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The Calendar
The Egyptians determined the true length of the year-- 365.242 days and divided it into 12 months of 30 days each. The 5 extra days (or 6 extra days in Leap Year) were devoted to festival holidays. The month was divided into three 10-day periods.
After the conquest of Egypt, Julius Ceasar, in 46 B.C. adopted the Egyptian calendar for the Roman Empire, except, says George Eastman, that he did not continue the equal months of the Egyptians. He distributed the 5 extra days throughout the year by adding one day to every other month, January, March, May, July, September and November, and took one day off February.
In 28 B.C., Augustus Caesar, in order to have as many days in the month of his birth (August) as there were in the birth month of Julius Caesar (July) and also to be known in history as having altered the calendar, moved the 29th day of February to August.
Property owners who rented by the quarter objected to the unequal quarters caused by his change, as there would have been 90 days in the first quarter and 93 in the third. Augustus compromised by moving September 31st to October 31st. That caused two 31-day months to come together, and a further change was made by moving November 31st to December 31st.
The calendar of the two Caesars, Julius and Augustus, was based upon a 365.242 days, therefore, .008 of a day was accumulated every year. By 1582, the accumulation had amounted to 10 days, and Pope Gregory XIII in that year ordered the 10 days between October 5 and October 15