[EMAIL PROTECTED] (John Carmichael) writes: > Let's say you want to build a large sundial using the ground as the dial > face. The ground is somewhat irregular and not quite horizontal. You > decide to draw the hour lines, not by calculation, but by using the > technique of building the gnomon (style) first and then marking the position > of the shadow on the ground at selected time intervals using clock time and > correcting for EOT and longitiude. > > You draw the hour lines from the edge of the dial face to the dial center, > tracing the shadow. Since the ground is irregular and not flat, you notice > that the shadow line is not straight, but irregular also, depending on the > terrain. This produces hour lines that are not straight. > > Because the sun's declination changes during the year, changing the angle > that the sun strikes the style, will this technique produce the same shape > hour lines if it is done at any time of the year or is the declination > irrelevant? Will this technique produce the same shape hour lines at any > time of the year? I think it should. but I'm not sure.
Yes. The hour lines will always have the same shape. This is even true if the gnomon is not aligned with the axis of the Earth, as long as it is straight. If the shadow passes through a point P, then it will pass through all the points of the plane containing P and the gnomon. If it does not pass through P, then it will pass through none of the other points in the plane (except those of the gnomon). The intersection of this plane with the ground (the shadow line) is just a subset of the points of the plane, so the same holds there. Art
