Re: re how italian hours
Hello Friends, I've been asked for more information about how I made the H2SS card dial. There is an excellent account on Carl Sabanski's site: http://www.mysundial.ca/tsp/qbasic_Mac_Oglesby_H2SS_Card_Sundial.html Carl has extensive material on using QBASIC at: http://www.mysundial.ca/tsp/qbasic.html And quite a bit about some of my other sundials at: http://www.mysundial.ca/tsp/qbasic_Mac_Oglesby.html If, by any chance you aren't familiar with Carl's extensive sundial pages, here's a link to his index. Enjoy! http://www.mysundial.ca/tsp/tsp_index.html Best wishes, Mac Oglesby --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
Dear Chris, Your diagram is a masterpiece! I still find it intriguing that the simple-to-define concepts of Babylonian and Italian hours open the way to a feast of geometric delights. With you dreaming up such eloquent mappings, this feast clearly has more courses to come! All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
Dear Friends, I hope my attached diagram will help show the relationships between Italian, Babylonian and modern hours, and ways to plot Italian and Babylonian hours on any horizontal, vertical (or reclining) dial. To keep the file size down, I put in only minimal instructions. My diagram shows a cylindrical dial wrapped around a polar gnomon with a nodus. Surprisingly, perhaps, it shows that the Italian hours line for hour H and the Babylonian hours line for the same hour number H are just different ends of the same line! Frank makes the point that the horizon line IS the Italian 24 hour line and the Babylonian 24 hour line, but Gianni's original statement was meant, I feel sure, to refer to the useful observation that intersections of the horizon line with each of the *other* hour lines enable them to be plotted very easily. But he got two of the equations wrong. The correct equations for lines crossing the horizon are: HIT=2 HMOD for 0 To: "Roger Bailey" ; "Gianni Ferrari" Cc: "LISTA INGLESE" Sent: Saturday, April 03, 2010 8:46 AM Subject: Re: how italian hours > Dear Gianni and Roger, > > Thank you very much for the clarifications. > Gianni's table is especially clear about > the two cycles of 12 for Italic hours as > used in the Muslim world. > > Chris Lusby Taylor's comment is true in a > way but, equally, your original remark can > be interpreted as being correct. You > said: > > Also for each point of the line of horizon > (on the sundial) pass one hour line with > Modern, one with Italic *and* one with > Babylonian hours. > > I interpreted this as being *correct*. The > horizon line IS either B=0 or I=24 so you > have triple points like B=0, F=8, I=16 > and B=8, F=16, I=24. These points are > on the horizon line! > > I do agree that HMOD=11, HIT=22, HBAB=2 > is an inconsistent trio but it can be made > correct just by changing HBAB to 0 and > you have another triple point on the > horizon line! > > Best wishes > > Frank > > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > <>--- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
Dear Gianni and Roger, Thank you very much for the clarifications. Gianni's table is especially clear about the two cycles of 12 for Italic hours as used in the Muslim world. Chris Lusby Taylor's comment is true in a way but, equally, your original remark can be interpreted as being correct. You said: Also for each point of the line of horizon (on the sundial) pass one hour line with Modern, one with Italic *and* one with Babylonian hours. I interpreted this as being *correct*. The horizon line IS either B=0 or I=24 so you have triple points like B=0, F=8, I=16 and B=8, F=16, I=24. These points are on the horizon line! I do agree that HMOD=11, HIT=22, HBAB=2 is an inconsistent trio but it can be made correct just by changing HBAB to 0 and you have another triple point on the horizon line! Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
My responses are interspersed below. -- From: "Frank King" Sent: Friday, April 02, 2010 10:18 AM To: "Roger Bailey" Cc: "Gianni Ferrari" ; "Frank King" ; "LISTA INGLESE" ; Subject: Re: how italian hours > Dear Roger, > > You are right... > >> This gets more interesting with each note. > > The business of labelling gnomonic features > elegantly can be a nightmare! > > With an ordinary sundial you have a chapter > ring of one kind or another for the labels of > the hour-lines and life is straightforward! > > When you try to label Babylonian hours and > Italian hours it is easy to get into a mess. > > [You especially get into a mess if you > insist on using Roman Numerals. A time > like XVIII takes up a lot of space!] On the Istanbul sundials they only put numbers on the Italian hours. Those hours go to 12 at sunset as they use two 12 hour cycles' The French hours are numbered but this is on a different scale around the outside of the dial. They do not use our Arabic numbers. That would be too easy. They use Indo-Turk numerals that can be confusing. The Al Shatir dial dated 1371 in Damascus has Italian hours for the afternoon and Babylonian hours for the morning. > > You say that... > >> ... on the sundials in Istanbul, Topkapi >> Palace ... they assigned 6 to noon. On >> the equinox all the lines cross the meridian >> at 6. The others then fall into place. > > This certainly makes things easier but could > you confirm my interpretation of what you > are saying? > > Are you saying that at the crossing point, > on the equinoctial line, at one hour before > noon, they number the four times: > > Babylonian = 5 Yes, 5 hours from dawn > French = 5 No because the polar gnomon and point gnomon are not the > same. The point gnomon is half the height of the polar gnomon directly above it > Italian= 5 Yes as it 7 hours to sunset and 12-7=5 > Temporary = 5 Yes, 5 hours from dawn > > > Clearly Babylonian and Temporary would be > called 5 anyway but not French and Italian. > > Have I misunderstood? > >> The horizontal 12 line on the south facing >> dial is interesting. > > Sorry. I am lost here! Is this the line > which I would call Italian = 24 but which > is now being numbered 12 because it is 6 > at equinoctial noon? Yes but not because noon is 6 but because sunset is > 12, not 24 > >> In Istanbul they used two 12 hour cycles >> so there were no numbers in the teens and >> twenties. > > Given your assertion that noon = 6 are you > saying that when there are 14 hours of > daylight the French hours are numbered: > > 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 Yes, just as we go through noon > as 11 12 1 but we could go 11 12 13 with a 24 hour clock > > Also, do they use *real* Arabic numerals? No a Indo-Turk or Eastern > Arabic. See http://en.wikipedia.org/wiki/Ottoman_Turkish_alphabet > > Very best wishes > > Frank > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
Sorry , I forgot the table :-) Gianni F. TabOre.pdf Description: Adobe PDF document --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
Chris Lusby Taylor, has very kindly written me that in my first Email *“How trace the italic hour lines” *I have made an error: it’s true! The error is serious enough and I thank Chris and apologize to all L I wrote *Also for each point of the line of horizon (on the sundial) pass one hour line with Modern , one with Italic AND one with Babylonian hours.* But, as Chris writes, *there is no point on the horizon common to both an Italian and to Babylonian hour line. * The correct sentence had to be *pass one hour line with Modern , one with Italic OR one with Babylonian hours.* * * When F <12 (or HMod<12) the modern hour line intersects the horizon in a point that is West of the meridian line and where also the Italic line I=2F passes. When F >12 (or HMod>12) the modern hour line intersects the horizon in a point that is East of the meridian line and where also the Babylonian line B=2F-24 passes. So the line B=2 crosses the line of the horizon for F=13 and NOT for F=11, as I have written. Best wishes Gianni - Mail to : gfme...@gmail.com Lat.44;38,18.5N Long. 10;56,05.3E Ita_Bab.pdf Description: Adobe PDF document --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
Dear Roger, You are right... > This gets more interesting with each note. The business of labelling gnomonic features elegantly can be a nightmare! With an ordinary sundial you have a chapter ring of one kind or another for the labels of the hour-lines and life is straightforward! When you try to label Babylonian hours and Italian hours it is easy to get into a mess. [You especially get into a mess if you insist on using Roman Numerals. A time like XVIII takes up a lot of space!] You say that... > ... on the sundials in Istanbul, Topkapi > Palace ... they assigned 6 to noon. On > the equinox all the lines cross the meridian > at 6. The others then fall into place. This certainly makes things easier but could you confirm my interpretation of what you are saying? Are you saying that at the crossing point, on the equinoctial line, at one hour before noon, they number the four times: Babylonian = 5 French = 5 Italian= 5 Temporary = 5 Clearly Babylonian and Temporary would be called 5 anyway but not French and Italian. Have I misunderstood? > The horizontal 12 line on the south facing > dial is interesting. Sorry. I am lost here! Is this the line which I would call Italian = 24 but which is now being numbered 12 because it is 6 at equinoctial noon? > In Istanbul they used two 12 hour cycles > so there were no numbers in the teens and > twenties. Given your assertion that noon = 6 are you saying that when there are 14 hours of daylight the French hours are numbered: 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 Also, do they use *real* Arabic numerals? Very best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
This gets more interesting with each note. The time system used on the sundials in Istanbul, Topkapi Palace and various mosques, makes it easier to assign all the hour numbers. They assigned 6 to noon. On the equinox all the lines cross the meridian at 6. The others then fall into place. The horizontal 12 line on the south facing dial is interesting. On a horizontal dial, the lines continue as summer days have more than 12 equal hours. In Istanbul they used two 12 hour cycles so there were no numbers in the teens and twenties. Roger Bailey Walking Shadow Designs -- From: "Frank King" Sent: Friday, April 02, 2010 4:12 AM To: "Gianni Ferrari" Cc: "LISTA INGLESE" Subject: Re: how italian hours > Dear Gianni, > > Your analysis has silenced the Lista Inglese! > > I will summarise what you said so that new > readers may start here... > > You have: > > D = length of day (sunrise to sunset) > > Whenever D is an integer number of hours, the > associated constant-declination curve passes > through a hyperbolic arc of points at which > Babylonian and Italian hour-lines intersect. > > Whenever D is an EVEN integer number of hours, > the associated constant-declination curve passes > through a hyperbolic arc of points at which > Babylonian, Italian AND French hour-lines > intersect. > > Whenever D is 6, 12 or 18 hours, the associated > constant-declination curve passes through a > hyperbolic arc of points at which Babylonian, > Italian, French AND Temporary hour-lines > intersect. > > This makes 58.49 degrees North an interesting > latitude to set up a dial because: > > At the winter solstice D = 6 hours > At the equinoxes D = 12 hours > At the summer solstice D = 18 hours > > I attach a PDF which shows a dial marked out for > a direct south-facing wall at this latitude. > > The Babylonian, French and Italian hour-lines > are obvious and I have drawn the Temporary hours > in blue to distinguish them. > > Design exercise for the reader: > >Number all the lines in an elegant way! > > The equinoctial line has quadruple crossing points > all along it. > > The winter and summer solstice curves have these > quadruple crossing points at noon and at: > > B=6, F=9, I=12, T=4 and B=12, F=15, I=18, T=8 > > There are, of course, triple crossing points along > the D=6, 8, 10, 12, 14, 16 and 18 hyperbolae where > Babylonian, French and Italian hour-lines intersect. > > There are a few "surprise" triple crossing points > too such as those at: > > B=5 I=14, T=4 and B=10, I=19, T=8 > > The French hours at these points are half-integers. > > One more thing: > > Babylonian, French and Italian hour-lines are > STRAIGHT on a plane dial. Temporary hour-lines > are narrow S-shapes. Print out my attachment > and squint along the blue lines. You will see > that they are gentle curves. > > It is very cold here at 52 degrees north so I shall > not be moving to 58.49 degrees north myself :-) > > Best wishes > > Frank > > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
Dear Gianni, Your analysis has silenced the Lista Inglese! I will summarise what you said so that new readers may start here... You have: D = length of day (sunrise to sunset) Whenever D is an integer number of hours, the associated constant-declination curve passes through a hyperbolic arc of points at which Babylonian and Italian hour-lines intersect. Whenever D is an EVEN integer number of hours, the associated constant-declination curve passes through a hyperbolic arc of points at which Babylonian, Italian AND French hour-lines intersect. Whenever D is 6, 12 or 18 hours, the associated constant-declination curve passes through a hyperbolic arc of points at which Babylonian, Italian, French AND Temporary hour-lines intersect. This makes 58.49 degrees North an interesting latitude to set up a dial because: At the winter solstice D = 6 hours At the equinoxes D = 12 hours At the summer solstice D = 18 hours I attach a PDF which shows a dial marked out for a direct south-facing wall at this latitude. The Babylonian, French and Italian hour-lines are obvious and I have drawn the Temporary hours in blue to distinguish them. Design exercise for the reader: Number all the lines in an elegant way! The equinoctial line has quadruple crossing points all along it. The winter and summer solstice curves have these quadruple crossing points at noon and at: B=6, F=9, I=12, T=4 and B=12, F=15, I=18, T=8 There are, of course, triple crossing points along the D=6, 8, 10, 12, 14, 16 and 18 hyperbolae where Babylonian, French and Italian hour-lines intersect. There are a few "surprise" triple crossing points too such as those at: B=5 I=14, T=4 and B=10, I=19, T=8 The French hours at these points are half-integers. One more thing: Babylonian, French and Italian hour-lines are STRAIGHT on a plane dial. Temporary hour-lines are narrow S-shapes. Print out my attachment and squint along the blue lines. You will see that they are gentle curves. It is very cold here at 52 degrees north so I shall not be moving to 58.49 degrees north myself :-) Best wishes Frank GF.pdf Description: GF.pdf --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: re how italian hours
Hello friends, I've been following the discussion about Italian hours sundials with great interest, since dials with Italian hours labeled in countdown fashion have been a passion of mine for many years. The focus of the discussion has been on dials where the Italian hour lines appear as straight lines and the number of hours since sunset (or, hours to sunset -- H2SS) are read by looking where the shadow of a nodus falls on the dial face. I have made a lot of such dials (but always as H2SS) and still do, but I want to point out to those who don't see the NASS Compendiums regularly that one doesn't have to use a nodus. Over the past 18 months or so I've made H2SS dials which use shadow planes and H2SS dials which use polestyles. The shadow plane models I wrote about in the December 2008 issue have no shadow casting unit, either nodus or polestyle, but rather have a moveable vane to be turned edgewise to the Sun. The H2SS are read on a scale. See photo1.jpg. The June 2009 issue has a brief description of another shadow plane H2SS dial, one which permits more accurate reading. See photo2.jpg. In the September 2009 issue are pictures of two polar H2SS dials which use polestyles. See photo3.jpg. Most recently, the March 2010 issue has pictures of horizontal and direct south-facing H2SS dials which use polestyles. These sundials also work as shadow plane dials. See photo4.jpg. These designs might not be to everybody's liking, but I did want to show that there are alternatives to the usual Italian hours dials. If anyone wants better photos, let me know off list and I'll send some along. My last mentioned article concludes with the statement, "It has been said often that new ideas are rare in dialing, so I am pretty sure polestyle H2SS dials have been made before. I would be pleased to learn when, and by whom." No replies so far. Best wishes, Mac Oglesby <><><><>--- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: re how italian hours
I suppose it depends on how many diallists there are and if he/she/they are old or is it an old trick. It is now at last sunny in Brighton. Jackie Jones -Original Message- From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Frank Evans Sent: 01 April 2010 09:58 To: Sundial Subject: re how italian hours Greetings, fellow dialists, Re my suggestion of laying out an italian hours dial ninety degrees away: Did you ever feel, the moment after you had hit the "send" button, that you should not have written what you did? Of course, it would not work. But I am pleased that the subject of italian and babylonian hours has had such a good run. Off topic: I wrote about using "the old dialist's trick" of laying out a dial ninety degrees away from site. Should it have been "the old dialists' trick"? Either? Frank 55N 1W --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
re how italian hours
Greetings, fellow dialists, Re my suggestion of laying out an italian hours dial ninety degrees away: Did you ever feel, the moment after you had hit the "send" button, that you should not have written what you did? Of course, it would not work. But I am pleased that the subject of italian and babylonian hours has had such a good run. Off topic: I wrote about using "the old dialist's trick" of laying out a dial ninety degrees away from site. Should it have been "the old dialists' trick"? Either? Frank 55N 1W --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
*Some other curious properties of the Italic and Babylonian hours.* I will adopt here the Frank’s notation : F=French or modern hours; I=Italic; B=Babylonian. Moreover T=Temporary and D = duration of the clear day (from dawn to sunset). The simple following formulae are valid: I=F+(24-D)/2 (1) B=F-(24-D)/2 (2) T=6+12(F-12)/D (3) I+B = 2F (as usual) I-B = 24-D= duration of the night (1) and (2) suggest one method to draw the daily lines (hyperboles) corresponding to the days whose length is equal to an integer of hours =D. If the duration D is an odd number it is necessary to have the hour lines with modern hour every half an hour. If we take , for instance, D=14 they become I=F+5 and B=F-5: the hour lines with modern hours F, Italic I and Babylonian B meet in a point that belongs also to the daily line corresponding to the day whose length is 14 hours. If we connect all the points that we obtain changing the value of F we have daily line. For instance F = 7; I=12; B=2 or F=16; I=21; B=11 For instance: with D=9 we have I=F+7.5 and B=F-7.5 -- In the points of the daily lines corresponding to a duration D=6, 12, 18 we find four hour lines with an integer number of hours : with modern, Italic, Babylonian and Temporary hours. (see formula n. 3) For D=18 it is necessary to consider only the values of F multiple of 3. For D=6 we have T=2F-18 and, for example, the lines with F=10, I=19, B=1, T=2 pass all through the same point. For D=18 we have T=2F/3-2 and, for example, the lines with F=15, I=18, B=12, T=8 pass all through the same point. This is a simple ( J ) method to draw the Temporary hour lines. Best wishes Gianni Ferrari --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
Dear Gianni, I enjoyed your explanation and (I liked the deliberate mistake which you included to make sure we were paying attention)... > If we have a horizontal sundial we > cannot use the method that I have > described yesterday. Of course, we CAN use your yesterday's method provided we accept that the horizon line is at infinity! Today is just a special case of yesterday! In general: B + I = 2.F(1) B = Babylonian I = Italian F = French = Local Sun Time = Modern = ... This means two things: 1. Local Sun Time, F, is the average of Babylonian and Italian Time 2. At ANY crossing point (when B and I are both integers) then Local Time is an integer or half-integer. The horizon line (even when at infinity) indicates sunrise or sunset when: EITHER B = 0 OR I = 24 B or I is an integer so all intersections on the horizon line are for integer B and I. At sunrise or sunset we have from (1): EITHER I = 2.F OR B = 2.F - 24 [I do not agree with HBAB=24-2HMOD this is the deliberate mistake you included to test us all :-) ] Worked examples for a horizontal dial: 1. To set out I = 18 Mark P on the equinoctial line at F=12 [I-6] Noting that I=2.F, draw a line through P parallel to the F = 9 line. 2. To set out B = 6 Mark P on the equinoctial line at F=12 [B+6] Noting that B=2.F-24, draw a line through P parallel to the F = 15 line. The world needs educating. Let's have more Italian-hours sundials outside Italy!! Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how Italian hours
Roger Bailey wrote: > The conversion of the > presentation to an article fro the compendium is stalled at 80% complete. > This follows the classic 80 20 rule defining work progress. Which is to say that the remaining 20% of work will consume the *other* 80% of time? Dave --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
A small addition If we have a horizontal sundial we cannot use the method that I have described yesterday. In this case, however, the point where the Modern hour line HMOD and the Italic hour line HIT=2 HMOD cross the " horizon line" becomes a “point to infinity” (I hope that this is the mathematical term in English :-) ) , that is a direction. Therefore the modern hour line HMOD is parallel to the Italic hour line HIT = 2 HMOD and to the Babylonian one HBAB=24-2HMOD Gianni Ferrari P.S. I am completely in agreement with Frank on the difficulties that the method (simple) can introduce: as often happens, the things theoretically simple become difficult in the practice . 2010/3/30 Frank King > Dear Gianni, > > I like your explanation and I like the > extra comments too. > > You have: > > P1 on the equinoctial line and > > P2 on the horizon line > > This is good in theory but not so > good in practice. For example, my > line for Bab = 11 does not run > as far as the equinoctial line or > the horizon line!! > > Several other lines do not reach > one or other of the equinoctial > line and the horizon line. > > Another practical problem is that P1 > and P2 can be quite close together > and a small error in either will make > for a large error in the extension > towards the summer solstice curve! > > I very much agree with this: > > When a friend asks me a suggestion to > draw a sundial, I always recommend him > a sundial that marks the hours to sunset, > that is a sundial with italic hours... > > My practical problem here is that it has > taken me 20 years to find a client who > agrees with this suggestion :-)) > > Now, when I look at the finished sundial, > people keep coming up to me to ask, "How > do I tell the time, the REAL time?" > > I explain that Babylonian hours and > Italian hours ARE real times but this > is not the answer they want. > > "OK," I have to say, "take the average of > Babylonian and Italian hours and you will > find the time on an ordinary sundial!" > > It is VERY nice to have an Italian Hours > sundial so close to home!! > > Cordiali saluti > > Frank > > -- Mail to : gfme...@gmail.com Lat.44;38,18.5N Long. 10;56,05.3E --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how Italian hours
I am also a fan of Italian and Babylonian hours as they are based on the significant solar events in the day. They cannot be legislated to be something different. OK, the definition of sunrise and sunset need to be arbitrarily defined. I use the mathematical zero altitude that ignores refraction and semi-diameter. I agree with Gianni that establishing hour points along the equatorial line is a good practice. This shows quickly what the dial will look like and as a check on the calculation of the Italian and Babylonian lines as they cross on the equinox. Once while vacationing without access to files and computers, I set myself the challenge of designing a sunset sundial from scratch. This used the journeyman's procedure with the following steps. Calculate polar sundial using equatorial disc Solve for sunset times at solstices: Cos t = Tan Lat x Tan Dec Tabulate t = sunset time – N hours (15º/hour) Calculate Altitude for t knowing Lat & Dec Sin Alt = Sin Lat x Sin Dec + Cos Lat x Cos Dec x Cos t Calculate Azimuth for t knowing Altitude Sin Az = Cos Dec x Sin t / Cos Alt Project point onto wall knowing declination of wall, altitude and azimuth Plot the results and join the points for hours to sunset and solstice declination lines This exercise was successful and I left a mock up of the design for the owner of our rental suite. The results presented at the NASS Conference in St Louis. The presentation "Designing a Sunset Sundial from Scratch" is available on my website"www.walkingshadow.info" . Click on Walking Shadows (Sundials) for the index page of publications. The presentation contains drawings showing the geometry both spherical and plane. Also included are the program steps for a programmable scientific calculator like the ones distributed at the NASS Conference in Chicago. The conversion of the presentation to an article fro the compendium is stalled at 80% complete. This follows the classic 80 20 rule defining work progress. Regards, Roger Bailey Walking Shadow Designs -- From: "Frank Evans" Sent: Monday, March 29, 2010 3:47 AM To: "Sundial" Subject: how italian hours > Greetings, fellow dialists, > Following the pictures of the fine dial of Frank King in Selwyn College, > Cambridge (congratulations) I began to wonder how it was laid out. Most > of the commonly consulted books on dial construction (in English), > Waugh, Mayall & Mayall, Cousins, etc. do no more than glance at Italian > and Babylonian hours. Only Rohr has some account. His practical method > appears to be to find the time and nodus point of sunrise and sunset at > the solstices, count the hours back from them and join the winter and > summer nodus points for each hour. This seems a pretty journeyman’s > procedure (nothing wrong with that) but I wonder if there is some more > sophisticated method. > > Also, the assumption seems to be made that sunrise and sunset occurs > when the altitude of the sun’s centre is zero. This is far from sunset > in any practical sense. Any comments, please? > Frank 55N 1W > > > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
Dear Gianni, I like your explanation and I like the extra comments too. You have: P1 on the equinoctial line and P2 on the horizon line This is good in theory but not so good in practice. For example, my line for Bab = 11 does not run as far as the equinoctial line or the horizon line!! Several other lines do not reach one or other of the equinoctial line and the horizon line. Another practical problem is that P1 and P2 can be quite close together and a small error in either will make for a large error in the extension towards the summer solstice curve! I very much agree with this: When a friend asks me a suggestion to draw a sundial, I always recommend him a sundial that marks the hours to sunset, that is a sundial with italic hours... My practical problem here is that it has taken me 20 years to find a client who agrees with this suggestion :-)) Now, when I look at the finished sundial, people keep coming up to me to ask, "How do I tell the time, the REAL time?" I explain that Babylonian hours and Italian hours ARE real times but this is not the answer they want. "OK," I have to say, "take the average of Babylonian and Italian hours and you will find the time on an ordinary sundial!" It is VERY nice to have an Italian Hours sundial so close to home!! Cordiali saluti Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
*HOW TRACE THE ITALIC HOUR LINES (in not horizontal sundials)* *The sundial with Modern hours (Local Solar Time) must have been already drawn. * For each point of the Equinoctial line pass one hour line with Modern , one with Italic and one with Babylonian hours. The values of the different hours are HIT = HMOD + 6, HBAB=HMOD-6 and HIT-HBAB=12 For example: HMOD=11, HIT=17, HBAB=5 --- Also for each point of the line of horizon (on the sundial) pass one hour line with Modern , one with Italic and one with Babylonian hours. Now the values are : HIT = 2 HMOD , HBAB = 24 - 2 HMOD , HIT=24 - HBAB For example: HMOD=11, HIT=22, HBAB=2 I remember that the horizontal line on the sundial is the line where the plane of the sundial is cut by the horizontal plane through the nodus (or the end of the style) --- Then to draw the hour line with the Italic hour HIT we have to find: - the point P1 of intersection with the Equinoctial line of the line with modern hour HMOD = HIT - 6 - the point P2 of intersection with the line of horizonof the line with modern hour HMOD = HIT / 2 The straight line through P1 and P2 is the Italic hour line that we are looking for. Example: if we want HIT = 22: - P1 where Equnoctial meets Modern hour line HMOD = 22 - 6 = 16 - P2 where Modern hour line HMOD = 22/2 = 11meets the horizon line. --- When a friend asks me a suggestion to draw a sundial, I always recommend him a sundial that marks the hours to sunset , that is a sundial with italic hours.. This because when a person sees a sundial, immediately looks at his wristwatch to check if it works correctly: almost always immediately he affirms that the sundial is wrong L, because he don’t know that the sundial says the time of the Sun and not our mean and artificial time . With a sundial with hours to sunset this cannot happen and the observer can never realize if I have made an error, obviously unless he is one of the readers of this list J These sundials are enough used in places where it is important to know how many hours of light remain, as fields for games, small airports, sea places, wide parks, etc. Best wishes Gianni Ferrari 2010/3/30 Jack Aubert > I have been thinking the same thing. > > That slate dial is strikingly beautiful and I like the idea of using a > completely different type of hour that does have to offer any excuses for > not being the same as what is on one's watch. Frank King's narrative write > up answered one of my questions. I had assumed that Babylonian hours must > be something from Babylon and therefore unequal hours but apparently they > came into vogue along with "Italian hours" after the arrival of mechanical > clocks. They are equal hours. > > I was struck by the fact that the Italian and Babylonian hours coincide > (cross each other) at the equinox line but not at the solstice lines. > After > staring at the two types of hours, which seem like they should be > reciprocal, so to speak, for a while I was not able to come to any > intuitive > understanding of how they work and why they are not symmetrical. > > The only detailed instructions I have been able to find for construction of > Italian hour dials is Mac Oglesby's paper on the dial he made for Moore's > Field: http://www.mysundial.ca/files/H2SSManual040801.pdf. This method > uses > trigonometry and requires calculating the sun's azimuth among other things. > > > I have no objection to using trig or computer software, but I wondered if > there any geometry-based methods for laying out Italian/Babylonian hours? > Were older dials with Italian and Babylonian hours always laid out using > trigonometry? Also I wonder about combining a vertical sundial with a > polar > gnomon with a nodus for Italian/Babylonian hours. It might be too > cluttered > and complex to be worthwhile in practice but I wonder about the > relationship > if any between the two types of dial > > Jack > > > -Original Message- > From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] > On > Behalf Of Frank Evans > Sent: Monday, March 29, 2010 6:47 AM > To: Sundial > Subject: how italian hours > > Greetings, fellow dialists, > Following the pictures of the fine dial of Frank King in Selwyn College, > Cambridge (congratulations) I began to wonder how it was laid out. Most > of the commonly consulted books on dial construction (in English), > Waugh, Mayall & Mayall, Cousins, etc. do no more than glance at Italian > and Babylonian hours. Only Rohr has some account. His practical method > appears to be to find the time and nodus point of sunrise and sunset at > the solstices, count the hours back from them and join the winter and > summer nodus points for each hour. This seems a pretty journeyman's > procedure (nothing wrong with that) but I wonder if there is some more > sophist
Re: how italian hours
Dear Jack, You go straight to the heart of the matter... > I was struck by the fact that the Italian and > Babylonian hours coincide (cross each other) > at the equinox line but not at the solstice > lines. It is, of course, these criss-crosses which make having the Babylonian+Italian hour-lines so appealing. You are right that you don't get crossings at the solstices but you DO get crossings at EIGHT other declinations besides the equinox. If sunrise is a half-integer number of hours before or after 6am then, during the day, the shadow of the nodus will trace a path through a sequence of crossing points. At each such point both the Babylonian hour and the Italian hour is an integer. This is in the latitude of Cambridge. In theory, it means there are 18 days a year when the trace goes through crossing points. In practice this doesn't happen at an equinox because the declination doesn't stick at zero all day! The extreme declinations are when the sun rises two hours before or after 6am. At you go towards the equator the number of declinations where you get this effect reduces. If you really want crossing points at the solstices, then you need to move to a latitude where sunrise, at the solstices, is a half-integer number of hours before or after 6am. I rather fancy Babylonian hours myself. I could happily get up every day at 0h Babylonian and accept that sunset may be anything from 7.5 hours to 16.5 hours later where I live. I think this means joining a rather exclusive Religious Order! All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
Dear Frank, You pose two questions: 1. How do you lay out Babylonian and Italian hour-lines? 2. Why use dubious definitions of sunrise and sunset? I attend to the dubious definitions below but let's live with them for a moment. BABYLONIAN AND ITALIAN HOUR-LINES Let B = Babylonian = Hours since sunrise Let I = Italian= Hours since sunset Let F = French = 'normal' local sun time At an equinox you can trivially convert B or I to F: F = B + 6 F = I - 6 Checks: At sunrise B = 0 F = 6 I = 12 At noon B = 6 F =12 I = 18 At sunset B =12 F =18 I = 24 When the solar declination is not zero the conversions are modified slightly: F = B + 6 - xd F = I - 6 + xd Here xd is the amount of extra dawn or extra dusk compared with an equinox. If sunrise is at 5 [local sun time] then xd = 1. Expressed as an hour-angle: sin(xd) = tan(dec).tan(latitude) Of course, xd is negative when dec < 0. All I did was to set up a spreadsheet and for each Babylonian hour I chose five declinations and worked out the equivalent French hours. That gave me five hour-angles and declinations which I translated into (X,Y) points on the slate. I checked that the straight line of best fit through the five points didn't miss any by more than 0.5mm and drew the line. Job done. Well, job nearly done... When you are cutting slate by hand, you lose the line the instant you make the first cut! Accordingly, you actually draw THREE lines: the middle one and one on either side. You then make a vee-cut between the two outer lines and accept that you lose the middle one. Where possible, the five declinations I choose were +/- eps0, +/- 12 and 0. Many of the lines went out of reach at the solstices so I chose smaller declinations in such cases. SUNRISE AND SUNSET You say (correctly): ... the assumption seems to be made that sunrise and sunset occurs when the altitude of the sun's centre is zero. This is far from sunset in any practical sense. I certainly won't disagree. Like industry standards, the great thing about definitions of sunrise and sunset is that there are so many of them! If you are unfortunate enough to have to measure the sun's altitude with a sextant when the sun is low, you have to make all kinds of tedious corrections... If you are really doing the job properly you have to allow for your height above sea level and refraction. You therefore have to allow for temperature, pressure and humidity and, probably, allow for pollutants too. All this would make it hard to deal with even a simple conventional horizontal sundial. The 6-6 lines run west to east but the sun is (apparently) due east detectably before 6am on occasions: when the declination is small and negative. You can't win! My understanding is that Babylonian and Italian hours came in AFTER the advent of mechanical clocks when (of mechanical necessity) equal hours took over from unequal hours. With an equal-hours instrument you needed a reference point to start and end the 24-hour period. There are four obvious choices: Midnight, Noon, Sunrise, Sunset [Aside: there is a fifth utterly insane choice which is 'one hour before midnight' and, curiously, that is the one which is chosen for most of the civilised world at the moment. Gh!] If you want to set a clock, midnight is not a good time to do it by the sun. Noon IS a good time but it is not easy to estimate noon if it is cloudy and raining. Sunrise and sunset can be estimated approximately (within 30 minutes) even in the foulest of weather conditions. This made these times attractive as references on early clocks (which didn't keep very good time). It was common in Italy to deem sunset to be half an hour after dark when the Ave Maria Office would be said. Some Italian Hours sundials are marked out in this way with the crossing points on the equinoctial line displaced half an hour. With that kind of history, I don't feel unhappy about using a simple geometric definition of sunrise and sunset. You will now make a note to keep me well away from the Navigation Officer's chart table! All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: how italian hours
I have been thinking the same thing. That slate dial is strikingly beautiful and I like the idea of using a completely different type of hour that does have to offer any excuses for not being the same as what is on one's watch. Frank King's narrative write up answered one of my questions. I had assumed that Babylonian hours must be something from Babylon and therefore unequal hours but apparently they came into vogue along with "Italian hours" after the arrival of mechanical clocks. They are equal hours. I was struck by the fact that the Italian and Babylonian hours coincide (cross each other) at the equinox line but not at the solstice lines. After staring at the two types of hours, which seem like they should be reciprocal, so to speak, for a while I was not able to come to any intuitive understanding of how they work and why they are not symmetrical. The only detailed instructions I have been able to find for construction of Italian hour dials is Mac Oglesby's paper on the dial he made for Moore's Field: http://www.mysundial.ca/files/H2SSManual040801.pdf. This method uses trigonometry and requires calculating the sun's azimuth among other things. I have no objection to using trig or computer software, but I wondered if there any geometry-based methods for laying out Italian/Babylonian hours? Were older dials with Italian and Babylonian hours always laid out using trigonometry? Also I wonder about combining a vertical sundial with a polar gnomon with a nodus for Italian/Babylonian hours. It might be too cluttered and complex to be worthwhile in practice but I wonder about the relationship if any between the two types of dial Jack -Original Message- From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Frank Evans Sent: Monday, March 29, 2010 6:47 AM To: Sundial Subject: how italian hours Greetings, fellow dialists, Following the pictures of the fine dial of Frank King in Selwyn College, Cambridge (congratulations) I began to wonder how it was laid out. Most of the commonly consulted books on dial construction (in English), Waugh, Mayall & Mayall, Cousins, etc. do no more than glance at Italian and Babylonian hours. Only Rohr has some account. His practical method appears to be to find the time and nodus point of sunrise and sunset at the solstices, count the hours back from them and join the winter and summer nodus points for each hour. This seems a pretty journeyman's procedure (nothing wrong with that) but I wonder if there is some more sophisticated method. Also, the assumption seems to be made that sunrise and sunset occurs when the altitude of the sun's centre is zero. This is far from sunset in any practical sense. Any comments, please? Frank 55N 1W --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: how italian hours
dear Frank, I use the trigonometric sphere. I get the formula for the angle (alpha) between the max slope line and the n italian line, then the distance (s) of the italian line from the base of the orthostyle O. The formula is for any oriented dial. I attach: - the trigonometric sphere: P is the observer, N the North, P0 the horizontal equivalent dial, I1, I2, In are the italic planes - a picture with the lines on the dial: s is the distance between the italic hour line and the base of the orthostyle - the formula, where: phi 0 and lambda 0 are the coordinates of the horizontal equivalent dial; they are calculated with i, the zenithal inclination, d, the declination and phi, the latitude. Jn is the dihedral angle between the n italic plane and the dial; it is useful to calculate s omega n is the angle between the n italic hour line and the substyle; with sigma, the substyle angle, you get alpha, the angle between the max slope line and the n italic hour line. s is calculated with Jn and a, the height of the orthostyle. ciao Fabio Fabio Savian fabio.sav...@nonvedolora.it Paderno Dugnano, Milan, Italy 45° 34' 10'' N 9° 10' 9'' E GMT +1 (DST +2) <><><>--- https://lists.uni-koeln.de/mailman/listinfo/sundial
