Subdividing a section: the center of section and the quarter-quarter corners

The original survey delivered a section with eight monumented points: four section corners and four quarter-section corners, one at the middle of each side. Everything inside was left to be established later, by the local surveyor, when someone first needed to describe a piece smaller than a half section. That interior work is the subdivision of the section, and it is governed by rule rather than by discretion.

The rule is proportional and it is short. The center of the section is the intersection of the straight lines joining opposite quarter corners. The quarter-quarter corners are the midpoints of the lines joining the corners on either side of them. Applied consistently, these two statements subdivide any regular section completely.

What the original survey left you

Only the first two rows are original evidence. Everything below them is a construction, correct if it applies the rule to properly identified original corners and incorrect otherwise. That distinction matters when two surveyors disagree about a quarter-quarter corner: the argument is never about evidence, because there is none, but about whether the rule was applied to the right controlling points.

The center of section

Center of section

The point at the intersection of the straight line joining the north and south quarter-section corners with the straight line joining the east and west quarter-section corners. It was not monumented by the original survey.

Three things it is not. It is not the geometric center of the section, because the four sides are unequal and the quarter corners are rarely at the exact midpoints. It is not the average of the four section corners. And it is not a point on the ground that anyone can recover as original evidence, because no original surveyor ever set it.

The two center lines are straight lines between opposite quarter corners, run as straight lines and not as curves or cardinal lines. If the north and south quarter corners are not directly north and south of each other, which is normal, then the north-south center line is not a cardinal line, and that is correct. The rule says join the quarter corners, not run a meridian.

Subdividing step by step

1. Recover the four section corners and the four quarter-section corners from original evidence, restoring by proportion only those that are genuinely lost.
2. Run a straight line from the north quarter corner to the south quarter corner, and another from the east quarter corner to the west quarter corner.
3. The center of section is at their intersection. Monument it and record it.
4. On each section boundary, set the quarter-quarter corner at the midpoint of the line between the section corner and the adjacent quarter corner.
5. On each center line, set the quarter-quarter corner at the midpoint of the line between the quarter corner and the center of section.
6. To subdivide a quarter section into quarter-quarters, join the opposite quarter-quarter corners of that quarter with straight lines; their intersection is the center of the quarter.
7. Repeat the halving as far as the description requires, always by joining opposite established corners and taking midpoints.

Fractional sections are different

In the north and west tiers of a township, and in sections closing against water or another survey, the rule changes because the original survey deliberately placed the excess or deficiency in the outer half-mile. There, quarter-quarter corners on the outer half of the section are set at 20.00 chains from the interior corner, at full record measure, and whatever remains falls into the outermost tier of lots.

The center of a fractional section also needs special treatment when an opposite quarter corner does not exist. Where a section is fractional on the north, for example, there may be no north quarter corner to join to the south one. In that case the center line is run from the existing quarter corner in a cardinal direction, or as the record indicates, to the meander line, reservation boundary or other governing line, and the center of section is established on it at the proper proportional position.

• Establish first whether the section is regular or fractional, from the plat, before choosing a rule.
• In a fractional section, the government lots shown on the plat define the outer tier; do not attempt to force it into aliquot quarter-quarters.
• Where only one of a pair of opposite quarter corners exists, run the center line cardinally from the existing corner unless the record shows otherwise.
• Where a section is fractional on two sides, as section 6 usually is, both the north and the west center lines require the special treatment.
• The plat and the field notes govern in every case of doubt.

Why this is the part that goes wrong

Subdivision of a section is where the most boundaries are created and the fewest monuments exist, so it is where errors are both easiest to make and hardest to detect. A center of section established from a mistaken quarter corner will be wrong by half the error, and every quarter-quarter corner derived from it will be wrong too. Occupation lines built to a mistaken subdivision decades ago will conflict with a correct one made today, which turns a computation problem into a boundary dispute.

The defences are unglamorous and effective. Prove every controlling corner before using it. Apply the correct rule for the kind of section you are in. Monument what you establish and file a record of it. And when a previous surveyor's subdivision differs from yours, find out which controlling corners each of you used before assuming the difference is a mistake, because in section subdivision the answer usually lies in the control rather than in the arithmetic.