Dear Roger et al, Many thanks for your delightful message and for the associated diagram.
> Your improvements to the Braunschweig dial > are very interesting. The procedure I proposed for an "Improved Braunschweig Temporary Hours Dial" must surely be reinventing a well-known wheel? > To respond to your "question", I have seen no > examples of such corrections... I am just waiting for someone to tell me that there is an example from 1500 or thereabouts! > ... being in the "new world" my experience > and historical depth is quite limited. My historical depth is close to zero but you and Gianni and Frans and Karlheinz are doing a good job remedying this! > I enjoy your challenges... You are getting very close to solving the latest ones! > Demonstrating the curvature of the unequal > hours is fairly straightforward... See > attached sketch. Yes, this nicely shows the S-shapes if you squint along the temporary hour lines! > I can visualize the celestial sphere... That's exactly the right place to start. > I have yet to resolve the translation in > spherical geometry between the two time > coordinates. The good news is that you need consider only temporary hours as they appear when drawn as lines (which are not great circles) on the celestial sphere. Ignore these new-fangled equal-hours impostors! The proof is pure geometry without need for a single trigonometrical expression. > So far I cannot prove the "corollary"... That too needs not a single trigonometrical expression and is almost a one-line footnote to the main proof. > As I said, this is an interesting pair of > sundials. They have certainly got me hooked! I especially enjoy the fact that you can use the procedure on a dial which (within limits) has arbitrary orientation. Best wishes Frank --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
