Dear Friends, I hope my attached diagram will help show the relationships between Italian, Babylonian and modern hours, and ways to plot Italian and Babylonian hours on any horizontal, vertical (or reclining) dial. To keep the file size down, I put in only minimal instructions. My diagram shows a cylindrical dial wrapped around a polar gnomon with a nodus.
Surprisingly, perhaps, it shows that the Italian hours line for hour H and the Babylonian hours line for the same hour number H are just different ends of the same line! Frank makes the point that the horizon line IS the Italian 24 hour line and the Babylonian 24 hour line, but Gianni's original statement was meant, I feel sure, to refer to the useful observation that intersections of the horizon line with each of the *other* hour lines enable them to be plotted very easily. But he got two of the equations wrong. The correct equations for lines crossing the horizon are: HIT=2 HMOD for 0<HMOD<12 HBAB=2 HMOD -24 for <12<HMOD<24 HIT=HBAB ...so Gianni's example should read HMOD=11, HIT=22, HBAB=22 But, while it is theoretically true that HBAB=22, this represents two hours before dawn, so would be dark except very close to, or inside, the Arctic Circle. However, a dial showing HIT=11 and HBAB=11 is very plausible - these are collinear, separated only be the summer solstice declination curve. On my diagram I introduce a line I call the Baseline, which is a declination line for dec=90-latitude. If this line is plotted on a horizontal dial, it will be found that the modern hour line, and the Italian/Babylonian hour line meeting there all have the same number. This could be a neat solution to the numbering question raised by Frank - a single number serves all three hour systems. Best wishes to all Chris ----- Original Message ----- From: "Frank King" <frank.k...@cl.cam.ac.uk> To: "Roger Bailey" <rtbai...@telus.net>; "Gianni Ferrari" <gfme...@gmail.com> Cc: "LISTA INGLESE" <sund...@rrz.uni-koeln.de> Sent: Saturday, April 03, 2010 8:46 AM Subject: Re: how italian hours > Dear Gianni and Roger, > > Thank you very much for the clarifications. > Gianni's table is especially clear about > the two cycles of 12 for Italic hours as > used in the Muslim world. > > Chris Lusby Taylor's comment is true in a > way but, equally, your original remark can > be interpreted as being correct. You > said: > > Also for each point of the line of horizon > (on the sundial) pass one hour line with > Modern, one with Italic *and* one with > Babylonian hours. > > I interpreted this as being *correct*. The > horizon line IS either B=0 or I=24 so you > have triple points like B=0, F=8, I=16 > and B=8, F=16, I=24. These points are > on the horizon line! > > I do agree that HMOD=11, HIT=22, HBAB=2 > is an inconsistent trio but it can be made > correct just by changing HBAB to 0 and > you have another triple point on the > horizon line! > > Best wishes > > Frank > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial >
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