Related articles on the IMaGe website:
The Spatial Shadow:  Light and Dark--Whole and Part
Analogue Clocks (pp. 71-87)
An Analemma in Northern Italy.

John D. Nystuen

The University of Michigan
Community Systems Foundation

        On a recent trip through the less traveled parts of northern Italy (less traveled compared to the crowds encountered in Rome, Florence, and Venice) our traveling party found expected, and surprising, evidence of the great contributions to our modern world made by Italians in the first and second millennia.  The evidence is set in stone. 
        In the fifth and sixth centuries A.D. Ravenna, on the Adriatic Sea, was the seat of authority of the emergent church at the time the division was opening between the eastern and western churches.  Evidence of both Byzantine and western Christian traditions are preserved in the beautiful mosaics of the churches, mausoleums, and other religious places in Ravenna.  The images, made of stone and colorful glass, have remained bright and clear over time.   The interior of Basilica di Santo Vitale (6th century) is an example.  Many mosaics in the basilica cover walls, ceilings, and floors as do others in various religious structures throughout the city.  Ravenna has been continuously occupied; it was an intellectual center during the Renaissance.  Dante’s tomb next to the old churches is evidence of the importance of the city in the thirteenth and fourteenth centuries (Dante 1265-1321).
        Urbino is a well-preserved Renaissance town in the mountains to the south of Ravenna.  It was prominent in Italian history for two short centuries after which fortunes declined and it was annexed to the Papal States in 1631 and left to languish in obscurity.  Its rise to fame was due to Duke Federico di Montefeltro (1444-1482) who was most influential in advancing its political, artistic, and intellectual achievements. The value of this history to us is that the magnificent Ducal Palace (the linked photo shows its courtyard) and other renaissance buildings in the city were not demolished or scavenged in the process of building new structures suited to subsequent eras.  In the decline, the Palace fell into a state of abandonment and many of its art treasures were scattered to Rome, Florence and other seats of power.  Restoration began in the early part of the 20th century and the Palace is now the National Gallery of the Marche.  Also, fortunately, the Palace appears to have escaped the ravages of World War II despite the fact that heavy fighting occurred in the vicinity.  Urbino was by-passed by the battles of that conflict. 
        Restoration of the Ducal Palace, along with the new acquisition of Renaissance art, has created a magnificent museum of the Renaissance.   Here, within limestone and marble walls more delicate evidence of high civilization can be seen in the paintings, sculptures, and inlaid wooden cabinets and doors.  The Duke's study, paneled with inlaid wood, celebrates the discovery of perspective views used by artists to depict, with mathematical precision, three dimensional images on two dimensional surfaces.  The panels in the Duke's study have several versions of the illusion of three dimensions executed on a flat surface.
        Padua is another mid-sized Italian city just to the north of Ravenna with architecture and art dating back before the renaissance.  It is also the site of some of Galileo's experiments with telescopes and of the first scientific studies of the human body carried out by careful dissection of cadavers.  These medical demonstrations took place on the stage of a steep-sided amphitheater located at the University of Padua, one of the oldest universities in Europe, founded in 1222 (Leslie Nystuen, M.D. attempts to enter the amphitheater).  The careful, dispassionate demonstrations by professors in front of medical students were meant to impart knowledge to medical students as it was being created through use of the new empirical tradition of science.  The walls of the loggia enclosing the old courtyard of the Bo Palace, one of the core buildings of the university, are lined with stone seals and crests of graduates of the medical school.
        Bergamo is a city located at the foot of the Alps northeast of Milan.  The city is divided into the old, Alti Calli (high city) located high up steep-sloped hills with the new town spread out across more level surfaces at lower elevations.  The central piazza might serve as a setting for a Shakespearean play (photo; sketch by author).  A medieval cathedral and a renaissance church stand close together at one end of the main piazza and are separated from it by an open-sided arcade covered by a high arched and vaulted ceiling. 
     An unusual feature located under this covered space is an analemma (and meridian) made of marble inlaid in the stone floor.  An analemma is a graduated plot of the declination of the sun observed at solar noon throughout the year.  A beam of sunlight passes through a small hole  in a shield mounted high on the south facing wall.  Through the course of a year the beam traces out the equation of time in an elongated, asymmetric figure 8 .  The months and days of the year are marked on the analemma and each day is illuminated in turn by the sunbeam as it traces out a calendar year. The centerline of the structure marks the line of the meridian (north/south direction).  At solar noon on the day of the Winter Solstice (December 20 or 21) the sun is at its lowest declination and casts its pencil of sunlight onto the crossing of the meridian by the analemma trace at the extreme northern extent of the larger of the loops of the figure 8 shape.  On the summer solstice (June 20 or 21) the sun is at its highest
point in the sky and the pencil of sunlight illuminates the crossing of the analemma trace with the meridian on the southern extreme of the smaller of the loops of the figure 8.  The light beam crosses the meridian twice more during the year; in the center of the figure 8, once on the Spring Equinox and again on the Fall Equinox but with the pencil of light approaching from opposite directions.
     On our visit, we immediately recognized the inlaid figure on the floor to be an analemma but we were puzzled because it was located under a roof and surrounded by large buildings.  How could direct sunlight fall on it?  Close observation revealed that to the south just enough open sky existed to permit the sun to shine through the shield and onto the floor at noon on any day of the year (with a view of the shield in mind, now check back to the broader general picture to see it in context).  Analemmas are specific to the latitude at which they are located.  Inscribed in the floor along with the analemma is a record of the latitude, longitude and elevation of the figure.  The inscription reads, <‘Latitude 45° 12’ 11” Nord, - Longitude 9° 39’ 46” Est> and on another line, <Altitudine M 360.85 sul livello Dell Adriatico>
     A compass rose is also present to which is affixed the presumed date of the work, 1857.  That date is 137 years after telescope-equipped theodolites came into wide use for accurate measurement of angles (1720) (Wilford, p. 97).  In that era, more accurate and stable surveying equipment was introduced and used for land surveys and earth measurements.  In 1666, Isaac Newton had predicted that the earth might be better modeled as an ellipsoid or oblate spheroid (a solid figure generated by rotating an ellipse around its short, or minor, axis) than as a sphere (Wilford p.99).  Using the improved surveying instruments and techniques, the French investigated this hypothesis by undertaking to measure an arc of the earth near the North Pole along the Meridian of Kitts (Lapland) (1736-37) and similarly along the Meridian of Quito (Ecuador) (1735-43) (Wilford, p. 101).  The arc nearer the pole proved flatter than the arc at the equator, that is, a degree at high latitudes is longer than a degree near the equator.  The curvature of the earth is greater at the equator and flatter near the poles.  The technology increasing the precision in the measurement of angles and distances had been put to great scientific purpose, establishing the shape of the earth by empirical means in support of theory. 
     That more precise earth model was needed for the Bergamo analemma to be constructed with sufficient precision of shape and position for the sunbeam to stay on the track laid in stone.  The Italians had undertaken cadastral and topographic surveys of northern Italy by the time the Bergamo analemma was constructed.  Knowledge from such surveys would have been used to fix the location and altitude of the analemma.  The two decimal figures for altitude implied high order geodetic control. 
     I wonder though whether theory alone was sufficient to predict the placement of the analemma relative to the shield mounted on the wall.  It could be closely predicted but I speculate that the theory might have been backed up by empirical observations made throughout the seasons.  Theory would direct how the construction should proceed; practice, on sunny days throughout the year, would suggest the location of the beam of light that could then be checked and recorded empirically.  This presumes that they could determine the moment that high noon occurred.  Over the months the precise path of the spot of light could be traced out. 
     Our overnight (May 15) visit to Bergamo was too short for us to learn of the history of the construction.  A large library located on the piazza no doubt has a record of the project and perhaps on another day we will return and look into it.  We were able to conduct some empirical observations of our own.  Jeffrey Nystuen, one of our party, had a portable GPS (global positioning system) receiver.  The instrument was a hand held Magellan GPS receiver that he named Enrico, after Henry the Navigator (1394-1460).  Despite being under cover with little open sky visible, Enrico could fix the location and altitude of the analemma.  The receiver recorded the same latitude to the exact second as that written in the stone.  There was one-second difference in longitude.  Enrico reported elevation as five meters higher than that recorded in stone.  Fixing elevation with a GPS is less exact than fixing position. 
     The length of one second of longitude at 45 degrees north can be approximated by multiplying the cosine of latitude by the length of a second of longitude at the equator of the authalic sphere (a sphere with the same surface area of the ellipsoidal model of the earth) (Robinson, et al.).  This works out to be about 22 meters .  Using the GPS Precise Positioning Service the positioning error of the Magellan GPS receiver should be less than 2 meters. [The circumference of the authalic sphere is 40,030.2 kilometers; thus, dividing the circumference by 360 yields one degree as equal to 111.195 kilometers and, subdividing further, one second as 30.89 meters.  Cosine 45 degrees times 30.89 meters equals approximately 22 meters (Robinson, et al.).]
     In May of 2000, the Selective Availability feature of the GPS  was turned off by the U.S. government.  Prior to this date, for military purposes, deliberate degrading of the stability of the on-board atomic clocks in the GPS satellites degraded the GPS signals.  The Standard Positioning Service that had been previously available (worldwide) provided at best 100 meter accuracy.  As it was, this degradation could by overcome by using differential GPS procedures in which a base receiver station with a well-known position could be used in conjunction with a roving receiver.  This procedure was being routinely applied by a variety of civilian users.
     Today relatively inexpensive GPS receivers are being employed in myriad tasks not at all envisioned by the designers of the system.  For example Enrico, the hand-held receiver, provides the basic latitude, longitude, and altitude with error terms attached but it can also indicate direction and speed of movement -- even walking speed.  One can fix a position in Enrico's memory, such as the location of the parked car, and then wander off through a maze of medieval Italian streets and Enrico can show the path to take to return to the car.  It has in its memory the locations of most towns and cities with population greater than twenty thousand, at least, in North America and Europe where Enrico has been put to use.
     Precise agreement in latitude and one second discrepancy in longitude seems very good for the performance of a hand-held GPS receiver and for the older methods that were employed to locate and design the analemma.  Yet given the assumed accuracies, a 22 meter discrepancy may be too large.  The likely explanation is in the differences in the theories applied.  The Italians in 1858 modeled the earth as an ellipsoid using the best available datum (values for earth radii and eccentricity) perhaps the Bessel, 1841 model that is widely used in Europe.  This datum differs from WGS84 (World Geodetic System, 1984) which now is used in conjunction with modeling the satellite orbits.  Those orbits respond to the earth's center of gravity, not its geometric center.  The same basic assumption must be made to achieve identical results.  What the good correspondence we observed indicates is that both models are very good. 
     The Italians have made many contributions to Western Civilization and to our modern global society.  Fortunately records of some of these achievements have been set in stone.  I wonder, in this new informational age that we live in today and that is so rapidly becoming digital and electronic, are we leaving imprinted forms so durable that after one hundred fifty years, a thousand years, or fifteen hundred years they will be fresh and bright, full of grace and beauty and intellectual achievement?  Will they charm passing travelers? 


  • Alfred Leick, 1990 GPS Satellite Surveying. New York: John Wiley & Sons, Inc. 
  • John Noble Wilford, 1981 The Mapmakers, New York: Alfred A. Knopf, Inc. 1981.
  • Arthur H. Robinson, Joel L. Morrison, Philip C. Muercke, A. Jon Kimerling, Stephen C. Guptill, 1995 Elements of Cartography, sixth edition. New York: John Wiley & Sons, Inc.

Related articles from the internet:
     Sundials on the internet
     Equation of Time