Hi John, It is back to the basics on this one: Waugh, Chapter 10, Page 79, Verse 1 to 4. The concepts of Sub-style Distance (SD), Sub-style Height (SH), Difference in Longitude (DL) and Angle with the Vertical (AV) so well developed in Waugh, are not evident in the computer programs that we now commonly use. You can determine the wall declination from the Sub-Style distance if you know the latitude as Tan SD = Sin Dec / Tan Lat. The Sub-style Distance is the angle from the sub-style line to the vertical. This is the same angle that the perpendicular to the sub-style, the equinoctial, line, makes with the horizontal.
As wall declination increases from zero, the sub-style distance (and equinoctial angle) increase but at a reduced rate, reaching a maximum, equal to the co-latitude, when the declination is 90 degrees. Using your examples and your latitude of 32.3 degrees and Tan Lat = 0.632: Dec = 0, Sin Dec = 0, Tan SD = 0 Dec = 45, Sin Dec = 0.707, Tan SD = 0.707/.632 = 1.118, SD = 48.2 Dec = 90, Sin Dec = 1, Tan SD = 1 / 0.632 = 1.582, SD = 57.7, or your co-latitude. Zarbula had it easy as he worked at latitude 45 degrees where the Tan = 1. For him, Tan SD = Sin Dec. Similarly you can calculate the Sub-style Height, the angle of the gnomon to the wall, as Sin SH = Cos Dec x Cos Lat. But this is not how Zarbula did it. He only had available a stick, some string and the sun. I will leave that as a homework exercise. Regards, Roger Bailey Walking Shadow Designs N 48.6 W123.4 -----Original Message----- From: John Carmichael [mailto:[EMAIL PROTECTED] Sent: December 4, 2004 8:46 AM To: Roger Bailey Cc: Sundial List Subject: Re: Zarbula's Method for Wall Declination Hi Roger: I followed your whole letter with great interest, and understand it all, except for one thing. Is it possible to determine the wall's declination once I have drawn the equinoctial line and the substyle line using this method? At first I thought that if I drew a horizontal line on the paper and determined the angle of the sloping equinoctial line, that this angle would equal the wall's declination, but it doesn't in all the examples I've tested. For examples, I played around with a sundial drawing program and entered different wall declinations (0, 45 and 90 degrees East of South) for my latitude 32.3 deg N. and then I measured the sloping angle of the equinoctial lines. Here are the results: 1. If the wall is due south, then the equinoctial line is horizontal which means the declination is 0. so far so good. 2. But if the wall declines say 45 degrees to the East of South, and I draw a sundial face using Shadows or Zonwvlak, then I thought it's angle is should be 45 also, but it's not. It's 48.2 degrees. 3. If I draw a dial the declines 90 degrees East of South, then the angle of the equinoctial line should be 90, but it's not. It's 57.7 degrees. So obviously my supposition is wrong. The angle of the equinoctial line is NOT equal to the wall declination. How can I get the wall declination using your Indian Circle method? Thanks John -
