For the past eight years Bob Kellogg's Sundials for Starters begins the list of articles in each Compendium. For example in Sundials for Starters in September 2019 Bob asks "What Makes an Elegant Gnomon?" This question brings together mathematics, mechanical precision, and artistry. Focusing on large and small horizontal dials, the gnomon is perhaps the most visible part of the sundial from a distance. Some dials have needle like gnomons, creating a thin line in the sky that points toward the north celestial pole. On the other hand, many artists have chosen to embellish the area underneath the gnomon. Early in the 20th century Paul Manship was the leading artist-craftsman. He not only created a graceful sculpture, but through it, told a relevant story: known as Parcae in Roman mythology, and as the three fates in Greek mythology, they sit under a tree that holds the sundial gnomon. The goddess of necessity, Themis, brought forth three lovely daughters, Clotho, who spun the thread of life; Lachesis, who measured the thread and determined life direction; and Atropos, who cut the thread of life, causing death.
Sundials in the shape of statuary are common, but it is the true artist who can integrate the gnomon successfully into the artwork as for example the Sundial of Mourning at St. John, New Brunswick. Other artists push the boundaries of the gnomon function. A bird gnomon with parts at the correct angle are esthetically curved to the shape of a bird by dialist and artist Cecilia Lueza. She and other artists take the mathematical triangle and incorporate beauty, memorials, and recall of history and mythology...all with the gnomon of a sundial.
Fred Sawyer takes a look at gnomons on a horizontal dial as well. But in his article on "Polar Envelope Gnomons" he pushes the sundial gnomon to the extreme. The goal is to have equal time marks on the edge of a circular dial. This cannot be done with a thin, fixed gnomon as is done in a traditional dials. But why not widen the gnomon and allow different off-center portions of the gnomon cast the shadow? Fred develops the mathematics to make this happen and Steve Lelievre takes the challenge to create this odd shaped dial using a 3D printer.
Rounding out The Compendium is a wonderful article "The Honey Bee Haven Dial - An Analemmatic Sundial Using Ceramics." Rick Williams walks us through the process of selecting and using clay for tile months that adorn the central walkway of an analemmatic (human) sundial. The clay is wedged, forcing the air out, and then carefully dried over a period of several weeks. As Rick says, "Drying the tiles took time and practice." but in the end, he had pieces that he could underglaze with bright colors and fire to a bisque. Black "stroke and coat" glaze was applied to recessed letters an numbers, and then fired again up to 2100 F. In the end, these hand techniques produced one of the most colorful analemmatic dials ever made.
Read these articles and join NASS where art, history, mathematics and craftsmanship converge.
The June 2019 issue of The Compendium as usual begins with a "Sundials for Starters" that looks at the sun during the moments of sunrise and sunset, particularly the phenomenon of the Green Flash. What time is sunset anyway? Read and find out.
Robert Adzema presents an article on his design, fabrication, and installation of the "Van Vleck Observatory Sundial - My Design Process". Robert relates "William Herbst, the senior astronomer at Wesleyan, was my principal guide along with his colleagues, in determining the functions that the sundial would provide. He wanted a dial that was not too complicated and that would serve as an educational tool for the students..... We agreed on a design for a 6′ × 6′ square vertical south dial.... I researched other vertical south dials on the web and kept coming back to the Queens’ College dial in Cambridge, England. It is a beautiful dial, but has too many functions and layers for easy reading. What I found striking and used was the layout of the border and the Roman hour numbers that take their shape from their corresponding hour angles." Read along with Robert to see how a professional dialist designs a beautiful dial and finds the occasional hazards in building it. And of course, "To install the sundial, we used an all-terrain scissor lift to lift and maneuver the dial into position."
Then join Mark Montgomery article about the "Tres Riches Heures" with his examination of the Duc de Berry's Book of Hours, a famous prayer book for the Catholic layman of the Middle Ages and art connoisseurs of today. "During daylight hours, monks used mass dials to determine the time to start prayers. Mass dials were seasonal (unequal) hour sundials with Terce, Sext, and None usually marked by extra thick hour lines or crosses on the prayer hours.... To keep track of saint's days and other feasts, most of the books of hours begin with a calendar. One page for each month listed all of the holy days. The most important feast days were marked in red; hence ... red letter days."
The topic of sunrise and sunset comes up again, this time in Steve Lelievre's article "An Hours to Sunset, Solar Declining Dial using a Mirror in a Box". Steve describes the dial thus: "A ray of light entering a small hole in the vellum is reflected by the mirror onto the reverse side of the vellum. Because the vellum is translucent, the position of the reflected spot is easily seen amid the dial face drawn on the vellum." Steve provides the appropriate mathematics for anyone to construct a similar dial for their latitude in five easy equations.
A most interesting historical dial is written in an article by Gianni Ferrari who died in March 2019. It is "The Roman Sundial known as the Ham of Portici". The Ham dial, made of silver-plated bronze, had in some ways the same principles of theSteve's Mirror Box sundial, "It is a portable dial with a fixed stylus, showing the ancient temporal hours. Time was read by turning the instrument, while suspended, to bring the shadow of the extreme point of the tail to the vertical line corresponding to the date of observation day." One read the time along that vertical line. What is fascinating is the number of drawings of this dial since its discovery in 1755. Only several of a dozen drawings accurately portrayed the sundial markings. Gianni presents the mathematical equations for analyzing this small dial. In further issues of The Compendium Fred Sawyer presents with clarity the mathematics for a whole range of these sundials including the ability to read civil (clock) time.
Read about these adventures in history, art, and mathematics and how they all converge in telling time with sundials. Join the North American Sundial Society today.
The Compendium from September 2016 exemplifies the idea of "giving the sense and substance of the topic within small compass.” To begin, the article "Sundials for Starters" looks at the surprising antiquity of the Pythagorean Theorem and the hidden secrets of the right triangle. This foundational mathematics is extended by Ortwin Feustel in his article "Globe Sundial of Prosymna - The Enigma of its Ancient Construction is Solved". The Prosymna Globe was discovered in 1939 by the American archaeologist Carl Blegen while excavating the ruins of the ancient Greek city of Prosymna (near Corinth on the Peloponnese peninsula in Greece). The globe is currently kept in the Archaeological Museum of Nauplion. If you like to solve ancient mysteries or the intricacies of spherical sundials, this article clearly explains the curves that can be seen and measured on the globe. How does the dial work? One finds the time at the shadow terminator, the line that divides the sphere from sunlight and dark.
Then there is an article on the "Linear Equant Sundial", one of many elegant and modern sundials designed by Fred Sawyer. The idea is to have a horizontal sundial that uses a second dial face that can be easily rotated to account for the sun's delay and advance across the meridian known as the equation of time. This dial is brought to life by craftsman and dialist Bill Gottesman.
For a change of pace, read Roger Bailey's article "Sundials and Smartphones" where he ponders if a modern compact smartphone could meet all the traveling needs of a modern sundial enthusiast. He demonstrates the smartphone's usefulness to search for the famous Zarbula's sundials in the French Alps... or determine how far you must walk from your hotel to find a sundial in Rittenhouse Square in Philadelphia. Roger presents many more resources for dialing that can be found on the web and are accessible via smart phone for the dialist.
Does this make you curious? Are you interested in the intersection of history, art, and mathematics? Why not join the North American Sundial Society. You may download this Compendium issue from the link below. But why not subscribe and receive this quarterly journal of sundialing?
This issue begins with "Sundials for Starters" by Robert Kellogg from Maryland, describing the Cahokia Mounds American Woodhenge built by Mississippian Indians. Robert then discusses the mathematics of astro-archeology to compute the alignments of the wooden posts for sunrise at summer and winter solstices and at the spring-fall equinox. During the mathematical investigation Robert exclaims, " Our euphoria at becoming the next Indiana Jones is shattered however when we realize that (1) we have ignored refraction, (2) we've used the center of the sun and may need to use the uppoer or bottom limb of the sun as a realistic, observable marker, and (3) we have ignored the Collinsville Bluffs that rise above the true horizon." So how do we solve the problem? Read The Compendium and find out.
The Alessandro Gunella from Italy discusses the "Discovery that Lines for Unequal Hours are Not Straight", or at least this was the thinking during the 16th century. Are they curved or straight?
Next the Connecticut Historical Society discusses the Sheldon Moore Sundial, a popular dial manufactured in Kennsignton, CT during the 1840's. "The manufacture of sundials was commenced prior to August 1840, in which month, a supply was sent to Breck & Company of Boston for sale at 20% commission. In six months they sold 18 dials, which apparently encouraged Sheldon Moore to expanc his facilities". How much did they cost? Read The Compendium and find out.
John Davis of the UK discusses a Triple Horizontal Dial for California. John starts his article with an introduction "There are not many clients for a horizontal sundial that have consulted an original copy of William Leybourn's 1682 book on dialing before arriving to discuss their dial design. But Dr. Rudy Light of Redwood Valley, California, had done so and also brought a copy of Leybourn's diagram of 'An Horizontall Dial with its Furniture' ... with him when he visited me in the summer of 2003. When he explained that he wanted a large scientific dial to position ouside his house and that he 'wasn't aftriad of complications', I knew it would be an interesting project." The result of the project is on the cover of this issue of The Compendium.
And did you know that The Entrance Exam for Japaneese Junior High School students contains questions about gnomonics? Could you answer the questions correctly? See if you qualify for Shibuya Kyoiku Gakuen Makuhari Junior High School, Chiba City, Japan. Barry Duel, an NASS member interviewed the author of the gnomnics questions to find "The science teacher who made the test explained in an interview that he tries to prepare problems that students cannon easily memorize in advance. He wants students who can think ..."
Read this issue of The Compendium to find these articles and much, much more.
This issue begins with several articles about shadow sharpeners, the ability to change the penumbral edge of a shadow that is created by the fact that the sun is a disk, not a point, of light. William Walton from Vermont and Gianni Ferrari from Italy each offer there thoughts and solutions to getting a sharper shadow for reading time more precisely.
Then John Carmichael from Arizona ponders the McMath-Oierce Solar Telescope as a giant sundial gnomon, and then mathematically analyzes what happens if you choose a "fat" gnomon of various shapes such as a cylinder, hexagon, pentagon, square, or triangle. In the end, John presents the mathematics so that you can accurately draw hour lines on a horizontal dial face given one of these gnomon shapes.
Next, Claude Hartman from California discusses the fundamentals of the Celestial Sphere, and what we mean by the "pole" and "equator". Then Claude explains those terms used by astronomers and sundialists to define the position of the sun, definining "solar declination" as equivalent to measuring where we are on the earth by latitude and "solar right ascension" as the equivalent of longitude.
Mohammad Begheri from Iran describes the first analemmatic sundial in Iran, starting with "Iran has a long and rich tradition in many branches of astronomy, including gnomonics. Untial a few decades agon, sundials were used in mosques and madrassas (traditional religious schools) to show the times of the day, especially to determine the times of the five daily ritual prayers." Read more in The Compendium to find out about the first analemmatic sundial.
Four times a year the North American Sundial Society publishes The Compendium, the journal of sundialing. Edited by Sterve Lelievre, the journal illuminates various aspects of sundials,both new and old. The Compendium presents sundial mathematics, sundial histories, and sundials of interest since 1994.
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