Julius was Julius Caesar. His adopted son Octavius later became the Great Empereor, or Caesar Augustus. Probably had an inferiority complex. So he honored his murdered father and himself with the month name changes. And with it he moved the start of the year from just before the Ides of March, to January--but why I don't know/remember. The other, or course, more closely matches the spring start of the year in so many cultures and religions.
And (as I put in a non-posted mailing to Gary), he caught me. The year length was from a faulty memory, and is not 365.248. I'll try to track it down more precisely. But I do agree him, Judy, and others that there some wonderful potential lessons here connecting other cultures with different calendars, history, and math. I've done some of it with middle school students, and pre-service teachers. The lesson starts with a Tower of Hanoi activity, but I won't tell you how we get here from there!
In addition to the books mentioned, Key Curriculum also has those wonderful Math Around the World posters, some of which relate to calendar math.