"The lunar year of 354 days fell short of the solar year by 111⁄4 days: in 8 years this amounted to 90 days or three months. These 90 days he divided into two months of 22 and two months of 23 days, and introduced them alternately every second year for two octennial periods: every third octennial period, however, Numa intercalated only [...] three months [...] because he adopted 355 days as the length of his lunar year". Daniel Spillan, Livy's History of Rome, Book I. 19. Footnote 24. This is the theory of Macrobius in Saturnalia (c. AD 430).
