The difficult questions connected with this subject cannot be discussed here. Since Mommsen wrote his _Römische Chronologie_ it has at least been possible to give an intelligible account of it, such as that in the _Dict. of Antiquities_ (second edition), in Marquardt’s _Staatsverwaltung_, iii. 281 foll., and in Bouché-Leclercq, _Pontifes_, p. 230 foll. There is a useful summary in H. Peter’s edition of Ovid’s _Fasti_ (p. 19). Mommsen’s views have been criticized by Huschke, _Das Römische Jahr_, and Hartmann, _Der Röm. Kalender_; the former a very unsafe guide, and the latter, unfortunately, an unfinished and posthumous work. The chief ancient authority is Censorinus, _De die natali_, a work written at the beginning of the third century A.D., on the basis of a treatise of Suetonius. Footnote 2: _Chron._ 48 foll.; Marq. 284 and notes. Footnote 3: Huschke, _op. cit._ 8 foll.; Hartmann, p. 13. Footnote 4: 1 Censorinus, _De die natali_, 20. 4. Footnote 5: Mommsen (_Chron._ 13) believes it to have been a Pythagorean doctrine which spread in Southern Italy. Hartmann, on the contrary, calls it an old Italian one adopted by Pythagoras. See a valuable note in Schwegler, _Röm. Gesch._ i. 561, inclining to the latter view. Footnote 6: Probably by the Decemvirs, B.C. 450, who are said to have made some alteration in the calendar (Macrob. 1. 13. 21.) Footnote 7: See _Dict. Ant._ i. 337 and 342. It is highly probable that there was a still older plan, which gave way to this at the time of the Decemvirate: the evidence for this, which is conjectural only, is stated by Mommsen in the first chapter of his _Chronologie_. The number of days in this cycle (also of 4 years) is computed at 1475, and the average in each year at 368-3/4. Footnote 8: Or, according to Mommsen, in alternate years after the 23rd and 24th, i. e. in the year of 378 days 23 days were inserted after the _Terminalia_; in the year of 377 days 22 days were inserted after the 24th (_Regifugium_). Thus February would in the one case have 23, and in the other 24 days; the remaining 5 and 4 being added to the intercalated period. The object of the Decemvirs (if it was they who made this change) in this curious arrangement was, in part at least, to keep the festival of the god Terminus on its original day (Mommsen, _Chron._ 38). Terminus would budge neither from his seat on the Capitol (Liv. 1. 55) nor from his place in the calendar. Footnote 9: Probably in order that the beginning of the year might coincide with a new moon; which actually happened on Jan. 1, 45, and was doubtless regarded as a good omen. Footnote 10: He added 10 days to the normal year of 355: January, Sextilis, December, receiving two; April, June, September, November, one only. These new days were placed at the end of the months, so that the days on which religious festivals fell might remain as before. Footnote 11: