Mike Cowham wrote: > > Dear Friends, > I have a vertical east declining sundial that I believe was once > fixed to a church building. Its gnomon is missing. > What I wish to calculate is the latitude of the dial, and its > declination. I am sure that it is a very easy problem to solve, but so > far I have failed. > When I have this information, I hope to be able to locate its > original site, (I already have a rough idea of the area of England), and > maybe find some evidence of where it was fixed to the building. > The only real clue to its location is given by the angles made > by its hour lines - assuming them to be accurate. > Thanks in advance to anyone who may be able to help. > Regards, > Mike Cowham. > Cambridge, England.
Dear Mike, Here I give just a number of formulae by which the latitude phi and the declination d of a vertical sundial can be calculated, assuming the pattern is well drawn. Measure the angles of the following 2 hourlines : - for east decliner : hour 6 and 9 - for west decliner : hour 18 and 15 Name these angles t45 and t90 and use positive signs for the angles. Calculate : P = cot(t45) - cot(t90) Q = cot(t90) X = P*P Y = Q*Q a = Y b = X + Y - 1 c= -1 Z = (-b + sqrt(b.b - 4.a.c)) / (2.a) or Z = (-b - sqrt(b.b - 4.a.c)) / (2.a) Take the positive answer for Z Then phi = atn(1/sqrt(Z)) d = asin(Q/tan(phi)) ( sqrt is square root out of... ) Example : t45 = 29 degrees t90 = 68.78 degrees X = 2.0044 Y = 0,1508 a = 0,1508 b = 1.1552 c = -1 ( of course ) Z = 0,7852 phi = 48.4552 degrees d = 20.1244 degrees ( east or west ) I hope I didn't make any typing error. Otherwise have a look in bulletin of De Zonnewijzerkring, 88.3, page 31. Best wishes, Fer. -- Fer J. de Vries [EMAIL PROTECTED] http://www.iaehv.nl/users/ferdv/ lat. 51:30 N long. 5:30 E
