Re: Astrolabe
The site mentioned below by Angelo Merletti does a wonderful job of creating an astrolabe like device. It is a form of astrolabe in the sense that any instrument that uses altitudes to position celestial objects can be called an astrolabe. It is not, however, the instrument that is usually meant by 'astrolabe'. I would be happy to answer any astrolabe related questions that can be contained in normal e-mail. My e-mail address is: [EMAIL PROTECTED] Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm -Original Message- From: Angelo Merletti <[EMAIL PROTECTED]> To: sundial@rrz.uni-koeln.de Date: Friday, April 17, 1998 6:14 AM >>-Original Message- >>From: Tinkler [mailto:[EMAIL PROTECTED] >>Sent: Thursday, April 16, 1998 8:22 AM >>To: sundial@rrz.uni-koeln.de >>Subject: Astrolabe > > >>By chance would anyone here happen to have any instructions on making an >>Astrolabe? Or mayby a copy of some of the varous treatise on the subject >>from >>some old manuscripes. that could be scanned in? > > >>David R. Carlson ([EMAIL PROTECTED]) > > >at the address: > >http://www.ifa.hawaii.edu/faculty/meech/education/astlabe.html > >you find a hystory, description, method on make an astrolabe. >You find also a program for a complete calculation of plates. > >best regards > >Angelo Merletti > >University of Torino (Italy) >Dep. Neuroscience >C.so Raffaello 30 >10125, Turin (Italy) >
Easter
An interesting sidelight to the date of Easter in the early Christian church, and one of the most divisive and contentious subjects, related to the date of Passover. Passover was not as well defined back then. The beginning of each lunar month was declared by a committee appointed by the Sanhedrin based on the physical observation of the first crescent moon. The choice of which lunar month represented the beginning of spring was based on crude observation of such things as the state of vegetation; the astronomical event of the vernal equinox was not a consideration. We will never know whether the Crucifixion was in March or April because no one noted if that year was warm and wet or a cool, dry one. The death of Jesus was originally observed on Nisan 14 and Easter was celebrated three days later (particularly in the east) regardless of the day of the week on which it fell. In the west, Easter was generally (but not always) celebrated on a Sunday . The supporters of the eastern practice became known as quartodecimians due to their adherence to Nisan 14 and the supporters of Easter Sunday became known as quintodecimians. Since the time of Passover was determined empirically, the quartodecimians had to ask Jewish authorities when Passover began in order to know when to celebrate Easter. To many church leaders, the quartodecimians represented an unacceptable dependence on Jewish customs that had to be eliminated (the so called "quartodecimian heresy"). This was a major motivation for the First Council of Nicea (AD 325). The Nicean Council did not define a method for determining the date of Easter but said only that it should be celebrated on Sunday. The practice of using the vernal equinox to define the beginning of spring originated with the bishops of Alexandria (probably using the resources of the great library). The method of using the Metonic cycle to predict when the Paschal moon would occur also originated in Alexandria and this lunar cycle is still known as the "Alexandrine cycle" in church literature. The process of determining the date of Easter was far beyond the capabilities of all but the most learned and the practice of paschal letters from the Pope originated to ensure that all Christians celebrated Easter at the same time. Summary: Discussions concerning the date of Easter are not new. Footnote: Nisan, the month of new grain, is the seventh month of the Jewish year in the current Jewish calendar but it was not always so. According to the Mosaic law, Abib, the month the Israelites came out of Egypt, would be the first month of the year and Passover would be celebrated during Abib. Abib was probably in about April. After the captivity in Babylon, the names of the months were changed to names of Chaldean origin and Nisan became the first month. Also, the civil year was changed to begin at the start of Tishri and Nisan became the seventh month, although Nisan is still the start of the Jewish ecclesiastical year. James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Webster Astrolabe
The astrolabe kit designed by the late Rod Webster, curator emeritus of the Adler collection, is available from the Adler Planetarium Shop, 1300 South Lake Shore Drive, Chicago, IL 60605, and probably other places such as Celestaire or The Time Museum. I have a few (10 or 15). It consists of a kit reproduction of a 15th or 16th century European astrolabe in gold foil covered cardboard. It takes about a half hour to assemble. The result is a very good reproduction of an old instrument with all the attendant fragility and accuracy problems. The booklet that comes with it is very basic. James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Sundial haiku
Stop for a minute. Stand and enjoy the sun. Time passes too fast. James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
The Electric Astrolabe
Although astrolabes are not sundials in the strictest sense, many sundial enthusiasts are also interested in astrolabes. I just wanted to let anyone who is interested know that I have just made a fully animated planetarium program in the form of a planispheric astrolabe available for free download from my astrolabe web site. It gives very accurate positions of the Sun and the equation of time and can be quite useful for sundial design and testing. The program is called The Electric Astrolabe and requires an Intel processor of 386 or later vintage with a math coprocessor. Instructions for downloading and installation are on the web site below. Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Electric Astrolabe Update
Fer de Vries found a small problem in The Electric Astrolabe related to the calculation of local sidereal time when dynamical time is applied. An updated version as been placed on the astrolabe web site at http://myhouse.com/mc/planet/astrodir/electric.htm. You can download just the updated executable program (astro.zip - 70Kb) which is a good bit smaller than the full package. Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Re: Translation of Chaucer
An invaluable aid to understanding Chaucer's astrolabe treatise is: North, John D., "Chaucer's Universe", Clarendon Press, Oxford (1988). Chaucer's treatise assumes the reader is familiar with 14th century cosmology, an assumption that is no longer valid, particularly in the astrological conventions. The first half of 'Chaucer's Universe' has an overview of medieval cosmology that is interesting in and of itself, and absolutely required to understand the text of the astrolabe treatise. The second part is concerned with the astronomical content of "The Canterbury Tales". In addition, it is useful to have parts of 'Horoscopes and History', also by North, which explains the various astrological 'house' conventions. The method used by Chaucer is not the one popularized by Regiomantanus that appeared on many astrolabes. Diligent study of these three sources provides a wonderful opportunity for getting a feel for the medieval mind and will open many doors for the study of the history of astronomy. Be advised, however, that it is not easy going and commitment is needed to wade through it. Another source for a more readable Chaucer text is Skeats' edition, from the late 19th century. North is better. Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm -Original Message- From: Mac Oglesby <[EMAIL PROTECTED]> To: sundial@rrz.uni-koeln.de Date: Sunday, April 19, 1998 11:09 AM Subject: Translation of Chaucer >Greetings all, > >Does anyone have a web address where I might find a translation of >Chaucer's Treatise on the Astrolabe? I have the text (from Richard M. >Koolish: http://www.fordham.edu/halsall/source/chaucer-astro.html), but I >confess I need some help understanding the old English. > >Thanks, > >Mac Oglesby > >
Reproductions
I would appreciate any reference to someone in the UK who is qualified to make a reproduction of a mariner's astrolabe from the 15th century from drawings. Such a device would be made of a solid wood disk with a brass edge and a brass alidade. The reproduction is for a BBC documentary. Best regards, James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Off topic: Eclipses
Does anyone out there in sundial land have a source that gives the circumstances of lunar eclipses in 1582? I am trying to help a young man with a project related to efforts to determine the longitude of Mexico City in that time period. We need an eclipse that is visible in both Madrid and Mexico city around 1582. Thanks. Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Off topic: Eclipses
I want to thank everyone who responded to my request for information on an historical lunar eclipse. Thanks to Tony Kitto, the correct eclipse was found to be on September 26/27, 1577. The Sundial list is a fabulous resource for practical astronomy information. Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Population and Latitude
A quick glance at the Rand-McNally, "New International Atlas" seems to indicate that a the most populous band is about 20 degrees +/- 5 degrees. This band includes much of India, Bangladesh, Southern China and Mexico City. Number 2 appears to be 45 degrees +/- 5 degrees which includes much of Europe, the populous east coast of North America and Japan. This is not very analytical, but it seems to make sense. Best regards, James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Fw: Off topic: transit of Venus in about 1770
Cook's was one of many astronomical expeditions attempting to observe the 1769 Venus transit. The objective was to measure the solar parallax which is a fundamental quantity for determining the distance from the Earth to the Sun (1 astronomical unit) and, hence, all distances and dimensions in the solar system. Basically, the problem was to time the exact instant when Venus' disk enters the solar disk from as many different places on Earth as possible. The technique used was first described by Edmund Halley in 1716. Several observations were made of the 1761 transit and even more in 1769. Cook, who was a pretty good astronomer in his own right, escorted a group to Tahiti. Other groups went to California (Chappe), San Domingo (Pingre), Hudson Bay (Wales), Siberia (Vardoe) and still others observed from their home observatories. The values measured for the solar parallax varied from 8.55 sec to 8.88 sec., which is very close to the true value and a great improvement over previous values. Note that the accuracy of the measurements was greatly enhanced by tremendous progress in the 18th century in determining the size and shape of the Earth itself. Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm -Original Message- From: John Pickard <[EMAIL PROTECTED]> To: sundial@rrz.uni-koeln.de Date: Monday, March 15, 1999 8:33 PM Subject: Off topic: transit of Venus in about 1770 Greetings all, When I was a kid at school more years ago than I care to remember, I was taught that Lieutenant James Cook RN came out to Australia in 1770 (or was it 1772??) to have a look around, and also to observe the "transit of Venus" in Tahiti. OK, I know what the ToV is, but why go half-way round the world at great expense and logistic difficulty just to see it? No one ever explained this to me. Apparently the education department assumed that it was self-evident! So my question (which I am sure will be answered) is simple: why would anyone cross the road (let alone the world in a small sailing ship) just to see a ToV? Thanks, John Dr John Pickard Senior Lecturer, Environmental Planning Graduate School of the Environment Macquarie University, NSW 2109 Australia Phone + 61 2 9850 7981 (work) + 61 2 9482 8647 (home) Fax + 61 2 9850 7972 (work)
Re: Sun Compass
My wife's uncle was in an artillery battery in the 1st Infantry Division in W.W.II. I asked him about the use of the sun compass and he said he seemed to remember that some sort of sundial device was used to locate the artillery pieces in North Africa where they did not have accurate maps. He could not remember any details and it is not clear whether this applies to this specific device. Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Fw: WHEN DOES EOT=0
I get Julian Date 2451284.52918 which is UT 0:40:57.6 on April 16, 1999. I think this corresponds to 17:40:57.6 MST on April 15, 1999, in Tucson. It will be interesting to see what other people come up with. Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm - Original Message - From: Phil Pappas <[EMAIL PROTECTED]> To: Sent: Tuesday, April 13, 1999 11:20 AM Subject: 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 > >
Re: EOT=0
I calculate the Equation of Time as: Sun's Mean Longitude - Sun's Apparent Right Ascension. This is equivalent to: Right Ascension of the Fictitious Mean Sun - Right Ascension of the Sun (which is the definition of the Equation of Time) even though the Sun's mean longitude is measured on the ecliptic because the fictitious mean sun used to define civil time keeping is defined is such a way that its mean right ascension is always equal to the Sun's mean longitude. It has never been totally clear to me whether it is more accurate to use the Sun's mean right ascension or the apparent right ascension in calculating the equation of time. In the Electric Astrolabe, I used the Sun's apparent right ascension (calculated using VSOP87 corrected for light time and the true nutation of date and optionally corrected for dynamical time). This calculation might more correctly be called the 'apparent equation of time'. I don't think it makes much difference. I suspect the reason that the Dialist Companion gives a value for when the Equation of Time is 0 that is quite a bit different than Luke and I got is because it uses a series expansion for the calculation. Perhaps someone involved in Dialist Companion can tell us. The general series expansion gives a pretty good value, but is not accurate, in the astronomical sense, for any specific day or year (but is good enough for sundials). The US Naval Observatory used to publish the series expansion for calculating EQT for a given year, but I don't know if they still do. Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm - Original Message - From: Luke Coletti <[EMAIL PROTECTED]> To: Phil Pappas <[EMAIL PROTECTED]> Cc: Sent: Friday, April 16, 1999 7:18 PM Subject: Re: EOT=0 > Hello JOHN, > > I think the difference between my reported time and that given by Jim > Morrison converges very closely the same value, if as I suspect, Jim has > incorporated DeltaT in his calculation i.e., the difference between > Dynamical Time and Universal Time. I know that I have not, still on the > punch sheet though! I don't have the exact current value handy but it is > on the order of a minute of time. Therefore, I would say you have two > values that are quite close to one another. The interesting thing to me > is that like Jean-Paul I too use the VSOP87 periodic terms to calculate > solar position however the two EoT zero times based upon it are quite > different, I guess I would suspect a different computation method of the > EoT itself. > > > Regards, > > Luke Coletti > > > John Carmichael wrote: > > > > 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. >
Re: bad people on the list
I'm not sure how to respond. I've never been called a fraud before. Perhaps it is about time. At any rate, the primary source for my calculation of the equation of time is W.M. Smart, "Textbook on Spherical Astronomy, Sixth Edition", Dover (1979), sections 85-91, with additional material from The Explanatory Supplement to the Astronomical Almanac. It makes sense to me. As for being a 'true' dialist, I have been designing and making sundials for 22 years. I also worked as an orbital mechanic on the Apollo program. There's an old saying where I come from: "When you're in a hole, stop digging". Given that, I will just slip into the background. Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm - Original Message - From: Fernando Cabral <[EMAIL PROTECTED]> To: Sent: Saturday, April 17, 1999 11:24 PM Subject: bad people on the list > Hello to All. > > I hate to start something, but I think that Jim Morrison is a fraud. > I have check his equations for EOT, and I believe that he just made > them up. Here in Brasilia, we have a saying to translate which means, > "even a stupid man may be considered wise if he keeps his mouth shut". > If you don't know something Jim, than be graceful enough to ask for > help for someone who does. But please don't make up non-factuous > nonsense. I know that Jim is not a true dialist, that his interests > are elsewhere, and maybe he is just jealous of the rest of us. I hope > I have not to offend anyone, I'm just helping to keep everyone aware > of the facts. > > Fernando > > ___ > Get Free Email and Do More On The Web. Visit http://www.msn.com > >
Re: "accurate" vs "precise"
I am reminded of a particularly relevant cartoon: An "Old Timer" is looking over the shoulder of a very young man in what is obviously an engineering drafting room. The caption was: "I'm not sure about those last eight decimal places, but the first one is wrong." Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Off topic: Mirages
I have a desk "Space Calendar" that has a tear-off page with an outer space related picture for each date. The picture for April 30, shows the Space Shuttle on the ground at Edwards Air Force Base with a perfect reflection of the vehicle in what appears to be a lake. It is not a lake, but a mirage caused by the extreme heating of the of the ground. Can anyone explain what is happening that causes such a perfectly reflected image? I scanned the picture. Send me a note if you want me to send the small image (50k GIF). Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Re: Sundials in Prague
The astrolabe clock on the Prague City Hall is spectacular. Best regards, James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm - Original Message - From: Michael Koblic <[EMAIL PROTECTED]> To: Chantale Dumas <[EMAIL PROTECTED]> Cc: Sent: Tuesday, April 27, 1999 12:05 AM Subject: Re: Sundials in Prague > At 04:30 PM 5/25/99 -0400, you wrote: > >Dear All, > > > >I am looking for information about sundials to see in Prague, Czech Republic. > > > >Thanking you for your help, > > > >Chantale Dumas > >Chicoutimi (Quebec) > > > It has been 30 years since I lived there and in those days I did not care > about sundials. However, try Umeleckoprumyslove Muzeum (Museum of Decorative > Arts) in Prague. They are supposed to have 39 different sundials on display, > mainly "table" and "travelling" variety. It would seem a good point to start. > > Mike Koblic, > Quesnel BC > >
Fw: frame & grid method
Here is one way to calculate the intersection points of two circles: Given circle of radius r1 at origin: x^2 + y^2 = r1^2 Circle at (x0,y0) with radius r2: (x-x0)^2 + (y-y0)^2 = r2^2 Intersection points between the circles lie on a line: y = mx + b Where: m = -x0/y0 b = - 1/2y0 (r2^2 - r1^2 - y0^2 - x0^2) x = (-mb +/- SQR(m^2 b^2 - (m^2+1)(b^2-r1^2)) / (m^2 + 1) If the roots of x are imaginary (i.e. the radical is negative) then there is no intersection. Adjust coordinates of intersecting circle relative to base circle. I have this function coded in C, QBASIC and assembler if anyone wants it. Best regards, Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm - Original Message - From: John Carmichael <[EMAIL PROTECTED]> To: Ron Anthony <[EMAIL PROTECTED]> Cc: Sent: Wednesday, May 26, 1999 10:43 AM Subject: Re: frame & grid method > Ron: > > Very cool! Point C is the intersection of two offset circles with centers > at A and B, whose radii is known. I wonder what the exact mathematical > formula for this is? Wouldn't it come out as an (x,y) coordinate? > > John Carmichael > http://www.azstarnet.com/~pappas > > >All, > > > >I'm sorry I was only half awake when this thread started so forgive me if > >I'm off course. If I had to lay out a large dial (say 100 ft) to a high > >degree of accuracy (say .1 of an inch) I would plot all the points not as > >x,y co-ordinates. I would plot them all out as the intersection of two > >lines from two fixed points. > > > >To see what I mean pick 2 points that are well established, e.g., point A > >where the gnomom meets the dial face, and point B some number of feet due > >north (in line with the gnomon base) of point A. Every point on the dial > >face is now at the intersection of two tape measures that start at points A > >and B. Assuming that the dial face is flat the accuracy would be good as > >the tape measures used. For the points that are almost inline with the AB > >line, a third point C could be used as one of the points. Point C could be > >calculated from points A and B. Of course the computer would have to > >calculate all of the points for you. > > > >As a crude ASCII art: Point X is 30" 1 1/4" from point A, and 22" 3 7/8" > >from point B. (A metric tape measure would be a lot handier) > > > > > > B > > \ > > \ > > \ > > \ > > \ > >/ X > > /C > > / > >/ > > / > > / > > / > >/ > >A > > > >
Fw: epure
John, My French is not what it once was, but I think an épure is just a working drawing. Jim James E. Morrison Astrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm - Original Message - From: John Carmichael <[EMAIL PROTECTED]> To: Sent: Friday, June 04, 1999 10:05 AM Subject: epure > Hi Dialists: > > I'm halfway through reading Rohr's sundial book for the first time. In > laying out hour lines for many types of sundials, Rohr uses a devise called > an "epure" (w/ an accent mark over the last e.). He assumes that the reader > knows what this is. From the context I think it must be some sort of > drawing tool or something like a trigon, but I'm not sure. Does anybody > know? Is it still used by any of you? Supposedly it aids in laying out > hour lines using graphic methods, but many of Rohr's drawings are so > complicated, that they are very difficult to understand. > > I'm so glad that my first sundial book was the easy to read Mayalls' book. > I think that if I had started with Rohr I would have given up! > > Thanks, > > John Carmichael > http://www.azstarnet.com/~pappas > >
Electric Astrolabe
I thought it might be useful to those of you who use The Electric Astrolabe to know that I have just uploaded a new version that provides graphical display of lunar eclipses and has a new facility to make it a bit easier to customize under Windows 95/98. Just drop me a note if you have any comments or questions. Best regards, Jim [EMAIL PROTECTED] James E. MorrisonAstrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Copiers and laser printers
There have been several notes on the general subject of the reproduction accuracy of photocopiers and laser printers. Some years ago I had product management responsibility for IBM's copiers and laser printers so I have a bit of background in this general area. Technologies change, but the principles seem to be the same. Neither office copiers or desktop printers claim to be high precision devices and are really designed to reproduce printed text efficiently and with good resolution. They are not designed to provide accurate reproduction of high precision graphics, although both do a pretty fair job. Basically, almost all copiers use an optical system to transmit the image from the paper to be copied to the reproduction engine. The optical system, which consists of several lenses and mirrors, can be calibrated and adjusted to make perfectly accurate copies but the process is very involved and time consuming so many field engineers do not try to make all of the required adjustments. Most copiers from reliable manufacturers are calibrated at the factory to provide images that are very close to 1:1. There will be some variation in the field because some of the motors in the system may be slightly voltage sensitive which may cause variations in the speed of paper in the paper path and may change the rates that the optical system moves in relation to the photoresistive drum. If you are making copies at a copy center, all you can do is try several copiers and use the one that does the best job. Usually, the big, fast machines do a good job. Small copiers often use a different imaging system that suffers from the same problems as laser printers. Small laser printers use an imaging system that usually consists of a single row of LED's that expose the photoresist. The latent image on the photoresist is transferred to the paper in the developer where the toner is added. The resulting image is then fused by a heated platen. Small laser printers often have trouble printing in exactly the same resolution in both the horizontal and vertical directions due to the variations in the speed of the paper through the machine, which may vary depending on the line voltage, paper weight and surface finish. This manifests itself in elliptical circles and unsquare squares. The error is often too small to see with the naked eye, but can be measured with an accurate rule. To compensate, you can try adjusting vertical and horizontal scales for a particular paper weight (which I do on the Personal Astrolabe). Even that may not be perfect because papers change size differently when they are heated depending on the paper grain and moisture content. PostScript has many features that allow you control this sort of thing and the microcode parameters can be adjusted for most printers to provide some compensation. You are then in the position to start all over if very high accuracy is needed when the humidity is very high or very low or the line voltage varies . I use a scale divided into 1/64 inch and try to estimate the center of lines with a 10x loupe. I consider it close enough if it seems accurate to this precision, which may not be sufficient for more demanding applications. I use my test sheets for scratch paper. The pile is currently about two feet high. Summary; You can't rely on either copiers or small laser printers to produce exact figures that require high two dimensional accuracy without detailed attention to a lot of variables. However, either will produce images that are accurate to within about .5 mm if properly adjusted. Laser printer images can be adjusted by software to compensate for variations in paper path speed. One thing that I have never been able to find a solution for is page to page registration. You must print registration marks if pages must match as in color separations or photomasks. Professional print shops have very expensive printers that will reproduce anything with very high accuracy, but the cost is high, particularly for a short run. Getting accurate images on paper is kind of like getting to Wink, Texas; you have to want to get there to get there. Best regards, Jim James E. MorrisonAstrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
16th century navigating/surveying
The attempt by the Spaniards to find the longitude of Mexico City was done on September 26/27, 1577. Observers in Madrid and Mexico City both observed the end of a total lunar eclipse. The value they came up with was 94.5 degrees longitude difference between Madrid and Mexico City, versus the true value of 95.46 degrees (+ or - depending on the exact location of the observers). The one degree difference resulted from attempting to determine the exact time the eclipse ended and the Mexico City team was late by four minutes. This result seems pretty good to me for two guys working with the naked eye and an ephemeris derived from Ptolemaic astronomy. Best regards, Jim James E. MorrisonAstrolabe web pages at: http://myhouse.com/mc/planet/astrodir/astrolab.htm
Astrolabe Web Pages
The astrolabe web site URL has changed to www.astrolabes.org. Those of you who have links to the old URL may want to change it, even though the old one is supposed to work for at least a year. Best regards, Jim James E. MorrisonAstrolabe web pages at: http://www.astrolabes.org
