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 x 8) 90 days.

These 90 days he divided into 2 months of 22 and 2 of 23 days, ([2 x 22] + [2 x 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 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.