suspicious. Other traditions existed alongside this one, however. Plutarch's Parallel Lives recounts that Romulus's calendar had been solar but adhered to the general principle that the year should last for 360 days. Months were employed secondarily and haphazardly, with some counted as 20 days and others as 35 or more. Republican calendar The attested calendar of the Roman Republic was quite different. It followed Greek calendars in assuming a lunar cycle of days and a solar year of synodic months ( days), which align every fourth year after the addition of two intercalary months. Two months were added at the end of the year to complete the cycle during winter, January and February, before the intercalary month inserted every two years; the intercalary month was sometimes known as Mercedonius. The inequality between the lunar year of 355 days and the tropical year of days led to a shortfall over four years of ( × 4) = 41 days. Theoretically, 22 days were interpolated into the calendar in the second year of the four-year cycle and 23 days in the fourth. This produced an excess of four days over the four years in line with the normal one day excess over one year. The method of correction was to truncate February by five days and follow it with the which thus commenced (normally) on the day after 23 February and had either 27 or 28 days. It did not acquire the alternative name Mercedonius until post-classical times. 23 February was the Terminalia and in a normal year it was Thus the dates of the festivals of the last five days of February were preserved on account of them being actually named and counted inclusively in days before the calends of March; they were traditionally part of the celebration for the new year. There was occasionally a delay of one day (a being inserted between 23 February and the start of the ) for the purpose of avoiding a clash between a particular festival and a particular day of the week (see for another example). The Roman superstitions concerning the numbering and order of the months seem to have arisen from Pythagorean superstitions concerning the luckiness of odd numbers. These Pythagorean-based changes to the Roman calendar were generally credited by the Romans to Numa Pompilius, Romulus's successor and the second of Rome's seven kings, as were the two new months of the