Credit for the squaring of the Midwest is often given to Thomas Hutchins, the first geographer of the United States.
Due partially to his influence, in 1785, Congress passed a law stipulating that the Midwest would be surveyed in a grid pattern of 6-mile squares, each square (or township) to be further subdivided into 36 1-mile squares (sections) of 640 acres each. Surveying the first tract, Hutchins stuck his Jacob staff on the north bank of the Ohio River, square on the Pennsylvania border, and ran a line due west 42 miles. And so it went.
Many towns, even before they were platted, were set aside as 1-mile squares. Platting started with a public square, then little squares or blocks pushed out in all directions until they ran blindly into a river or lake. Thus began the pattern of land survey that was to persist throughout the rest of the country, with few exceptions. The pattern provided a way to locate precisely any piece of land within a tract to be surveyed.
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Blame for the squaring of the Midwest goes to the road builders. A survey line is only a mark on a map, not visible on the land like a river or three oak trees growing from one root. In hill country, delineations of roadway by necessity followed the lines of least resistance. When the lines reached the flat land of Indiana and Illinois, it became possible to mark them physically. Roads were built on the section lines.
At least it is impossible to get lost: Heading west on a township road, you can count the perpendicular roads you pass and know how many miles you have gone. If the road you are on ends at a river, you just take a right angle and go until you find another east-west road that crosses the river.
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Unfortunately, you can’t lay down a straight line on a curved surface for very far. Furthermore, a magnetic compass will not keep to a consistently straight line over a great distance. For both of these reasons, Squaredom is not nearly as accurate as the square mind would like it to be. Many 640- acre sections of land actually contain a few more or a few less acres than 640. The extras may have been added on to all of the quarters of a section, or they may, as in Illinois, all have been thrown into the northwest quarter, so that three-fourths of the land possesses undefiled rectitude.
Another kind of inaccuracy is inherent in the rectitude of forcing imperfect Earth into perfect geometric squares: Deeply undulating terrain contains considerably more surface acreage than flat terrain of the same survey dimensions. And for that, many Midwesterners are grateful.