reality, until recently, the start (and end) of a month was set by [*observing*]{} the crescent new moon.\
However, the sighting of a crescent new moon could have been delayed by one or more days due to, e.g., bad weather, high extinction at low latitude, or difficult landscape. For that particular month ([*Shawwāl*]{} 158h), no calibration is kno- wn, e.g. no mentioning of a week day together with a date or an astronomical event (such as, e.g., an eclipse) with well-known precise date; a calibration point outside of that month, e.g. the day of the death of the caliph, may not be relevant, because such shifts (due to a delayed crescent sighting) were not neccessarily transferred to the next month nor cumulative, but could be corrected with the next new crescent. (If the length of a month would be fixed to, e.g., at least 29 days and/or at most 30 days, then a calibration in a neighbouring month and/or the knowledge of the start and/or end of a neighbouring month would also help, see at the end of this section.) However, there were some possibilities to find the start of the month even in case of bad weather: One can 