Re: About the circumpolar parabola

[Chris Lusby.Taylor]

The sundial park at Genk in Belgium has a dial where the gnomon is this very cone. See dial number nine at <http://www.biol.rug.nl/maes/genk/welcome-e.htm>. Its edges cast shadows on the horizontal dial that it rests on. They directly indicate Italian and Babylonian hours. Interestingly, these hour lines are identical to the half hour lines of a horizontal dial. So, if part of the cone were replaced by a polar gnomon the same lines could be used to show Italian (sunset-related), Babylonian (sunrise-related) and common (midnight/midday-related) local apparent time. They would merely need different numbering for each time system. Indeed, you don't need the entire conical surface - any complete section would do. So, the cone could be reduced to an equatorial circle or, in latitudes <45 degrees, a vertical ellipse. Thus, adding an equatorial circle to any horizontal dial allows it to indicate Babylonian and Italian hours, with no extra lines, but noting that every conventional hour line represents a two hour period - so 10am should be labelled as 20:00 Italian, 11am as 22:00 Italian, 1pm as 02:00 Babylonian, 2pm as 04:00 Babylonian... Chris Lusby Taylor 51.4N 1.3W   Anselmo Pérez Serrada wrote: Hello Fer and all,    Thanks for the reference. I hadn't seen Fantoni's book but I have heard that it is very good.As I told you, I heard about that topic from somebody else. Yes, you are right in saying that the curve can be some other conical if the sundial reclines, but ifit is horizontal it doesn't matter which the latitude is: the curve is a parabola (more or less open). An special case rises when the sundial is equatorial: the evolving curve of the ita-bab lines isa circle; and if we make an stereographical projection instead of a gnomonical one, we geta nice diagram that looks like a rose window or a ball bearing, if you prefer. Greetings, Anselmo Perez Serrada [41.652 N  4.723 W] ----- Original Message ----- From: fer j. de vries To: sundial@rrz.uni-koeln.de Sent: Sunday, March 17, 2002 11:30 AM Subject: Re: About the circumpolar parabola  Hello Anselmo, About the property you mention a description may be read in the Italian book "Orologi Solari" by Girolamo Fantoni, 1988.He describes the Babylonian and Italian hourlines and draw figures with the "Cerchio circumpolari visibili". Have in mind that you only get a parabola on an horizontal sundial.For other sundials the intersection of the cone with the sundial's face will be an ellipse or hyperbola . Best wishes, Fer.   Fer J. de Vries mailto:[EMAIL PROTECTED] http://www.iae.nl/users/ferdv/ Eindhoven, Netherlands lat.  51:30 N      long.  5:30 E