Section Subdivision

Overview#

The section is the fundamental unit of land description in the PLSS. Each standard township contains 36 sections, nominally one mile square and containing 640 acres. Sections are further subdivided into half sections, quarter sections, and quarter-quarter sections -- the "aliquot parts" that form the basis of most land descriptions in PLSS states.

The rules for subdividing sections are not arbitrary. They follow the order of the original survey and determine where excess or deficiency in measurement is placed. Understanding these rules is essential for every surveyor who subdivides a section, locates a quarter corner, or determines the center of a section.

"All the corners marked in the surveys, returned by the Secretary of the Interior or such agency as he may designate, shall be established as the proper corners of sections, or subdivision of sections, which they were intended to designate." -- Act of February 11, 1805 (2 Stat. 313; 43 U.S.C. 752), quoted in BLM, Manual of Surveying Instructions (2009), Sec. 6-1

The 36-Section Township#

Section Numbering Pattern

Sections within a township are numbered 1 through 36 in a serpentine (boustrophedon) pattern beginning in the northeast corner and ending in the southeast corner. The numbering proceeds west across the first row, drops down, proceeds east across the second row, and so on:

This numbering pattern has been standard since the early 19th century. The original 1785 surveys used a different scheme (numbered 1 through 36 from the southeast corner, south to north), but the serpentine pattern was adopted in subsequent legislation and has been used consistently since.

Note that Section 1 is always in the northeast corner and Section 36 is always in the southeast corner of the township. Section 6 is in the northwest corner and Section 31 is in the southwest corner.

The Order of Subdivision

The subdivision of a township into sections follows a specific order:

1. Township exteriors are established first (south and east boundaries from prior surveys; north and west boundaries as the survey progresses).
2. Section lines are run from south to north and from east to west within the township.
3. Quarter-section corners are established at the midpoint of each section line (at 40 chains from the section corner, nominally).

The critical rule is that subdivision lines are run from established corners toward the north and west boundaries. This means:

• Excess or deficiency in the east-west direction falls in the westernmost half-mile of each section line.
• Excess or deficiency in the north-south direction falls in the northernmost half-mile of each meridional section line.

"Corners are established from south to north on the line connecting the previously established township corners, at intervals of 40 chains and at intersections with meanderable bodies of water, marking the true line. By this procedure, the excess or deficiency in measurement is incorporated in the north half mile." -- BLM, Manual of Surveying Instructions (2009), Sec. 3-19

Standard Sections#

Dimensions and Area

A standard section is nominally 80 chains (5,280 feet or 1 mile) per side, containing 640 acres. In the Gunter's chain system used historically:

$640 \text{ acres} = 80 \text{ ch} \times 80 \text{ ch} = 6{,}400 \text{ sq. ch.}$

Since $1 \text{ acre} = 10 \text{ sq. ch.}$:

$\frac{6{,}400 \text{ sq. ch.}}{10 \text{ sq. ch./acre}} = 640 \text{ acres}$

In practice, the actual area of a section varies from the nominal 640 acres depending on the accuracy of the original survey and the location of the section within the township.

Interior vs. Boundary Sections

The interior 16 sections (sections 8, 9, 10, 11, 15, 16, 17, 20, 21, 22, 23, 26, 27, 28, 29, 33, 34, and others not on the north or west boundary) are intended to be standard -- 640 acres with regular quarter-section divisions.

The sections along the north boundary (sections 1--6) and west boundary (sections 6, 7, 18, 19, 30, 31) absorb the excess or deficiency from convergence and measurement errors. These are typically fractional sections containing lots rather than standard aliquot parts.

Section 6, in the northwest corner, is the most irregular section in any township. It absorbs both the east-west convergence error and the north-south measurement error, and may be significantly larger or smaller than 640 acres.

Aliquot Parts#

Definition

An aliquot part is a fractional subdivision of a section defined by running lines between opposite quarter corners or between the center of the section and midpoints of the section boundaries. Aliquot parts are the standard method of describing land within a section.

Half Sections (320 Acres)

A section is divided into two half sections by a line connecting opposite quarter-section corners:

• N 1/2 (North Half) -- the northern 320 acres
• S 1/2 (South Half) -- the southern 320 acres
• E 1/2 (East Half) -- the eastern 320 acres
• W 1/2 (West Half) -- the western 320 acres

$A_{\text{half section}} = \frac{640}{2} = 320 \text{ acres (nominal)}$

Quarter Sections (160 Acres)

Each section is divided into four quarter sections by lines connecting opposite quarter-section corners. The intersection of these two lines defines the center of the section:

$A_{\text{quarter section}} = \frac{640}{4} = 160 \text{ acres (nominal)}$

The 160-acre quarter section was the standard homestead claim under the Homestead Act of 1862.

Quarter-Quarter Sections (40 Acres)

Each quarter section is further divided into four quarter-quarter sections by lines connecting the midpoints of opposite quarter-section boundaries:

$A_{\text{quarter-quarter section}} = \frac{640}{16} = 40 \text{ acres (nominal)}$

The 40-acre "forty" was the smallest unit available under many federal land laws and remains the basic building block of PLSS descriptions.

Area Calculations for Aliquot Parts

For a standard section, the areas are computed by simple division:

$A = \frac{640}{n}$

where $n$ is the number of equal parts. For irregular or fractional sections, areas are computed from the actual surveyed dimensions:

$A = \frac{L_{\text{NS}} \times L_{\text{EW}}}{10}$

where $L_{\text{NS}}$ and $L_{\text{EW}}$ are the north-south and east-west dimensions in chains, and the result is in acres ($1 \text{ acre} = 10 \text{ sq. ch.}$).

Fractional Sections and Lots#

When Sections Are Fractional

A section is fractional when it does not contain a full 640 acres. This occurs when:

• The section is on the north or west boundary of the township (absorbing convergence and measurement errors).
• The section borders a meanderable body of water (navigable river or lake).
• The section is interrupted by a reservation, grant, or state boundary.

"Sections that are invaded by meanderable bodies of water or by approved claims at variance with the regular legal subdivisions are subdivided by protraction into as many aliquot parts as possible and then lots, as may be necessary to form a suitable basis for disposal." -- BLM, Manual of Surveying Instructions (2009), Sec. 3-106

Lots

In fractional sections, the irregular portions that do not fit into standard aliquot part descriptions are designated as lots and numbered sequentially within the section. Each lot has a computed area based on the dimensions shown on the plat.

For sections along the north boundary of a township, lots are typically numbered beginning in the northeast corner and proceeding west. For sections along the west boundary, lots are numbered beginning in the northwest corner and proceeding south. For sections along meandered water, lots are numbered in sequence along the water boundary.

Rules for Subdividing a Section#

The Fundamental Rule

The subdivision of a section is governed by the principle that lines are run from established corners to determine the position of the center of the section and the subdivision corners. The original survey established the section corners and the quarter-section corners on the section boundaries. The interior subdivision -- the center of the section and the sixteenth-section corners -- must be determined by connecting these established points.

Locating the Center of Section

The center of section is found at the intersection of two lines:

1. A line connecting the quarter-section corners on the east and west boundaries of the section (the "east-west centerline").
2. A line connecting the quarter-section corners on the north and south boundaries of the section (the "north-south centerline").

In a perfectly surveyed section, these two lines would cross at a single point exactly in the geometric center. In practice, because the section may not be perfectly rectangular, the point is determined by running straight lines between the established quarter-section corners.

Subdividing a Standard Interior Section

For a standard interior section (not on the north or west boundary of the township), the subdivision follows these steps:

1. Connect the quarter-section corner on the south boundary to the quarter-section corner on the north boundary with a straight line. The midpoint of this line is the center of section in the north-south direction.
2. Connect the quarter-section corner on the east boundary to the quarter-section corner on the west boundary with a straight line. The midpoint of this line is the center of section in the east-west direction.
3. The center of section is at the intersection of these two lines.
4. Sixteenth-section corners are placed at the midpoints of each half of the section boundary lines and at the midpoints of the centerlines.

Subdividing Sections on the North and West Boundaries

Sections along the north and west boundaries of a township are subdivided differently because the excess or deficiency in measurement falls in these sections. The rule is:

• On the north boundary (sections 1--6): the excess or deficiency falls in the north half of the section. Lots are formed in the north half, while the south half contains standard aliquot parts.
• On the west boundary (sections 6, 7, 18, 19, 30, 31): the excess or deficiency falls in the west half of the section. Lots are formed in the west half, while the east half contains standard aliquot parts.

For Section 6 (northwest corner), both the north and west halves are irregular, and the entire section may be lotted.

Double Proportionate Measurement for Interior Corners

When a section corner within the interior of a township is lost (cannot be recovered from any direct or collateral evidence), it is restored by double proportionate measurement -- a method that uses the four nearest identified corners (two on the meridional line and two on the latitudinal line) to proportionally determine the position of the lost corner.

"The term 'double proportionate measurement' is applied to a new measurement made between four known corners, two each on intersecting meridional and latitudinal lines, for the purpose of relating the cardinal equivalents intersection to both." -- BLM, Manual of Surveying Instructions (2009), Sec. 7-8

The method works by:

1. Determining the latitude (north-south position) proportionally between the two controlling corners on the meridional line.
2. Determining the departure (east-west position) proportionally between the two controlling corners on the latitudinal line.
3. Placing the restored corner at the intersection of these two proportioned positions.

Protraction vs. Survey#

Protracted Subdivisions

Not all section subdivisions were surveyed on the ground. When lines are protracted, they are drawn on the plat based on mathematical computation from the surveyed boundaries, without a surveyor physically running the line and setting monuments on the ground.

The most common protracted features are:

• Quarter-quarter section lines (the lines that divide quarter sections into four 40-acre parcels).
• Sixteenth-section corners on interior section lines.
• Lot lines in fractional sections along water boundaries.

Protracted lines have the same legal standing as surveyed lines for purposes of land description and conveyance. However, they are not monumented on the ground, and when a surveyor needs to establish them physically, the surveyor must follow the rules for subdivision of sections.

Surveyed Subdivisions

When a subdivision line is actually run on the ground and corners are physically set, the survey governs. The surveyed corners are established monuments and take precedence over protracted positions. This distinction matters in practice: if a quarter-quarter section corner was protracted on the plat but a local surveyor later physically established it by a proper survey, the monument controls over the protracted position (assuming the local survey was properly executed).

Area Computation#

Standard Aliquot Part Areas

For a standard 640-acre section, the areas of aliquot parts follow a simple geometric division:

Area of an Irregular Parcel

For a rectangular parcel with surveyed dimensions, the area in acres is:

$A = \frac{w \times h}{43{,}560}$

where $w$ and $h$ are in feet, or equivalently:

$A = \frac{w_{\text{ch}} \times h_{\text{ch}}}{10}$

where dimensions are in chains (1 chain = 66 feet, 1 acre = 10 square chains).

Excess and Deficiency

The original survey returns the area of each section and lot. By statute, these returned areas are the legal areas:

"Each section or subdivision of section, the contents whereof have been returned by the Secretary of the Interior or such agency as he may designate, shall be held and considered as containing the exact quantity expressed in such return." -- Act of February 11, 1805 (2 Stat. 313; 43 U.S.C. 752), quoted in BLM, Manual of Surveying Instructions (2009), Sec. 6-1

This means that if the original survey returned Section 14 as containing 640.32 acres, that is the legal area -- even if a modern resurvey measures a slightly different figure.

Key Takeaways#

• A standard township contains 36 sections numbered in a serpentine pattern from Section 1 (northeast) to Section 36 (southeast).
• A standard section is 640 acres (80 chains per side). It is subdivided into quarter sections (160 acres) and quarter-quarter sections (40 acres) by connecting established corners.
• Excess or deficiency from convergence and measurement falls in the north and west tiers of sections. Sections along these boundaries are fractional and contain numbered lots.
• The center of section is at the intersection of lines connecting opposite quarter-section corners. It is not necessarily the geometric center of the section boundary.
• Double proportionate measurement is used to restore lost interior section corners using four controlling corners.
• Protracted subdivisions (drawn on the plat, not surveyed on the ground) have legal standing but are not monumented. When established on the ground, the rules for section subdivision must be followed.
• The returned area of each section and lot is the legal area by statute, regardless of what a modern measurement may show.

References#

1. U.S. Department of the Interior, Bureau of Land Management. Manual of Surveying Instructions (2009). Chapter III: The System of Rectangular Surveys, Secs. 3-54 through 3-106. Chapter VII: Restoration of Lost Corners, Secs. 7-1 through 7-57.
2. Act of February 11, 1805 (2 Stat. 313; 43 U.S.C. 752).
3. U.S. Department of the Interior, Bureau of Land Management. Restoration of Lost or Obliterated Corners and Subdivision of Sections. Manual Supplement.
4. Robillard, W.G., Wilson, D.A., & Brown, C.M. Brown's Boundary Control and Legal Principles (7th Ed.). John Wiley & Sons, 2014. Chapter 18.
5. Skelton, R.H. "Subdivision of Sections and Restoration of Lost Corners." Surveying and Land Information Science, Vol. 64, No. 4, 2004.