Re: Reverse Engineer Oldest SGS

[Anselmo P�rez Serrada]

Fer J. de Vries wrote: Hi John,   Assuming the sundial is vertical (because the XII hourline is vertical) and assuming the sundial is well made, just measure two angles in the pattern and it is possible to recalculate the latitude and declination of the dial.   The angles you need are the hourlineangles for hour 6 and 9 for a morning dial or 15 and 18 for an afternoon dial.   There is a more general formula in case you can't measure these hours. I got it from Soler's book, page 395: Suppose that you have the angle z1 for hour H1 and z2 for hour H2,  let's define P = cotg(H1)   Q = cotg(H2) p = cotg(z1)     q = cotg(z2) A = (p-q) / (P-Q) B = (Pq - pQ) / (P-Q) Then you can get (and check!) the substylar angle from tan(zSS / 2) = 2B / (A^2 + B^2 - 1) and from it tan(LAT) = sqrt( B/tan(zSS) ) sin(DEC) = B/tan(LAT) = sqrt( B*tan(zSS) ) These formulae are complete general so it's worthwhile taking the effort to type them into a spreadsheet. Regards Anselmo