and his successor, the emperor Augustus; and the months Quintilis, Sextilis, September, October, November, and December are archaic adjectives formed from the ordinal numbers from , their position in the calendar when it began around the spring equinox in March. Others are uncertain. February may derive from the Februa festival or its eponymous ("purifications, expiatory offerings"), whose name may be either Sabine or preserve an archaic word for sulphuric. April may relate to the Etruscan goddess Apru or the verb ("to open"). May and June may honor Maia and Juno or derive from archaic terms for "senior" and "junior". A few emperors attempted to add themselves to the calendar after Augustus, but without enduring success. In classical Latin, the days of each month were usually reckoned as: Dates after the ides count forward to the kalends of the next month and are expressed as such. For example, March19 was expressed as "the 14th day before the April Kalends" (), without a mention of March itself. The day after a kalends, nones, or ides was also often expressed as the "day after" () owing to their special status as particularly unlucky "black days". The anomalous status of the new 31-day months under the Julian calendar was an effect of Caesar's desire to avoid affecting the festivals tied to the nones and ides of various months. However, because the dates at the ends of the month all counted forward to the next kalends, they were all shifted by one or two days by the change. This created confusion with regard to certain anniversaries. For instance, Augustus's birthday on the 23rdday of September was in the old calendar but under the new system. The ambiguity caused honorary festivals to be held on either or both dates. Intercalation The Republican calendar only had 355days, which meant that it would quickly unsynchronize from the solar year, causing, for example, agricultural festivals to occur out of season. The Roman solution to this problem was to periodically lengthen the calendar by adding extra days within February. February was broken into two parts, each with an odd number of days. The first part ended with the Terminalia on the 23rd (), which was considered the end of the religious year; the five remaining days beginning with the Regifugium on the 24th () formed the second part; and the intercalary month Mercedonius was inserted between them. In such years,