Re: Reverse-engineering oldest SGS

[Chris Lusby Taylor]

I've only just got around to looking into this. The question, if you remember, was how to find the latitude and wall declination for which a vertical sundial (such as an SGS) had been made, given that you can measure the style height (SH) and angle between the style and vertical (SD). Nobody posted a correct analytical solution to Roger Bailey's simultaneous equations, and several posters thought it had to be done by trial and error. The thread then turned to using the hour line angles, which is a valid approach. But there is an easy solution. It is:   Sin Lat = Cos SH x Cos SD    This doesn't tell us if the latitude is north or south. An easy way to resolve this is:   In the (upper or lower) half of the dial where the gnomon is, if one o'clock on the dial is to the right of twelve o'clock, it is for the northern hemisphere, else for the southern.   Another way is:   If the hour lines increase clockwise, the gnomon points north, else south. If the gnomon points up, the dial is for the same hemisphere, else the opposite hemisphere.   Given the latitude, from my equation above, you can find the wall declination from Roger Bailey's first equation. To get the correct sign, make Lat positive if north, negative if south, and measure SD anticlockwise from the vertical:   Sin Dec = Tan SD * Tan Lat   Take the answer in the range -90 to +90. Interpret a negative answer as a declination east of whichever pole the gnomon is pointing to. A positive answer is a declination west of the same pole. For instance, if the gnomon points south, and the equation gives Dec=-30, the wall declined 30 degrees east of south.   Best wishes to all Chris Lusby Taylor 51.4N 1.3W