The election of 1800 had ended with the following results in the electoral college :
(Candidate/Party/Home State/Electoral Votes)
Thomas Jefferson Democratic-Republican Virginia-73
Aaron Burr Democratic-Republican New York-73
John Adams Federalist Massachusetts-65
Charles Cotesworth Pinckney Federalist South Carolina-64
John Jay Federalist New York-1
Total-276
The members of the House of Representatives balloted as states to determine whether Jefferson or Burr would become President. There were sixteen states, and an absolute majority of nine was required to pick a winner. Jefferson had been the candidate for President and Burr for Vice President, but the lame-duck House was controlled by the Federalists, who were unwilling to vote for Jefferson. Most Federalists voted for Burr, giving Burr six of the eight states controlled by Federalists. The seven delegations controlled by Republicans all voted for Jefferson, and Georgia's sole Federalist representative also voted for Jefferson, giving Jefferson eight states. Vermont was evenly split, casting a blank ballot. The remaining state, Maryland, had five Federalist representatives to three Republicans. One of its Federalist representatives voted for Jefferson, forcing the state delegation to cast a blank ballot.
Over the course of seven days from February 11 to February 17, the House cast a total of 35 ballots, with Jefferson receiving the votes of eight state delegations each time, one short of the necessary majority of nine. During this time, Alexander Hamilton recommended to Federalists that they support Jefferson because he was "by far not so dangerous a man" as Burr. He said that he would much rather have someone with wrong principles than someone devoid of any. Hamilton embarked on a letter-writing campaign to get delegates to switch votes.
On February 17, on the 36th ballot, Jefferson was elected. Some Federalists in Delaware, Maryland and Vermont all cast blank ballots. This resulted in the Maryland and Vermont votes changing from no selection to Jefferson, giving him the votes of 10 states and the presidency.The final tally was Jefferson with ten states to Burr's four.
As we all know, the bad blood between Burr and Hamilton ended four years later when the two men duelled on July 11, 1804 and Burr fatally wounded Hamilton, who died the following day.