Note 561 — Chapter VI · LUNAR CALENDARS AND THE WEEK

The mean age of the moon when first seen being 30 hours + 24/2 hours = 1 day, 18 hours (above, p. 174 n.¹), and the mean age of the moon when full being (29 days, 12 + hours)/2 = 14 days, 18 hours, it follows that the mean interval between the first appearance of the moon and the full of the moon is about 13 days. “In other words the moon becomes full on an average at the end of the thirteenth day and the beginning of the fourteenth night. Hence, where the days are reckoned from sunset, we should expect the fourteenth day of the month to be regarded as the day of the full moon. And it is in fact one of the days most commonly so regarded. The fifteenth is a date obtained more simply. Fifteen is half thirty and, as the middle of the month, should be the date of full moon. In calendars based on calculations the month is frequently reckoned from the actual new moon, and in these the fifteenth is more correct than the fourteenth for the mean date of full moon.” It should be noted, also, that, as a general rule, the nearer the autumnal equinox, the later the first appearance of the moon and the shorter the interval between the visible new moon and full moon. If the first appearance is late, as it often is in September, the moon might be full on the night following the eleventh day. See J. K. Fotheringham, in Proceedings of the British Academy, 1909-1910, pp. 283, 286.