For the Annual Conference of the North American Sundial Society, Tucson lived up to its sunbelt reputation. The weather was clear sunny and hot. Our host, John Carmichael explained that it was a dry heat and actually quite pleasant. He was correct; the weather was ideal for studying sundials and cactus.

NASS Group at Tohono Chul Park

The conference was held at the Marriott University Park Hotel, on the edge of the quiet tree-lined streets of the University of Arizona campus, about a mile from the downtown core and “Old Tucson”

There were 38 participants registered for the conference. California, Texas and Arizona were well represented with eight, six and five participants respectively. Eight came from New England, five from Canada, three from the Pacific North West, two from the mid west and one (John Hayes) from England.

As usual, the conference started with an informal get together and light refreshments on Thursday evening. This provided a chance to meet old and make new friends and study the displays of shiny new sundials. Bill Gottesman had his Sawyer Equant dial on display. Carl Haskett was showing off the model of his patented SunClock.

Tom Hughes brought a model of his new Sidereal Sundial. Tom Kreyche displayed his large double horizontal dial and Fritz Stumpges his universal equatorial.

Fred Sawyer brought an excellent collection of door prizes. The unusual Cole altitude dial was won by Tom Hughes, the “Horilegium” book dial by Craig Huber, the set of drawings for the Pilkington-Gibbs heliochronometer by Fritz Stumpges, the Strode book, “A New and Easie Method To The Arte of Dyaling” by Claude Hartman.

The proceedings started Friday morning with a welcome by NASS President, Fred Sawyer. Fred noted that all speakers would be presented with a replica of the "Fugio cent", America’s first coin issued in 1787. Benjamin Franklin designed this coin showing a sundial and the motto “Fugio” meaning “Time flies” and “Mind Your Business”.

Len Breggren, the first speaker of the day, took us way back in the history of sundials to 200 BCE and the work of the Greek geometer Diocles. In his treatise “On Burning Mirrors”. Diocles seems to describe the earliest Greek sundial, a hemispherical mirror that indicates the hours of the day from a burning trace. Len stated the postulates of Diocles and then went through the geometric proofs and explanations.

1. To find a mirror surface, when placed facing the sun, the rays are reflected onto the circumference of a circle and
2. To find the mirror surface, when placed facing the sun, the rays are reflected to a single point.

In the questions, Sara Schechner asked if the Greeks could shape these surfaces or was the work theoretical. A lively discussion followed on methods that the Greeks might have used to form concave hemispheres. The Campbell-Stokes sunshine recording instrument using focused sunshine to burn a trace was noted.

Fred Sawyer continued the historical theme in the next presentation, noting the overlap between Dialing and Cartography. Both are based on the mathematics of curves and lines in three dimensions projected onto a two dimensional plane. Following the historical overview, Fred discussed the orthodromic or compressed gnomonic projection that preserves azimuth angles measured from either of two focal points. He then introduced a new family of compressed gnomonic dials and a Bipolar Azimuthal Equant Dial that he has developed based on this projection.

The ecliptic and equatorial discs on the polar axis Larger Photos

The partial ecliptic disc attached to the equatorial disc

The picture on the left shows the ecliptic and equatorial discs on the polar axis rotated so the shadow of both discs project as lines. The equatorial disc shadow is a line at the equinox and the date of this picture, 27 September, is pretty close.

The picture on the right shows the more compact version with the partial ecliptic disc attached to the equatorial disc. Again the discs are rotated on the polar axis until the ecliptic shadow projects as a line. Sidereal time is then read from the rotation from the intersection node of the two discs, the Vernal Equinox. Local solar time is read the usual way for an equatorial sundial. The equatorial disc is rotated so noon is the zenith and time is read from the angle of the shadow of the polar axis from the zenith. In the discussion Roger Bailey noted that a proper armillary sphere with a rotating basket could be used in this way to tell sidereal time. The shadow of the ecliptic ring on itself would be the same as the disc projecting as a line.

John Schilke’s presentation Oh, East Is East and West is West was a note on the Prime Vertical, that great circle which passes through the zenith and nadir and the east and west points of the horizon. The Prime Vertical is thus orthogonal to the meridian and to the horizon. It has a few properties that make it useful for the dialist; several terms of formulae in common use vanish, simplifying calculations. For example, the time angle when an object is on the prime vertical reduces to Cos t = Tan Dec / Tan Lat. John outlined two methods of establishing the Prime Vertical, the Indian Circle method of equal altitudes and the two string and candle method. He also gave examples of dials for which a readily determined local east-west line is even more convenient than the meridian. In the discussion Roger Bailey noted a couple of good reasons for using the Prime Vertical rather than the meridian to determine the axis of a sundial. The shadows are longer and the rate of change of azimuth angle with time is less. Unfortunately the Prime Vertical is only available for the sun for half the year, when the declination is the same sign and smaller than the latitude.

In his presentation, Stephen Luecking outlined a method for Constructing Daylines using a compass, straight edge and geometry rather than trigonometry. Daylines are trickier to construct than are hourlines. This talk introduced the point-wise construction of hyperbolas and its application to daylines. During the Renaissance, artist/scientists such as Leonardo Da Vinci, Albrecht Dürer and Piero Della Francesca began experimenting with methods for constructing these curves. Their experiments and those of others led to the point-wise construction of conic curves, a method which was to presage the plotting of curves in analytic geometry. The method outlined enables the constructing of a dayline on a horizontal dial for any particular date. In the discussion Len Berggren noted that a “Perfect Compass” had been developed in the Moslem world that generalized geometric methods to draw all conic sections similar to those Steve outlined here for hyperbolas.

The Informal Presentations were expected to be quick talks on specific topics that did not warrant a full presentation. The reality was different. In most cases these short talks were fascinating and generated interest that made it difficult for the Chairman and speakers to keep within the time constraints.

Bill Walton’s slide show on Pinholes and Shadow Sharpening was a necessary prerequisite for the tour on Saturday. Bill went over the pinhole camera effect used to remove the penumbra fuzziness from a shadow. A small hole 1/16” in a card projects a fairly sharp image of the sun. A larger hole, say 1/4”, projects a brighter but fuzzy image. In the partial penumbral shadow, both show the eclipsed solar image. As the response of the eye to brightness is logarithmic, people perceived middle of the shadow when about 80% of the solar disc was covered. Bill then went on to show the effects of compound shadow sharpeners, using two holes in series, a dot in a ring, etc. These simple devices showed the importance of the partial penumbra shadow and how the accuracy of sundials can be significantly increased using shadow sharpeners.

Bill Gottesman then presented a method for measuring wall declination using a carpenter’s square.

Place the square on the vertical wall with the short end projecting perpendicular to the wall. Orient the square until it is aligned with the sun and casting the thinnest possible shadow. Measure the length of the shadow from the base of the square.Note the exact time. Determine the azimuth (A) and altitude (B) for the sun at that date and time using the NASS Dialists Companion or whatever method you prefer.

Calculate the Wall Declination = A+/- ArcCos[Sin(C)/Sin(B)] where C is the ArcTan(Height of Square/Length of Shadow). A and B are the azimuth and altitude of the sun.

The method seems simple and straightforward. Bill also offered a simple spreadsheet available on his web site www.precisiondials.com to do the calculations including the solar azimuth and altitude.

After lunch, the dials on display were brought out to the sunny courtyard for testing and display.

Claude Hartman demonstrates his model that incorporates ten separate sundials. These dials can be read on the walls and inside the stained glass structure.

Claude Hartman and the model

Ten separate sundials

Bill Gottesman showed his Sawyer Equant dial with the adjustments for latitude, longitude, equation of time and daylight savings time.

Bill Gottesman with his Sawyer Equant Sundial design

Bill Walton displayed an analemmatic “Sun Compass” and an interesting Pelekinon (double axe) dial.

The Analemmatic Sun Compass

The Pelekinon dial

After lunch the Annual General Meeting was held.

Fred Sawyer’s talk on Dialing Scale Techniques - Old & New was based on the dialing scale and instruction set published by E.C. Middleton early in the 20th century. Fred showed how to use the Middleton scale and then went on to demonstrate a new technique for drawing vertical declining dials using only dialing scales.

Tom Kreyche then presented a paper on Projections of the Sphere for Astronomical Instruments. His inspiration was the planispheric astrolabe. He showed how the planispheric astrolabe and double horizontal dials are closely related “kissing cousins”. Tom displayed his large brass double horizontal sundial that incorporated this math through computer based design and machining techniques.

Following the break, the winner of the Sawyer Dialing Prize was announced and the prize presented to John Carmichael. In recognition of his efforts to bring dialing to the high tech world of a leading solar observatory, and his demonstration that it is still possible in the modern world to prosper as a traditional craftsman of high quality heliochronometers

John then presented his paper on “Polar Axis Gnomons with Multiple Styles” This outlined the project to utilize the structure of the McMath-Pierce Solar Telescope as the gnomon for a sundial. Although the telescope tube is at the correct polar angle for use as a gnomon, the design was complicated by its size and thickness. The “style shift” as the shadow was projected from different edges of the structure and the fuzziness of the penumbral shadow were complicating factors in the design.

Proceed to the Saturday Bus Tour of Sundials

Sunday morning We started with an informal presentation by Fritz Stumpges on his “Portable Equatorial Sundial and Spherical Compass”. Here Fritz is seen demonstrating the features of his dial to Craig Huber. Level the base plate, adjust for latitude, and rotate the dial until the shadow of the face plate hits the date setting on the gnomon. The dial is now correctly aligned to north and time can be read as with any equatorial dial.

The next informal presentation was a slide show on Sundials of France by Warren Thom.

This was followed by Claude Hartman’s talk Back to Basics, sundial topics by a novice for novices, a series of articles he is writing for the Compendium. These articles outlining basic sundial design information and techniques are aimed at non-mathematical novices interested in making a sundial. One tip was how to fold a dollar bill for use as a sundial. Claude asked people to send him tips like these for his Compendium articles.

Sara Schechner then showed us what a Savvy Traveler in the Renaissance might carry as portable, packable items to guide them in their travels. Sara gave us a look at pocket sundials and astronomical compendia, with their remarkable components (including gazetteers, specialized hour scales, astrolabes, quadrants, nocturnals, maps, and travel guides). Most of the items described are from the Collection of Historical Scientific Instruments at Harvard University, where Sara is the curator.

Roger Bailey then outlined the development of Seasonal Sun Rise and Set Markers for analemmatic sundials. There is a point on the east/west axis of analemmatic sundials that can be used with the date table on the north/south axis to show where and when the sun rises or sets. Stand on the seasonal sunrise marker and look past the date mark to see where on the horizon the sun rises or sets. Stand on the date mark and sight past the seasonal mar-ker to the hour ellipse to determine the time of sunrise or set. These marker points are an excellent addition to analemmatic dials to demonstrate the seasonal changes of the sun’s position. The presentation outlined the discovery of this brilliant idea, the theory and calculations to determine the points, the construction of the first seasonal dial using these markers, and techniques to improve the accuracy to compensate for periodic error and horizon pollution.

In the Informal Presentations Paul Lapp described A Practical Application Of Dialing Knowledge, the alignment of solar cells to recharge batteries for market stalls in Boppal, India.

Ken Clark told of his efforts to publicize NASS and sundials.

In his presentation A Mandl Abac Sundial, Fred Sawyer told us what he did on his summer vacation. As he hiked along, he thought of how to develop a new universal altitude sundial from a simple nomogram or abac by J. Mandl.

The final presentation was by Stephen Luecking on Projective Meridians and Sundials. This talk focused on the aesthetics of public sculptures, specifically sundials. His historical perspective reminded us of how solar orientations at the solstice are built into the architecture of many civilizations, from the Great Kiva at Casa Rinconada, Stonehenge and standing stones to the cathedrals of Europe. He then outlined design proposals for large projective sundials including these elements.

	Fred Sawyer was able to close the conference on time in spite of the interests raised and discussions started. He thanked John Carmichael for being an excellent host and invited us to come together at the NASS Conference next year, 21 to 24 August at the Banff Centre where Roger Bailey will be our local host.
	See our 2003 Conference in Banff

Conference review by Roger Bailey (Canmore, Alberta).
Photos by Roger Bailey and Carl Trost