Dear Frans, Like Gianni, you produce splendid scholarly input to this list!
I promised not to challenge your answer so I will constrain this reply accordingly! You have made me think about Zinner's imagination... If you have a medieval sundial such as you describe [a vertical dial, assumed direct south-facing, and a horizontal gnomon] AND a clock (no matter how bad) there will be a natural temptation to compare the clock and the sundial. If you choose noon as your start-of-day, then you can set the clock each day at the moment of transit (vertical shadow) and then mark the position of the tip of the shadow of your gnomon at hourly intervals (as timed by the clock) from noon. If you keep this up for six months, then you will see that the marks for a given hour join up in a straight line. Moreover, the set of straight lines all intersect at a point some way above the foot of the gnomon. Then one night, someone looks up at the dial and notices that the line from the tip of the gnomon to the magic point is at an angle to the horizontal that corresponds to the altitude of Polaris. Wow! This way you get to invent the polar-oriented gnomon. :-) Now, if you choose sunRISE as your start of day, you set the clock at sunrise and you can again mark the position of the tip of the shadow at hourly intervals. Again you get straight lines but they don't intersect at a common point. You don't get to invent the polar-oriented gnomon but you do get to invent a Babylonian hours sundial. If you choose sunSET as your start of day then you can do the same thing but you will have to wait until daylight before you can mark the positions. The early clocks would have drifted during the night so it would be more difficult to notice the straight lines but not impossible. For completeness I could note that (accurately laid out) temporary hour lines are not (quite) straight (because they are not projections of great circles). They DO intersect at the sub-nodus point but only because they curve towards that point. The straight sections of temporary hour lines approximately intersect at a point a little above the sub-nodus point. I assume that it is this higher point that was used for the medieval gnomon? This is already suggesting a reason for bending the gnomon downwards. Zinner could be right! As you can tell, I am very weak on the history side of this business :-( Best wishes Frank --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
