Fig 5.11 ref 3
It is stated above that for the lunar crescent to be visible, the Moon’s age from conjunction must be of the order of 20 to 30 hours. The age criterion has been studied by various people by taking random observations and is usually stated in the form of general rules such as the sightings of the Moon younger than 20 hours are rare and the sightings of Moon older than 24 hours are not uncommon although its visibility may at times require it to be more than 30 hours old.
Dr. Ilyas, Head of the Astronomical Research Unit at the University of Science in Malaysia, has made much more thorough investigations of the Moon’s age requirement for the earliest visibility at various latitudes throughout the year, and spread over a number of years. Fig.5.11 taken from his book (ref: 3) shows a tabulation of his results. The results show, without any doubt, the enormous variations possible. Based on his results he goes on to suggest, for the purpose of approximate calculation of the earliest visibility of the Lunar Crescent, a figure of 24 plus or minus 2 hours from conjunction. This, in round figure, means that we have to assume that the Lunar Crescent will be most likely visible on the day after the Astronomical “New Moon”, i.e. from the conjunction. Thus, Islamic calenderical months could be reckoned from the day after the conjunction, as published by the astronomical almanacs. It must be pointed out that in the field of the Islamic Calendar, the contribution of Dr. Ilyas is very extensive and his book (Ref: 3) is a must for anyone interested in this subject.