Sentence:  For the modern reader of Latin the most irritating pecularity of this system of dating is that the days after the <WSD>Ides</WSD> of any month carry the name of the following month... Another trap for the unwary lies in the fact that the Roman calendars given in most reference books are Julian, not pre-Julian. When Caesar added ten days to the Roman year he put them near the ends of the seven 29-day months, one or two in each. As a result, instead of the day after the <WSD>Ides</WSD> of all months being "a.d. XVII Kal.", in these seven months it is either "a.d. XVIII Kal." or "a.d. XIX Kal.", and all the following days change correspondingly. 
Meaning of the word marked with <WSD> tags:  The notional full-moon day of a Roman month, occurring on the 15th day of the four original 31-day months (March, May, Quintilis or July, and October) and on the 13th day of all other months.