George Washington's Farewell Address was written to the people of the United States at the end of his second term as President of the United States. It appeared in many American newspapers on September 19, 1796. Technically speaking, it was not an address, but an open letter to the public published in the form of a speech. Washington's fellow Americans gave it the title of "Farewell Address" to recognize it as the President's valedictory to public service for the new republic.
In 1792, Washington was prepared to retire after one term as the President of the United States. To that end, Washington, with James Madison, wrote a farewell address to the public of the United States of America. Faced with the unanimous desire for him to remain in office from his Cabinet, Washington agreed to stand for another term. In 1796, Washington refused a third term. Starting with his 1792 draft, Washington rewrote the text to better fit the problems that were emerging in the new political landscape. He had much help from Alexander Hamilton, and some passages do sound like Hamilton's writing, but all the key ideas were those of Washington.
Full Text of Washington's Farewell Address from Avalon Project, Yale Univ. Law School.
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