too low and too close to the Sun on Aug 31, see Fig. 3. According to Gautschy (2011) (footnote 7), the crescent new moon of this particular month was not visible before AD 775 Sep 1 at 15:49h UT at Babylon, actually visible at the first dawn after the time given. These dates are Julian calendar dates (the difference between the old Julian calendar and the new Gregorian calendar was 10 days in AD 1582, so that, by the time of AD 775, the shift was three days). Hence, the month of [*Shawwāl*]{} ended probably on Sep 1, but maybe one day later (in case of bad weather on Sep 1) or possibly on Aug 31 (in case of a false early sighting).\
We can therefore conclude that the month of [*Shawwāl*]{} 158h started with the sighting of the crescent (new) moon on AD 775 Aug $2 \pm 1$ (Julian calendar). The end of this month was then shortly after the next new moon (AD 775 Aug 30, 22:44h UT, $\pm 2$ min according to Morrison & Stephenson 2004), i.e. probably at sunset on AD 775 Sep 1 ($\pm 1$ day) in the Julian calendar.\
According to de Blois (2000), 