A "normal" sundial has the gnomon coaxial with the Earth. This is done to keep the errors with respect to clock time to a minimum during the course of the year. If we have the ambition to make our sundial read clock time to better than +/- 15 minutes, then we have to correct for the Equation of Time. There have been many public discussions here and private ones in my head about the best way to do this. Simply reading a table or graph is inelegant and subject to errors of sign. Methods which use the declination of the sun, either by using a specially shaped gnomon or by observing the shadow of a nodus, rather than an edge, are perhaps more esthetic, but they are inherently ambiguous at the solstices and double-valued the rest of the time.
One way of thinking about the nodus methods (which has come up here in discussions of the EoT with respect to leap years) is that the declination tells you what the date is, and the figure-eight-analemma allows you to find (with the restrictions mentioned above) the EoT for that date. It seems reasonable to suppose that everybody has a pretty good idea of the date already, so we are making the sundial do unnecessary work. If we make the user do this work instead of the nodus, the figure-eight can be unfolded and made unambiguous. (I am sure I have seem such a dial design somewhere, but I can't remember where.) For example, the date-lines can be made concentric circles, from Jan 1 innermost to Dec 31 outermost, and the EoT for each hour marked as a nearly radial wavy line. We could even trivially accommodate the change between standard-time and daylight-saving-time. As a practical matter, I think it would be easier to read clock time (corrected for EoT) from such a dial than from any alternative. The freedom opened up by this arrangement is astounding: The date-lines can have (nearly) any shape, and they could all have different shapes (as long as they don't cross). The gnomon need no longer be parallel to the Earth's axis; it doesn't even have to be straight! I could envision a Salvador Dali sundial, but maybe I should start with something for John Carmichael: Draw the outline of Arizona many times at different scales and put them inside of one another, but so that all the Tucsons overlap, and of course properly oriented with respect to the compass. Put an obelisk at the location of the Tucsons. Label each outline with a date and calculate (the hard part!) where the shadow of the obelisk will fall across that outline for that date and each hour of the day. For each hour, connect the points for all the dates and label the resulting wavy line with the hour. Voila! I'd love to do the design myself, but realistically I know I won't find the time any time soon, so I'd rather through the idea out to the world. Is the description clear enough? (The idea is probably between 500 and 2000 years old anyway.) Regards, Art Carlson
