Chris, John, Dave, Anselmo and others, I would like to add something to this discussion.
All dials like the analematic dial, the Foster-Lambert dial and many more, including the usual horizontal dial are members of just one family: the eqatorial projection dials. Imagine an equatorial ring with hourpoints and a scale of date on the polestyle. Project this ring vertical onto the horizontal plane, from the zenith point, and you get the usual analemmatic sundial with an ellipse of which the long axis is east-west and in the center a scale of date. Project this ring in the direction of the polestyle onto the horizontal plane and you get the usual horizontal sundial with an ellipse of which the long axis is in the north-south direction as Chris noted. The scale of date now is just a point and therefore we can draw complete hourlines and not only hourpoints on the ellipse. An article about this you may read at the web site of De Zonnewijzerkring. Follow the links: Calculate and construct Analemmatic sundials-Equatorial projection dials. Article (in English) The article is by Bruno Ernst = J.A.F. de Rijk. I think this article is of great importance and a must for all gnomonists. Best wishes, Fer. Fer J. de Vries De Zonnewijzerkring mailto:[EMAIL PROTECTED] http://www.de-zonnewijzerkring.nl Home mailto:[EMAIL PROTECTED] http://www.iae.nl/users/ferdv/index-fer.htm Eindhoven, Netherlands lat. 51:30 N long. 5:30 E ----- Original Message ----- From: "Chris Lusby Taylor" <[EMAIL PROTECTED]> To: <[email protected]>; "Anselmo Pérez Serrada" <[EMAIL PROTECTED]> Cc: <[email protected]> Sent: Saturday, June 07, 2003 9:38 PM Subject: Re: Dial calculation mystery > > ----- Original Message ----- > From: "Dave Bell" <[EMAIL PROTECTED]> > To: "Anselmo Pérez Serrada" <[EMAIL PROTECTED]> > Cc: <[email protected]> > Sent: Saturday, June 07, 2003 7:04 PM > Subject: Re: Dial calculation mystery > > > > On Sat, 7 Jun 2003, [ISO-8859-1] Anselmo Pérez Serrada wrote: > > > > > I think I can help you on this. They use a very elegant method to draw a > > > sundial based on geometrical > > > affinity that traces back to our High School days: > > > > > > 1. Draw two concentrical circles : one of radius r and the other one of > > > radius r*sin(Lat) > > > 2. Now draw a sheaf of 24 equispaced lines from its center as if it > > > were an equatorial dial. > > > 3. These lines intersect the circles at points I' and I'', II' and > > > II'', and so on up to XXIV' and XXIV''. > > > 4. Now trace horizontal lines from the inner points and vertical lines > > > from the outer points. Let's call > > > I the point where the lines from I' and I'' intersect, II the point for > > > II' and II'', and so on. > > > 5. If we connect these points we just have the analemmatic ellipse, > > > right? Well, but if we trace lines > > > from the center to these points we get a horizontal dial for that > > > latitude. Isn't that nice? > > > > Very well described, Anselmo! > > > > Everything agrees perfectly with the original article, except you have one > > circle of radius 1 and the other of 1*sin(lat). Now, if I am looking at > > this correctly, that would make the second circle smaller than the first > > (and also avoid the singularityat 0 degrees!) However, is the ratio of the > > two circles' size the same in both constructions? I'll have to draw them > > up, and scale one to match the other... > > > > Dave > > 37.28N 121.97W > > Yes, the ratio is the same. The ratio of 1 to sin(lat) is the same as the > ratio of 1/sin(lat) to 1. > > But I think Anselmo makes one small error. Yes, the points at step 4 are the > hour marks of an analemmatic dial if, by 'horizontal lines' he means > east-west lines, but to draw a Horizontal Sundial you want to draw > north-south lines from the inner points and east-west ones from the outer > points. > This is because an analemmatic dial's major (longer) axis is east-west, > whereas for a horizontal dial constructed this way the major axis is > north-south. > > Chris Lusby Taylor > 51.4N 1.3W > > - > -
