The origin of the square grid in America’s western lands is Thomas Jefferson’s Land Ordinance of 1785.
Surveyors were sent out far into the wilderness to fix meridians and base lines; from these, half a continent was divided into six-mile square townships, each split into 36 square sections of 640 acres (a square mile), then sold at a fixed minimum price of a dollar an acre.
Having never stepped foot on their property, someone could point to a map, make a purchase, and start their wagon westward knowing precisely where they were going.
Today, a cross-country flight will easily show the physical ramifications of Jefferson’s decision to subdivide this territory upon the grid. The vast majority of America’s western land is so arranged in a logical lattice-work.
By superimposing a rectangular grid on the earth surface, a grid built from square miles, you will have to fix the spherical deviation. After all, this grid has only two dimensions. Somehow and somewhere corrections have to be made.
I have been looking for these Grid Corrections in Google Earth and found these on the Kansas/Nebraska border.