Dear Frank &all, Frank King wrote:
> The expression now turns into a function of time: > > a . (coslat/cos(dec(t)) . sqrt(coslat^2 - sin(dec(t))^2) > > THIS is the expression to integrate over a whole year and > whose average should be found. THAT result is where the > markers should be placed. Now getting back to your initial question: > What I want to know is where these markers should be placed... it seems to me that this expression calls for numerical integration, isn't it? Or in other words: > > The mathematics becomes cumbersome... > Yes indeed! Interesting perhaps for the mathematically inclined, but remember that we were discussing APPROXIMATIVE sunrise/sunset indicators. I therefore would like to make a plea for the original Lambert circles. They are "the real thing", no integration or approximation needed. The circle through any point of the date scale and the foci of the ellipse intersects the hour scale exactly at the times of sunrise and sunset for that date. One just needs a compass, or a pin and a piece of rope for a human-sized dial! An example of an analemmatic dial with a set of 7 Lambert circles (for the zodiacal months) can be found in Ootmarsum (NL). The dial was designed and constructed by Bote Holman. See my website www.fransmaes.nl/sundials, choose Index and browse to Ootmarsum, for pictures and details. By the way, the most elegant proof of the Lambert circles I know of has been given by Willy Leenders in Zonnetijdingen, the bulletin of the Flemish Sundial Society (in Dutch). Best regards, Frans Maes --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
