Schaefer 1993), while most sightings are even later. Hence, the month of [*Shawwāl*]{} 158h should have started with the first sighting of the crescent in the evening on Aug 2 or 3, see Fig. 3; the crescent new moon was theoretically visible on Aug 2, but if the weather was bad, the month of [*Ramaān*]{} ended one day later on Aug 3. According to Gautschy (2011) (footnote 7), the crescent new moon of this particular month was not visible before AD 775 Aug 2 at 16:23h UT at Babylon (not far from Baghdad, Iraq), actually visible at the first dawn after the time given. Hence, this month probably started on Aug 2 (in case of good weather), but maybe one day later on Aug 3 - or possibly on Aug 1 (in case of a false early sighting).\
The next new moon was 29.5 days later on AD 775 Aug 30 at 22:44h UT ($\pm 2$ min according to Morrison & Stephenson 2004), so that the end of the month of [*Shawwāl*]{} (and the start of the next month, called [*Dhū al-Qa$^{\rm c}$dah*]{}) should have been on AD 775 Sep 1 or 2, while the crescent new moon was still 