Let's fix the nomenclature!
Hello All: I'm glad the azimuthal discussion didn't die as I think we are finally coming to grips with understanding it. I think it is that it is important to point out that much of the confusion on this subject has resulted from poor understanding and misuse of sundial terms. The terms "Dali, azimuth, azimuthal, Singleton and monofilar" have all been mistakening used interchangably in this discussion causing a great deal of frustation and lost time. Before we go any further I think that we should first all agree upon the proper nomenclature, so we are all speaking the same language. According to The John Davis Glossary, a monofilar sundial is a dial "in which time is marked by the point where the shadow of thread held between the dial face and the sun intersects a set of date lines." This definition seems to apply to either to a Singleton dial (polar axis thread (or cable) gnomon with EOT hour lines and date rings) or to an azimuthal dial ( vertical thread or cable gnomon with unwrapped analemma hour lines and date rings). It seems that the only important requirements of a monofilar dial are that it have date rings and use a string type gnomon. If an azimuthal Spin dial has a vertical cable instead of a rod for the gnomon, then it also fits perfectly the Davis definition of monofilar. We need to come up with and decide upon a term that describes a Singleton sundial. Should we just continue to call it a "Singleton" for lack of something better or should we call it monofilar and ask John Davis to modify his definition to exclude azimuthals? John Carmichael p.s. I see no reason why a Singleton has to have a thread (or cable) gnomon. Won't it also work with a traditional solid triangular gnomon? Since monofilar means "single thread", it seems that it's definition should be the following: "a sundial that uses a thread, string, cable or rod", with no date ring requirement. This would make my current cable sundials monofilar. Or should I call my sundials "string sundials"?
total lunar eclipse
Hello dialists: My new Celestial Products moon calendar says that there will be a total lunar eclipse at 4:41 UT on January 21 (the evening of Jan. 20th in North America). We have already discussed on the list the fact that moonlight should indicate the correct time on a sundial during totality if corrected for EOT and longitude and if its light is bright enough to cast a shadow. But what happens to the declination readings on a sundial during a lunar eclipse? I'm thinking that the shadow of the nodus should indicate a date which is exactly six months from the date of the eclipse. In this case a sundial with declination lines would show the date to be July 21. Is my theory correct about this? Those of you who have sundials with declination lines might want to check this out during totality. I'm also curious if there will be enough moonlight to even see a shadow. Mark this date on your calendars and please let us all know the results of your observations. Thanks John Carmichael Tucson Arizona
Re: coordinates
Dear Francois: I ran your coordinates through the mapblaster program and determined that indeed they are for the location of City Hall, downtown. I didn't check other cities, though. In the mapblaster program there is an option similar to your's for which you give mapblaster the name of the city that you want and it gives you a city map with its coordinates. For some reason, the coordinates that mapblaster gives for Tucson are precicely for the entrance gate to Davis Monthan Air Force Base which is several miles from City Hall on the outskirts of Tucson! Thanks so much for getting back to me with your answer, and please excuse my mistake in confusing your program with Fer's. John Carmichael http://www.azstarnet.com/~pappas >Hi John and everybody > >I can give some information about the coordinates of the cities included in >my program Shadows. I took the coordinate from the "Grand Atlas de >geographie de l'Encyclopedie Universalis" published in France. In the >copyright notice they say that it is originally a book from Rand McNally & >Company. > >The coordinates are given for the approximate center of the town. In some >cases, they give the coordinate for another place near the town (i.e. the >Niagara falls: 43*15'N 79*04'W and Niagara Falls city: 43*05'N 79*03'W) but >I included only the coordinates for the town. > >It can't be absolutely accurate, and may be I included also some typing >errors in editing the coordinates for the 750 cities by hand, reading the >book!! > >For Tucson, they only give 32*13'N 110*55'W. > >François Blateyron >EMail: [EMAIL PROTECTED] >Web: http://web.fc-net.fr/frb/sundials/ (cadrans solaires / sundials) > > > >-Message d'origine- >De : John Carmichael <[EMAIL PROTECTED]> >À : sundial@rrz.uni-koeln.de >Date : dimanche 22 août 1999 21:57 >Objet : excuse me Fer > > >>p.s. >> >>I wrote to Fer pleading forgiveness for saying that his program contained a >>list of cities with their coordinates. I was confused and should have said >>that this program is from the "Shadows" program by Francois Blateyron . >But >>I'm still interested in knowing to which exact part of a particular city >>these coordinates apply and how these coordinates were selected. I guess >>I'll have to check out the mapblaster website to find out, now that I've >>made the creators of both these wonderful programs mad at me! >> >>John Carmichael >> >> >> > >
a peculiar sharpener
Hello dialists: Three years ago I built an equitorial interactive mechanical heliochronometer of brass and wood based on the design described in chapter xII, pgs. 193-202 of the Mayall's book. "The heliochronometer consists of four basic parts: base, dial plate, alidade or sighting instrument, and analemma. The alidade is attached to the dial plate so that it can be rotated about its center, which is coincident with the center of the dial plate. Consisting of a flat plate, the alidade has two fixed upright arms perpendicular to the dial plate. One arm contains the style or nodus, the other the analemma." The Mayall's suggest that the style or nodus may be either a simple pinhole (a shadow sharpener), the intersection of two crosshairs, or a bead centered inside of a small hole. They didn't say which type is better, however. To determine this, because I didn't know the necessary optical mathematics, I conducted over thirty different experiments using all sorts of hole, crosshair and bead diameters. The objective, of course, was to find the style which cast the smallest point of light or shadow onto the analemma. The design which worked the best was a 1/8 inch spherical bead, suspended by thin brass crosswires, in the exact center of a 1/4 inch round hole. (The style was about 24 inches from the analemma). A very curious thing happens with this type of style. The bead alone, by itself, casts a shadow that was twice as big as the bead; but when the 1/8th in. bead is in the center of a 1/4" hole, with a space of 1/16th of an inch between the bead's edge and the hole edge, the bead's shadow miraculously sharpens into a tight, dark shadow that is only 1/16th of an inch in diameter, smaller than the bead itself The wires which keep the bead suspended in the middle of the hole are so thin that they don't cast a visible shadow onto the analemma. This arrangement somehow has the ability to sharpen the shadow of the bead. I don't know how this works, but it does. It probably has something to do with the wavelength of light or diffraction. My experiments showed that this effect only worked for a style with these dimensions; larger or smaller beads, holes or gaps did not exhibit this strange focusing phenomena. I don't know why this works, but it does. Can any of you explain this? John Carmichael p.s. I believe I sent photos of this style on my heliochrometer to several of you to whom I sent copies of my manual (Roger, Ross, Susan, Harold, Fred?)
Re: Center of penumbra....or not?
Hello all: I was just thinking that on a horizontal sundial that the true shadow point would ONLY be at the center of the penumbra at high (apparent) noon. In the late afternoon or early morning, the sun would be to the side of the style, causing the shadow to strike the dial face at an angle. Wouldn't this shift the true shadow point towards the center of the sundial, away from the center of the penumbra? (wish I could make you a little drawing of this as a picture is worth a thousand words). John Carmichael >
A GIANT PRECISION SUNDIAL
Hello Charles & all others: You're right, the "fuzz zone" is the prenumbra, not the umbra. (mia culpa) It seems that we are in agreement that the center of the preumbra is the place where the shadow of the style's edge would be if the sun were a point light source, and that this point can be estimated either by the eye or determined exactly using a shadow sharpener (a great invention!). When reading a large sundial this point must be determined because, in the calculation of the hour lines, the math specified this point, right? Does this mean that there is no upper limit for the size of a sundial? * Assuming that the fuzziness of the shadow is not a limiting factor for maximum size, because you can get precise readings using the fuzz zone's center, then a huge sundial could be built that could have extremely small time divisions. Couldn't it? If this is true, then one second time line markings could be placed on the dial face, couldn't they? I haven't done the math, but if the one second lines at high noon ,when they are closest, were spaced at an easy to read distance of about a 1/2 inch apart on a giant horizontal sundial, then the height of the style and the diameter of the face could be determined. It would be a large sundial indeed! It has long been my dream to design and construct such a sundial, maybe not with one second markings, but with 30, 20, or 10 second time lines. (What are the time divisions on the large sundial in Japur India, does anyone know?) I'd like to use the same basic design that I use for my horizontal string sundials (see website). The sundial face could be located in a park and people could walk on it. The cable style would reach way up to a pulley attached to a building roof edge or southern wall. A very heavy counterweight suspended from the cable would apply tension, making the cable straight. The diameter of available stranded metal cable may be the limiting size factor here because if the sundial were too large and the cable too narrow then the shadow would completely disappear (like telephone lines do on the ground). I know that I've asked more than my fair share of questions of you all, but of all of them, these are the questions to which I would most appreciate an answer. I need your help on this one guys! A dollar for your thoughts, John Carmichael Tucson website: http://www.azstarnet.con/~pappas I >At 09:23 AM 5/2/99 -0700, you wrote: >>Hello Nit Picking Old Timers: >> >>Roger states what we have all thought to be true, that as the >>style recedes from the sundial face, the shadow's edge becomes fuzzy which >>limits the degree of precision attainable. This effect is most noticible on >>large sundials. However, it's not as bad as we think because the eye is >>very good at estimating where the CENTER of the fuzz zone (the umbra) is. > >This is just a gut level feeling, and I don't know enough math to prove or >disprove it, but I don't think the correct point would be in the center of >the fuzzy zone. (Am I correct in my belief that the fuzzy zone is the >penumbra shadow?) > >Assuming you could safely look at the sun directly, stand so the entire >disk of the sun is hidden behind the building in question. As you >gradually step back, the percent of the sun's disk that is visible will >grow at an increasing rate until half the disk is visible. After that the >percent will continue to grow but at a decreasing rate until the entire >disk is visible. I'm not sure this would put the correct point in the >center of the penumbra shadow or not. > >As a test, you could make use of a device I read about called a "Shadow >Sharpener", supposedly used by Chinese astronomers centuries ago. > >The shadow sharpener is simply a stiff sheet of opaque material with a >clean edged round hole in the middle. I made one from the thin cardboard >backing of a pad of paper, with a hole about half a barleycorn in diameter. > >To use, hold the sharpener a short distance (1 to 3 feet) away from the >fuzzy zone, with one side facing the sun. An image of the sun will appear >on the surface the shadow is on. Move the sharpener around until the image >of the sun is bisected by the edge of the roof of the building, (or >whatever comprises the gnomon). I believe then that the image of the >gnomon will be in the exact place it would be if the sun was a point >source. Try this and see if this point falls in the same place that your >eye estimates it would. > >Charles > >
Re: Penumbral Head Swelling
Hello Nit Picking Old Timers: Well, well, well; you are all truely amazing. I have given up on trying to write to each of you individually to thank you for your answers to my question about the definitions of "precise" and "accurate". The response was unbelieveable. I lost count at about 30! I have already incorporated some of your ideas into the last draft of my "Sundial Owner's Manual" manuscript. I hope you don't mind. In fact, I 've printed out hard copies of the RELEVANT answers,(no lice, barlycorns, or barnyard atmospheres!), and am putting them into my heliochronometer folder for future reference. By the way, I have made similar folders that contain our previous discussions of EOT, DST, sunrises & sunsets, etc. etc. Might make a good book someday! I was going to let the present discussion die down, then go to heart of the matter: "What makes a sundial precise"? But Roger Bailey beat me to it. (see below). Roger states what we have all thought to be true, that as the style recedes from the sundial face, the shadow's edge becomes fuzzy which limits the degree of precision attainable. This effect is most noticible on large sundials. However, it's not as bad as we think because the eye is very good at estimating where the CENTER of the fuzz zone (the umbra) is. I was downtown the other day, sitting in the shade of a very tall building right next to the roof edge shadow fuzz zone which was about 18 inches wide. (Ross Mccluney could tell you how tall the building is). I was imagining that the edge of the building's roof was the style. At first I thought that that would make the sundial difficult to read. But then I realized that if you use the center of the umbra then your reading can be extremely precise. The diameter of the face of this huge sundial would be the size of a small park. What would be the smallest time divisions possible on such a large dial? one min., 30 sec., 5 sec.? Is a sundial with one second markings even possible? I think so, if and only if one reads it using the CENTER OF THE FUZZ ZONE. I'd love to hear your opinions on this one: What size would a sundial have to be to achieve one second precision (not accuracy) or better? And, for extra credit, what would be the velocity of the moving shadow on this giant sundial? A sincere thank you to all of you who have made the sundial discussion site such a valuable, educational, and entertaining experience. Please forgive me if I don'tt answer you all back personally. Back to the old grindstone, John Carmichael website: http:/www.azstarnet.com/~pappas (from Roger Bailey >Dear John Carmichael, > >Well done John, Your simple question again triggered an avalanche* of >responses from us nit picking old timers. > >By now the difference between accuracy and precision is well defined. I >would like to return the discussion to sundial design. The accuracy of a >dial depends on the skill of the designer, builder and installer. It should >take into account the latitude, longitude and orientation of the dial. > >The precision of a sundial is limited by the fact that the sun is not a >point source of light but is a disk about half a degree wide. The shadow >edge is fuzzy for half a degree as the sun is partially covered (penumbra >shadow) and then totally covered by the umbra shadow. Size does not matter. >A small dial seems to have a sharper shadow but it cannot be read as >precisely. A large dial allows division into smaller units of time but the >shadow is too fuzzy to read precisely. For a rod type of gnomon, the >problem is even worse. It may be too narrow to completely cover the sun >and produce the dark umbral shadow. > >There is a simple demonstration of this phenomenon that I observed one >morning. Stand by a window with the sun at your back and casting your >shadow on the floor. Move away from the window until the shadow of your >head is about 4 inches (10 cm) from the shadow of the top of the window. >Then slowly more to bring your shadow up to the window shadow. As the >penumbra shadows of your head and the window start to intersect, the dark >shadow will grow. The top of your head will seem to swell upward as the >shadows come together. Repeat to confirm the phenomenon. This is best done >in the privacy of your own home. > >In that twilight zone of partial shadow, a sundial cannot be precise. Half >a degree is two minutes of time. But there are techniques to minimize the >problem and read a dial to a precision of less than a minute. One is to use >a disk or ball on the gnomon to cast the shadow. A properly sized disk will >project a small dark umbral shadow at the center of the large fuzzy >penumbral shadow. The Romans used this technique by topping their obelisks >with spheres. > >Cheers from a swelled headed, nit picking, old timer, > >Roger Bailey >Walking Shadow Designs >N 51 W 115 >*where triggering an avalanche is not just a figure of speech! > > > >
a mathematical definition
Hello Ross: So good to hear from you again. I should have known that you would be the one to come up with mathematical definitions of "precise" and "accurate". It is obvious that you have thought about this before, in connection with your own sundials. Yes, your definitions and explanations make a lot of sense, as I still remember a little bit from college statistics. Thought it very instructive to see how your definition could be applied to anything that is measurable, even darts! Seems that the dictionary closely agrees with the mathematical definitions, in much simpler terms, of course. Thank you once again for another one of your thoughtful, in-depth answers. John Carmichael new website: http:/www.azstarnet.com/~pappas p.s. After seeing your amazing Disney sundial, I can't wait to see any new projects that you have in the works. Keep us informed, I'm sure everybody in the group would be interested. >>From my recollection of the principles of experimentation, >accuracy has to do with the magnitude of the spread of a series >of repeated measurements of the same quantity around the mean or >average measured value, representing something like the >reproducibility of the measurement. The greater the accuracy the >narrower the spread. > >Precision has to do with how far the mean measured value is from >the "correct" value. Of course there is a logical difficulty >here. If you knew the "correct" or "true" value, why make any >measurements? > >In the context of sundials, however, where presumably one can >calculate or otherwise determine the correct time with great >accuracy and precision, a sundial's indication of time can have >both a random spread of values around the mean of a series of >measurements of the same thing, and a fixed, error of that mean >from the independently know true value. > >This also brings up a paradox. How do you perform a number of >repeated measurements of 1:23:00 PM? If you cannot do this >(because time is always changing on you), then perhaps we could >compare our measurements only with the moving correct time, >independently determined. In this case I suppose we could speak >of the precision of each measurement being its departure from the >correct time. If we repeat this measurement often over a period >of time and discover that the time differences do not add to >zero, then the non-zero amount would be an indication of the lack >of precision of the measuremenet. The standard deviation of the >time differences could be an indication of the accuracy. > >Does this make sense? > >-- >Ross McCluney, Ph.D. Principal Research Scientist >Florida Solar Energy Center, 1679 Clearlake Rd., Cocoa, FL >32922-5703 >Voice: 407-638-1414 Fax: 407-638-1439 e-mail: >[EMAIL PROTECTED] >Florida Solar Energy Center: http://www.fsec.ucf.edu >Sundials: http://www.sunpath-designs.com >Introduction to Radiometry and Photometry: >http://www.artech-house.com >-- > >
"accurate" vs. "precise"
Hello Old Timers: I've got another knit-picky question for you all to ponder. But you're a rather knit-picky group, so I don't think you'll mind. In proofreading the new fifth edition of my "Sundial Owner's Manual", when discussing sundials, I think that I mistakenly used the words, "precise" and "accurate", interchangeably, as if they meant the same thing. Is it possible to have an accurate sundial that is not precise? (I think so) Is it possible to have a precise sundial that is not accurate? (I think not) Should the word "precise' refer to sundials that have small time divisions; ie. large sundials? (One definition of "precise" in my dictionary says "minutely exact"). Using this definition, only large sundials with small time divisions can be precise. A ring sundial can never be precise. Size is everything! The word "accurate" is defined by my dictionary as "free from error". This suggests that an accurate sundial is properly designed and constructed. Does'nt it? There is a very large public vertical wall dial here in Tucson that appears to have been correctly designed and constructed but it has no hour lines at all, only numerals. It's anyone's guess what the precise time is. This would be an example of an accurate sundial that is not precise. On the other hand, a heliochronometer would HAVE to be precise and accurate because it is well-made and has small (1 min?) time divisions. Right? Do you think my train of thought is correct? John Carmichael Tucson tel: 520-696-1709 website: http://www.azstarnet.com/~pappas
excuse me Fernando
Hello Fernando, the jerk in New Mexico, and everybody else: Since I was the first person on the list to read and reply to the faux Fernando's insulting message, and not suspecting that a forger was at work, I publically denounced Fernando. Thank goodness that many of you quickly identified the forgery, through the analysis of e-mail adresses and writing styles. I would like to redirect my ire towards the New Mexican imposter and offer my sincere apologies to Fernando, who has been vindicated. (From now on, Fernando, I will double-check your return addresses!) I hope this is the last we all hear about this matter, execpt for the confirmation from the site managers that the forger has been expelled from the sundial group. I'd rather spend my limited time talking sundials than dealing with this sh... John Carmichael Tucson
Shame on you
Hello All: I too just read Jim Morrison's EOT equations with great interest but I have not digested them yet. I don't know if they are true or false. Even if they are incorrect, that is no reason for Fernando to have lashed out against Jim. I think Jim has been a valuable and intelligent member of this discussion group. He comes up with his own theories, like we all do, then he presents them to the group for discussion, correction, affirmation, fine-tuning or whatever. If you think he is wrong, Fernando, then you should tell him so, privately, in a friendly, civilized manner. I think that you might have been projecting when you called him "a fraud, a stupid and bad man". I think Fernando owes Jim Morrison a sincere apology. John Carmichael Tucson
4/15:EOT=0=Taxes
Hello yall: What I've been trying to do is to tell my sundial customers that there are four "magical" days of the year when their sundial keeps perfect Standard Mean Time. (The dials are already corrected for longitude and DLS Time). On these four days, they don't need a copy of the EOT to tell time. These are also the only days that a sundial can be set, without EOT corrections, using the time method. >From what I've learned, with your help, is that these dates may change from year to year mostly due to leap year adjustments. This anual variation may be as much as 24 hrs. But the exact moment of the event, EOT=0, is absolute and occurs at the same time everywhere. The date, however, may be different due to longitudinal time zone differences. I guess what I need is the AVERAGE four dates for The United States. Do you think that it is ok to stick with: April 15, Jun. 14, Sep 1, and Dec 25 ? I can accept an error of about 1 minute (EOT=0 plus or minus 1), as my dials can only be read to about 1 min. EOT will be -1 min. tomarrow. Thank you all, John Carmichael Tucson
EOT=0
Hello all: The reason that I inquired as to when the Equation of time equals zero is because I state in my Sundial owner's Manual that on these four days (Apr 15, Jun 14, Sep 1, and Dec 25) my sundials need no EOT correction. I realize that this statement is not entirely correct as the date when EOT=0 depends on the specific longitude of the observer. For example, this year, EOT=0 early in the morning in Greenwich on Apr 16th but late at night on the 15th here in the US. Also, I asume that the exact time when EOT=0 must vary slightly from year to year. Does anybody know what the maximum amount of variation would be? Is it more than 24 hours? Several people wrote me with their calculations of when EOT=0. I hope they don't mind if I sumerize their answers for you here. Jim Cobb:4/16/1999 3:04:36 UTC (xephem version 3.0) Luke Coletti:4/16/1999 0:40:00 UT(Solar Calculator) Jean-Paul Cornec: 4/16/1999 1:06:04 UT(VSOP87) James Morrison: 4/16/1999 0:40:57 UT(?) As you can see, all the calculations are different. I assume this is due to the different calculating methods that were used. Surely there can only be one correct answer.(Or should I use the average time of all the answers?) Thanks again to Jim, Luke, Jean-Paul, and James for taking the time to do the calculations. John Carmichael Tucson
WHEN DOES EOT=0
Hello all: Does anybody know the exact time (UT) when the Equation of Time equals zero this April 15th (or is it the 16th)? Thanks John Carmichael Tucson
double blue moon
Hello all: Will two full moons always occur in a March that follows a Febuary with no full moon? John Carmichael Tucson
time & rotation
Hello All Timekeepers: First of all, let me say that this has been a very interesting discussion! To summerize, it seems that our measurement of time will always be linked to the earth's rotation rate, because as daylength changes, so will our biological clocks. Consequentially, if we keep a 24 hour timescale in the future, then as the earth's rotation slows, the length of seconds, minutes and hours will increase because 24 hrs. will always equal one day (one rotation). Therefore, won't clock mechanisms have to evolve also, slowing down and running slower? Sundials would't have this problem, would they, since they measure the rotation rate directly? John Carmichael Tucson
slowing rotation
Hi guys, If the earth's rotation is slowing, due to lunar tidal drag, then in what year will it stop completely? Will one face of the earth, presumeably the side with the most mass, permanently be facing the sun, just as one side of the moon permanently faces the earth? Which side of the earth will be facing the sun when slows to one rev./year? John Carmichael
UT & face numbers
Hello all, If in the future, everybody everywhere switches to Universal Time then all timepieces would have to have twenty-four hour timescales. Right? Would'nt all twelve hour clocks, sundials, watches, etc. become obsolete, becoming anachronistic collector items? Sort of like vinyl record albums. But I suppose you could always refit Big Ben with a new 24 hr. face! John Carmichael Tucson
Internet Time
Hey, did anyone see the CNN story last night about the watch company ,"Swatch" that is now selling timepieces which tell "Internet Time"? I can't remember exactly, but they said one minute of normal time=about 1 1/2 minutes Internet Time, and that the idea behind it is to facilitate timekeeping around the world for internet users. Everybody everywhere (even on Mars?) will be using on the same time! Arthur C. Clarke believes that the current timezone system will be abandoned and everyone will use Universal Time in the future. I agree with Arthur. Or am I wrong, will we all be using Internet Time instead? John Carmichael p.s. What about Mars?
website address
Hello dialists: Ooops! Yesterday I made a little typo error in my new website address. The CORRECT address is: http://www.azstarnet.com/~pappas Mia culpa John Carmichael p.s. thank you John Pickard for persevering!
My new website
Hello all dialists! My new website, "Sundial Sculptures by John L. Carmichael Jr.", is finally completed and ready for your critical inspection. I did not realize how difficult it would be to do this, which explains why it took so long. I think, though, that it will constantly change as my sundial design and construction methods and education evolve. I used much of my "Sundial Owner's Manual" and an upcoming article for "The Compendium" as the basis for the text of my website. Also, there are seven pictures of my sundials (thumbnails and blowups). I especially want to thank all of you who have helped me so much with all my sundial questions over the past few months. I have incorporated much of your invaluable information and suggestions into both the " Sundial Owner's Manual" and my website. I hope that there are no mistakes, but I know that this is just wishful thinking. PLEASE let me know if you think I should make any changes. My new website address is: http:www.azstarnet.com/~pappas Thank you all so much, John L. Carmichael Sundial Sculptures 925 E. Foothills Dr. Tucson AZ 85718 tel: 520-696-1709
heliochronometers
Hello everyone: Well my new website is finally up and running WITH PICTURES! But I am still working on the text and I have a question. I'd like to say that my sundials are "heliochronometers". My sundial books state that heliochronometers are very accurate sundials. But what criteria is used? At what point does a sundial become a heliochronometer? If my sundials are accurate to one minute or less would they qualify? I'd appreciate any comments or suggestions about this or anything else on my site. The address is: http://www.azstarnet.com/~pappas Thanks again for your help, John Carmichael
