Sentence:  The interesting thing about these ceremonies is that they must have originated in a period when the Romans were using true lunar months based on the observation of the crescent moon. The Kalends then would have been the day after the evening on which the crescent had been first sighted, the <WSD>Nones</WSD> would have been the first day when the moon was at the first quarter... In the calendar of the late Republic the lunar months have disappeared and the days have been fixed into a rigid pattern. 
Meaning of the word marked with <WSD> tags:  The notional first-quarter day of a Roman month, occurring on the 7th day of the four original 31-day months (March, May, Quintilis or July, and October) and on the 5th day of all other months.