Jehovah's Witnesses used to think that 1799 was a very important date. The Watchtower of March 1, 1922 said, "The indisputable facts, therefore, show that the "time of the end" began in 1799..."
The actions of Napoleon were seen as confirmation of this important prophetic date.
"Having thus furnished grounds for establishing the identity of this character (Napoleon), whose deeds mark the beginning of the 'Time of the End,' the prophecy proceeds to show which particular event of that time is to be understood as definitely marking the exact date of the beginning of the 'Time of the End.' This event is shown to be Napoleon's invasion of Egypt, which covered a period of a year and nearly five months. He sailed May, 1798 and, returning, landed in France Oct. 9, 1799." -Studies in the Scriptures-Thy Kingdom Come (1915) page 44
They also thought 1799 was significant because it was 1260 years after the fall of the Ostrogothic monarchy in 539 AD. Daniel 12:7 mentions three and a half times or 1,260 days. They just converted the days to years. Jehovah's Witnesses now believe that these 1,260 prophetic days refer to the 684 days (from June 21, 1918 to May 5, 1920) that the second president of the Watchtower Society, Joseph Rutherford, spent in prison on charges of espionage.
See also this page of Watchtower quotes about 1799.