Re: moving asteroids
Dear Brent, I think your proposals should be examined by the Organisation Overseeing Orbital Parameters (OOOPs). They would note: > I might move the moon closer to the earth > to create better surf. Indeed it would. Total eclipses would last longer too. > Think of all the unfortunate people suffering > at the mercy of droughts or floods or typhoons > caused by the tilted axis. Wouldn't some of these unfortunate people suffer from your "better" surf? > This would also clean up the messy sundial > situation. Hillaire Belloc has something to say about messy sundials: I am a sundial. Ordinary words Cannot express my thoughts on Birds. I don't see that changing the orbital parameters would help too much with that! All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: special events
Dear John, You are not wandering too far off topic... > I used to train architectural students to > pace a metre accurately. When I take a party on a local Sundial Walk I always start off by congratulating them on each bringing along their own sundials. I ignore their blank looks and explain that every individual is a self-contained altitude dial. By pacing out the length of your own shadow you can determine the time. I then pick someone who looks psychologically robust and stand him with his back to the sun. I point to the shadow of the top of his head and ask him to see how many steps it takes to walk that far. The whole party instantly sees the problem. It is not only rainbows that are difficult to get hold of :-) I expect this practice counts as treating an individual as an experimental subject and I should ask for written consent and evidence that it is "informed consent". No doubt shadows have rights too especially if they are human! All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: special events
Dear Frank,
I must read your reference...
> I have a little book ("A Manual of
> Modern Navigation" by S. M. Burton,
> 1941) with a chapter on the particular
> case of very high altitudes.
The more I think about this, the more snags
I see. If I am very close to the sub-solar
point, and I try sweeping the horizon, I am
sure I would find that bits of ship got in my
line of sight! With the sun zipping past the
zenith I would be bound to miss the critical
moment!
I must clearly think some more :-)
You add...
> On land I believe a theodolite can be used
> to give very accurate sun altitudes.
Ah. Here I do have a tiny bit of experience
and I hit another snag. Take a look at
http://www.surveyequipment.com/total-stations
You will see what modern instruments are like.
They all have handles across the top which stop
you looking close to the zenith.
Even with a lowish-altitude sun there are snags.
You can't (sensibly) look at the sun through the
telescope without suitable precautions which
require a special purchase. When you fix it all
up you then find that the bottom part of the unit
gets in the way. You can't get your eye near the
eyepiece.
Alas, I am definitely a theoretical navigator
and surveyor rather than a practical one!
Very best wishes
Frank
---
https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Falling Tree
Dear All, We must assume that the tree casts shadows when the sun shines! That keeps the topic relevant! The topic was much discussed by 18th century philosophers. The debate centred on the Latin maxim Esse ist percipi to be is to be perceived. If it isn't perceived then does it exist? Someone wrote a limerick on the subject and referred to a tree which he could see in the middle of the college quadrangle: There was a young man who said "God must find it exceedingly odd, that the tree that I see continues to be when there's no one about in the quad." Unsurprisingly he received a prompt reply: Dear Sir, your astonishment's odd. I am always about in the quad, so the tree that you see continues to be since observed by, yours faithfully, God. All the best Frank H. King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Leap year
Dear Brooke, You ask: > Can you say more about how to read the photograph > you attached? Yes. On a given day around Local Mean Solar Noon you watch the splodge of light from the aperture nodus cross the analemma. The analemma is, in some sense, drawn with a very wide brush and it takes four minutes for the splodge to cross this width. That's one degree of hour-angle. When the splodge is half-way across the time is local mean noon. The analemma is broken up into strips. The design has 366 strips, one for every day of the year including 29 February, but the strips at the solstices are impractically thin. You note which strip the splodge is travelling along and this gives you the date. Fortunately, at the end of February the declination is changing quite rapidly so the strips are quite substantial and even the (almost) quarter-height strip is easy to see. > Is there an existing dial that incorporates > detection of 29 Feb? The photograph IS of an existing dial. The limitations of the Gregorian calendar mean that it will drift out of sync with the dates after 40 years but the design life of the building isn't much more than that and I won't be around to bother about it!! Life would be so much better if we had the Omar Khayyam calendar that Roger Bailey was writing about. That would take a very long time before things went out of sync. All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Unique Old British Sundial
Dear Roger, This is all good fun. You note... > The underlying image of the sundial is clearly > for a 1755 sundial at 55°... If you zoom in on the pelican version you can see that the 55° turns into 53°. This squares with the latitude of Eyam which is 53°20'. On Patrick Powers's photograph the 53 does look like 55 but the "20 minutes" shows up clearly. All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Portable Sundials
Dear Mike, I see that Amazon are claiming that your book "A Dial in Your Poke" about portable dials and suchlike is "currently unavailable". Can you confirm this? I am copying this to the SML in case anyone else has wondered. All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Proceedings for Future of UTC meeting
Dear Rob, No one seems to have responded to your message of 1 December in which you drew attention to: http://futureofutc.org/preprints Apart from the nice picture of the Prague clock this is rather heavy going! For lighter reading, I turned to the comments that were sent in from round the world: http://www.cacr.caltech.edu/futureofutc/preprints/18_AAS_11-668_Epilogue.pdf Numerous contributors familiar to readers of this mailing list sent in comments including: Tony Finch Rob Seaman Patrick Powers Frank King John Davis Christopher Daniel The summary showed that there were about 450 contributors of whom 76% were in favour of the status quo [keeping the leap second]. Two comments especially appealed to me: John Davis said: I (or my descendants) do not wish to have noon drift into the middle of the night. An anonymous contributor said: If you want a timescale with a constant offset from TAI, why not just use TAI? Many others said much the same less succinctly! The Royal Institute of Navigation seem to have been allowed the last words and say: In summary, making this change to UTC has a rather esoteric rationale, limited benefits and potentially significant costs. Unfortunately, the matter remains unresolved. Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Proceedings for Future of UTC meeting
Dear Mac, You say: > May I ask a stupid question? They are often the best. Remember the recent thread started by someone who thought it wrong to imagine that the sun moved across the sky? [I didn't respond to that one, but insisting that the sun stays in the same place would mean you couldn't say "Oh, what a beautiful sunset." You would have to say "Oh, look at that beautiful horizon-rise" instead!] > What was wrong with AD and BC? There are strange people who seem to suffer an attack of the vapours when they come across anything hinting at religion. This pretty much rules out studying a good many subjects. You can't study architecture, astronomy and certainly sundials for very long without coming across Egyptian gods, Greek gods, Roman gods, Christian practices, Muslim practices and all the rest. In the case of AD there is the additional problem that it stands for two Latin words and other strange people think that using a dead language isn't user-friendly. They won't get far studying the history of science either! Happily, Latin isn't quite dead. I am one of 40 or so people in my neck of the woods who is actually paid to declaim Latin in public (loudly and with enthusiasm!). Enjoy your 2011 Christmas. Now just what was it that was going on 2011 years ago? Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Proceedings for Future of UTC meeting
Dear John, I like your story about the times quoted by the Darwin control tower. In some of my introductory talks about sundials I mention Unequal Hours, Babylonian Hours, Italian Hours and so on. Just when the audience thinks this is offering more choice than they can cope with, I explain that things are little better when you use clock time. Your story illustrates this nicely AND also illustrates the use of different levels of precision. I may plagiarise this next time I give such a talk! All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Proceedings for Future of UTC meeting
Dear Dave, Hmmm. Hard to comment on this... > "... Jesus was only 7 years old..." Given the absence of zero, 2011 years ago takes us to 1BC. There is a little uncertainty but current best estimates of the date of birth seem to fall in the range 6BC to 4BC which would make the age between 3 and 5 years. I guess we agree that not a whole lot was going on! There is a well-known sundial near where I am sitting which has an inscription that uses A.S. instead of A.D. Brookes and Stanier say that this stands for Anno Salvationis but I feel that Anno Salutis is also a candidate. Both mean In the Year of Salvation and I wonder whether using A.S. might cause less distress to those who need smelling salts when they read A.D.? No doubt someone can tell me how common it is to see A.S. on sundials? We can be fairly sure that you don't often see B.C. on sundials, at least not as the date of manufacture :-) Felix Nativitas Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Sundial and the Leap Second
Dear All, Patrick Powers has drawn my attention to the recent non-vote on the future of the Leap Second. Those interested will probably already know that the vote that was planned for this week has now been delayed until 2015. If you Google... Leap Second Future or Leap Second Vote You will find more hits than you can cope with. The one with the best picture is: http://www.dailymail.co.uk/news/article-2088798/Leap-second-Conference-bigges t-timekeeping-change-centuries.html?ito=feeds-newsxml There is a nice view of a sundial resting on a plinth but not bolted down. Could this be a Tony Moss or John Davis dial? The caption "...rendering sundials useless" is a little over the top in my view! The impression I get is that the Canadians, the Chinese and the British are in favour of keeping leap seconds but the French, German and U.S. authorities want to get rid of them. Would any French, German or U.S. contributors to this mailing list care to comment!! Frank King Cambridge U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Sundial and the Leap Second
Dear John, You are right... > I think I recognise it as one of the > Connoisseur Sundials range. Take a look at: http://www.sundialsonline.co.uk/ You will see the very dial as the second from the left. It is the same one right down to the absence of screw heads! > But the bad (UK) news yesterday was about > the upcoming parliamentary vote proposing > (yet again) that we adopt permanent BST. What this really means is extending the Central European Time Zone westwards. Can we lobby that this is just as unwise as joining that other Eurozone? All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Decision to eliminate the leap second deferred
Dear Wolfgang, Your report on the UTC and leap second discussion notes: The suppression of the leap second would make a continuous time scale available... This is quite true but there are already at least three continuous time scales available: International Atomic Time TAI Dynamic Time TD GPS TimeGPS Those who don't like UTC don't have to use it. That's no reason for denying its use to those who do want to use it. Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: medieval astronomy (was: Georg of Peuerbach)
Dear Roger, Sara's message merits serious study! We here in Europe weren't totally asleep in medieval times or even in the so-called dark ages following the Fall of Rome. [A fair proportion of Europe seems to be falling asleep just now but that's not the period you are referring to :-) ] There is a street in a town in Italy (probably Perugia but my memory may have failed me) where there are examples of architecture of every century from the first to the 20th. This is a very convincing way of seeing the continuity of design and craftsmanship. A quite different way of pondering continuity in Europe is to look at the complete list of Popes at: http://www.newadvent.org/cathen/12272b.htm There is a biography of each one. Things really were going on even at times that historians seem not to have popularised. Take Pope 33 for example, S. Sylvester. He may or may not have convened the Council of Nicea in 325 but he took part in it. This Council discussed how to determine the date of Easter which motivated much study of the length of the year. Pope 227, Gregory XIII, set up the commission which gave us the current calendar and led to the setting up of the Vatican Observatory which is one of the oldest astronomical research outfits in continuous existence. Pope 244, Clement XI, commissioned the great meridiana in the Basilica di S. Maria degli Angeli in Rome, again to study the length of the year. Now I need a nap. All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Ante diem bis sextum Kalendas Martii
Dear All, A Happy Leap Year Day to everyone... Those who think that I am a few days early should read my little article in the December issue of the BSS Bulletin. The explanation lies in the almost obsolete English term "bissextile year". Few people with English as their mother tongue use this term these days but it is alive and well in Italian. Key "bisestile" into Google Translate and ask for an Italian to English translation; you will get the answer "leap". Amazing, albeit misleading! The Romans dealt with leap years by doubling the length of the sixth day before the first of March and this was referred to as: ante diem bis sextum Kalendas Martii before day twice sixth first of March It took a while before the fiction of a single 48-hour day was accepted as two ordinary days and, importantly, it was the first of these two days which was deemed the intercalary day. As far as I know, only Finland and Sweden have enacted legislation to change what the Romans bequeathed to us so, unless you are reading this in Finland or Sweden... Today is the intercalary day. Enjoy it! The next time I design a date-showing sundial I shall probably show the extra day for leap years between 23 and 24 February rather than between 28 February and 1 March. It is interesting to compare the English, German and Italian Wikipedia entries for bissextile years: http://en.wikipedia.org/wiki/Bissextile http://de.wikipedia.org/wiki/Schaltjahr http://it.wikipedia.org/wiki/Bisestile The English gives the Latin as: ante diem bis sextum Kalendas Martii This is correct post-Classical Latin. The German gives the Latin as: ante diem bis sextum kalendas martias This is incorrect: martias is here accusative when it should be genitive "of March". The Italian gives the Latin as: bis sexto die ante Kalendas Martias This is most interesting. The Martias is again incorrect but the "sexto die" is correct PRE-Classical Latin using the ablative for point of time. For reasons of euphony, the word order has been changed to put "ante" after sexto die; an ablative after ante, while correct, didn't sound right! MORAL: when using Wikipedia be very careful; read an entry in at least three languages before making up your mind! Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Ante diem bis sextum Kalendas Martii
Dear Roser, You are right that checking Wikipedia entries in several languages is interesting. They all make mistakes!! Spanish: this entry is correct to say that 24 February is the extra day but has little to say about the Latin. Curiously it mentions the Italian word but asserts that this is bisestil instead of bisestile. Catalan: this has a big error (in my view) by saying the extra day is inserted 'entre el "sextus" i el "quintus" de les calendes'. The extra day is inserted between the seventh and the sixth, not between the sixth and the fifth. French: this makes the same mistake as the Catalan entry but expresses it differently: 'Ce jour "additionnel" se plaçait entre le 24 et le 25 février.' No! The extra day is between the 23rd and the 24th February! If the extra day were between the 24th and the 25th then there would be no need to shift S. Matthias's day in Leap years. The original concept of a single 48-hour day had some merits. You still had only 365 different dates and no problems of being born on 29 February. Indeed there was the advantage that anyone born on 24th February would have a double-length birthday every four years. If we still had a single 48-hour day, date-showing sundials could simply have the strip for 24 February a little thicker than its neighbours. Maybe I'll do that next time! I have heard it said that another merit was to make life easier for astrologers. Translated to the present day, your horoscope should be the same tomorrow [25th Feb.] as it is today [24th Feb.]. I had better check the down-market press. Make the most of today, all 48 hours of it! Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Charles V document...
Dear Ruben, That is an interesting document and what you say is strictly true but it requires thinking backwards!! The document says: San Matias 24 febrero en los anos comunes, y 25 en los bisiestos This is right. The difficulty, as you say, that we are "in reverse mode"! Thus, when you are counting I, II, III, IV, V, VI, VII and so on and you add something "after the sixth day" this goes between VI and VII as: I, II, III, IV, V, VI, [extra], VII BUT when we think of this as a count-down it all gets reversed: VII, [extra], VI, V, IV, III, II, I S. Matthias (in English) has his day 6 days before the Kalends of March, WHATEVER kind of year it is so he sticks on VI. BUT when you measure from the start of February, as we do nowadays, he gets shifted from 24 February to 25 February. It is only a question of how you label things. When the labels are stuck on in reverse order it is best not to talk about "before" and "after" because you need to say which way you are going :-) The bisextus is really the full 48-hour period which, these days, account for 24 February and 25 February. So, we can continue enjoying the bisextus tomorrow! All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Pridie Kalendas Martii
Dear All, A Happy 29 February to everyone... Even I recognise that this date is out of the ordinary, while not acknowledging it as the extra day in a bissextile year! My plan is to visit Paternoster Square but there are hazards aplenty: Strong Police presence Heavy presence of the Square Security people Even heavier presence of the Stock Exchange Security people Total absence of sun Sometimes planning a sundial visit means packing a lawyer alongside your camera! I shall not be taking a tent! This must be the most challenging public sundial to get at in Britain. I accept that sundial visits to the Great Mosque in Damascus just now are probably even more challenging. Tomorrow is the Calends of March and we can all get back to normal after recent calendrical excitements! Frank King Cambridge, U.K. Dear Patrick, Thank you for your message and the notes. It looks to be a big room for the talks. > Perhaps you could let me have 60-80 > words for inclusion in the programme... You add... > I'm very intrigued... Yes. I wondered what you made of the slides :-) Well, try the following... See Naples and Dial - An Italian Job This is a fast-moving story. A contemporary English diallist works in harness with the Roman poet Virgil (and a number of others) to produce an unlikely analemmatic sundial in a truly exotic setting. There is a mystery courting couple, the brooding presence of Vesuvius, hints of Mafia involvement and a Fred Sawyer style geometry lesson. You will need to pay close attention. Alas, there is a sad ending. Now I wonder whether this has made things a little clearer! All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: When the Transit of Venus Transits the Meridian...
> Publicity is already building to its expected crescendo on > 8 June 2004 when Venus will transit the Sun's disk... > So how can a dialist participate in the fun? A truly fascinating question but, sadly, I suspect the answer is to use a telescope! > I notice that the six-hour event's final minutes transpire > just as the Sun culminates over Italy... Indeed so. The Italians have all the luck and it probably won't be cloudy there either! > ... the location of several marvelous meridiane. As you say these can be thought of as pinhole cameras and you can do some simple calculations... A very crude model of a pinhole camera is to think of it as constructing an image out of pixels with each pixel the same size as the pinhole. [This is crude because the pixels all overlap but you get the idea.] At the time of transit, the angular diameter of Venus will be almost exactly one arc-minute so you want your pinhole to subtend an angle no more than this if you are to stand a good chance of seeing Venus. At Milan Cathedral, for example, the pin-hole is 25.2mm in diameter (information from Gianni Ferrari whose reply will be definitive!) and for this to subtend an angle of one arc-minute you have to be about 87m away. Unfortunately the height of the pinhole above the Cathedral floor is under 24m and, being close to the solstice, the solar altitude will be high too. You are going to get only one third of a pixel or so and I don't think you will notice the smudge. Gianni: please tell me I'm wrong! Frank King Cambridge University England -
Re: When the Transit of Venus Transits the Meridian...
Hi Gianni, Thank you for your illuminating calculations. I have now reproduced your figures. As always, I find your explanations both fascinating and challenging! At noon on 8 June I think the altitude of the sun will be about 67.4 degrees in Milan. If the hole height is 23821mm then the hole-to-image distance is about 25802mm but this is close to your value of 2570cm. I agree with your description of the image of Venus: it has an inner diameter of about 18mm and an external diameter of 33mm. Of course, this is the minor axis of the image. The image is really an ellipse and the major axis is slightly longer than this. Is my understanding correct here? Here is another calculation and I would welcome your comments... If you put your eye at the centre of the image (at noon on 8 June) and look at the hole, you will see that the hole is slightly elliptical (because you are not looking at it from directly underneath). I think the angular measurements of the hole are: major axis = 1/1024 radians minor axis = 1/1108 radians The angular diameter of Venus (which is still circular in this view because you are looking at Venus and not its image) is 1/3440 radians. The proportion of the elliptical hole which is taken up by Venus is: (1/3440).(1/3440) / (1/1024).(1/1108) = 0.096 [This is pi.r.r / pi.a.b ] So, with Venus in the centre of the hole, you are still getting 0.904 of the brightness of the rest of the image. This roughly agrees with your figure... > The illumination is 0.92 that of the Sun image... Is my calculation sensible? The contrast is indeed very low but if you can persuade the Cathedral authorities to cut out all the ambient light then it just might be possible to see Venus. That would be utterly amazing! It is late at night for me so my calculations may contain mistakes! Frank -
Re: Wall Declination Measurement
Dear Alex, Thank you for your rapid reply... > As architect my comment on no.1. is that the north arrow which > we place in drawings (at least the ones I place) are based on > the North direction on large scale survey maps supplied by > planning authorities and on which the drawing would be based. That certainly makes sense. Here in the U.K. we would have to know whether the large scale map used true north or grid north but, subject to that caveat, your arrow ought to be within a degree or two of being right. The main reason for errors of 15 degrees or so seems to be a result of modern surveying practice using instruments which measure distance as well as angle... What seems to happen is that the surveyor takes ONE primary point on a building site and marks this on the ground with a pin and a little circle. This is the origin of an x,y,z coordinate system in which positive z is vertically up and the x-y plane is horizontal. This still lacks an orientation. In theory, positive y is due north and positive x is due east. Surveyors don't actually use the letters x, y, and z but talk about Easting, Northing and Height respectively. I have watched these guys at work. When they start off, they choose a reference origin quite carefully (you don't want a spot which is going to be built over or have huts on it) but they are much less fussy about orientation. They will simply guess which way is north (or east if that is more convenient) and slap a target on a wall and use that as their reference orientation for the whole construction period. If it is 15 degrees out no one seems to mind! Maybe surveying practice is more rigorous in Malta! Frank -
A Sundial Drama in One Act
Dear All, I have just had an unnerving experience. I may even need counselling... There was a hint of sun first thing this morning so I decided to go to London to look at some sundials close to the winter solstice. [Yes, I know that is not until tomorrow but there may not be any sun then. I am writing from England!] All went well for a while until I set myself up in a nice square in the City. [I daren't say exactly where for security reasons but it was approximately 51d 30m 54.5s N and 0d 5m 58.7s W.] I had my usual kit with me: tripod, camera, binocular, radio-controlled watch, note-book and so on. All was fine for about 10 minutes but I suddenly found myself surrounded by about a dozen burly security men. The Chief Security Man (CSM) advanced menacingly... CSM: Can you tell us exactly what you are doing? ME: Er yes, I'm looking at that sundial over there. CSM: But we have been observing you taking photographs of that building. ME: Well yes, the sundial is on that building. CSM: But on at least one occasion you photographed one of my security officers. ME: Oh yes, I remember one of them getting in the way. CSM: Do you not appreciate that you cannot just go around photographing buildings without arousing suspicion? ME: Er, this is London. Even at this time of year it is full of tourists taking photographs of buildings. CSM: But you are taking photographs of just one building. ME: Well it's the only one I am interested in just now. We continued talking nonsense like this for quite a while when a Police Sergeant (PS) arrived on the scene. In the end he rescued me but not without more fuss... PS: Is there a problem. CSM: We have been observing this man taking photographs and making notes. PS: Is this true? ME: Indeed so, that's why I came here. PS: May I look in your bag sir? ME: Yes, here it is. He had a good look at a collection of suspicious looking spreadsheets and my heart sank when he spotted a large-scale map with markings that could be interpreted as lines of fire. Fortunately none of this seemed to worry him and he moved down the pile to a collection of photographs of sundials. Then my heart stopped... PS: I see you have a photograph of the Houses of Parliament? ME: Well it's really of the sundial in the street outside. PS: Oh, is that what it is? ME: Er yes, it's one of mine. Perhaps you would like to hear about analemmatic sundials? PS: Not today I think. Happily he was clearly able to distinguish the ordinarily insane from the criminally insane and he explained to the bemused security men that he had decided that I was not a threat. Moreover he gave me his rank and number and said that I could mention his name if I came again. Phew! I'm glad he didn't search my pockets where he would have found my Class III Laser pointer. Frank King Cambridge, UK -
[no subject]
Hi Daniel, > The Equation of Time is zero today so Christmas is a great > time to give, receive or set sundials. Yes, but don't forget the offset for longitude! > Are the dates of perihelion and solstice close at this time > by coincidence... It's coincidence. The most recent occasion that they were (almost) coincident was in 1246 (see Meeus) when the analemma was symmetric about a vertical axis. The shape of the analemma steadily changes with precession. Sadly, this means that all of us who have designed sundials which incorporate analemmas have to accept that they steadily go out of date. Not that we live long enough to notice! Happy Christmas Frank King Cambridge, U.K. -
Re: Oblate Spheroid correction for computing distances?
Dear Thad > As many of us know, we can geometrically compute the distance > between two locations (lat, long) and (lat2, long2) assuming > that the Earth is a perfect sphere (which of course it isn't). > > Has anyone seen a correction for this flattening at the poles, > or bowing around the equator? As always, Meeus has the answer. The crucial difference is that between geographic latitude and geocentric latitude: The geographic latitude is the apparent altitude of the nearer celestial pole measured above the northern (or southern) horizon. Meeus calls this phi. The geocentric latitude is the angle that a radius from the centre of the Earth to the observer makes with the plane of the Equator. Meeus calls this phi'. The difference is given as: phi - phi' = 692.73 sin(2 phi) - 1.16 sin(4 phi) The constants are arc-seconds. The greatest difference is at a latitude of 45 degrees when the difference is about 11.5 arc-minutes. This translates into about 11.5 nautical miles. This is the about the error where you live! Geographic latitude is what is normally measured and used. This is what is marked on maps. There is an implicit assumption that the plane of the horizon is perpendicular to the local gravitational vector. This means you can use a normal sextant or other instrument that measures relative to the horizon or you can use an instrument that has some kind of spirit-level built in. Beware of massive mountains nearby! Frank King University of Cambridge England -
Re: Birthday
> Happy birthday > Nikolaus Copernicus! > February 19, 1473 in Thorn Thank you for sharing this with us. I appreciate the thought even if others grumble. Of course, his name wasn't Copernicus, the date is open to doubt and he wasn't born in Thorn. He was born in Torun (Thorn is the Prussian version) where, by the way, there are many interesting sundials. Never mind. I like to be reminded of this revolutionary! He is a hero of mine. Frank King University of Cambridge England -
Re: Magnetic variation.
Dear Tony, > As any diallist is painfully aware the most probable event for > dial installation is an obscured sun all day... Indeed so! > ... we may be forced to do the diallistically unspeakable > viz. a temporary magnetic alignment... May I suggest that you equip yourself with a cheap handheld GPS station? The last time I was in Longyearbyen was before the days of GPS but several of my pals have been there more recently and confirm that GPS works perfectly well there. If there is a decent amount of space round your intended site you can simply walk northwards (or southwards) from the site of the sundial, checking that your longitude doesn't shift in the last decimal place. The further you can walk the better! Walking eastwards or westwards is just as good but holding any other course with cheap GPS kit is less easy. You should then obtain a true north-south line better than a magnetic compass will ever give you. Richard Langley has already explained why. He is right! If you want really good results with the GPS then you need to use very expensive kit that uses a master-slave system but that won't be necessary if you just want to be within a degree or so. Frank King University of Cambridge England -
Re: calendar
Dear Frank Everything Mike Shaw says is right. My own eclectic notes suggest that the 10 so-called `missing days' were accounted for by the leap days in 300, 500, 600, 700, 900, 1000, 1100, 1300, 1400 and 1500. These would have been omitted under the Gregorian leap-year rule. In my view it would have been better to have missed out 11 (but I wasn't consulted!) which would have had the added bonus of putting the Vernal Equinox on 21 March (at the longitude of Rome) more often than is the case. Noting Mike Shaw's comment about the late change in Greece you might think about what happened in Alaska... Alaska changed when it was bought from Russia by the United States which, as an English Colony, had adopted the Gregorian Calendar in 1752. It was decided not only to change to the Gregorian Calendar but also to re-route the International Date Line from the east of Alaska to the west. That action by itself retards the date by one day. Further thought is merited... The old calendar continued throughout Friday 6 October 1867 (Julian). The change was not made at midnight but early next morning. There was a brief period of Saturday 7 October (Julian) which was equivalent to Saturday 19 October (Gregorian) but the shift of the International Date Line meant an abrupt backward change to Friday 18 October (Gregorian). Accordingly, the citizens of Alaska went to bed on Friday 6 October and woke up on Friday 18 October having experienced a few hours of Saturday 19 October while still asleep. They then duly lived through Friday again and before experiencing Saturday 19 October once more, this time for a whole day! To make life more interesting still, these citizens had also to adjust to being part of a different country, having a different language, a different currency and a different culture. You many need to read all that three times to take it in but I am pretty sure it is true! Frank King University of Cambridge England -
Re: sundials in Rome (Capitel of Italy)
> I can send you 2 files with a complete list of topic sundials in Rome. The > files are scannerized from the catalogue "Meridiane dei Comuni d'Italia". > The file size is around 1 Mb. Please, let me know if you want. Please could you send me these two files. I should be most interested. Thank you very much. Frank King Cambridge University England. -
Re: explain analemmatic (human) sundial to children
> Are there any suggestions as to how to explain to children > ...the way the analemmatic sundial functions? Here is a simple explanation that I use when giving talks in schools to children aged about 8. I stand in the middle of the class holding a yellow balloon at the end of a long stick. [They like this and some lucky child gets the balloon at the end.] I stand facing north. [I stick up a large letter N on a wall so they know where north is.] I then do a lot of pointing... 1. At an equinox the sun rises at 6am due East and sets at 6pm due West. I make one child stand at the 6am hour mark and another stand at the 6pm mark. 2. At the summer solstice the sun rises much earlier AND much further to the North. By 6am it is quite high but STILL North of due East. At 6pm it is equally high but North of due West. 3. If your 6am and 6pm hour marks are due East and West of where you are standing you obviously have to walk forward (North) a bit for your shadow to be in the right place. They seem to accept this explanation even though it has a few holes in it! Sometimes I get an assistant to walk round with a 3kw light to make a shadow. Oh! I usually start with the vernal equinox and wear a green pullover to indicate spring. At the summer solstice I take this off and put on a sun hat. At the winter solstice of course I put on a fur hat. One child wrote me a letter afterwards: `I did like the way you kept changing your clothes'. Frank King Cambridge University England. -
Another human sundial for children
Len Berggren, Ronit Maoz... Several people have been kind enough to comment on my tips for entertaining children so I will divulge one more... I ask for eight volunteers to step forward and I give each one a flag. The tallest child gets a flag saying `12 noon' and the smallest gets one saying `12 midnight'. The others get flags at three hourly intervals: 3am, 6am,... I arrange the children in a circle facing outwards with the 12 midnight child facing due north. I explain that I will walk round with my yellow balloon pausing at the positions of the sun at the different times. I explain that the relevant child will then have to point at the balloon with the flag. I start with the vernal equinox and begin at 6am. The 6am child has to point horizontally due east, the 9am child points up a bit and roughly south-east and so on... The 6pm child points horizontally due west of course but then comes a difficulty. What happens after the sun sets? No problem. `Imagine we have a see-through Earth', I say. [To demonstrate that this is perfectly reasonable, I bring out a blow-up transparent globe which you can buy in stores. `Look', I say, `a see-through Earth'.] I then continue round the circle holding the balloon very low at 9pm and 3am and right on the floor at midnight. I then have to do a bit of adjusting to get the effect I want but I can usually get the children's arms to be roughly co-planer so that they form the spokes of a fairly convincing disc shape. What I want to get across is that this disc isn't horizontal. It dips towards the north. [Later I do the Summer Solstice and show that we get a cone shape and later the Winter Solstice which also gives a cone but the other way up. Different hats of course!] Then I say, `Now we have a sundial made out of boys and girls and I am going to show you how to use it...' I explain that you tell the time by seeing which flag is most closely pointing to the balloon. I might hold the balloon so that the 9am flag is pointing at it. I ask the class as a whole, `What time is it now?' and they will say `9 o'clock'. `But we can do better than this,' I say. `This sundial is made out of boys and girls so we can ask the flag-holder what the time is. I duly ask the boy or girl holding the 9am flag, `What is the time on your flag?' `9 o'clock' will be the reply. `So, children, you see what a magnificent sundial this is. It is a SPEAKING SUNDIAL and it is the only one in the whole world.' Frank King Cambridge University England -
Re: Declination approximation?
Dear John > Is there an approximate formula for the declination of the > sun vs day number? This is a tantalising story which doesn't really have a happy ending! Only gluttons for punishment should read any further... Your solution is a good starting point: > I just tried the obvious > > 23.44*SIN[(day number)*360degrees/365.2422] You have taken the obliquity of the ecliptic as 23.44 degrees which is close enough. You implicitly start at the Vernal Equinox (day number = 0 gives declination = 0) and you have taken the length of the year as 365.2422 days. You can improve on this by looking at: http://www.sundialsoc.org.uk/glossary/frameset.htm This is the truly wonderful Glossary of the British Sundial Society (it is edited by John Davies) and you will find under Equations (look for number 9) the following Fourier transform: D = 0.006918 - 0.399912 cos w + 0.070257 sin w - 0.006758 cos 2w + 0.000907 sin 2w - 0.002697 cos 3w + 0.001480 sin 3w where D is the declination in radians. The parameter w is also in radians and represents a proportion of the year scaled to the range 0 to 2pi. Using your scaling, you could take w as: w = (day number)*2pi/365.2422] Here, though, day number = 0 corresponds to somewhere around 1 January. The maximum error is said to be 0.0006 radians (less than 3 arcminutes). If you want to do better than that, you can implement the appropriate algorithms described by Meeus and you will find yourself keying in over 500 constants. It is very rewarding to get these right but it takes quite a while! The real difficulty is what you mean by `day number'. If you are just interested in the fraction of the year from the Vernal Equinox then you need take in no more. If you want to relate `day number' to a date then you will be defeated by the Gregorian Calendar. You can see the problem by asking the reverse question, `What is the day number corresponding to a given declination?' Even if you take a nice easy declination, like 0 degrees, you find the date varies by over two days over the 400-year Gregorian cycle. On the Greenwich Meridian the instant of the Vernal Equinox varies from late afternoon on 21 March (e.g. 1903) to early afternoon on 19 March (e.g. 2096). If you are in a different time zone you may well be the other side of midnight so the date changes again. Worse still, counting days from 1 January involves having to include 29 February one year in four which throws out the count by one day for the rest of the year. I said there wasn't a happy ending but if you want some light relief you can read a nice article that alludes to this kind of thing in the latest, March 2004, Issue of the British Sundial Society Bulletin. I wrote it myself and it's about a sundial I did for the Queen a couple of years ago! Frank H. King Cambridge University England -
Re: Declination approximation?
Dear John, > ... by now, you will have received a copy of the scanned and > OCRed paper which was the first publication of this equation. That's fascinating. Many thanks. It's always good to see the original paper and this seems not to be acknowledged in the BSS Glossary under `Sources'. I didn't copy the expansion for the Equation of Time but I note that the BSS Glossary has reversed the sign used by Spencer. I take the Spencer view myself. > I wonder what Spencer would think if he knew that his research > on air-conditioning of buildings would be helping diallists > 30 years later? It is amazing that the Equation of Time can have any relevance to air-conditioning! Are Australian air-conditioning units fitted with time-clocks that come on up to a quarter of an hour early or late depending on E? Do the guys who install the plant take longitude offset into account too? Hey, you could even have your air-conditioning plant controlled by a sundial on the roof. Perhaps there is a new market for our trade waiting to be exploited! Frank -
Re: Roman Numerals - as a test message
Message text written by Patrick Powers > ...out of 446 dials which show 4am or 4pm and where I have now > entered this sort of detail, 273 use and 173 use IV. This is wonderfully quantitative information and my guess is that the ratio would not be much different for clock faces. > ... usage actually varies with type of dial... Other things being equal, I would naively expect on vertical dials to find (for 4pm) used more on an east decliner where the pm time lines are more widely spaced and IV used more on a west decliner where they are closer together. Of course, other things are often not equal because one can deliberately choose to place the noon line off-centre and so so on but it would be interesting to know whether your data support the naive hypothesis! Frank King Cambridge University England -
Re: Wall Declination Measurement
he hyperbolic path followed by the image of the sun on a given day and, with luck, the image will cross some of the circles twice, once before and once after noon. Taking these crossing points in pairs, find the mid-points. They should align with one another and with the point perpendicularly below the hole. This is your north-south line. Verdict: Fine if you are Cassini; I haven't tried it! 8. Using Stars A technique used by the surveyors responsible for digging railway tunnels in the 19th century was to follow a circum-polar star round the celestial pole and note its most easterly and most westerly points. Half-way between is due north. This sounds easy in theory but needs the right kit, the right kind of experience, a clear night, thermal clothing and considerable skill. I cannot imagine how they avoided freezing to death in the U.K. winters! Verdict: Not for beginners Incidentally, real walls can be a right pain! They aren't flat and they aren't vertical and you can easily come to grief. For large wall dials, a good deal of practical dialling amounts to a hard slog analysing survey data and undertaking laborious error analysis, but that's another story. Frank King Cambridge, U.K. -
Re: Turtle Bay Sundial Bridge opens
Hi John, At last signs of the truth... > Theoretically it's correct that the projection of a circular > disc on to a flat surface parallel to the disc will be a circle. > Unfortunately the sun's apparent size results in the disc becoming > very blurred when you get a couple of hours off of local noon. The theory suggesting that a circular disc casts a circular shadow depends on the sun being a point source of light which is isn't! If the model on which the theory is based is refined to take the angular diameter of the sun into account, you find that the shadow is generally degraded into an approximate ellipse whose major axis is less than the diameter of the disc and whose minor axis is smaller still. The actual shape at a given time can be determined by noting the shape that the image of the sun that would form if the sun were projected through a pin-hole at the centre of the nodus (this image really is a true ellipse). You then draw the circular shadow that the simple theory suggests and at each point on the rim you draw this ellipse, being careful to preserve its orientation. You then get two envelopes, the inner of which is a fair approximation to the true shape of the shadow. The inverse of this effect occurs with an aperture nodus. The anti-shadow of a circular hole likewise distorts into an approximate ellipse but its major axis coincides with the minor axis of the shadow of the surrounding disc and vice versa. Of course the anti-shadow is bigger than the original hole. You have to use the outer envelope. Unless a nodus designer understands all this, it is ever so easy for the anti-shadow from the hole to exceed the size of the shadow of the surrounding disc. The result is indeed pretty useless! Frank King Cambridge University England -
Re: Turtle Bay Sundial Bridge opens
Hi John, > This little distortion effect must be quite small... You are right. > For practical purposes, you can call the shadow a circle... Right again. > ... even though it's a tiny bit elliptical. Yes again (though the tiny bit isn't quite an ellipse!). > If the disk is large, this effect becomes almost insignificant > doesn't it? Yes, again absolutely right. With a sufficiently large disc the distortion is indeed a trifle but... Some designers, hoping for a nice small shadow to pin-point the features on their dial furniture, like to have the disc as small as possible subject to it casting a shadow. This is when you have to be careful. There is nothing wrong with an elliptical shadow (that's what you get from a spherical nodus almost all the time) provided it doesn't fade away to nothingness! > I'm going to do the simple experiment tomorrow if I have time. > I also want to test how useful a horizontal disk is in the early > morning and late afternoon and I want to try a disk with a central > aperture hole. This can be a profitable experiment. You may not find any distortion at all unless you look out for it. The effect is best if the solar angle of incidence is about 70 degrees (that is the angle off the normal) so, on a horizontal surface, the altitude would be 20 degrees. If you hold a circular disc about 100mm in diameter about 1500mm from the surface you should see the effect. The anti-shadow from a hole about 15mm in diameter should distort nicely too and much more noticeably than the shadow of the outer rim of the disc. In my home town, many of the street lights have circular fittings at the top about 300mm in diameter and about 4500mm above the pavements. These distort nicely when the sun angle is low. You have to be careful. I found I got a lot of funny looks from passers-by when I was studying the shadows cast by street lights! It is important to note that for a wall dial you can easily get angles of incidence greatly in excess of 70 degrees. At noon on the summer solstice with a direct south-facing wall at latitude 52 degrees the angle of incidence is about 61 degrees and that is the *minimum* angle of incidence for the day. If the wall isn't direct south-facing, the angle of incidence is higher even at noon. I hope your experiments are rewarding. Frank King Cambridge, UK. -
Re: Dawn shadows on an east/west wall
Noam Kaplan queried: > ... why does Waugh write that the sun will never shine on > a vertical direct south dial before 6 AM or after 6 PM? Hmmm. The erudite answer from Tony Moss notwithstanding, this assertion, as written, is not strictly true. With his recent travels to the Far North fresh in his mind, Tony will know that once you cross the Arctic Circle all kinds of rules start to go awry. Let us start with Tony's example: ...on midsummer day the sun rises at my latitude - 55° north - at just after 3.0am (GMT) and at a point on the horizon approx. 45° north of due east. Before/after 6.0 am/pm it is shining on the north face of an east/west wall. This is correct. The sun shines on the south side of the wall for only about 9 of the 18 hours that it is above the horizon. As you go further north, the time the sun shines on the south side of a direct south-facing wall gradually increases until, when you reach the arctic circle, it shines on the south side for about 11 hours. The tantalising bit comes next... On the day of the summer solstice the sun is above the horizon for all 24 hours at the arctic circle so it is on the NORTH side for about 13 hours. This still doesn't violate Waugh's assertion but... Translate your wall to the ANTarctic circle and here, at OUR winter solstice, the sun shines on the SOUTH side for about 13 hours. These are the hours from roughly 5:30pm to 6:30am which include ALL the hours between 6pm and 6am that Waugh is denying us. All we need now is a client for Tony Moss who wants a wall dial in the Antarctic and we can see this at work. Frank King Cambridge University England -
East/West walls and the North/South divide
Hi Gianni, > In my opinion the Waugh's statement is correct if we think only > to the sundials in the North hemisphere (as Waugh did). Yes, you (and Mr Waugh!) are quite right of course... > For this reason it seems to me a little " trick " to consider the > period of illumination of the South face in a sundial to the > ANTarctic polar circle :-) Yes, this is indeed one of my tricks! I like to think that every wall has TWO sides and the `wrong' side can be very interesting. North-facing dials are quite common but not many people realise that it is (theoretically) possible to have more than 12 hours of continuous sun on the same face of a wall. You just have to be in the right place! > For curiosity I send some approximate values... These are the figures I was thinking about, especially: > Latitude 66° 27' > Dawn 3h 27m > Start of the illumination 6h 43m > Length of the illumination 10h 33m It is the last figure that is responsible for my `trick'. Here the sun is on the `wrong' side for 24 - (10h 33m) = 13h 27m, well over 13 hours. Here is another `trick' concerned with the difference between the north and south hemispheres... If `summer' in northern latitudes is taken as the period between the March equinox and the September equinox and `summer' in southern latitudes is taken as the period between the September equinox and the March equinox then: a) Is summer longer in the north than in the south? or b) Is summer the same in the north as in the south? or c) Is summer shorter in the north than in the south? The correct answer is (a) but what is interesting is that the difference is OVER A WEEK. In Europe we have almost 8 more days a year where the sun is above the horizon for longer than it is below, than the poor people in Australia! Frank King [In Cambridge where it is raining heavily and all thoughts of sundials are purely theoretical at the moment :-(( ] -
New Zealand Puzzle
Dear All, One of my colleagues recently took some photographs of a couple of items of gnomonic interest in Hamilton, New Zealand. These can be seen at: http://www.cus.cam.ac.uk/~ph10/hamsun.html You can click on the thumbnails to make them bigger. Object one is a car-park-sized sundial with constant declination lines for the first day of each month, and analemmas for six or seven hours (apparently set for New Zealand time since there is nothing central for local noon). The concentric circles seem to have no obvious purpose other than ornamentation. Object two is curious. Can anyone identify it? It is in poor condition and some components appear to be missing. The photographs were also taken in pouring rain! It might be the remains of a heliochronometer but there are no obvious markings and no plaque to say what it is or how to use it. The mount can adjusted for altitude and azimuth. Suggestions welcome! Frank King Cambridge, U.K. -
Re: Horizontal equivalence
Tony Moss says: > If the plumb bob is suspended with its tip in e.g. a petri > dish of water, but just clear of its bottom, it can be > aligned with a mark on the plane and has much of the > wind motion safely damped out. I have tried putting a plumb bob in a bucket of water and that certainly damps the motion. The bad news (or my ineptness) is that the string just forms a nice arc in the wind and you aren't really much better off! Cassini and Bianchini dropped their bobs through long pipes to shield them from draughts. They would then spend days observing the tip swinging around before settling on a perceived centre of swing. Of course, with the string enclosed in a pipe it won't cast a shadow. If that is not a problem then this was probably the best that could be done with 17th century technology. We are jolly lucky to live in an age where we can use surveying instruments equipped with solid-state gyros for levelling purposes! Frank King Cambridge, UK -
Re: Author of poem
Dear John Yes, both Patrick Powers and Mike Shaw are spot on in identifying your author but, like most renderings, what you wrote is not what Shakespeare would have recognised. The best (pure ASCII) rendering I can do of the key lines as they appear in the First Folio is: To carue out Dialls queintly, point by point, Thereby to fee the Minutes how they runne: How many makes the Houre full compleate, How many Houres brings about the Day, How many Dayes will finifh vp the Yeare, How many Yeares, a Mortall man may liue. In this, the f of fee and the second f of finifh should not have cross-bars. Each is of course an early 17th century s but they are not like integration signs, they do not have descenders. Readers who know how bawdy Shakespeare can be might note that there is a good deal of double meaning in all this. Indeed the word quaint (with an a) is still in use as a slang word in Scotland. This has nothing to do with sundials! Interested readers can look up quaint in the full OED for more. I am ashamed to say that a particularly bad rendering of this quote appears on a dial I set out in 2002 in Old Palace Yard at the east end of Westminster Abbey. I couldn't persuade my clients (a Joint Committee of the House of Commons and House of Lords) to use proper Shakespeare. Grrrrh! Frank King Cambridge, U.K. -
Re: On the greatest size of an analemmatic and more
Dear All, I have been following this analemmatic thread with particular interest since I have recently been giving advice to a Swedish stone-cutter who wants to set a dial out in her garden. She lives on the cold side of 60 degrees north. I especially noted: > I have been talking to people who know about road > construction... So have I and I have been learning about `slab-on-grade construction' and `nominal maximum expected frost depths' and so on. In England, the standard frost depth code is 450mm but in Canada it is typically 1200mm and in places which have really cold winters the figure is 1800mm. In my limited experience, the solution has been to use a truly wonderful material called SAND! This works fine in England. You just dig a shallow pit, put in 150mm or so of sand, lay your slate (or whatever) on top and provided you have been careful this will stay level for many years. When I looked at the Brooklyn bathroom-tile dial that John Carmichael kindly drew to our attention my first thought was, `How will that look after a New York winter?' Worse, `How will it look after 20 or 50 winters?' I am very much minded of the maxim `Beauty is only skin deep'. Can some U.S. reader who knows all about cold winters kindly let this temperate Brit know what is likely to be found underneath this dial? Is there really 1200mm of hard-core and elaborate drainage? My Swedish friend advises that they can expect two to three months of -25C temperatures with occasional dips to -35C. Whenever I have stuck tiles on a bathroom wall I find the wretched things peel off after a year or so inside a nice warm house. With frost heave, ice penetration, and differential thawing effects that the Swedes call `shooting', there wouldn't be much to look at come spring if I had laid the tiles on an outside dial. I am feeling a serious lack of experience! Can anyone help? Frank King Cambridge, U.K. -
Re: On the greatest size of an analemmatic and more
Dear All, Many thanks to Tony Moss and Brian Albinson for the most erudite comments so far... Tony: I vaguely recall the constructions techniques used in Spitsbergen, namely very deep piles as you note. Here, of course, there is permafrost and one can rely on the ground being permanently frozen below a certain depth which gives stability. I am not sure how this translates when you go to not-quite-so-frozen latitudes a little further south! Brian: I am most interested to hear of your method (ii) for mosaic work. This sounds well worth pursuing. What kind of foundations did you have below the surface? How do you stop water getting into the ground beneath the dial and doing nasty things when it freezes and thaws? Frank King Cambridge, U.K. -
Re: Is the USA 'Daylight-Saving' period to be extended ?
> Daylight Saving Time should be abolished... > that's my 2 cents worth... Hmmm! I have so many objections to this tinkering with clocks that I could easily run to 2 dollars worth! I will try to be temperate. I shall fail! 1. The principal purpose, one assumes, is to get people out of bed earlier. That's fine but I don't see why Government's have to tell lies about the time to achieve this. 2. To a pedant like me the terms a.m. and p.m. become silly in summer. Where I live (close to longitude 0 degrees) from 12 noon BST until 1 o'clock BST we are still anti-meridiem (before the middle of the day) so it is strictly 12:30 a.m. at what is actually 11:30 GMT but is legally 12:30 p.m. BST. 3. The concept is inherently inflationary. We now hear talk of using GMT+1 all through the winter and GMT+2 in the summer, `double summer time'. Wait 50 years and it will be GMT+2 and GMT+3. 4. Worst of all, in U.S. terminology at least, is the term `daylight saving' which is an even bigger lie since no daylight is saved at all. The only good news is that this term is not used much in the U.K. Brian Albinson correctly cites the 1925 (British) Act of Parliament. The most recent relevant Act came into force in 1972 and the pertinent passage is: `the period of summer time for the purposes of this Act is the period beginning at two o'clock, Greenwich mean time, in the morning of the day after the third Saturday in March or, if that day is Easter Day, the day after the second Saturday in March, and ending at two o'clock, Greenwich mean time, in the morning of the day after the fourth Saturday in October.' That's clear enough so what happens this year? This year the clocks went forward at ONE o'clock Greenwich mean time on Sunday 27 March. This was THREE-ways illegal: it was one hour earlier than specified in the Act, it was on the morning of the day after the FOURTH Saturday AND it was Easter Day itself. In summary: the whole business is about introducing a law that tells lies about the time and then not following that law properly having enacted it. [Aside: this is because European legislation on clock-changing supersedes national legislation.] I use God's Magnificent Time, all the time, even when many time zones displaced. No doubt I shall be clamped in irons for this eccentricity! Frank King Unrepentant Sinner Cambridge, U.K. -
Re: Is the USA 'Daylight-Saving' period to be extended ?
> It was clearly illegal if you compare it with the > quoted text. But it was at exacltly the same moment > as all other EU-countries... Yes, this is indeed true. > So I guess there will be an EUrule which became in > force also for the UK. Technically the British 1972 Act is STILL in force in the U.K. but some quite separate small print has been exploited which I chose not to mention :-) This says: The duration of Summer Time can be varied by Order in Council In recent years this has duly happened to bring the U.K. more in line with the procedures in other E.U. countries. I suppose the Queen has to sign this Order each year! This doesn't make me any happier! I want sundials on the Greenwich meridian to average around GMT. There are, of course, many sundials with 1 at the bottom (or at the north point) rather than 12 but such numbering doesn't look right to me. I will accept that this is largely a matter of taste. Frank King Cambridge, U.K. -
Re: Which longitude/latitude to use?
Dear Wee-Meng You raise some very interesting points... > When I read about longitudes/latitudes in GPS articles, > there are loads of different types of projection used. Indeed there are. These all represent different models of the shape of the Earth and the best one is kept secret by the U.S. Military who probably know the shape of the Earth better than anyone else! > In my GPS, if a point is specified using the wrong > projection, it may be way off. Sadly this is true. We in the U.K. like to think that Longitude 0 degrees has been fixed since 1884 by the position of Airy's Transit Circle telescope at Greenwich. For some purposes this is still true but certainly not for all purposes. Even the much-acclaimed British Ordnance Survey Maps use a different Longitude 0 (for the simple reason that the Ordnance Survey started long before 1884 and they haven't wanted to change!). The WGS84 model was established by the U.S. who used a secondary longitude (probably one in Washington) as a reference during the refining of the model. When they finished, it turned out that 0 degrees on the WGS84 model is about 6 arc-seconds to the EAST of the longitude of the Airy Transit Circle. I am writing all this from memory so someone else may correct this figure of 6 arc-seconds. If my memory is right this translates into about 0.4 seconds of time or (very roughly) 100 metres at the latitude of Greenwich. I don't think diallists should worry too much about this error. UTC is allowed to differ from UT1 by over twice this amount and I expect most diallists use UTC for checking sundials without correcting to UT1. [A few serious pedants like me make this correction!] To those readers who are familiar with the difference between UT1 and UTC I should like to have it confirmed that UT1 STILL uses the Airy Transit Circle as defining reference longitude 0 degrees. In short: is it still the case that 12h UT1 is the instant of superior transit of the mean sun at Airy's Transit Circle? I am fairly sure the answer is yes but I would be happier if some expert could confirm this. Frank King Cambridge, U.K. -
Re: Reading at a Distance
Dear John, You have had sound advice from several on this list but there is an extra point that might be of interest to you and to others... Those who cut inscriptions on stone walls take into account that the top is likely to be further away from the observer than the bottom. Accordingly, they adjust the heights of the letters (but NOT the widths) so that the lettering at the top is taller than that at the bottom. When read from the most natural standing position the letters all APPEAR to be the same height and this is easier on the eye. I can imagine circumstances where this kind of adjustment might be appropriate for diallists, a tall wall dial in a confined public square for example. > ... I'm going to make a linear graph relating distance > to character size. Yes, but character `height' would be more strictly accurate than character `size'. Any serious letterer will tell you that characters do not scale linearly as you increase their size. All kinds of subtle tricks (subtle in that they are there so you DON'T notice them) are brought into play. A simple example is the letter X for 10. Usually, the stroke from top-left to bottom-right is fat and that from top-right to bottom-left is thin. If you have all the proportions correct for an X on a wrist-watch and then naively enlarge it 100 times for an X on a public clock, then both lines will be much too fat but the thin line more so than the fat one. Those who cut inscriptions in Roman times 2000 years ago knew many of these tricks! Frank King Cambridge, U.K. -
Re: Meridiana of Milan
Dear Rodrigo > Do you know if in the "Duomo" of Milan there is a big > "meridiana" in the pavement? There is indeed. > Do you know if there is some bibliography? The Bookshop in the Duomo sells a very nice booklet `La Meridiana Solare del Duomo di Milano'. This gives a good deal of basic information and many measurements though, strangely, not the diameter of the hole. That and other things I had to ask Gianni Ferrari about :-) This booklet is in Italian of course. I am sending you separately some private notes about this meridiana which I wrote a couple of years ago. These are in English and are quite technical but are not really fit for general consumption. Frank King Cambridge, U.K. -
Save the Leap Second
down of the Earth's rotation. Consider, for instance, the transit of Venus of 14 June 2984. First exterior contact (for the Earth's center) will take place at 10:10:23 Dynamical Time. This will be 10:09 UTC if the US proposal is accepted. However, if the leap hour is introduced before A.D. 2984, then the instant would become 09:09 UTC. Consequently, presently we don't know whether the transit will begin at 09:09 or at 10:09 in the proposed UTC scale, and hence it is not possible to create a long list of events with the instants expressed in UTC. (6) Finally, for sundials, too, the situation would be complicated. Presently, to convert true solar time (as given by a sundial) to "official" time, we have to take into consideration: the longitude difference with Greenwich, the equation of time, and the fact that we use or not the "summer" time. But if the US proposal is accepted, a further correction would be needed: the difference between UT and UTC, a difference that is now negligible, but that will gradually increase over the years if the US proposal is accepted. Finally, I don't understand why the ITU and the people of GPS insist to suppress the leap seconds. Are they really unable, notwithstanding the modern technique of the 21th century, to handle this "problem"? Should astronomy suffer because those guys cannot handle the leap seconds easily? Jean Meeus (Belgium) --- End of Forwarded Message For further details see: http://www.cl.cam.ac.uk/~mgk25/time/leap/ http://www.ucolick.org/~sla/leapsecs/ I regard all this as bad news. Quite apart from anything else, having a leap hour some time in the future seems like building up a problem that will make the Y2K nonsense seem a trivium. What do others think? Should we take to the streets? Frank King Cambridge, U.K. -
Re: Save the Leap Second
Dear Fer, > Does "another correction for sundials", as Jean Meeus > writes, also means an extra shift in the system > wintertime/summertime?. I suppose that will be up to individual Governments or, in our case, some group in Brussels but it seems almost inevitable. A cumulative drift of up to an hour will surely be noticed, just as it was eventually noticed that the Julian Calendar was causing the seasons to drift. > What is the concequence for our daily lives? Well it won't be very much. As Jean Meeus says, it will take a long time to accumulate an hour's worth of drift. I'll be dead long before I care too much, though it won't take too many left-out-leap-seconds before people who read sundials carefully will notice. Those who look at Jupiter's satellites will notice even more quickly. > Because of my interests I agree with Jean Meeus. > Keep the leap second, no leap hour. Exactly my opinion. Long Live the Leap Second!! Frank -
Re: Save_the_Leap_Second
Dear Wolfgang, You ask: > Who cares about UTC in every-day life? Well all diallists and anyone who uses astronomical tables care about UTC precisely because it is, currently, guaranteed the same as UT1 to within 0.9s and we can ignore that difference. When UTC-UT1 is even a few seconds, never mind a large fraction of an hour, we won't be able to ignore the difference. I'll go further. Everyone who ever sets a clock or a watch uses UTC or some very simple offset from UTC (usually an integral number of hours). There are quite a lot of people who own watches! Moreover, most e-mail headers, certainly including yours, implicitly refer to UTC. Your header said... Date: Tue, 12 Jul 2005 08:10:15 +0200 (MEST) That +0200 refers to the offset from UTC. So the answer to your question is simple: `Almost everyone in the civilised world cares about UTC.' It is true that some of them don't know that they care :-) Frank H. King Cambridge, U.K. -
Re: WSJ.com - Why the U.S. Wants To End the Link Between Time and Sun (fwd)
Dear Fred, Thank you for this snippet about the Leap Second... > Copy and paste the following into your Web browser to access > the sent link: > > http://www.emailthis.clickability.com/et/emailThis?clickMap=viewThis&etMailToID=1114314915&pt=Y I am impressed that the Wall Street Journal should take up the cause! I can't imagine a British newspaper being much interested though maybe I am wrong. Those who have been following this debate might note that the Royal Astronomical Society met in London last Friday and the subject came up then. There was a senior Civil Servant there representing the British Government. There was not a single voice in favour of abolishing the Leap Second and the Civil Servant was at one with the rest. Steve Allen of the University of California certainly has the right idea: "Time has basically always really meant what you measure when you put a stick in the ground and look at its shadow," Indeed so! Frank H. King Cambridge, U.K. -
Re: The J. Carmichael stone technique...
Dear All, I was fascinated to read... John Carmichael's Stone Cutting & Carving Technique This eloquently describes an interesting set of procedures. What is particularly noteworthy to me is that there is almost no overlap with standard stone cutting procedures that I have come across in traditional stone workshops in the U.K. All the sundials I have ever worked on have been in stone (mostly slate but several in limestone and one in granite) and different workshops use different practices. There is clearly no `right' approach. That said, I consulted the most gifted stone-cutter I know, Annika Larsson from Sweden, and I asked her to spell out her own procedures in an analogous step-by-step way. Here (very slightly edited) is what she wrote... ANNIKA LARSSON'S STONE CUTTING & CARVING TECHNIQUE 1. Draw a scale design. 2. Order stone to size. 3. Organise fixings in the back, if required. 4. Rub surface, if necessary. 5. Draw out the design ON THE STONE a. set out guidelines b. draw design [ Review the design at this stage: Does it work? Will small adjustments have to be made? ] c. have a final LOOK 6. Spellcheck a. check papers/correspondence [with client] b. do a letter by letter check of the text on the stone 7. Cut. (or drill, or engrave or whatever) 8. Wash. Leave to dry. Time varies depending on type of stone. 9. When stone is dry, gild and paint. Methods vary depending on type of stone again. 10. Leave paint to dry over night. With gilding leave for a week. 11. Wash and burnish if necessary. 12. If pins/fixings are required, attach at the end. Annika was rather astonished when showed her John's procedures (which are self-evidently sound). There seemed to be several steps which are not obviously needed. In particular: If you can draw it on paper, you can draw it on stone, and the result will be more real. You can use the space much better. A paper surface and a stone surface are different. Paper is flat. The stone has depth. This is very subtle, though. Most people wouldn't think there was a difference. I hope this may be of interest to some readers. Frank H. King Cambridge, U.K. -
Re: The J. Carmichael stone technique...
Dear Andrew and Jack, Your observations definitely resonate with me, especially the comment that... > ... a relatively inexperienced stone cutter can use John's > technique and produce something that is at least acceptable > without years of practice. I have been incredibly lucky to have worked with a number of traditional stone workshops in the U.K., most particularly David Kindersley's Workshop in Cambridge where they still run an apprenticeship system. Even after 25 years of watching this place operate I continue to marvel at how people can be trained to do extraordinarily intricate things in stone. It is incredibly disciplined. On day one, new apprentices are simply asked to place a piece of drawing paper on a drawing board without creasing it. They are then given ten reasons why they got it wrong! One kink and its a failure. In stone, no mistakes are allowed, so they are taught early on that even perfection is only just good enough! Many tears get shed! > Drawing out the design directly on the stone means that > you have to do the whole thing by hand. Well yes and no. We are happy to use computers for producing a scale version of the design. The hour lines are calculated by computer as are constant declination curves and, indeed, anything mathematical. What happens next depends on the scale. If you have a big slab of stone wall, say 7m x 3m, then you are going to have a very unwieldy piece of paper if you insist on direct transfer! In these circumstances I mark the whole surface out in 1m squares using modern high-tech surveying kit (i.e. one of the more expensive total stations) and then fill in each square in turn, all by hand. In a particular case the summer solstice curve might be 6m long and will be represented by 100 points on a spreadsheet. I just accept that it takes a couple of hours to mark all the little Xs on the wall and then another hour to join these up satisfactorily with the aid of a piece of bendy wood. At its ends such a curve may deviate from a straight line by only a few mm in a couple of metres. It is important to get a continuous curve; the eye is very sensitive to short stretches of flatness. We then put tick marks on either side of this line and draw two other curves on on each side. Standard cutting techniques are then used to make a vee-cut. Often, constant declination curves are used as guidelines for lettering. These curves are again points on a spreadsheet which are transferred to the wall as Xs and the guidelines are then drawn through them. That's when people like Annika come along and, using the guidelines, simply draw letters by hand and get it right first time. Magic! > ... engraving the numbers would be particularly difficult for > me to do without a direct trace. I am totally sympathetic! I certainly couldn't do this either. I marvel at those who can but there seem to be plenty of them about! > Annika Larsson's step 7, "Cut. (or drill, or engrave or > whatever)" would be my downfall. Mine too! > Also, note that John developed the technique using sandstone. Yes, this IS noteworthy. Sandstone is pretty hellish! (though not as bad as granite) and EATS chisels! > I am now going to give it a try on limestone... Limestone has different problems. It is much kinder to chisels but it has fossils in it! Worse than that it may have huge holes where fossils used to be!! I remember the first time I worked on a limestone wall. I was shocked to find huge pits, maybe 5mm deep in places, where fossils had dropped out often EXACTLY where I wanted to place an X. I had had every intention to working to 1mm precision. Real life can be so hard!! This was the highest quality Bath stone and I didn't know how lucky I was. On a later dial, I had Portland stone and the wretched clients had specified that they wanted stone with `feature'. This is a euphemism for truly gigantic pits. Even Annika was a little perturbed when she found she could push a pencil 100mm into one of the holes! > I guess my point is that a relatively inexperienced stone cutter > can use John's technique and produce something that is at least > acceptable without years of practice. Indeed so and it is hard to see the apprenticeship system that supports these `years of practice' surviving indefinitely. Frank -
Re: Many a slip....
Dear Tony, You certainly have my sympathy... > VII VIII XI X XI XII This is definitely a case of `There but for the grace of God go I'! So far I have avoided this particular mistake but, measured in terms of embarrassment factor, I have had a far worse experience... A Workshop which will remain anonymous asked me to do the calculations for a vertical slate dial to go on a local mansion. I did the site survey myself, I did the calculations and I oversaw the marking out of the slate. I checked everything that mattered several times during the cutting and paid a final visit to the Workshop just to make sure. There was this beautifully cut slate, embellished with lots of gold leaf, all perfect. There were two slots along the sub-style for the gnomon and, just to make extra sure, I made one final check of all the time lines and, of course, the sub-style too. No problems. All that remained was to fabricate the gnomon, fit it into the slots and then fix the slate on the wall. Usually I went along to watch the fixing but this time I was about to go away for three weeks. Since the Workshop had done all this numerous times before I had no concerns. I explained that the sub-style height had to be 35.75 degrees and I handed over a template with a rough outline of a nice gnomon for them to work from. Someone would cut the design from quarter-inch brass plate and then it would be gilded. When I returned three weeks later there was an invitation to a really posh dial-inauguration party at the mansion. This would be fun! I arrived at the appointed time and headed straight for the dial. It looked magnificent. Moreover, there seemed to be a good chance that there would shortly be some sunshine. I was happily enjoying myself when a little doubt suddenly came into my head. There was something distinctly odd about the gnomon. The style height looked to be more than 45 degrees, and there is a trivial dialling theorem which says that on a vertical sundial, the style height cannot exceed the co-latitude. [I don't think I have seen this in books but it is so obvious that it must be well known!] Sure enough, when the sun came out it was instantly clear (to me at least) that something was seriously wrong. The indicated time was over three hours out. Most of the guests took the view that `sundials are completely hopeless at telling the time' so showed no signs of surprise. For once, I was content to let this view go unchallenged! Sadly, not all the guests were so accommodating and someone asked the wealthy hostess who had done the calculations. I was reduced to mumbling incoherently. The truth was that I didn't really know what had gone wrong but I said I would return to make some more checks. Next day I climbed up a ladder equipped with a protractor. The style height was just over 54 degrees. What had happened was that the fabricator had used my template on a rectangular brass plate and had marked out a line from one corner. The line was correctly angled at 35.75 degrees to one edge and the plate was then neatly cut into two pieces exactly along this line. I speculate that there must have been a tea break at this point and the fabricator got muddled. Instead of using the piece with the 35.75 degree angle he used the other piece which had a 54.25 degree angle. This explained why the style height was very obviously over 45 degrees. Of course, this led to all kinds of grovelling to the client and we had to saw the gnomon off (very difficult to do without scratching the slate) and provide a new one. I don't want that experience again! It is not quite so easy to change XI to IX though perhaps you could ink in a little minus sign to give X-I. Just an idea :-) Frank King -
Re: east and west, an afterthought
Dear Chris > I would argue that the rhumb line is itself virtually obsolete. I readily accept your line of thought, but a rhumb line legacy is still very much with us. I refer, of course, to Mercator's Projection where all straight lines are projections of Rhumb Lines. Mercator's is probably the best known of all map projections and it will be a while before it becomes obsolete. In particular, all British Ordnance Survey maps use it though their base great circle is not the equator but a line of longitude through the Isle of Wight. Mercator's Projection is quite a mathematical challenge and it and rhumb lines lead to interesting puzzles. For example, if you set out from Greenwich and follow a strict north-EASTerly course you will eventually pass over Canada. Of course, you will also cross the Greenwich meridian an indefinite number of times as you approach, but never quite reach, the north pole. Frank H. King Cambridge, U.K. -
Re: Firenze clock
Dear Willy, It is hard to find definitive information about clocks which show Italian hours. A number survive in Italy mostly in the Rome area. What I write now should not be taken as wholly reliable! Napoleon wanted French time everywhere of course and most Italian hours clocks were changed during his era. Papal influence in the Rome area meant that a few Italian hours clocks escaped Napoleon's attention! The date given for the Paolo Uccello clock is 1443 and you can be fairly sure that such a clock would be a very poor timekeeper compared with clocks today. The typical daily error would greatly exceed the difference in time of sunset from one day to the next so there would be no need for any special mechanism. Clocks of that period would have to be reset frequently, using a sundial of course, and you could choose to set it to Italian hours or French hours as you wished. Of course, the clock weights were probably wound daily anyway (and in early clocks the winding process stopped power to the clock thereby contributing further to the errors) so the added task of resetting the clock was hardly a great one. As clock time-keeping improved, the daily error reduced and, by the Napoleonic era, the effort of resetting an Italian hours clock daily would have started to seem a little irksome. I believe some of these later clocks (18th century) did have special mechanisms but they were pretty crude. I can imagine clock-keepers being quite grateful to Napoleon! There is an interesting paper by Nicola Severino on Italian hours clocks: `Le Ore Italiche... Perdute!' Also, have a look at his web page... http://www.nicolaseverino.it/orologio%20italiano.htm You will some pictures of Italian hours clocks (I took a couple of them myself). The majority of these clocks have dials running I, II, III, , V and VI. The single hand turns about four times a day if you are lucky. I don't know of ANY that remotely keep to Italian hours time today and most are in a very poor state of preservation. Frank H. King Cambridge, U.K. -
Re: Holbein's `The Ambassadors'
Dear All, Nicola Severino's article on the Holbein painting, The Ambassadors, is most interesting and adds to the corpus of understanding of this fascinating picture. For those who read English but not Italian, there are many references to The Ambassadors, including BSS articles which Nicola refers to. An account that I particularly enjoyed is in the book `The Secret Life of Paintings' by Richard Foster and Pamela Tudor-Craig, where the painting is the subject of Chapter 6. Those who are not familiar with this work should first appreciate just how big the painting is. The figures are life size. This explains how all the detail can be accommodated. There are so many incredible things about the details in the picture. For example, the globe shown on the lower shelf is the first known representation of a terrestrial globe in a painting. Moreover it emphasises the so-called (but not-yet-discovered) North-West Passage from the Atlantic to the Pacific. The little book in front of the globe can be identified as an arithmetic primer of the day. Even the page can be inferred. The polyhedral dial clearly shows polar oriented gnomons, quite a novelty in 1533. Intriguingly, and deliberately, one dial shows 09:30 and another 10:30. One detail which Foster and Tudor-Craig draw attention to is the declination indicated by the Shepherd's Dial. This corresponds to a date of 11 April or 15 August (remember that the Julian Calendar was in operation) but there is good reason to believe the April date is intended. Why is this significant? Here, it seems, we can reconstruct a 16th Century news flash. Recall that the painting is dated 1533. The indicated date, 11 April, was a Friday. Moreover it was Good Friday and it had been quite a week... On Monday 7 April, the English Parliament decreed that henceforth there should be no appeal to the Court of Rome. [Interestingly, Nicola doesn't mention this!!] Why so? Well, this was the culmination of `The King's Great Matter', Henry VIII's desire to extricate himself from his marriage to Catharine of Aragon. In fact, Henry had secretly (and bigamously) married Anne Boleyn in February and she was now four months pregnant. The Great Matter was daily becoming greater and Henry set 11 April 1533 as the deadline for resolving it, and there is the date, in the painting, on a sundial. Amazing! Many apologies to readers who are familiar with all this! Frank H. King Cambridge, U.K. -
Seeing in 2006
Dear All, How should a diallist see in 2006? After all, the new year starts at midnight when there is no sun (except in the Antarctic) and, this time, it is new moon too so those who like moon dials (always a disappointment in my experience) will also be out of luck. Well, we do have a Leap Second to savour. This will be the first Leap Second since the end of 1998, and just might be the last, so we should enjoy it to the full. Accordingly, I present three suggestions for making the most of an event that lasts just one second: 1. Listen to the speaking clock on a telephone. 2. Tune into a broadcast seven-pip time signal. 3. Stare at a radio-controlled clock or watch. The first two can readily be recorded so you can play them back to your friends later. The third needs a camcorder. Don't forget that the Leap Second is just before midnight UTC. Those in most of Europe will have to wait until almost 01:00 and for those in the U.S. the event will take place in the afternoon or evening depending on time zone. In the U.K. the speaking clock has (or had) two machines, one set a second behind the other. The change-over is made manually just before you hear `At the third stroke...' heralding midnight UTC. If the technician doesn't get it spot on you hear `Ahht the third stroke...' instead. The BBC generally make a mess of the seven-pip time signal. I have heard a ghastly disc jockey talking all through it and, once, they gave us the Chimes of Big Ben at the same time. Staring at a radio-controlled clock is likely to be gravely disappointing and you may have to look at it for rather a long time. Clocks controlled by Rugby (U.K.) and Frankfurt (Germany) seem not to resynchronise until two or three hours after the event. Can anyone explain why? Enthusiasts will have noted that the coming Leap Second will (so the International Earth Rotation Service tell us) result in UTC changing from being ca 0.66s ahead of UT1 to being ca 0.33s behind. Users of heliochronometers should be able to detect the difference. If savouring the Leap Second is not to your taste you can always open a bottle of your favourite wine instead. Indeed, why not do both? Happy New Year Frank H. King Cambridge, U.K. -
Rods versus Knife-Edges
> > It seems to me it would work, but I can't see any > > advantages over a cylindrical gnomon. > > I just tried the shadows of a knife edge and of a > 3/4" diameter rod and they look about equally sharp. > I should do a more careful experiment, but to first > order, it appears to be true. Indeed so, at equal distances you get equal fuzz, but this misses the main point... With a rod you can readily estimate the centre of the shadow ignoring the (approximately equal) fuzz on either side. With a knife edge you have to estimate where in the fuzz is the true centre-line of the shadow of the edge. This is error prone and, to some extent, subjective. I say `spare the rod and spoil the sundial'. Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Exact Time and date conventions
Douglas Bateman writes: > What is a poor scientist to do, especially when he tries > to understand 'time'? Just for once, I incline to the ISO standard here. This has considerable (though not universal) support by Scientists. Astronomers in particular seem to favour its use. Today is 2005-04-07 and the time as I write is 08:34:46Z. The hyphens and the semi-colons are the standard separators but they may be omitted unambiguously. The Z stands for Zero Meridian (i.e. Greenwich) and means UTC. The Z is usually omitted in which case the time is deemed to be the user's local time. Since I don't like my local time I need the Z! A good easy guide to ISO standard time and date is to be found at: http://www.cl.cam.ac.uk/~mgk25/iso-time.html Frank King Cambridge, UK --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Exact Time and date conventions
Hmmm, apologies for the deliberate mistakes! Today is 2006-04-06 and not 364 days earlier. Finger trouble. Frank King --- https://lists.uni-koeln.de/mailman/listinfo/sundial
S.M. Maggiore Puzzle
Dear All, On 19 April, Claus Jensen sent this list an interesting attachment showing a representation of a sundial in a painting in Santa Maria Maggiore in Rome. Claus and I have been in correspondence about this and we have failed to interpret the dial. I have not been able to reverse-engineer this dial to my satisfaction. I work on the risky assumption that artists who include sundials in their pictures either have some familiarity with their subject or are copying a real dial. Of course this one may be quite bogus, but let's assume provisionally that it has some legitimacy. Here are the obvious features: 1. There is a roughly square dial with the gnomon/nodus in the top right-hand corner. 2. The hour lines start from XII and go round anti-clockwise through XIII and XIV. After that the labels run out but the lines continue. 3. The inner ends of the hour lines (the ends nearer to the nodus) do not outline a convincing winter solstice curve but this might be artistic licence. 4. The XII line is roughly horizontal. 5. At the instant depicted, the shadow appears to be close to the inner end of the XIII line. The position of the nodus, the orientation of the labels, and the anti-clockwise progression suggest a vertical dial which declines to the west. So far so good. The obvious problem lies in interpreting the labels on the hour lines. What kind of hours are represented? If they were regular hours you would expect the XII line to be (roughly) vertical not almost horizontal. If they were Italian hours you would not expect to see the XII line at all. Certainly, one wouldn't expect a shadow XIII hours after sunset at the winter solstice! OK, let's be a bit more imaginative. Maybe it is supposed to be a HORIZONTAL dial set up in the southern hemisphere and is drawn with north at the top? The hour lines would go round anti-clockwise and the inner ends of the hour lines now correspond to what in the southern hemisphere is the summer solstice. With a horizontal southern-hemisphere Italian Hours dial the depiction should have the XII line parallel to the top and bottom edges of the dial. The fact that it is not quite parallel suggests that the dial dips slightly to the west. This almost works but seems terribly unlikely! OK, we can try Babylonian hours and Equal Hours but they don't seem to fit at all. Interestingly, the little bit of the line that corresponds to XVIII is almost vertical. This is tantalising because, using Italian Hours, XVIII is noon at the equinoxes. Could the artist be confusing regular hours and Italian Hours and drawn (rather imprecisely) regular hour lines but labelled them with a six-hour shift? Is this a well-known picture? Is there some sinister significance about drawing attention to hour XIII? Have I altogether goofed? Someone must know the answer!! If anyone has lost Claus's photograph please let me know off-list and I'll resend it. Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Buyer's Guide
Dear Mac > Here in Vermont a sundial is lucky to see the > sun 15% of the hours in a year. Hmmm, sounds worse than the U.K. :-( > Heck, half of the time it's night! Interestingly, this isn't true. The number of days from the March equinox to the September equinox is about 8 more than the number of days from the September equinox to the (following) March equinox. This is much more than a second-order effect! In the northern hemisphere, therefore, we get more day than night taking the year as a whole. Down in the southern hemisphere the reverse is true. Only on the equator can you say `half the time it's night' and even there you risk being told by a pedant that night excludes the period of twilight. Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Buyer's Guide
Dear Mac, > I would have wagered a small amount that I had seen > a map showing average annual sunshine in Vermont to > be less than 30% of possible sunshine. However, I > just found a NOAA map which appears to show mean > annual sunshine here as 51 - 55 percent. That's pretty good by U.K. standards! > ... my point remains that, since a sundial functions > as a sundial only part of the time, it really ought > to be a pleasant thing to look at when it's not working. Yes, agreed 100%. > Do you have an estimate for the percentage of working > hours during a year for a sundial at your location? That's an embarrassing question and I have had to look up the answer. It seems that in Cambridge, England, we average about 1700 hours of sunshine a year. If you take the year as being 8766 hours this means we get sun about 19% of the year. This is about 40% of daylight hours. As this list has been reminded in recent weeks, even when the sun is shining there are many reasons why a sundial might still be in shadow. The sun might be on the `wrong' side of the dial or blocked by trees, buildings, hills or other items of horizon pollution. I see, from Wikipedia that the maximum sunshine ever recorded in the U.K. in a single month was 383.9 hours at Eastbourne (East Sussex) in July 1911. That is almost 52% of the total hours in the month. You are right. We had better make our sundials good to look at even when they are in the shade! Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Conical Gnomon Advantages
> ... the shadow on a wall of any thin flat object parallel to the > wall is exactly the same shape and size as the flat object... > if you ignore fuzziness. Indeed so but the crucial phrase is "if you ignore fuzziness" because if you DON'T ignore fuzziness a whole new world of interest opens up! The greatest examples which use an aperture nodus are the camera obscura dials in continental cathedrals. You will certainly find that a circular hole results in an elliptical spot of light even though the hole and floor are parallel. Moreover, the spot of light is an image of the sun so it is a bit unfair to use the term "fuzziness". Super pedants will note that the image isn't quite elliptical but is an ellipse with a fuzzy border whose width is the diameter of the hole. You can get a low-quality version of this effect with an ordinary circular nodus with a circular hole. If the nodus is parallel to the dial what you see is a roughly circular shadow with a roughly circular spot of light. Both circles are distorted by fuzz (I am happy with this term here!). The shadow is a false ellipse and the spot of light is too. The major axis of the shadow is aligned with the minor axis of the spot of light. The extent of these distortions very much DOES depend on the angle of incidence of the sun. Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
The Gnomonic Cipher - An Italian Job
Dear All, I am going to regret this... After my request for comments on the dial that features in the Santa Maria Maggiore painting, several list members sent me helpful suggestions. The general view, summarised by one who wishes to remain anonymous, is that maybe this was more a puzzle to pass on to Dan Brown than to diallists. In an idle moment I found I was able to hack into Dan Brown's word processor and I discovered that he has already solved the puzzle. There is a whole chapter relating to this dial (and to other sundials in Rome) in his latest work in progress which has the provisional title The Gnomonic Cipher. I have put a PDF copy of this chapter in: http://www.cl.cam.ac.uk/users/fhk1/Maggiore.pdf Mr Brown's agent explains that numerous acknowledgements (or apologies) are due to many people who unwittingly contributed to this new work. The following are noted in particular: Claus Jensen, Chris Lusby Taylor, Tony Moss, Patrick Powers, Francesco Bianchini, Nicola Severino, Tonino Tasselli and other Italian gnomonisti who are referred to in the text. Remember: you saw it here first! Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: The Gnomonic Cipher - An Italian Job
Dear Dave > Excellent hacking job, Frank! Thanks for the accolade! > I make the location of Bar La Meridiana a few meters south > of 41:54:11, but not at any particularly "interesting" longitude > On the other hand, the Basilica di Santa Maria Maggiore > appears to be at 41:53:51, and very darned close to > E12.5 (12.4986?)... Yes those figures sound right. The latitude 41:54:11 is that of the foro gnomonico at the Basilica di Santa Maria degli Angeli. This is the figure quoted in the splendid book `Il Cielo in Basilica' by Mario Catamo and Cesare Lucarini. Interestingly, again quoting from the book, Bianchini himself calculated the latitude as 41:54:27. Bar La Meridiana is a fairly standard Italian bar. Most of the serving staff don't know what a Meridiana is unfortunately but they can usually dig out someone who does! I still haven't seen this fragment of the Augustus dial. The excuse given last time I was there was that the basement was flooded. Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Bitter at Twisted
Dear Mike, Gee, what amazing sundials. I particularly enjoyed (!) what you so eloquently list as Crap_002.jpg (with the cat and mice). These sundials, or at least your snaps of them, are ideal for showing at lectures. You can say: `OK, now you understand sundials, see how many mistakes can you find in these in two minutes!' I looked at your poems page. By chance, I spent the first three afternoons of this week assessing a sundial exercise I set to 465 first-year scientists. Some of the candidates included little poems in their write-ups. [Don't ask me why!] These were mostly pretty poor but one, from a guy at Queens' College (noted for its moon dial), lent itself to heavy editing and comes out like this: An applicant visiting Queens' said I simply can't tell what it means. The sundial says seven, Yet it's just on eleven. Oh what a mistake to choose Queens'. If you want to attribute this to anyone, you could say `Inspired by Oliver Shortle of Queens' College.' The limerick illustrates the difficulties faced by a novice user of a moon dial. I regard moon dials as the strangest of curiosities. If you need to tell the time at night, use a nocturnal! Frank King --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Nodi Shadow Experiment
Dear John That is an interesting experiment... > I think you will all agree on the following: > > the cone's shadow is without a doubt the easiest to read at > low and medium solar angles. Yes, but don't be misled by this result! One way to analyse the performance of a nodus is to imagine looking at the sun from the shadow of the nodus on the dial. [You *imagine* this but don't actually do it of course!] Suppose you draw a line from the centre of the solar disk through the tip of your cone and on to the dial surface and look back from the point where the line intersects the surface. You will see the tip of the cone in the centre of the solar disk. If your cone has an 18-degree angle then you will see nineteen-twentieths of the solar disc. That is almost indistinguishable from full sunlight. Where you THINK you see the point of the shadow is actually not where you would like it to be but further into the geometric shadow. You get a false reading. For all their faults, spheres and discs and holes are better bets because you can estimate the centres of their shadows (or spot of light) better. Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Sundial Motif to Be Featured on New Canadian $10 Coin
> Now if they'd just put the a.m. VI diametrically > opposite the p.m. VI... No need. On a circular plate that would be appropriate for an equatorial dial but, for a horizontal dial the VI-VI line on a circular plate is invariably not a diameter. Look again at the original at... http://users.eastlink.ca/~srgl/louisbur.htm There are many ways a sundial can make a botch but this isn't one of them! Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: McDonald's billboard (A sundial?)
Good thinking Roger... > Of course it is a sundial, a very clever one. It does not > show regular hours but the original "stomach time". The > design is similar to Mass dials... It does indeed share many of the properties of Mass dials but it is a good deal more colourful! The implicit hyperbola is upside down for the summer months but let's overlook that detail! For example, at 6a.m. the shadow of the nodus would be on the road a couple of blocks away! This nodus is the major novelty and I invite an enterprising diallist to exploit it. The double-arch M offers all kinds of possibilities... With a little mathematics and careful design one can arrange that the outer limbs of the M serve as error bars. The central limb indicates a specific time and the outer limbs bracket a range of times. I would fix it that there was a 68% chance of the local mean time falling within the indicated range. This corresponds to a well-known property of the normal distribution that there is a 68% chance of being within one standard deviation of the mean. It would be better to have the nodus parallel to the plane of the dial (rather than horizontal) to keep the shape of the shadow (almost) constant. We should be grateful to the McDonald's Ad Agency for pointing the way to some potentially useful theory! The only snag is that anyone who exploits this idea may fall foul of some U.S. patenting law! Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Dear John, That is a splendid experiment... > http://advanceassociates.com/WallDial/NodusShadowExperiment.pdf It illustrates all kinds of interesting aspects of nodus design The Purpose, Setup and Execution all earn top marks. The Conclusion, though, is subject to a little caveat... Let's concentrate on just three of your designs: the disc with the 0.25" hole at the top (or leftmost), the cone at the bottom (or rightmost) and the 1" ball next to the cone. Now look at the two sets of shadows: 1. When the shadows are short... (a) the centre of the anti-shadow of the disc with a hole is about 6.1" along your board. (b) the centre of the shadow of the ball is just a little shorter. It seems to be almost spot on the 6" mark. [This is possibly because the supporting stick is not quite vertical. This is not important.] (c) the shadow of the tip of the cone is almost exactly in line with the anti-shadow of the disc with a hole, about 6.1" along your board. 2. When the shadows are long... (a) the anti-shadow of the disc with a hole is no longer clear (as you say) but because there is an equal amount of fuzz at the extremities of the shadow of the disc as a whole you can fairly easily estimate the centre. It seems to be about 23.3". (b) the centre of the shadow of the 1" ball is just a little less easy to estimate because the supporting stick disturbs the fuzz at one of the extremities but one can see that the centre is about the 23" mark. This, as expected, is shorter than the shadow to the centre of the disc and is consistent with 1(b). So far everything ties up. (c) the shadow of the tip of the cone though has now fallen behind the shadow of the centre of the disc. The shadow may be easier to read but IT IS GIVING A FALSE RESULT. The big big trouble with any asymmetric nodus is that you cannot cancel out the fuzz. You have to decide just where in the fuzz is the point of interest. This is difficult. Different people will estimate different points. As noted at 2(b), each of your ball nodi is slightly asymmetric because of the supporting sticks. If you had mounted the balls sideways (as you have the disc with the hole) it would be easier to estimate the centre of the shadow. To my mind, the disc with the hole gives the most accurate result even if its shadow isn't the prettiest! Incidentally, it is worth analysing the hole in your disc in the long shadow case... Diameter of hole 0.25" Height of hole above the board 4" Approximate length of shadow 23.3" Distance of centre of anti-shadow from centre of hole 23.6" Angle of incidence arctan(23.3/4) = 80.3 degrees Now consider the hole viewed from the centre of the anti-shadow. Given that the disc is parallel to the board, the hole will appear as an ellipse whose angular dimensions in radians are: Major axis0.25/23.6 approx 1/94.4 radians Minor axis 0.25 x cos(80.3) / 23.6 approx 1/558 radians This last figure should be compared with the angular diameter of the sun which (by a diallist's rule of thumb) is about 1/107.5 radians. Now imagine an insect (wearing eye protection) at the point where the centre of the anti-shadow should be. As seen by the insect, the minor-axis of the hole appears to be less than one-fifth the diameter of the sun. The anti-shadow is entirely penumbra and impossible to detect. In my opinion this is NOT a design error. My eccentric view is that a disc with a hole IS the best form of nodus, especially for big sundials (well ALMOST the best) because... when the angle of incidence is small (short shadows) you observe the centre of the anti-shadow and... when the angle of incidence is high (long shadows) you observe the centre of the shadow of the disc as a whole. I say ALMOST the best because there is a special case of a disc with a hole, and that is the great camera obscura sundials which one comes across in Europe. There the angular diameters of the holes are even smaller than yours. [According to Gianni Ferrari, Cassini took the view that the hole should be 1/1000th of its distance to the floor, half the size of your hole at 23.6".]. The disc though is effectively of infinite diameter because the entire building surrounds the hole and you DO see a splodge of light. This is not anti-shadow though; it is actually an image of the sun and you can estimate its centre VERY precisely. Try making your disc of infinite size and you will see how this works :-) MORAL: Sticks and cones are seductive but should be resisted! I hope this hasn't been too tiresome a message for this list! Frank H. King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Dear John (and Edley), Your experiment continues to fascinate me and I have some fresh comments which include an experiment that everyone can carry our very easily and which amplify Edley's remarks. First, many thanks for your dimensions: > the cardboard thickness: 3/32" > the hole diameter: 1/4" > the disk diameter: 2") I got the external diameter wrong but that's not too important. My guess at 0.1" for the internal diameter was almost exactly right! Accordingly, my figures don't really need amending. THICK VERSUS THIN I have some comments on your practical points... > ...if I were to make one for a real sundial, I'd use strong, thin > metal instead of cardboard! Interestingly, you don't have to use thin material for a disc nodus. You could use quite thick material PROVIDED you taper the internal and external rims to knife edges. Even a thick disc then works as though it were paper thin! CONES AND CLOCK HANDS > On the practical and artistic level, I love the cone gnomons' > shadows because they look like clock hands. Yes, I very much accept this. The shape of the long shadow of your cone is very elegant. It is such a shame that such a shadow gets foreshortened when the shadows are long. One thing that hasn't been suggested is to use TWO cones arranged so that they meet tip to tip. Approximations to this arrangement are not uncommon. I am thinking of statue sundials where perhaps two fingers meet almost tip to tip. AN EXPERIMENT ALL CAN TRY This isn't what you have in mind when you seek a shape that looks like a clock hand but it prompts me to suggest a simple experiment that anyone can do anytime the sun is shining without any equipment at all. Here's what you do... 1. Stand with your back to the sun about 6 to 10 feet from a plane surface which is approximately facing the sun and look hard at this surface. [The experiment doesn't work well if the sun is shining through glass, especially double-glazing, so do this outside or, at least, open the window!] 2. Point your two forefingers at each other so that there is about a 1" gap between them and arrange that the shadows of the fingers fall on the plane surface. 3. Now, very slowly, bring the fingers close together. You will find that, sometime before they actually touch, a mysterious blob appears between the shadow fingers. The result is that the shadow fingers appear to touch before the real fingers do. This effect is, of course, because the sun is not a point source of light. The critical moment comes when the angular separation of the fingers becomes less than the angular diameter of the sun. The gap between the shadows stops receiving full sunlight and becomes penumbra instead. You will get something of the same effect if you bring two of your cones together tip to tip. I mention all this to demonstrate that curious effects occur in the vicinity of the shadows of tips. If you have a PAIR of tips this doesn't matter too much. You can look at the symmetry and estimate fairly accurately where the mid-point is. If you have just ONE tip, estimating gets much harder. Edley's message alludes to this difficulty. BALL NODI There is something else your experiments showed up that I hadn't really appreciated before... If you are going to use a ball nodus, then the supporting stick should go RIGHT THROUGH THE BALL so that it sticks out a little bit, perhaps half a ball diameter. This thought struck me when I tried estimating the centres of the shadows in printouts of your photographs. The point on the shadow where the stick meets the ball is not matched by a corresponding point on the far side. Once again, the lack of symmetry makes estimation a little harder. Often a ball nodus is mounted on a regular gnomon, perhaps half-way along, so you get the symmetry for free. Amazingly, I have somehow missed out analysing the shadows of balls at the ends of sticks (rather than in the middle) so I am most grateful to you for thrusting these images my way. I have also become very impressed by the quality of PDF format. I found I could enlarge your images many times without serious degradation of quality. All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Dear Mac, Thank you for sharing Bill's sketch with the list. I really appreciate his phrase... > I'm a bug on symmetry... I think that pretty much describes me too! Moreover, his design satisfies the symmetry goal well. In particular, the fat rod extends beyond the crossing which keeps me happy! The main snag is that the relatively thin rods might disappear into fuzz when the main shadow is long, especially when there is light haze. Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hi Gianni, It is always good to hear from you on this list. Most of what I know about nodus design is a result of reading your papers so your message is of very great interest. You made this comment... > I think that it is advisable that the plane of the hole is a > polar plane with the hole axis on the intersection among the > equator and the meridian planes. Ah. You want the axis of the hole to point at the position of the equinoctial sun at 12 noon. At that instant, the other end of the axis meets the dial where the noon line intersects the equinoctial line. This idea has good features and less good features... GOOD FEATURES The design is very symmetrical. The axis aligns with the sun at a position halfway between the extremes of declination and halfway between sunrise and sunset. Having the hole in a polar plane is particularly good if the dial is also in a polar plane. Of course, the hole is then parallel to the dial. LESS GOOD FEATURES Unfortunately, having the hole in a polar plane does not work well in general. An extreme example is a direct east-facing wall. The hole would then be in a plane perpendicular to the wall. You get no spot of light falling on the dial when the sun is due east. I think you were considering horizontal dials. Your suggestion certainly lets more light fall on the dial at the winter solstice. Let's look at an example... A CAMERA OBSCURA MERIDIANA To make the calculations easy, consider the situation at 12 noon. As an example, I shall consider a camera obscura meridiana at: Latitude 45 degrees Hole diameter 20 mm Height of hole above the pavement 20,000 mm Although millimetres were before their time, Cassini and Bianchini would have been familiar with these dimensions! The brightness of the spot of light falling on the pavement at 12 noon is proportional to the solid angle of the hole as seen from points in the spot. In a really simple case: The hole would be horizontal The altitude of the sun would be 90 degrees In this impossible case, the spot of light would be at the point perpendicularly below the hole. The solid angle is: RSA = (pi x 10 x 10) / (2 x 2) I call this RSA for Reference Solid Angle. This is the area of the hole divided by the square of the hole-to-pavement distance. In reality, the altitude of the sun varies from 45-23.5 degrees (at the winter solstice) to 45+23.5 degrees (at the summer solstice). In general at latitude 45 degrees and at 12 noon: altitude = 45 + dec(where dec = declination) When the altitude is changed from 90 degrees, the hole-to-pavement distance increases by a factor 1/sin(altitude) AND the hole will appear elliptical when you look at it from the spot of light. The semi-minor axis of the hole will be 10 x sin(altitude) if the hole is still horizontal. You suggest that the hole should be 45 degrees to the horizontal. Let's make this angle arbitrary: Let ang = angle of hole to the horizontal The semi-minor axis of the hole is now 10 x sin(altitude+ang) The solid angle is now: SA = RSA x sin(45+dec) x sin(45+dec) x sin(45+dec+ang) In the impossible case where the sun is in the zenith, dec = 45 and, if ang=0, we are back to SA = RSA the reference solid angle. The factor RSA is a constant. It is much more interesting to look at the other terms. Consider the function: sa(dec,ang) = sin(45+dec) x sin(45+dec) x sin(45+dec+ang) If the hole is horizontal ang = 0 and two special cases are: sa(+23.5,0) = 0.805 andsa(-23.5,0) = 0.049 The spot of light is 16 times brighter at the summer solstice than it is at the winter solstice. Now let's try the Ferrari angle. When ang = 45 we have: sa(+23.5,45) = 0.794 andsa(-23.5,45) = 0.123 This give a MUCH better balance. The spot of light is only 6.5 times as bright at the summer solstice as it is at the winter solstice and there is only a slight reduction in brightness at the summer solstice. Your suggestion looks VERY good... We can do even better. Why not align the axis of the hole with the winter solstice point on the noon line? Here ang = 68.5 and: sa(+23.5,68.5) = 0.590 andsa(-23.5,68.5) = 0.134 Now the spot of light is only 4.5 times as bright at the summer solstice as it is at the winter solstice. From the winter solstice point the hole now appears circular. This point is, of course, much further from the hole so it still receives less light. If you really want to achieve balance you can try the King angle. This is over-the-top in at least two senses but it really works. You set ang = 104.267 when: sa(+23.5,104.267) = 0.109 = sa(-23.5,104.267) = 0.109 The hole faces due south and is actually leaning backwards away from the noon line on the pavement. Also, the punto perpendiculare will probably be outside the building but, with modern surveying technology, this should not be a problem! We are severely restricti
Re: Expanded Nodi Shadow Experiment
Hi Gianni, Thank you for your splendid response... > I hope that our Emails, interesting for us, don't bore > other readers :-) I promise this one will be short!! Oh, and your image arrived first time (a little corrupted but I could read it). This time I agree with EVERYTHING in your reply. > For a declining sundial I think that the direction of the axis > of the hole should coincide with the intersection of the plane > of the equator with the substyle plane (hour plane normal to > the dial and on which the polar style lies) Ah. Now that IS a good rule and, as you say, it works for walls that face east and west too. > In the figure Yes, I agree with your calculations. > CAMERA OBSCURA MERIDIANA I am most grateful to you for your comments here. You are, of course, absolutely right to use sin(h) cubed. I was comparing solid angles. You compare brightness which is definitely better. > sin(45+dec) x sin(45+dec) x sin(45+dec) x sin(45+dec+ang) Yes!! Agreed. > I try to explain this in the note at the end, so the readers not > interested can jump it :-) Yes, your explanation is very eloquent and easy to follow. I see from a very old message that I once omitted a sin term before and you corrected me. I must do better! > Then in my opinion the function to use is > >sa(dec,ang) = sin(h) x sin(h) x sin(h) x sin(h+ang) > or >sa(dec,ang) = sin(45+dec) x sin(45+dec) x sin(45+dec) x sin(45+dec+ang) Yes but we must change the name... I chose sa for Solid Angle. My function is correct for comparing solid angles but solid angles are not (quite) what we want!! Using your function, the King angle is now 108.829 degrees... sa(+23.5,108.829) = 0.038 = sa(-23.5,108.829) = 0.038 This is very academic! The plane of the hole almost aligns with the sun at the summer solstice. The difference is only 2.67 degrees. The hole would have to be in a very thin part of the wall or the summer solstice point would get no light at all. You could make the hole elliptical which would help... If the height of the hole is 20,000mm then the hole could have a major axis of 160mm and a minor axis of 20mm. This would give you an image all year I think. At the summer solstice 1/R would be about 3000 and at the winter solstice 1/R would be about 450 which is acceptable. Unfortunately, at the equinoxes, 1/R would be about 400 which is getting rather low. I don't think Cassini would accept that! I think we can conclude this most interesting exchange. I must find an English church which will let me try some experiments! Thank you again Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: RE Dials - ore francesi
Dear Colin > In the description of the dials, one is said to be in french > hours ... Are these the same as equal hours? Roger Bailey has already confirmed your guess. You will rarely hear English-speaking diallists using the term French Hours but Italian diallists (gnomonisti) refer to `ore francesi' quite commonly. Intriguingly, ordinary Italians do not know this term. If you ask a non-dialling Italian about ore francesi you will get a blank look. This is not surprising. Few non-diallists in the English-speaking world ever use the term `equal hours'. You can read about Italian hours and French Hours (and just a hint about what makes them French!) in my frivolous spoof in: http://www.cl.cam.ac.uk/users/fhk1/Maggiore.pdf Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Message from Giovanni Bellina
Dear All, For those who do not read Italian, the message from Giovanni Bellina refers to a site about `Sundials in the Czech Republic and Slovakia'. Giovanni suggests that is worth a look. Indeed it is. You can choose English, French, German or Czech (but not Italian!). There are lots of nice pictures that are new to me. There is also a dialling schema (you key in parameters and it does the calculations). Yes, this site might interest a few... http://www.astrohk.cz/slunecni_hodiny.html Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Dials
Dear Mario, > > the French hours are equal to astronomical hours. I have some comments on your most interesting message but I would like a proper expert to comment further... 1. LANGUAGE > Here in Italy, by now from a long time, the term 'meridiana' is > used as synonym of sundial. To comment on this point I need some translations... Italiano English orologio solaresundial meridiana meridian line (or noon line or noon mark) gnomonista diallist A pedantic Italian gnomonista would use the terms on the left and a pedantic English diallist would use the terms on the right. A meridiana is of course a special kind of orologio solare but in Italy I find that `meridiana' is used not just as a synonym for `orologio solare, it is used INSTEAD! If I use the term `orologio solare' with Italian friends who are not gnomonisti they think I am being very pedantic. Perhaps the term `orologio solare' is too long for ordinary Italians! In England, very few people who are not diallists would use the term `meridian line'. Most people use `sundial' for ANY kind of solar instrument. 2. FRENCH HOURS > ... if you look for a precise description, without ambiguity, we > cannot say that the French hours are the same as astronomic hours. > French hours are the same hours used all over Europe from the half > of the 14th century till now (we call them French just because > Napoleon forced us to use them). I think that it is impossible to give a precise description of French hours without ambiguity! You say... > French hours are 24 equal hours parted in two group of 12, and > they start to be counted from midnight up to noon (first group > of 12), then from noon till next midnight (second group of 12). Yes, I agree BUT, if we are being precise, this is still a bit ambiguous. The problem is that `midnight' can be defined in several ways: A) It could be the moment of local inferior transit of the sun in a particular place. This is OK for a sundial of course. B) It could be the MEAN moment of local inferior transit of the sun in a particular place. This is what French clocks used in Napoleonic times and is probably what Napoleon forced on you! C) It could be the MEAN moment of local inferior transit of the sun at the French observatory in Paris. D) These days, in Italy, it is midnight UTC+1 (or +2 in summer). Does anybody know whether Napoleon understood the difference between local sun time and local mean time? He very probably did. In his day, sundials were used for setting clocks and he would surely have known this? I guess that when he imposed French hours on Italy what he did was to use meaning (A) for sundials and meaning (B) for clocks. Fortunately, Napoleon was not totally successful! There are still numerous Italian-hours sundials in Italy AND there are still a few Italian-hours clocks, especially in the Rome area. Unfortunately, there seem to be only two people in the world who are interested in Italian-hours clocks! I am one and Nicola is the other! I hope I am wrong!! Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Dials
Dear Gianni, I am most interested in your comments and those of Roger Bailey and Nicola Severino... > ... in my opinion, the Italian-hours clocks have never existed This is a big disappointment to me :-) > I ... asked a question that now I repeat: > > What are the differences from a mechanical "Italian-hours > clock" and a "Not-Italian-hours clock"? Yes, this is the important question. Roger Bailey answers: > ... there would be no difference in the mechanism or dial of > a mechanical clock for Italian or French hours. He explains... > Both are 24 equal hours... Roger also says... > The time of sunset shifts on a daily basis but resetting the > clock at the reference sunset time would be a easy normal > activity, no different than using a noon mark or meridian > to set a clock for French hours. Hmmm. Yes and no! In the 14th century, Roger would be right! Clocks were so bad that they had to be reset frequently. The daily error was much greater than the shift in the time of sunset or the shift (due to the equation of time) in the time of noon. By the time of Napoleon, clocks were much better. Importantly, the daily error was less than the effects of the equation of time and MUCH less than the shifts in the time of sunset. Here I need help with history... At some date, people began to set clocks to MEAN time instead of sun time. Clocks were still reset using sundials but you had to use a table (or a chart) with the equation of time to help you. The improvement in technology made a huge difference to the people who maintained clocks. If your clock used French hours AND mean time, you could leave your clock for a whole week or perhaps a month without resetting it. If your clock (with the SAME mechanism) used Italian hours you would still have to reset the clock every day, especially near the equinoxes when the time of sunset changes so rapidly. Here I need more help with history... Did the people who made clocks think about this problem? Did they invent a new mechanism so that a clock could keep to Italian hours? The mechanism would be quite simple... Here is some personal experience... I am `the University Clock-keeper' here in Cambridge and my clock has a pendulum almost 4m long. It has a period of 4 seconds. If I change the period to 4.08 seconds the clock will lose nearly 3 minutes each day. At the time of the March equinox, this would be fine for Italian hours, because sunset (here) is later each day by about this amount (not so much in Italy!). To change the period by 0.08 seconds I have to make the pendulum about 16mm longer. At the September equinox I have to make the pendulum 16mm shorter. At the top of the pendulum there is a long metal spring. It should be easy to change the swinging point +/- 16mm using a simple mechanism that goes round once a year. I would use a cam. The BIG question is: Did Italian clockmakers introduce this mechanism or something equivalent? If this mechanism existed, then I would be very happy! You ask: > the watchmakers built mechanically different clocks if > they had to send them in Italy, and if they had to send > them in Germany or in France? I don't know, but my mechanism is so simple that it would be easy to leave it out when you sent an Italian-hours clock to Germany or to France. You also say: > ... all the Italian tower clocks were transformed from > Italic to French hours after the Napoleonic empire. I have three points: 1. If my mechanism existed, this transformation would be simple. You take out the cam. 2. If my mechanism did not exist, this transformation would be a transformation of use rather than a transformation of mechanics. 3. Is it true that ALL tower clocks were transformed? I have an idea that the Pope had dispensation for some clocks in the area of Rome. Maybe this idea will be another disappointment! I shall be very sad if Italian-hours clocks never existed :-( Frank PS I have a comment on Roger Bailey's point... > ... resetting the clock at the reference sunset time would > be a easy normal activity, no different than using a noon > mark or meridian to set a clock for French hours. Of course it IS a little different. It is much easier to observe the time accurately at noon than it is to observe the time accurately at sunset. For this reason, I believe that it was common in Italy to use a special instrument called a temperatore. [Is that the correct spelling?] The idea is that you observe the time on a French-hours sundial and, with this instrument, you can read the equivalent time in Italian hours. I do not know of an English translation for `temperatore' but I have made a nice one for my latitude out of paper and transparent foil! F --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Equal hours?
Dear Mac, Fer de Vries has answered your question but he could be misinterpreted... > Of course you are right that an Italian hour and a > Suntime hour aren't of the same length each day. > But we are talking about 30/24 second of time per > hour as maximum... This is true if you take 24 hours as the time between successive transits, but the difference can be MUCH greater if you take 24 hours as the time between successive sunsets... The maximum difference depends on your latitude. Where I am at 52 degrees north the difference can be nearly THREE minutes either side of 24 hours measured on a watch. A sundial CAN certainly notice that. At the equator, sunset is at 6pm (by the sun) every day so Italian hours don't change any more than astronomical hours. Inside the arctic circle things go mad! On some magic date (again depending on latitude) you experience a sunset that is the last you are going to have for some weeks or even months. Italian hours are not well defined then but, if you insist on deeming an Italian hour to be one 24th of the time between successive sunsets, then an Italian hour can last several days! In summary: Italian hours are rather boring in the Tropics and go mad near the poles. They are at their most interesting somewhere in between like, ahem, in Italy! I think it is most unlikely that, when the famous Italian explorer Umberto Nobile was making his expeditions to the Arctic, he used Italian hours! Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: sundial on a cylindrical wall
Dear Willy, That is an interesting sundial... > I made the calculation for the hour lines and datelines > for a sundial ... on a concave cylindrical wall... When I first heard about this project, I imagined that the nodus would be hidden in shadow for most of the day by the wings of the wall. Now I see the finished sundial, all is clear. The top of the wall appears to be your horizon line. Is this right? > I am in search of other sundials on a concave cylindrical > wall. I do not know of any other examples but, in my experience, there is no such thing as a flat wall. Every stone wall has undulations, some of which are concave and some are convex! On a big dial you have to allow for this in the calculations... I am interested to know whether you assumed that your surface was a perfect mathematical cylinder? Did you survey the wall carefully to see where it goes in and out? With a big wall, which is supposed to be flat, I use the following procedure: 1. Note the latitude. 2. Survey the wall using, say, a 500mm grid. 3. Determine the best-fit *vertical* plane. 4. Determine the declination of the best-fit vertical plane. 5. For each intersection point on the 500mm grid, determine how far it is behind or in front of the best-fit vertical plane. 6. Determine the perpendicular distance of the centre of the nodus from the best-fit vertical plane (the ortho-style distance). 7. For each feature (e.g. constant-declination line) calculate the positions of a number of points assuming the ortho-style distance is constant. 8. For each calculated point, estimate the offset from the best-fit vertical plane and add or subtract this from the ortho-style distance. Then recalcualte the point. Repeat as necessary. Of course, what I am describing is an iterative procedure and I certainly claim no originality for it! Essentially, I am assuming that the wall consists of lots of parallel planes, each with its own ortho-style distance. I developed this procedure for a wall where the undulations were of the order of +/- 10mm over an area 10m x 4m. Some of the deviation was accounted for just by the wall leaning over (9mm in 10m). In fact, the procedure works perfectly wall if the wall is any shape at all. Since a cylinder is easy to describe mathematically it works well for that. Even your wall has a best-fit vertical plane! It is just that the ortho-style distance varies rather a lot from the mean! What I am interested to know, is: 1. `How close to a true cylinder is your wall?' 2. `How did you allow for the inevitable undulations? All the best Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: sundial on a cylindrical wall
Dear Mac Many thanks for your message... > Would you be willing to expand on the eight steps > you listed in your procedure for dealing with a > supposedly flat wall? Yes, I am willing but this is a bit of a risk! Each step could be a whole chapter of a book! I don't think the list would be too pleased with me. Also, I don't claim any special expertese. There must be many who subscribe to this list who do things differently and better! I shall take as my starting point Willy Leenders' comment: > When I calculated the sundial for this wall > there was no wall at all. Ah! One general remark is that there is a big difference between Mathematics and Engineering: Mathematics is nice and friendly. You can do it late at night in winter when its raining and would prefer to be in Italy. This is the fun part of dialling, at least for me. Engineering is what happens when real life takes over. Things go wrong! The scaffolding isn't ready. The sun stays in for days. Someone 10m above you drops a pencil which goes through your thumb! This is the hard part of dialling but it is probably the most rewarding because you end up with something real, not just an abstraction. OK, I'll give a fuller account of the steps I take. Most list subscribers should hit the delete button about here! 1 LATITUDE As you say, this is easy. You can use a map or you can use your hand-held GPS kit. Actually, I use GPS in a more elaborate way to determine the declination of a wall but we needn't consider that now. 2, 3, 4, 5 and 6 THE WALL SURVEY I confess here that I am almost as fascinated by modern surveying techniques as by sundials. Certainly I freely mix the two activities. Typically I make use of a Total Station... A Total Station is a modern theodolite which can measure distance (using a built-in infra-red laser) as well as angle. It readily converts positions to X,Y,Z coordinates. Using the associated software you can arrange for ANY particular point on a building site to be the origin. You are constrained to have the X-Y plane horizontal and the Z-axis vertical, but otherwise the orientation is arbitrary. For a diallist, the obvious plan is to have the nodus at the origin and to arrange for the X-Z plane to be parallel to the plane of best fit to the wall surface. Of course, you have to look at numerous points on the wall before you know the plane of best fit. Accordingly, you may change your mind a few times but it really doesn't matter too much if the assumed plane of best fit is not the actual plane of best fit. You end up with a system of coordinates... The positive Y-direction is horizontal, through the nodus, INTO the wall. Surveyors call this north (whatever the actual direction!!). The positive X-direction is then nominal east and the positive Z-direction is UP. The plane defined by Y=0 is taken as the reference plane. The nodus is in this plane, at the origin, and the best-fit plane in the wall is parallel to it. The separation of the best-fit plane from the Y=0 plane is the reference ortho-style distance. The real surface of the wall deviates from this best-fit plane and you make as many observations as you feel necessary. If the wall is very uneven, you make a lot. What you end up with is a chart of the wall showing the ins and outs relative to the best-fit plane. If the wall is good, the numbers will be like +2, +3, -4, -1, 0 being the deviations from the best-fit plane in millimetres. The average of all these values would be zero if you really have got the best-fit plane (at least if you use the term `best-fit' in a naive way). You can get some feeling for the wall just by looking at the numbers. If you notice that the `ins' are in the majority high up and the `outs' win low down, then the wall must be leaning backwards a little. Sometimes, the `outs' win at the west and east margins and the `ins' win in the middle. This means the wall has a concavity. You could take the view that the Willy Leenders dial is just an extreme case of this! Indeed, that is exactly how I would survey his cylinder. If you are hoping for a true, flat surface, then you will be lucky if the `ins' and `outs' are better than 1mm in 1m. If you have a wall 10m high then you will probably find deviations of the order of +/- 5mm. This seems to be the tolerance that builders work to. 7 and 8 ALLOWING FOR THE IRREGULARITIES I'll give you an almost real example with the figures rounded for simplicity. A client accepted a design for a big dial, about 10m x 5m, high up a wall at latitude 51 degrees N. The nodus support was put in place and the ortho-style distance verified to be 5000mm. On the first sunny day after that, the declination of the sun was 21 degrees so the altitude at noon was 60 degrees. You would expect the shadow to be at a point 5000 x tan(60) down the from the sub-nodus point. This is 8660mm. In fact the shadow was over 17mm lower than this. Why? We
Re: AW: Summaries of bulletin - Block dials
Dear Ruud, I very much agree with your comment... > Mathematically, a polyhedron ... need not be > regular or indeed convex. My favourite polyhedron is the Szilassi Torus. This is not just concave but, as the name implies, it is equivalent to a ring. This polyhedron has just SEVEN faces. Each face is an irregular hexagon. I find it remarkable that with just seven flat hexagonal faces you can make a torus. This polyhedron illustrates the Seven-Colour Map Problem: each face has an edge in common with each of the other six faces. Before you rush to Google, see if you can work out how such a torus is possible. I am certain you could make a sundial from a Szilassi Torus with one (or more) of its edges casting a shadow onto one (or more) of its faces There would be no need for vulnerable gnomons; the whole thing could be made out of stone. OK: that's my challenge for the week! Oh, I REALLY enjoyed your doggerel: > KonKAV ist eine Fläche dann, > wenn man KAFfee hineinschütten kann. I didn't know there were jokes like that in German! Does it translate into Dutch? Please send me more, but OFF List!! Frank H. King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Varying amounts of sundial correction
> For example, I think some countries may not subscribe > to the general rule of reference meridians and time > zone division every 15 degrees... It gets even worse than you thought. You can be a whole DAY out... The Line Islands in the Pacific keep their clocks at GMT+14. The International Date Line has a very curious wiggle (hey what am I thinking of?) which keeps them in the Eastern Hemisphere as far as the calendar is concerned but their longitude is about 150 deg W. [Source: Whitaker's Almanack] They really ought to be GMT-10 but they prefer their calendars to be in step with New Zealand which is the nearest land mass of any size. Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Chronograms on dials
Dear Phil and Giovanni If anyone is interested in seeing a photograph of the Rome chronogram, I have put one I took myself in 2005 in: http://www.cl.cam.ac.uk/users/fhk1/JamesIII.jpg I am entirely happy to relinquish copyright :-) In my view, the spacing of the lettering could have been better! > This chronogram is particularly interesting because > it is dedicated to: > > JAMES III BY THE GRACE OF GOD KING OF GREAT BRITAIN... He is indeed one of the best-known kings we never had. > For his biography and why his dial is in Rome, click > on http://www.royal.gov.uk/output/Page144.asp This is an interesting biography but, alas, doesn't explain why the chronogram is about 10 metres from the punto perpendicolare of the meridiana. The key to the motivation for the plaque is partly in the chronogram and partly in the phrase in the centre of the plaque FELIX TEMPORUM REPARATIO, Blessed Restoration of the Times. This is partly a reference to the 10-day shift which Pope Gregory had ordered in 1582 along with the reform of the Calendar. As wishful thinking it was also a hope that King James III would be restored to the throne. This, and more, is given in: http://www.jacobite.ca/gazetteer/Rome/SMariaAngeli.htm The chronogram is also referred to in the splendid book about the meridiana, Il Cielo in Basilica, by Mario Catamo and Cesare Lucarini but they do not say more than is found in this web site. It makes some kind of sense to place a thank-you plaque near an instrument that monitored the instant of the Vernal Equinox but neither the web-site nor the book explicitly says so and various things don't quite add up... The meridiana was laid down by Bianchini in 1703, long after the Gregorian reform of 1582. This particular meridiana cannot have had anything to do with the reform of the Calendar. James III recognised the Gregorian reform in 1721 which is the subject of the chronogram of course. Great Britain adopted the Gregorian Calendar in 1752. James III died 14 years later in 1766. I cannot find out when the plaque was placed in the pavimento of the Basilica. If it was placed shortly after 1721, while James III was still alive, this would make much more sense than if it were placed after his death. It would be fun to know that King James III saw the plaque himself. By 1766, surely, any irritation by Rome over Britain having taken such a long time to adopt the new Calendar must have been very slight? Can anyone supply further information? Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Europes largest horizontal sundial
> Have a look at Europe?'s largest horizontal sundial... How large is largest? No dimensions are given :-( There is a large sundial in Britzer Garten in Berlin for example and a huge compass rose dial in Lisbon. I don't have the dimensions of any of the three but they are all very big!! Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
GPS and Azimuth
Dear Doug and Roger, You are both right to doubt claims for 0.1 arc-second precision in azimuth using a hand-held GPS receiver but there is more to be said before dismissing GPS outright. Appropriately translated, 0.1 arcsec precision is equivalent to a 2km baseline with the end points known to 1mm. Unlikely! What you CAN do is set out a baseline of about 50m and, at each end, place matched up-market GPS receivers which are connected to the main kit close to the mid-point of the baseline. Typically, the system is left to run for 6 hours or so. All this time, both receivers are averaging their perceived positions. For any given pair of satellites all each receiver can do on its own is note the perceived difference in the clock times, which translates into a difference in distance. The locus of all points which are nearer to one satellite than another by some fixed amount gives a surface. By knowing the ephemeris data of each satellite, and taking several pairs, the intersections of these surfaces leads to a best estimate of position. In good conditions, you will end up knowing the positions of each receiver to within one or two metres. This is still pretty hopeless but now comes the clever bit... What the kit in the middle does is not merely compare perceived clock times but actually looks at the phase differences of the carrier waves from the different satellites as picked up by the two receivers. This way, they can determine the relative time differences to times corresponding to a fraction of a wavelength. This doesn't improve the estimates of the absolute positions of the two receivers at all but their RELATIVE positions can be determined to about 5mm. This is starting to look good. You are talking about 5mm in 50m or 1mm in 10,000mm which is about 20 arc-seconds or one-third of an arc-minute. With your theodolite you are (at the moment) getting an error of the order of 0.08 degrees which is about 4.8 arc-minutes. You should be able to get this down to 2 arc-minutes with practice unless there is lots of slop in your instrument!! GPS does rather better and doesn't need a clear sky. It DOES need a good view of the sky though and won't work well at street level with high buildings all round. You will need to set it up on something very solid high up. Concrete buildings don't sway as much as steel ones!! The snag is the cost of the kit. This is serious professional stuff costing between $50k and $100k. Specialist contractors who use this kit all the time are available for hire. I have used three different such contractors for big (and expensive!) sundials over the past 10 years. Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Australian Sun
Dear All, A nice insight into Australian understanding of the sun was reported in Monday's Daily Telegraph here in the U.K... Western Australia began a daylight-saving experiment last December ... largely to see whether it would lead to the energy savings forecast by the light lobbyists. In January one housewife in Perth tried to sue the state government. She was seeking compensation ... because the extra hour of daylight would fade the pattern on her curtains. Hey, wouldn't I just love to be brought in as an expert witness in such a case? I would happily appear for either side or, indeed, both sides! Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Australian Sun
Dear Roger, How splendid to hear from a fellow non-enthusiast for so-called Daylight Saving. > Although her suit may lack merit, I sympathise > with the lady in Perth. In fact, I feel sure I could contrive a way in which her case might be pursued!! Maybe she is in the habit of reading by a west-facing window in the late afternoons and when the low sun is troublesome draws her curtains across the window. Now she finds she has to do this for a whole hour longer :-) > This change was driven by profiteering not energy > conservation. Indeed so! > Give us back that hour of light in the morning... Yes, yes! I cycle to work about 6am (sun time) each morning and it was just getting so I could see the sun peeping over the eastern horizon but now I am put back in the dark for a few more weeks. The whole business is a confidence trick. You trick people into getting up an hour earlier by telling lies about the time. There was a U.S. State in the 19th century which got close to legislating that pi should be 3 because 3.14 was inconvenient. I regard changing the time of midnight by legislation in much the same way. Just imagine trying to change the time of sunset by legislation? At least Italian Hours are safe!! Frank King --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: strange longitude
> I looked with Google ... and I got a picture of the dial... > It is an east declining sundial for local suntime and I > think the value is the declination of the dial. That thought occurred to me too. In which case PL might be a slightly unusual use of the navigator's term Position Line? Strictly, a Position Line is the local arc of the circle centred on the sub-solar point that passes through the position you happen to be at. The plane of the dial stands on this arc when the outward normal to the plane is in the same direction as the sun. That is a good moment for measuring the declination of the dial which gives it some relevance. Maybe this is stretching the idea of a Position Line too far!! Frank King Cambridge U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: strange longitude
> But would anyone claim to measure declination to > seconds of arc? Hmmm. That's one reason why I hesitated to make the suggestion but there are three tiny points to note: 1. The meridian line in the Basilica di S. Maria degli Angeli in Rome was laid down in 1702 and that IS true north-south to within a few seconds of arc so it could be done in 1845. 2. In 1845 measuring longitude to seconds of arc probably wouldn't have been significantly easier than measuring declination to seconds of arc. 3. The quoted angle is 35 deg. 43 min. 40 sec. That could be interpreted as "measuring to the nearest third of an arc-minute" which doesn't sound quite so challenging. The use of Position Lines in navigation is attributed to Thomas Sumner in 1837. There must be readers of this list who know how things developed from then. It is conceivable that by 1845 the idea was well known to navigators and others. Writing PL on your sundial might be a way of showing that you were using modern ideas! OK. I'm clutching at straws! Incidentally, this quoted figure for longitude is within a few arc-minutes of being the co-latitude. Weird! Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Porcelain Sundials
Dear John, Thank you for your message. I was delighted to have the opportunity to meet you face to face at the BSS conference and to hear about the techniques you use... > especially our discussions about the possibility > of using durable fired porcelain instead of paint I shall certainly investigate this technology though my current client is keen to stick to paint! I have something else in mind for a year or two hence and may look very carefully at this technique then. I noted a number of intriguing linguistic differences in our discussions... I think we use the term `enamel' for `fired porcelain' which means something slightly different here. I also noted that when I talked about `fixing a dial' this was not a usage that you recognised!! Your CD, by the way, is full of absolutely splendid delights. Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: strange longitude
Dear Gianni, You are truly wonderful! You have, come sempre, solved the problem! We have all these people on the English list wondering about PL and we have to wait for you to interpret our English! I didn't think of the Geocentric Latitude and I certainly didn't think of the Reduced Polar Latitude but your calculations point to that conclusion. Your figure of f = 1/298.257 is used by Meeus but would not have been known in 1845. I agree that 1/280 is the value most likely used. You win the prize for solving this puzzle! Very best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Porcelain Sundials
Dear John, > Does anybody know if the four round blue dials on > the tower at Westminster Abbey in London are made > of porcelain (vitreous enamel)? They are on the Tower of the Church of S. Margaret's Westminster (quite different from Westminster Abbey) and are by Christopher Daniel. You can see a little about these dials in: http://www.sundials.co.uk/~thames.htm but it doesn't say what they are made of. I am fairly sure they ARE enamel! Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Porcelain Sundials
Dear Patrick, Your short message is a mine of information... > > I am fairly sure they (the dials on St Margaret > > of Antioch's Ch) ARE enamel! You are quite right to refer to this place as "the Church of S. Margaret of Antioch" and, likewise, I should have referred to "the Collegiate Church of S. Peter in Westminster" rather than the vernacular Westminster Abbey! I must try harder! As far as I know, the latter has no dials (though I put one in the street close to its Chapter House) whereas the former has four. Even more interestingly you say: > Yes, they are enamel > They are huge too - 8ft 6ins in diameter. This measurement raises further questions. John Carmichael explained that the biggest oven that his suppliers use will accommodate a maximum size dial of 46" square. The Margaret of Antioch dials are over twice that size. I wonder whether Brookbrae could still do a job that big. If so, they may have a customer! Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: strange longitude
Dear Frank, You present a splendid summary... > The most likely explanation, it seems to me, was > proposed by Fer de Vries. Indeed so... > In other words, at 9.37 am the sun will be directly > over the style and the cited longitude is the hour > angle. This explanation has the added advantage that > no geographical longitude is involved... Hmmm. Surely it would be even better to say... This explanation has the added advantage that it DOES involve a geographical longitude... The Pl longitude is the geographical longitude where, at 12 noon local sun time, anyone way to the west in Hawkshead could see the shadow of the gnomon falling along the sub-style of this dial. Thus "longitude" has its conventional geographical meaning. Just think: pupils at Hawkshead Grammar School could be taken outside for a break and told to watch for when the shadow fell along the sub-style. "Look at that boys", the schoolmaster would say, "It is now 12 noon everywhere along the Pl longitude". This has been the best thread for a long time!! Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Canted Dials
Dear All, One of the most interesting (to me!) side issues about the Hawkshead dial was noted by Patrick Powers: > On the matter of the dial being designed as a declining > dial yet also being canted out, it may be of interest > that there are only 16 dials known to the BSS Register > which have this property. I wonder whether the Register rules specify a minimum "cant"? If not, I shall, sotto voce, reveal a carefully guarded trade secret: Almost all vertical dials are canted. Here's why... When you have a real client who wants a real sundial on a real wall you do three things early on: 1. Assume the wall is vertical (this is rash) 2. You note the latitude (this is easy) 3. You estimate the declination (this is difficult) There then follow months of excitement and frustration (in equal measure) but you end up with a beautiful dial, complete with gnomon, ready to fix on the wall. With modern workshop techniques you have in your hands a dial that it just about perfect for a vertical wall at the noted latitude and with the ESTIMATED declination. You then go back to the site and discover the wall isn't quite vertical and, via a helpful sun, you find out that your estimate of declination is a bit wrong. If you have been careful, it should be correct to about a quarter of a degree. Even so, if your dial is 1m wide that will mean packing out one side or the other a little over 4mm. Of course, you have to pack out the top or bottom if the wall isn't quite vertical. Necessarily you do all this when the client isn't looking and keep quiet about it! And this, dear reader, is why most vertical dials are canted, even if only a little bit! Armchair diallists will now say: 1. Hey, surely you can do better than a quarter of a degree, and... 2. What about painting directly onto the wall where there is no scope for last-minute canting? The real-life problem about doing better than a quarter of a degree is that real walls are actually far from flat. They have bumps and dips and undulations and a horizontal line drawn on a wall will not be straight. The deviations can be well over a quarter of a degree. If you hold a 2m straight-edge horizontally against a wall you will find that it nestles against a couple of peaks that stand a little proud and you typically find dips of 5mm or more between these peaks. This is particularly true of old brick walls and, alas, even of 21st century walls made of stone blocks. If the wall is rendered you find gentle undulations. If you hold a 1m square piece of truly-flat slate against a real wall, it will typically rest against three local peaks. These define a plane of course but it may deviate significantly from the best-fit vertical plane which is what an expensive surveyor will come up with. Another real-life problem is that the client, at the very last minute, will say: "I think it would look better a little higher up". You then find you are resting against three different peaks. In some ways cutting directly into a wall (or painting on it) is actually easier. There you really can use the best-fit vertical plane and ALLOW for the deviations as you are setting the furniture out. Essentially, you regard the wall as being sectioned into little squares and treat each square as having its own separate nodus height. In a bad case, these separate heights may deviate +/- 5mm from the nodus height relative to the best fit vertical plane. Other practitioners will no doubt tell their own stories. I once had a client who suggested a quite different wall on the day of fixing! It's all good fun in the end! Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
