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1 Romulus had made his year to consist of ten months, the first month being March, and the number of days in the year being only 304, which corresponded neither with the course  of the sun or moon. Numa, who added the two months of January and February, divided the year into twelve months, according to the course of the moon. This was the lunar Greek year, and consisted of 354 days. Numa, however, adopted 355 days for his year, from his partiality to odd numbers. The lunar year of 354 days fell short of the solar year by 11 1/4 days; —this in 8 years amounted to (11 1/4 × 8) 90 days. These 90 days he divided into 2 months of 22 and 2 of 23 days, (\overline(2 × 22) + \overline(2 × 23) = 90,) and introduced them alternately every second year for two octennial periods: every third octennial period, however, Numa intercalated only 66 days instead of 90 days, i. e. he inserted 3 months of only 22 days each. The reason was, because [6??] he adopted 355 days as the length of his lunar year instead of 354, and this in 24 years (3 octennial periods) produced an error of 24 days; this error was exactly compensated by intercalating only 66 days (90 —24) in the third octennial period. The intercalations were generally made in the month of February, after the 23rd of the month. Their management was left to the pontiffs —ad metam eandem solis unde orsi essent —dies congruerent; “that the days might correspond to the same starting-point of the sun in the heavens whence they had set out.” That is, taking for instance the tropic of Cancer for the place or starting-point of the sun any one year, and observing that he was in that point of the heavens on precisely the 21st of June, the object was so to dispense the year, that the day on which the sun was observed to arrive at that same meta or starting-point again, should also be called the 21st of June: —such was the congruity aimed [7??] at by these intercalations.
Ille nefastus erit per quem tria verba silentur;
Fastus erit, per quem lege licebit agi.Ov. F. i. 47.
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