U.S. Public Land Survey System: Subdivision, Section Breakdown, and Restoration of Lost Corners
The frame
A principal meridian and base line intersect at an initial point; townships are laid out in 6-mile blocks in tiers north/south of the base line and ranges east/west of the meridian. Each normal township has 36 sections of 640 acres. Section 1 sits in the northeast corner and numbering runs westward to Section 6, drops south, then east to 12, serpentine, ending at Section 36 in the southeast corner. Halving produces the familiar ladder: half-section 320 acres, quarter-section 160 acres, quarter-quarter 40 acres.
Corners and lots
Standard corners are established on the line being governed (usually a standard parallel); closing corners are established where a meridian or township line closes upon that parallel. The north and west tiers of a township are short or fractional, and their parcels are described as numbered lots rather than aliquot parts, an error exam writers exploit by describing a fractional lot as "the NW 1/4 of the NW 1/4."
Obliterated versus lost
An obliterated corner is one whose position can be rehabilitated from direct or collateral evidence, and it is re-established at that evidenced position. A lost corner leaves no evidence of any kind, and its position is restored by proportionate measurement between the nearest acceptable found corners: single proportionate for a corner on one line, two-way or three-way proportionate for a closing corner on a standard parallel.
Worked rule of thumb
Two found section corners lie 80.20 chains apart and the field notes record a quarter corner at 40.00 chains. If the quarter corner is truly lost, straight-line proportion gives 40.00/80.00 x 80.20 = 40.10 chains from one end. If any evidence of the original monument survives, proportion is forbidden. Say it as a mantra: find first, proportion last, and never let proportion move a found monument.