passage of "An Ordinance for ascertaining the mode of disposing of lands in the Western Territory" of 1785 by the U.S. Congress (see Land Ordinance of 1785). This law provided that lands outside the then-existing states could not be sold, otherwise distributed, or opened for settlement prior to being surveyed. The standard way of doing this was to divide the land into sections. An area six sections by six sections would define a township. Within this area, one section was designated as school land. As the entire parcel would not be necessary for the school and its grounds, the balance of it was to be sold, with the monies to go into the construction and upkeep of the school. On May 20, 1862, President Abraham Lincoln signed into law the Homestead Act, by which settlers could "claim" 160 acres (a quarter section) of public land. Claimants were required to "live on" and “improve” their plot by cultivating the land. After five years, the original filer of the claim was entitled to the property, free and clear, except for a small registration fee. Roads and urban planning Numbering within a township Every township is divided into 36 sections, each usually square. Sections are numbered boustrophedonically within townships as follows (north at top): Section subdivisions Sections can be divided into quarter sections of , named by intercardinal direction (northwest, northeast, etc.). For instance, the southwest quarter of a section is named SW 1/4. Sections can be further broken up into blocks, or quarter-quarter sections. These add a second intercardinal direction label. For instance, the southeast quarter of the southwest quarter section mentioned above is labeled SE 1/4, SW 1/4: Measurement anomalies The curvature of the earth makes it impossible to superimpose a regular grid on its surface, as the meridians converge toward the North Pole. As the U.S. is in the Northern Hemisphere, if a section's or township's east and west sides lie along meridians, its north side is shorter than its south side. As sections were surveyed from south and east to north and west, accumulated errors and distortions resulted on the north and west lines, and north and west sections diverge the most from the ideal shape and size. The entire township grid shifts to account for the earth's curvature. Where the grid is corrected, or where two grids based on different principal meridians meet, section shapes are irregular. Sections