, relax, and count the stars > > **This message transmitted with 100% recycled electrons > > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > > -- Gianni Ferrari Mail to : [EMAIL PROTECTED] --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Frank, Maes and other friends, The question about the introduction of use of the polar gnomon is old. Actually, are very few the informations about this. Rohr wrote in his book that the polar gnomon was introduced in Europe with the Crusaders returning from the arabian country. I also think that the polar gnomon was re-invented in Europe from the Arabian astronomical science. Sure the mechanical tower clock with the equal hours was a good reason for the use of polar gnomon in the equal hours sundials, but I have some dubt about the importance of this "only one" reason. It is true that the first mechanical clocks was on the towers around the begin of the 1300. And the first vertical sundials with the polar gnomon was done arond the first half of 1300. The interesting articles of Curt Roslund in the BSS Bulletin, september 2005, pag. 116-119, show the vertical sundial of Braunschweig Cathedral of 1346 with the equal hour lines and a polar gnomon. A have find recently a important gnomonical manuscript attribuited to the end of 1300 with drawings of horizontal and vertical (also east and west plane) sundials with the equal hours line. But this is a new topic for a my next articles. Hence, we have the sources that the equal hours line on the horizontal and vertical sundials with an probable polar gnomon was used in the Europe at the end of 1300. Thanks for attention and the best wishes to all Nicola Severino --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Google quickly finds pictures and information on the Braunschweig Cathedral sundial. http://commons.wikimedia.org/wiki/Image:Braunschweig,_Dom_St._Blasii_mit_Sonnenuhr.jpg The pictures show a dial with the words Anno 1716 across the top. A text reference identifies "Hans Geog Hartel" with the sundial is 1659. http://historydb.adlerplanetarium.org/signatures/edit.pl?edit_id=6954 Is there an earlier sundial dating back to 1346 with the same characteristics, polar gnomon and equal hours? Can any of you scan Carl Roslund's BSS article and email me a copy? Regards, Roger - Original Message - From: <[EMAIL PROTECTED]> To: "Frank.King" <[EMAIL PROTECTED]> Cc: "sundial" <[EMAIL PROTECTED]> Sent: Saturday, August 23, 2008 8:54 AM Subject: Re: equal and unequal hours > > Dear Frank, Maes and other friends, > > The question about the introduction of use of the polar gnomon is old. > Actually, are very few the informations about this. Rohr wrote in his book > that the polar gnomon was introduced in Europe with the Crusaders > returning from the arabian country. I also think that the polar gnomon was > re-invented in Europe from the Arabian astronomical science. > > Sure the mechanical tower clock with the equal hours was a good reason for > the use of polar gnomon in the equal hours sundials, but I have some dubt > about the importance of this "only one" reason. > > It is true that the first mechanical clocks was on the towers around the > begin of the 1300. And the first vertical sundials with the polar gnomon > was done arond the first half of 1300. > The interesting articles of Curt Roslund in the BSS Bulletin, september > 2005, pag. 116-119, show the vertical sundial of Braunschweig Cathedral of > 1346 with the equal hour lines and a polar gnomon. > > A have find recently a important gnomonical manuscript attribuited to the > end of 1300 with drawings of horizontal and vertical (also east and west > plane) sundials with the equal hours line. But this is a new topic for a > my next articles. > > Hence, we have the sources that the equal hours line on the horizontal and > vertical sundials with an probable polar gnomon was used in the Europe at > the end of 1300. > > Thanks for attention and the best wishes to all > > Nicola Severino > > > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > > No virus found in this incoming message. > Checked by AVG - http://www.avg.com > Version: 8.0.138 / Virus Database: 270.6.7/1629 - Release Date: 23/08/2008 > 1:16 PM > > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Yuo can find a better picture on http://de.wikipedia.org/wiki/ Bild:Braunschweiger_Dom_kleine_Sonnnenuhr.JPG Willy LEENDERS Hasselt in Flanders (Belgium) www.wijzerweb.be Op 23-aug-08, om 19:35 heeft Roger Bailey het volgende geschreven: Google quickly finds pictures and information on the Braunschweig Cathedral sundial. http://commons.wikimedia.org/wiki/ Image:Braunschweig,_Dom_St._Blasii_mit_Sonnenuhr.jpg The pictures show a dial with the words Anno 1716 across the top. A text reference identifies "Hans Geog Hartel" with the sundial is 1659. http://historydb.adlerplanetarium.org/signatures/edit.pl?edit_id=6954 Is there an earlier sundial dating back to 1346 with the same characteristics, polar gnomon and equal hours? Can any of you scan Carl Roslund's BSS article and email me a copy? Regards, Roger - Original Message - From: <[EMAIL PROTECTED]> To: "Frank.King" <[EMAIL PROTECTED]> Cc: "sundial" <[EMAIL PROTECTED]> Sent: Saturday, August 23, 2008 8:54 AM Subject: Re: equal and unequal hours Dear Frank, Maes and other friends, The question about the introduction of use of the polar gnomon is old. Actually, are very few the informations about this. Rohr wrote in his book that the polar gnomon was introduced in Europe with the Crusaders returning from the arabian country. I also think that the polar gnomon was re-invented in Europe from the Arabian astronomical science. Sure the mechanical tower clock with the equal hours was a good reason for the use of polar gnomon in the equal hours sundials, but I have some dubt about the importance of this "only one" reason. It is true that the first mechanical clocks was on the towers around the begin of the 1300. And the first vertical sundials with the polar gnomon was done arond the first half of 1300. The interesting articles of Curt Roslund in the BSS Bulletin, september 2005, pag. 116-119, show the vertical sundial of Braunschweig Cathedral of 1346 with the equal hour lines and a polar gnomon. A have find recently a important gnomonical manuscript attribuited to the end of 1300 with drawings of horizontal and vertical (also east and west plane) sundials with the equal hours line. But this is a new topic for a my next articles. Hence, we have the sources that the equal hours line on the horizontal and vertical sundials with an probable polar gnomon was used in the Europe at the end of 1300. Thanks for attention and the best wishes to all Nicola Severino --- https://lists.uni-koeln.de/mailman/listinfo/sundial No virus found in this incoming message. Checked by AVG - http://www.avg.com Version: 8.0.138 / Virus Database: 270.6.7/1629 - Release Date: 23/08/2008 1:16 PM --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Roger, Yes, it is easy to get the "wrong" sundial when looking at Braunschweig Cathedral!! The bigger (17th century?) dial has recently been restored and I have in front of me a newspaper cutting which explains: Die Kosten von rund 700,000 Euro werden von der Dombaustiftung und von privaten Spendern getragen. This seems slightly expensive to me!! This Cathedral must have a large building fund and many wealthy patrons. Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear all, The DGC catalog mentions 4 sundials on the Braunschweig cathedral. The discussion does not refer to the 'new' ones from 1518 and 1715, but to two older ones, from about 1334 and about 1346. The hour line patterns (attached) show two ways of playing around with the lines, in the trial-and-error process that took place according to Zinner. Roger, I will send you a pdf with the last three pages of Karlheinz' BSS article (2.7 MB). I think they comprise the relevant part for this discussion. Roger Bailey wrote: Google quickly finds pictures and information on the Braunschweig Cathedral sundial. http://commons.wikimedia.org/wiki/Image:Braunschweig,_Dom_St._Blasii_mit_Sonnenuhr.jpg The pictures show a dial with the words Anno 1716 across the top. A text reference identifies "Hans Geog Hartel" with the sundial is 1659. http://historydb.adlerplanetarium.org/signatures/edit.pl?edit_id=6954 Is there an earlier sundial dating back to 1346 with the same characteristics, polar gnomon and equal hours? Can any of you scan Carl Roslund's BSS article and email me a copy? Regards, Roger <>--- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Willi and Roger, that sundial is not the one that Severino means. It is older. Mario - Mario Arnaldi Via Cavour, 57/c 48100 Ravenna Italy Lat. 44° 25' N - Lon. 12° 12' E Redazione di "GNOMONICA ITALIANA" rivista di storia, arte, cultura e tecniche degli orologi solari ID Yahoo Messenger: "mcardal" ID MSN Messenger: "[EMAIL PROTECTED] ID Skype: "mcardal" https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Frank King scripsit: Equal hours were not, though, used for governing ordinary life. - This is not quite right. Equal hours were not used from common people in their ordinary life, but used for civil porpouses. Censorinus and Gellius citing Varro say that in Rome the day was intended in 2 ways: natural and civil. Natural was the common day with 12 hours starting from sunrise and ending at sunset (other 12 hours for night from sunset to sunrise), wether the day was long or schort. Civil day was the complete period of day and night divided in 24 equal hours starting to compute at midnight. This was the civil roman day. But was used for civic meanings by lawyers and all those people involved in laws. because, it is written, lawyers must know the exat day of the birth of a man for marriage or for inheritances etc. people born before midnight, was born the day before and people born after midnight was born the day after. This was important to know exactly the age of one, and so establishing all the rights or duty by law. Also astronomer used the equal hours for the reason that Gianni sayd, but surely a lot of time before Ptolemy. It is known for example that the double hours of Babylon (Beru) were equal hours. Equal hours were measured with wather clocks. Mario - Mario Arnaldi Via Cavour, 57/c 48100 Ravenna Italy Lat. 44° 25' N - Lon. 12° 12' E Redazione di "GNOMONICA ITALIANA" rivista di storia, arte, cultura e tecniche degli orologi solari ID Yahoo Messenger: "mcardal" ID MSN Messenger: "[EMAIL PROTECTED] ID Skype: "mcardal" https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear all, [EMAIL PROTECTED] wrote: > > It is true that the first mechanical clocks was on the towers around > the begin of the 1300. And the first vertical sundials with the polar > gnomon was done arond the first half of 1300. The interesting > articles of Curt Roslund in the BSS Bulletin, september 2005, pag. > 116-119, show the vertical sundial of Braunschweig Cathedral of 1346 > with the equal hour lines and a polar gnomon. The 1346 dial now has a polar gnomon. As recent as 1964 there was no gnomon, merely a large hole (Zinner). It is not known, how the original gnomon was oriented. In my view, it is unlikely that it was a pole-style. The angles were laid out according to the 'Erfurt formula', as Zinner and Roslund point out. This rule does not say anything about the orientation of the gnomon. If it was intended to be pointing at the celestial pole, the formula would most probably have provided accurate instructions for that. To answer Roger's question: The dates of the 1334 and 1346 dials were deduced from the building history of the cathedral, assuming that they were laid out at the time of completion of the particular buttresses. Regards, Frans Maes --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Frank, the problem of equal or unequal hours, I left it out of the article but commented it only in my book on the Greek sundials. The reason is that the winter side of the Oropos dial looks as if made for equal hours and the summer side as if made for unequal hours. Strange thing! You have shown by the dotted lines in your drawing which gives the situation rather exactly that equal nd unequal hour lines do not differ very much. Sometimes we want to see things that are not intended, sometimes we do not want to see things because they cannot be. Who knows? Therefore my opinion is: they hour lines on the winter side could be equal hour lines. Hope, this answer your questions, best wishes Karlheinz -Ursprüngliche Mitteilung- Von: Frank King <[EMAIL PROTECTED]> An: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Verschickt: So., 24. Aug. 2008, 13:45 Thema: Re: Fwd: equal and unequal hours Dear Karlheinz, I have now read your article more carefully. It is excellent, one of the most interesting rticles I have read for a long time! I think now understand your comment... > ...you see that the winter circle is not divided in 12 parts as it should be for unequal hours. I misinterpreted this when I first read it. The winter circle IS divided into 12 parts ut the WAY it is divided is not as it hould be for unequal hours. Is that right? I attach a PDF showing the winter side of n equatorial sundial at latitude 40 degrees.0DThe two circles are for declinations of -24 degrees the value you used for the winter solstice) and or -2.5 degrees which has no special significance. I have drawn two sets of hour lines: 1. The solid lines are temporary hour lines which I have taken all the way to the horizon line by letting the declination run down to -50 degrees. This cannot really happen of course but it emphasises your point: "Strictly, the lines are curves..." 2. The dashed lines are (modern) equal hour lines which are at 15-degree intervals. Importantly, the equal hour lines radiate from the ittle black circle which (on the winter side) is BOVE the horizon line. It is, of course, where he polar axis through the nodus intersects the lane of the dial. It corresponds to your point W in Fig. 6. The temporary hour lines do not really *radiate* from point but they do *converge* to a point, your FW in ig. 6. There is one remaining puzzle. You say: Strictly, the lines are curves, but they diverge only slightly from the rectilinear, and so we may take them as straight lines... [Here you are talking about temporary hour lines and, of course, I agree.] ... This being so, the hour lines on our dial show a high degree of precision. This last sentence suggests that the hour lines on the ial are *temporary* hour lines. I don't understand :-( The lines in your Fig. 3 look very much like the dashe d ines in my PDF. They appear to radiate from a point BOVE the horizon line. Surely, these lines are *equal* our lines? Have I misinterpreted your sentence that begins: "This eing so..."? I am sorry to be so slow at understanding!! Best wishes Frank --- ttps://lists.uni-koeln.de/mailman/listinfo/sundial AOL eMail auf Ihrem Handy! Ab sofort können Sie auch unterwegs Ihre AOL email abrufen. Registrieren Sie sich jetzt kostenlos. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Mario, Many thanks for your kind explanation... > Censorinus and Gellius citing Varro say that > in Rome the day was intended in two ways: natural > and civil. I am slowly gaining some understanding of time in ancient Rome. Gianni Ferrari has pointed us at: http://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Dies.html This confirms what you say and refers to: dies naturalis and dies civilis Can you tell me how the common people knew what the time was? If the Circus Maximus announced a good chariot race next Friday, or the Colosseum announced a big fight next Saturday, how would people arrive at the right time? Did a Praeter go through the streets ringing a bell? Were there public klepshydras? Were there sundials on many buildings? It is hard to understand how a big city could work unless the citizens knew the time! Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Sorry, I think that my poor English made me misunderstood. When I wrote «Dear Willi and Roger, that sundial is not the one that Severino means. It is older.» I actually mean that Severino was speaking about other two sundials on the dome, older that the one shown in the photographs that you got in Internet». Mario --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Mario Catamo has suggested me that very probably the term "Italic" (in Italic hours) comes from the Latin word "Italicus" (that means "Italian"), that the word "Italianus" doesn't exist in Latin and that until the end of the XVIII century almost all the scientific texts (and also the gnomonic's ones) were written in Latin. I think he is right ! Best wishes Gianni Ferrari --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Gianni, the term "Italic" was not associated in the first time at the "Italian Hours". I believe in the first time the "italian hours" was named simply "ab occasum Solis". Because this hours was used spcially in Italy, in a second time was named "Italian hours". In the gomonic books written in Latin, the "italian hours" are named "ab occasum solis" and that this hours are used most in Italy. In the text not in Latin language, we read "Italian Hours". until > the end of the XVIII century almost all the scientific texts (and also the > gnomonic's ones) were written in Latin. I believe that only in part. Valentino Pini, Oddi Muzio, and others written about the gnomonica in italian, but many scientific text are written also in italian. Best regards Nicola -- Initial Header --- >From : [EMAIL PROTECTED] To : "LISTA INGLESE" [EMAIL PROTECTED] Cc : Date : Thu, 28 Aug 2008 16:48:52 +0200 Subject : Re: equal and unequal hours > Mario Catamo has suggested me that very probably the term "Italic" (in > Italic hours) comes from the Latin word "Italicus" (that means > "Italian"), that the word "Italianus" doesn't exist in Latin and that until > the end of the XVIII century almost all the scientific texts (and also the > gnomonic's ones) were written in Latin. > > I think he is right ! > > > > Best wishes > > Gianni Ferrari > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Gianni, It is good to have Mario's comment... > Mario Catamo has suggested me that very probably > the term "Italic" (in Italic hours) comes from > the Latin word "Italicus" (that means "Italian"), > that the word "Italianus" doesn't exist in Latin > and that until the end of the XVIII century almost > all the scientific texts (and also the gnomonic's > ones) were written in Latin. Mario makes a good point but I think Italicus AND Italianus both exist in Latin, and certainly in scientific Latin... You made the excellent comment: In our language today there is a small difference between the adjective "Italic" and the adjective "Italian": Italic is used only to make reference to things of the ancient Italy (as the civil law, the customs, the dialects) or to the ancient inhabitants of the country. The Oxford English Dictionary has entries for Italic and Italian. They almost repeat what you say BUT they add the Latin translations Italicus and Italianus: Italic, Latin Italicus Of or pertaining to ancient Italy or its tribes; especially in Roman History and Law... Italian, Latin Italianus Of or pertaining to Italy or its people; native to or produced in Italy... The Latin Italianus is used in scientific classification. For example you can read about diacyclops italianus in: http://copepods.interfree.it/diacy.htm The Oxford English Dictionary also explains the origin of the term italic for sloping text: (with small i) applied to the species of printing type introduced by Aldus Manutius of Venice, in which the letters, instead of being erect as in Roman, slope towards the right; first used in an edition of Virgil, published in 1501 and dedicated to Italy. This is interesting because I thought italic printing was an early 20th century development! It is good to see that it comes from Italy and you had it over 500 years ago!! In the context of time and sundials, I think italic is OK to describe the sundials of ancient. Equal hours that start at sunset were unknown in Roman times so I prefer to use "Italian Hours" :-) Mario is certainly correct to say that almost all scientific writing used to be in Latin. This practice went on for a VERY long time. Of course Mario's favourite example is: De Nummo et Gnomone Clementino by Francesco Bianchini about the meridiana in the Basilica di Santa Maria degli Angeli in Rome. Mario once showed me a copy of this dissertation. That is truly a "Sacred Text"!!! Te salutamus Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Braunschweig Cathedral sundial again ! I don't know the article of Curt Roslund in the BSS Bulletin, september 2005, pag. 116-119 about the the vertical sundial of Braunschweig Cathedral of 1346 with the equal hour lines and a polar gnomon but … in 1999 I have written a Note, published in our magazine Gnomonica, regarding the article of Nicola Severino "The most ancient vertical sundial with astronomical hours" published in the n. 4 - September 1999 of the same magazine In this note with few calculations I have put in evidence that in the Braunschweig Cathedral sundial (in Italy Brunswich) the style was certainly orthogonal and not polar. If someone is interested I can send this short note (in Italian !) Best Gianni P.S. – I write only now because I had completely forgotten this note : the old age :-( --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
I think, Severino is right. Actually I never found in the first texts the attribute "Italian" nor "Italic" (I mean medieval texts, usually chronicles). In the half of the 14th c. I've found only the attribute "complete". The attribute "Italian" or "Italic" was used surely by not Italian people that need to give a name to the hour system used in Italy. Like us in Italy called the European hours "French" or "German" or also "Spanish". Because the Italic hour system was used also in many other countries at that times, people next these countries called them "Polish hours" or "Czechoslovakian hours" etc. Mario - Original Message - From: <[EMAIL PROTECTED]> To: "gfmerid" <[EMAIL PROTECTED]> Cc: "sundial" <[EMAIL PROTECTED]> Sent: Thursday, August 28, 2008 5:36 PM Subject: Re: equal and unequal hours > > Dear Gianni, > > the term "Italic" was not associated in the first time at the "Italian > Hours". I believe in the first time the "italian hours" was named simply > "ab occasum Solis". Because this hours was used spcially in Italy, in a > second time was named "Italian hours". In the gomonic books written in > Latin, the "italian hours" are named "ab occasum solis" and that this > hours are used most in Italy. In the text not in Latin language, we read > "Italian Hours". > > until >> the end of the XVIII century almost all the scientific texts (and also >> the >> gnomonic's ones) were written in Latin. > > > I believe that only in part. Valentino Pini, Oddi Muzio, and others > written about the gnomonica in italian, but many scientific text are > written also in italian. > Best regards > Nicola > > > -- Initial Header --- > >>From : [EMAIL PROTECTED] > To : "LISTA INGLESE" [EMAIL PROTECTED] > Cc : > Date : Thu, 28 Aug 2008 16:48:52 +0200 > Subject : Re: equal and unequal hours > > > > > > > >> Mario Catamo has suggested me that very probably the term "Italic" (in >> Italic hours) comes from the Latin word "Italicus" (that means >> "Italian"), that the word "Italianus" doesn't exist in Latin and that >> until >> the end of the XVIII century almost all the scientific texts (and also >> the >> gnomonic's ones) were written in Latin. >> >> I think he is right ! >> >> >> >> Best wishes >> >> Gianni Ferrari >> > > > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Braunschweig Cathedral sundial again - 2 I am afraid but, perhaps, I have not understood anything! :-( Mario Arnaldi has written me that the Brunswick sundial on which time ago I have written a "Note" is one of the two ancient clocks of the cathedral, BUT IT IS NOT that on which we are speaking in these Emails. This clock ( of ours Emails) is on the contrary the second one, built few decades later. Since Frans affirms that the sundials were built in 1334 and in 1356 this means that the sundial of which we are speaking is that built in 1356. But I believed that my "Note" concerned just a sundial built around 1350 ! Questions: in which labyrinth I lose my way? who helps me to go out? And, most important, does someone have the images (good photos) of these mysterious clocks? I ask you to excuse me if also I have much contributed to entangle the things: - ( Best wishes Gianni Ferrari --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Hello Gianni, I conclude that your analysis is correct for the early dial (1334). See attached note. The 1334 lines are correct for an orthogonal gnomon. The later dial (1346) has the correct lines for a polar gnomon. Whether it had a polar gnomon before one was put on in 1985 remains inconclusive. I will send you the scanned document that Reinhold Kriegler sent me with pictures of the four sundials on the church. Regards, Roger From: Gianni Ferrari Sent: Thursday, August 28, 2008 3:46 PM To: LISTA INGLESE Subject: Re: equal and unequal hours Braunschweig Cathedral sundial again - 2 I am afraid but, perhaps, I have not understood anything! :-( Mario Arnaldi has written me that the Brunswick sundial on which time ago I have written a "Note" is one of the two ancient clocks of the cathedral, BUT IT IS NOT that on which we are speaking in these Emails. This clock ( of ours Emails) is on the contrary the second one, built few decades later. Since Frans affirms that the sundials were built in 1334 and in 1356 this means that the sundial of which we are speaking is that built in 1356. But I believed that my "Note" concerned just a sundial built around 1350 ! Questions: in which labyrinth I lose my way? who helps me to go out? And, most important, does someone have the images (good photos) of these mysterious clocks? I ask you to excuse me if also I have much contributed to entangle the things: - ( Best wishes Gianni Ferrari --- https://lists.uni-koeln.de/mailman/listinfo/sundial Brunswick Sundials.pdf Description: Adobe PDF document --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Mario, Gianni and other Friends, I found today a ancient codex written in Wien (not sure), dated 1508 in which i see very much quadrants, astrolabe and sundials (many quadrants unknowed) without description, but some word for the pictures. For the "Cylindri Horarii", the horis are named "Horis Italicis". This shown that in the 1508, out Italy, someone used the name "Italicis" for the italian hours! Gianni was not as wrong! Greetings Nicola -- Initial Header --- >From : [EMAIL PROTECTED] To : "sundial" [EMAIL PROTECTED] Cc : Date : Thu, 28 Aug 2008 23:46:04 +0200 Subject : Re: equal and unequal hours > I think, Severino is right. Actually I never found in the first texts the > attribute "Italian" nor "Italic" (I mean medieval texts, usually > chronicles). In the half of the 14th c. I've found only the attribute > "complete". The attribute "Italian" or "Italic" was used surely by not > Italian people that need to give a name to the hour system used in Italy. > Like us in Italy called the European hours "French" or "German" or also > "Spanish". > Because the Italic hour system was used also in many other countries at that > times, people next these countries called them "Polish hours" or > "Czechoslovakian hours" etc. > > Mario > > ----- Original Message - > From: <[EMAIL PROTECTED]> > To: "gfmerid" <[EMAIL PROTECTED]> > Cc: "sundial" <[EMAIL PROTECTED]> > Sent: Thursday, August 28, 2008 5:36 PM > Subject: Re: equal and unequal hours > > > > > > Dear Gianni, > > > > the term "Italic" was not associated in the first time at the "Italian > > Hours". I believe in the first time the "italian hours" was named simply > > "ab occasum Solis". Because this hours was used spcially in Italy, in a > > second time was named "Italian hours". In the gomonic books written in > > Latin, the "italian hours" are named "ab occasum solis" and that this > > hours are used most in Italy. In the text not in Latin language, we read > > "Italian Hours". > > > > until > >> the end of the XVIII century almost all the scientific texts (and also > >> the > >> gnomonic's ones) were written in Latin. > > > > > > I believe that only in part. Valentino Pini, Oddi Muzio, and others > > written about the gnomonica in italian, but many scientific text are > > written also in italian. > > Best regards > > Nicola > > > > > > -- Initial Header --- > > > >>From : [EMAIL PROTECTED] > > To : "LISTA INGLESE" [EMAIL PROTECTED] > > Cc : > > Date : Thu, 28 Aug 2008 16:48:52 +0200 > > Subject : Re: equal and unequal hours > > > > > > > > > > > > > > > >> Mario Catamo has suggested me that very probably the term "Italic" (in > >> Italic hours) comes from the Latin word "Italicus" (that means > >> "Italian"), that the word "Italianus" doesn't exist in Latin and that > >> until > >> the end of the XVIII century almost all the scientific texts (and also > >> the > >> gnomonic's ones) were written in Latin. > >> > >> I think he is right ! > >> > >> > >> > >> Best wishes > >> > >> Gianni Ferrari > >> > > > > > > --- > > https://lists.uni-koeln.de/mailman/listinfo/sundial > > > > > > > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear readers, two more informations to that subject: only in 1985 there were placed a polar gnomon on the dial from "1346" by the Braunschweiger Landeskirche. If the date of 1346 is correct nobody knows. See also my article that you may find on my web page www.antike-sonnenuhren.de/artikel.htm karlheinz -Ursprüngliche Mitteilung- Von: Frans W. Maes <[EMAIL PROTECTED]> An: [EMAIL PROTECTED] <[EMAIL PROTECTED]> Cc: sundial <[EMAIL PROTECTED]> Verschickt: So., 24. Aug. 2008, 12:57 Thema: Re: equal and unequal hours Dear all, [EMAIL PROTECTED] wrote: It is true that the first mechanical clocks was on the towers around the begin of the 1300. And the first vertical sundials with the polar gnomon was done arond the first half of 1300. The interesting articles of Curt Roslund in the BSS Bulletin, september 2005, pag. 116-119, show the vertical sundial of Braunschweig Cathedral of 1346 with the equal hour lines and a polar gnomon. The 1346 dial now has a polar gnomon. As recent as 1964 there was no nomon, merely a large hole (Zinner). It is not known, how the original nomon was oriented. In my view, it is unlikely that it was a ole-style. The angles were laid out according to the 'Erfurt formula', s Zinner and Roslund point out. This rule does not say anything about he orientation of the gnomon. If it was intended to be pointing at the elestial pole, the formula would most probably have provided accurate nstructions for that. To answer R oger's question: The dates of the 1334 and 1346 dials were educed from the building history of the cathedral, assuming that they ere laid out at the time of completion of the particular buttresses. Regards, rans Maes -- ttps://lists.uni-koeln.de/mailman/listinfo/sundial AOL eMail auf Ihrem Handy! Ab sofort können Sie auch unterwegs Ihre AOL email abrufen. Registrieren Sie sich jetzt kostenlos. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Karlheinz Thank you for sending us this information... > only in 1985 there were placed a polar > gnomon on the dial from "1346"... > > If the date of 1346 is correct nobody > knows. I think you said 1346 is the date of the buttress into which the sundial is cut. This is clearly a poor basis for dating a sundial! > See also my article that you may find on > my web page > > www.antike-sonnenuhren.de/artikel.htm I imagine this is the article with the title: Vertical Sundials of the 5-15th Centuries I had a little trouble navigating to this but it is an excellent article and gives a splendid summary of this thread. In this article you refer to the Brunswick dial of circ. 1350. This might be where Nicola and Gianni got that date from. You say that... in Roman times it seemed as a matter of course that only the tip of the gnomon shadow gave the hour. This must be a problem when trying to decide whether or not a missing gnomon was polar-oriented... For example, the winter side of the Oropos dial (which you date between 350 and 320 BC) seems to have hour lines that are almost perfectly set out for an equal-hours dial with a polar-oriented gnomon. You elegantly explain that the gnomon was in fact *horizontal* but the shadow of its tip, used as a nodus, would have indicated equal hours. I don't think such a gnomon is polar oriented (because it was horizontal) but others may say that such a gnomon has been described as polar-oriented sufficiently often in the literature that we must accept that usage. What do you think? Also, you say that: with an angle of 90 degrees minus half of the latitude, between the wall and south-facing pointer results in the sundial giving quite a reasonable approximation for equal hours. I haven't investigated this claim. For a proper polar-oriented gnomon, the angle is 90 degrees minus the latitude (not half the latitude). Can you tell us a little more about how this half-angle rule works? May I say just how much I have enjoyed reading your articles? Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
re: equal and unequal hours
I hope this is not off topic, but the discussion brought to mind a question that I have. Will a south facing vertical dial split into 15 degrees using a polar gnomon divide the day in the exact same way as an ancient Greek or roman sundial such as a haemuspherium with a vertical or horizontal gnomon? If it does divide the day in the same fashion, as I think it does, how great is the difference between the church dials that used a horizontal gnomon or if they would use a polar gnomon? PS Does anyone know the formula for breaking up the day on such a sundial with a horizontal gnomon? Thanks, Noam--- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: equal and unequal hours
Dear Noam, You pose interesting questions... > I hope this is not off topic... Certainly on topic for me!! > Will a south facing vertical dial split > into 15 degrees using a polar gnomon > divide the day in the exact same way > as an ancient Greek or roman sundial > such as a haemuspherium with a vertical > or horizontal gnomon? The key feature of a polar gnomon is that the direction of the shadow at a given time of day (hour-angle) is independent of the time of year (declination). Your dial with the polar gnomon will therefore divide the day in the same way every day of the year. If you label your 15-degree interval lines as equal hours, 6am to 6pm, and hope to read off equal hours, then the error at a given indicated hour will be the same each day. If you label your 15-degree interval lines as temporary hours, 0 (sunrise) to 12 (sunset), and hope to read off temporary hours, then the error at a given indicated hour will vary from day to day (because temporary hours vary from day to day). You will need an expert on Greek or Roman sundials to confirm the next point... My understanding is that, in Greek and Roman sundials, the *tip* of the shadow of the gnomon was used to determine the time so we are talking about an indicated point rather than an indicated direction. Also, such dials were usually intended to indicate temporary hours. They did this erroneously and the error at a given indicated time changed as the declination changed. > If it does divide the day in the same > fashion, as I think it does,... I may well have misunderstood your question but my interpretation is that the division is different. > Does anyone know the formula for > breaking up the day on such a sundial > with a horizontal gnomon? Assuming a direct south-facing vertical dial in the northern hemisphere there are two formulae to note: For a polar-oriented gnomon: tan(ang) = tan(H).cos(phi) Here ang is the angle of the shadow to the downward vertical when the hour-angle is H and the latitude is phi. Note that there is no term for the declination since the direction is independent of the time of year. For a horizontal gnomon: sin(H).cos(dec) tan(ang) = cos(H).cos(dec).cos(phi) - sin(dec).sin(phi) This is more complicated because the direction does depend on the solar declination dec. Notice that if the declination is zero, as at the equinoxes, the formula reduces to: tan(ang) = tan(H)/cos(phi) Karlheinz Schaldach and others have shown that the lines on the 1334 Braunschweig dial are close to the angles given by this formula. Accordingly, this dial would have indicated the time correctly at the equinoxes. That is not what you are asking about though! Try some experiments with the long formula and you will quickly get a feeling for how matters change as the declination changes and you will also, I suspect, be able to answer other questions that occur to you. Best wishes Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
