On Wed, 7 Apr 2004, Fer J. de Vries wrote: > 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.
The only clarification I might ask for is, exactly what you mean by the hourline angles. I would expect them to be measured from the Noon line, returning positive angles (in either morning or afternoon cases?) Is that correct? > The formulae: > I name the houline angles for an afternoon dial z15 and z18. > Calculate: > > A = ( cot z15 - cot z18 ) ^ 2 > B = ( cot z18 ) ^2 > a = B > b = A + B -1 > c = -1 > > Calculate y1 and y2 from : > > (-b +_ SQRROOT(b^2 -4ac)) / (2a) > > (A well known formula I think so typing it like this you should understand > it.) > (Only the positive y is interesting for our problem)) Well, y2 might be useful for imaginary dials! > Now calculte the latitude and declination from > > cot lat = sqrroot y > > sin decl = cot z18 . cot lat > > I learned this in 1988 from Mr. Martin Bernhardt, Germany after I once > made an iteration progam for a calculator to solve this question. > > I hope I didn't made a typing error but try it. > > Bernardt wrote more about these problems but for the problem you have > the above solution will do for many examples I think. > > Bet wishes, Fer. Dave Bell 37.277N 121.966W -
