How Washington DC became the capital of the US?

 
James Madison expounded the need for a federal district on January 23, 1788, in his "Federalist No. 43", arguing that the national capital needed to be distinct from the states in order to provide for its own maintenance and safety.

 An attack on the Congress at Philadelphia by a mob of angry soldiers, known as the Pennsylvania Mutiny of 1783, had emphasized the need for the government to see to its own security. Therefore, the authority to establish a federal capital was provided in Article One, Section Eight, of the United States Constitution, which permits a "District (not exceeding ten miles square) as may, by cession of particular states, and the acceptance of Congress, become the seat of the government of the United States".[9] The Constitution does not, however, specify a location for the new capital. In what later became known as the Compromise of 1790, Madison, Alexander Hamilton, and Thomas Jefferson came to an agreement that the federal government would assume war debt carried by the states, on the condition that the new national capital would be located in the South


On July 16, 1790, the Residence Act provided for a new permanent capital to be located on the Potomac River, the exact area to be selected by President Washington. As permitted by the U.S. Constitution, the initial shape of the federal district was a square, measuring 10 miles (16 km) on each side, totaling 100 square miles. During 1791-92, Andrew Ellicott and several assistants, including Benjamin Banneker, surveyed the border of the District with both Maryland and Virginia, placing boundary stones at every mile point