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Marcel wrote, about lengths of twilight-

| Since the problem has an Arab origin: Could it be that it was
| originally related to the prayer times? The duration of this twilight
| corresponds to the duration between evening and night prayer. One
| being done right after sunset and the other, depending on the
| understanding, when the  sun is 17 to 19 deg below the horizon.

I think he could be on to something. That seems plausible. If there was a 
prayer-time at sunset and another, when the sky became completely black, 
that might explain why it was useful to be able to predict the interval 
between them, to time with (say) a water-clock, if the sky wasn't clear. 
And similarly in the morning. But for such purposes, it's the actual length 
of twilight that needs predicting. Joel's posting relates, not to that 
length, but to the date of its minimum, which appears to me to be a much 
less interesting (indeed, entirely trivial) matter.

Other possibilities come to mind. Might it, I wonder, be related to the 
definition of the lunar month, in Jewish / Arabic calendar, in which the 
date of first viewing of a crescent Moon, shortly after sunset, becomes 
important? But that observation doesn't call for a very dark sky.

Or could it go back to earlier calendars still, from Babylonian times, in 
which the "heliacal rising" of a star (often Sothis = Sirius) became 
important in establishing the season of the year? Heliacal rising meant 
that the star could be observed, for the first time that year, just before 
the brightening dawn sky blotted it out. But again, I wouldn't expect that 
to call for astronomical twilight, with the Sun at -18�.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 

   

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