Hi Dave, The angles indeed are the angles between the noonline and the hourlines on the dial. I think the signs aren't important because at the start all is ^2. And there is symmetry between a west and east declining dial.
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: "Dave Bell" <[EMAIL PROTECTED]> To: "Fer J. de Vries" <[EMAIL PROTECTED]> Cc: "John Carmichael" <[EMAIL PROTECTED]>; "Sundial List" <[email protected]> Sent: Wednesday, April 07, 2004 5:01 PM Subject: Re: Reverse Engineer Oldest SGS > 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 > -
