We are accustomed to the use of azimuth, altitude, declination, hour angle etc., but Ptolemy used a different system. It was based on three surfaces: the horizontal, the meridian, and the first vertical, which is east-west. To describe a point on the celestial sphere, the surfaces are rotated about their intersections until all pass through that point. Ptolemy then identifies six arcs: three from the point to zenith (or nadir), east (or west) point and north (or south) point; and three describing the angles over which the surfaces are rotated.

Fred Sawyer designed a number of sundials based on this co-ordinate system. Remarkably, two of these designs are independent of latitude (Sawyer, Compendium vol. 5 nr 3 Sept 1998, pp 17-24).

Means are described to measure Ptolemaic angles of the Sun using a suitably placed card, the shadow of a pencil point and a degree scale around the card’s perimeter. The card carries a nomogram that will then tell time. Three examples are given, together with their generating formulae, but many more solutions should be possible. Readers are urged to send in their ideas on new nomograms or complete instruments.

An article by Maddux started a collaboration between Maddux, Oglesby, Thom and the author. Object is a card dial with Italian hour lines, also useable for Babylonian time. Literature was searched for similar dials, but only one possible example was found. Although conversion graphs were found, they do not allow direct reading in any other time system than LAT.

Mr. van den Beld suggested using EOT loops in the design. They are shown in the picture.

Mr. Strang van Hees suggested a different derivation, it is given here.

The author was corrected by both on mixing up the concepts of hour lines and hour angles.

The author had a fairly straightforward solution in mind. From Alt, Az and latitude, he solves for declination (giving the date) and hour angle. Accounting for equation of time and longitude, legal time is found. Mr. R. Vinck sent a solution along these lines. Mr. A. vd. Beld sent three pages of text! Had the author overlooked something? Mr. vd. Beld considered atmospheric refraction (negligible effect), size of sun disk (a difference of a day depending upper or lower limb), change of declination (leap years, tropical year slightly shorter than 365.25 days- see the spreadsheet results), and whether in the found year daylight saving time was in effect or not. And so a seemingly simple puzzle brought about rather more than the author had bargained for. In a random draw, Mr. vd. Beld turned out as the winner; deservedly, for all his work.

The author derives the x, y equations for date lines on the surface of a sundial. He does this by choosing the dial face as the z=0 plane, with the substyle determining the y direction. In the course of the day, the shadowline from the indicator on the style to the dial face describes a cone. The intersection of this cone with the dial face is the date line for that day. At the equinoxes the cone degenerates into the equator plane, and the intersection is then a straight line, perpendicular to the substyle.

[This contribution was sent in in reaction to two articles by Mr. vd. Beld (97.3 p23-29, 98.1 p24-27)]

Schoonhoven - The restoration of the sundial on the Weigh-house is still not done properly in spite of repeated directions. The lines are now painted on correctly, but the gnomon position is wrong. The author thinks it is also warped.

Valkenswaard 2 - Designed and constructed by S. Poos. Member J. Kragten helped him correct (as far as possible) a design flaw (98.1 p12-15). The dial is cast in brass, 80cm (32in) dia., pole style in the middle of a round surface showing radiant sky with little clouds. Also on the surface are children’s footprints and the words "Now here" and "Nowhere". Roman numerals LAT, Arabic MET and DST. Whole-hour lines.

Too many to list. Some that caught my eye: 1315: A new Italian gnomonic periodical. Editor: Nicola Severino, niksev@officine.it. Blue cover, photocopied pages. English language summaries of articles. From the overview given it looks like a very interesting magazine. Look also at the list of web sites. 1317.3: Helios XXII. A pump makes concentric ripples in the water surface of a pond. The reflection on a grid on the inside of a slanted dome gives the time. 1319: EOS "Science and technology for man", 15th/12 extra supplement: "The riddle Time". Various articles on the subject, from nanosecond timekeeping to the Milleniumbug, with psychological and farming detours in between. 1321.1: El Rellotge de Sol de Bangor. This equatorial dial was supposedly on the slanting surface of a buttress, but in that case the mottoes on it would have been for the birds (only). 1322.3: El Cañón Solar del Palais-Royal de Paris. The Paris noon-cannon from 1786 was restored in its own place in 1975. It has now been stolen, and thus ended the last mid-day cannon roar. -But according to the compiler there still are noon-cannons in service, see 97.3:1259.2, 98.1:1267.2. 1322.8: La mas sencilla fórmula para el Reloj Declinante. Mr. Lombardo suggests new formulae for calculating declining dials. They are derived from old geometrical constructions by Clavius.

Diverse berichtjes op blz. 4, 11, 12, 16, 25 en 31. - Mixed news on these pages

My copy only had the last half of the year- twice. ...