The Egyptian Year was a set of twelve months all of 30 days, at some early point the Egyptian's added added five extra days. As a year is 365 1/4 day this meant their years slowly became out of sync and once every 1,461 the Egyptian year once again started on the same day. This became known as the Sothis Cycle. 
At an early date they had been able to determine the longest day by observing the latest rising of Sothis before the sunrise. This, known as the Helical Rising of Sirius occurred on the first day of the month of Thoth when the calender was first adopted. 
They are believed to have occurred in AD139, 1321BC, 2781BC and 4241BC.