No township measures exactly six miles square. The original chaining had error in it, terrain made some lines long and some short, and meridians converge so that the north boundary of a township is genuinely shorter than the south. A rectangular survey has to decide what to do with the difference, and the PLSS made that decision once, in advance, for every township: all excess and deficiency is placed in the north and west half-miles.
This is not a rule about error in a vague sense. It is a specific instruction about where the surveyor set his monuments, and it explains the shape of the sections you will find on the ground. It also explains why a normal township with no water and no adjoining survey still has government lots along two of its sides.
The design decision
Any surveyor subdividing a township faces a choice. He can distribute the discrepancy evenly across all six sections in a tier, which keeps every section approximately equal but makes every section slightly wrong. Or he can hold the record measurement of 80.00 chains for as many sections as possible and let the last one take the remainder, which makes most sections correct and one section clearly fractional.
The PLSS chose the second. The advantage is certainty: a buyer of any section other than those in the north and west tiers received a full 640 acres as measured, and the lands whose quantity was uncertain were identified in advance so they could be lotted and sold by their actual computed acreage. The disadvantage is that eleven of the thirty-six sections in a township are irregular by design.
How the subdivision produces it
The interior of a township is subdivided starting from the southeast corner and working north and west. Section corners are set at 80.00 chains from the controlling corner, with quarter-section corners at 40.00 chains, tier after tier and range after range. When the survey reaches the north or west township boundary, whatever distance remains is simply the remainder.
Take a range line whose total length between the south and north township boundaries measures 479.14 chains rather than the record 480.00. The first five sections take their full record measure and the sixth takes what is left.
| Interval | Record distance |
|---|---|
| South township line to first section corner | 80.00 ch |
| Second section | 80.00 ch |
| Third section | 80.00 ch |
| Fourth section | 80.00 ch |
| Fifth section | 80.00 ch |
| Fifth section corner north to the township line | 79.14 ch |
The deficiency of 0.86 chains has landed entirely in the north tier section. But the rule goes one step further: within that section, the discrepancy is confined to the north half-mile, and within that half-mile to the outermost quarter-quarter tier.
| Interval | Record distance |
|---|---|
| South section corner to quarter-section corner | 40.00 ch |
| Quarter-section corner to quarter-quarter corner | 20.00 ch |
| Quarter-quarter corner to the north township line | 19.14 ch |
The three intervals sum to 79.14 chains, matching the measured length of the section. The south half of the section is a full 40 chains and its quarter-quarters are regular. Only the northernmost tier of forty-acre parcels is short, and those parcels are therefore returned as government lots rather than as aliquot quarter-quarters.
Lot area = 19.14 ch × 20.00 ch = 382.8 sq ch = 38.28 acresWhy north and west, and not south and east
The direction of the rule follows the direction of the survey. Interior lines were run north from the south boundary and west from the east boundary, so the surveyor's accumulated measurement necessarily terminated on the north and west township lines. Putting the remainder anywhere else would have required either resurveying backwards or distributing an unknown quantity before it was known.
The rule is also consistent with the treatment of standard parallels. Correction lines control the survey to the north of them, and townships are laid out northward from a correction line, so it is the northern edge of each block that absorbs whatever convergency and error have accumulated. The same logic operates at the scale of a single township.
What this means for retracement and for area
- In the interior sections of a township, treat the record 80.00-chain and 40.00-chain distances as the intended geometry and proportion any discrepancy across the whole line.
- In the north and west tiers, do not proportion the whole line. The intended geometry places full measure in the interior intervals and the remainder in the outermost half-mile.
- A short measurement in a north-tier section is not necessarily evidence of error. It may be exactly what the original survey intended.
- Where the actual measurement exceeds the record, the excess likewise goes to the outer tier, producing lots of more than forty acres.
- The plat governs. If the plat shows quarter-quarters rather than lots along the north tier, the survey did something other than the general rule and the plat controls.
The single most common mistake is to apply single proportionate measurement across the full length of a range line in a north-tier section, distributing the deficiency evenly among all six sections. That destroys the intended geometry, moves five section corners that were never in doubt, and produces a result the original survey never contemplated. Establish first which tier you are in, then choose the method.