Pressing Questions

Does anyone know why the city fathers of Washington decided to make the city a 10 square mile diamond centered on the White House and then divide it into four "quadrants" centered not on the center of the diamond, but on the Capitol, which is well southeast of the White House? And why was Arlington Country retroceeded to Virginia? The upshot is to make the Northwest "quandrant" much bigger than the Northeast and Southeast ones, while the Southwest "quandrant" is positively tiny. If they'd stuck with the original shape and centered the grid on the middle of the city, you'd have four actual quandrants of equal size.