If you have been watching John Adams on HBO, you may or may have not miss that he predicted to his wife Abigail that Americans would celebrate their Independence Day on July 2.   Well he was off by two days - not too bad for government work.

For Adams, it was the momentum towards achieving American independence initiated on July 2nd that future generations would consider worth celebrating, not the approval of this document on July 4.

Interestingly, in 1777, Congress did not think about commemorating the adoption of the Declaration of Independence until July 3rd, so the first organized elaborate celebration of independence occurred the following day: July 4, 1777, in Philadelphia. Ships in the harbor were decked in the nation's colors. Cannons rained 13-gun salutes in honor of each state.  

Since 1777, the tradition of celebrating America's independence on July 4th has continued.