days of the first decad were designated as ἱσταμένου or ἀρχομένου μηνος, and were counted on regularly from one to ten; thus, δευτέρα ἀρχομένου or ἱσταμένου is “the second day of the month.” The days of the second decad were designated as ἐπὶ δέκα or μεσοῦντος, and were counted on regularly from the 11th to the 20th day, which was called εἴκας. There were two ways of counting the days of the last decad; they were either reckoned onwards from the 20th (thus, πρώτη ἐπὶ εἰκάδι was the 21st), or backwards from the last day, with the addition φθίνοντος, παυομένου, λήγοντος, or ἀπίοντος; thus, the twenty-first day of a hollow month was ἐνάτη φθίνοντος; of a full month, δεκάτη φθίνοντος. The last day of the month was called ἕνη καὶ νέα, “the old and new,” because as the lunar month really consisted of more than twenty-nine and less than thirty days, the last day might be considered as belonging equally to the old and new month. Separate years were designated at Athens by the name of the chief archon, hence called _archon eponymus_ (ἄρχων ἐπώνυμος), or “the name giving archon;” at Sparta, by the first of the ephors; at Argos, by the priestess of JUNO, &c.--(2) ROMAN CALENDAR. The old Roman, frequently called the Romulian year, consisted of only ten months, which were called Martius, Aprilis, Maius, Junius, Quinctilis, Sextilis, September, October, November, December. That March was the first month in the year is implied in the last six names. Of these months, four, namely, Martius, Maius, Quinctilis, and October, consisted of thirty-one days, the other six of thirty. The four former were distinguished in the latest form of the Roman calendar by having their nones two days later than any of the other months. The symmetry of this arrangement will appear by placing the numbers in succession:--31, 30; 31, 30; 31, 30, 30; 31, 30, 30. The Romulian year therefore consisted of 304 days, and contained thirty-eight nundinae or weeks; every eighth day, under the name of _nonae_, or _nundinae_, being especially devoted to religious and other public purposes. Hence we find that the number of _dies fasti_ afterwards retained in the Julian calendar tally exactly with these thirty-eight nundines; besides which, it may be observed that a year of 304 days bears to a solar year of 365 days nearly the ratio of five to six, six of the Romulian years containing 1824, five of the solar years 1825 days; and hence we may explain the origin of the well-known quinquennial period called the lustrum, which ancient writers expressly call an _annus magnus_; that is, in the modern language of chronology, a cycle. It was consequently the period at which the Romulian and solar years coincided. The next division of the Roman year was said to have been made by Numa Pompilius, who instituted a lunar year of 12 months and 355 days. Livy says that Numa so regulated his lunar year of twelve months by the insertion of intercalary months, that at the end of every _nineteenth_ year