Dear Phil, You don't need any spherical trig or formulae. Here's how to do it for the south dial. First make two semicircular templates from stiff card or thin stiff plastic with radius equal to that of your hemisphere, so that each one fits into the recess across a diameter and with a flange at each end of the semicircle that can rest on the flat surface of the cube. On one, (A), that will sit in the vertical plane, mark lines on it from the semicircle centre to the perimeter that correspond (i) to the equator at (90 - lat) to the horizontal, and two others (ii) and (iii) that correspond to the tropics (+/- 23.5 deg). Place this semicircle vertically in the recess (in the meridian plane) and mark the positions of the equator and two tropics on the meridian (12 noon) line (also marked). On the other semicircle,(B) mark radii at 15 degree intervals, or divide the perimeter (if your recess is truly hemispherical) into 12 equal parts. Then hold B in the recess so that the flat-surface flanges are on the horizontal diameter and the perimeter is on the previously-marked equator position. Draw the whole equator line, and mark the 15 degree (hour) divisions. You're part way there, but the story is not complete. Is it clear so far, or do you want some drawings/sketches? David Brown Somerton, Somerset UK (51N3W-very ish!)
Phil Walker > Hi diallers, > I am considering a model cube dial with E. S and W faces, each with a concave hemisphere on it. It would have a pin gnomon with a ball nodus at > the end, at the centre of the hemisphere. I understand that this is based > in the Greek" hemicyclium" but there.are a few 16th century cube dials of > this type in England and Scotland. > I've two questions, > What are the dial equations for the hour- and day-curves for a > hemicyclium-based dial? Do they require some spherical trigonometry? How' in practice, could I draw/paint/scribe etc the said curves onto the concave shapes? > Your help would be appreciated, > Phil Walker > 52N2W (ish) > http://www.sundial.pwp.blueyonder.co.uk/ > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
