On Wed, 25 Aug 1999, Cordasco, Anthony (NJ Data Services) wrote: > Question: > If hour lines do not lie on the same plane as the base of the gnomon must > they shift and if so does anyone have a formula for this. > Lets imagine concentric circles with 4", 6", 8" and 10" concentric circles > each rising 1/4" above each previous one. If the hour lines are cut into the > surface of each circle, how would one compute the shift in hour lines? Would > it be a significant enough shift or would straight hour lines suffice? > Thanks, > Anthony > Interesting question! I'd say that *from one perspective* they do not shift: If you view the lines with your sight-line grazing the edge of the gnomon, they would appear continuous and straight - the Sun's point of view. That shows that from the machinist's point of view, the lines are intersections of the planes of the rings with the plane passing across the gnomon and through one of the calculated points on the base of the dial. If you were to *cut* the lines in, so they penetrated the rings right down to the base, the bottoms of the cuts would be exactly as calculated. However, the tops would be shifted towards the gnomon, resulting in an angled slice through the ring...
Does that make sense? Dave
