Township & Range

Overview#

The PLSS imposes a rectangular grid on the landscape, starting from an initial point where a principal meridian and baseline intersect. This grid divides the land into townships -- nominally 6 miles square -- identified by their position north or south of the baseline (township number) and east or west of the principal meridian (range number). Understanding the grid system is fundamental to reading any PLSS land description and to performing any survey in a public domain state.

The system accounts for the geometric reality that meridians converge toward the poles by incorporating correction lines at regular intervals. Without these corrections, the accumulated convergence would distort townships far from the initial point into trapezoidal shapes too narrow to contain full-sized sections.

"This 'rectangular system of survey' typically describes townships of 36 square miles comprised of sections of 1 square mile (640 acres, more or less), each subdivided into quarter sections (160 acres) and quarter-quarter sections (40 acres)." -- BLM, Manual of Surveying Instructions (2009), Sec. 1-1

The Grid Framework#

Initial Point, Principal Meridian, and Baseline

Every PLSS survey network begins at an initial point -- a precisely determined location from which the entire grid radiates. From the initial point:

• The principal meridian extends north and south along a true meridian of longitude.
• The baseline extends east and west along a true parallel of latitude.

These two lines divide the survey area into four quadrants. All townships are referenced to this intersection: north or south of the baseline, east or west of the principal meridian.

"The base line is extended east and west from the initial point on a true parallel of latitude. Standard quarter-section and section corners are established alternately at intervals of 40 chains and standard township corners at intervals of 480 chains." -- BLM, Manual of Surveying Instructions (2009), Sec. 3-10

The principal meridian is a true north-south line. The baseline is a true east-west line (a parallel of latitude). Corners are established along both at regular intervals: quarter-section corners every 40 chains (half mile) and section corners every 80 chains (one mile), with township corners every 480 chains (6 miles).

Standard Parallels (Correction Lines)

Because meridians of longitude converge toward the poles, a rectangular grid referenced to meridians will produce townships that narrow as you move north (in the Northern Hemisphere). To compensate for this convergence, the PLSS uses standard parallels -- true east-west lines run at regular intervals north and south of the baseline.

Under the modern system, standard parallels are established every 24 miles (every 4 townships) from the baseline. At each standard parallel, new measurements begin fresh, and the accumulated convergence error is absorbed. The townships immediately south of a standard parallel receive the excess or deficiency caused by convergence; townships immediately north begin with fresh, full-width ranges.

Standard parallels are sometimes called correction lines in older references, reflecting their function of correcting the accumulated convergence of meridians.

Guide Meridians

Guide meridians are true north-south lines run at intervals of 24 miles (every 4 ranges) east and west of the principal meridian. They extend from one standard parallel to the next and serve to limit the accumulation of errors in the east-west direction. At each standard parallel, guide meridians close and new guide meridians are initiated.

Together, the standard parallels and guide meridians create a network of 24-mile-square blocks (called "tracts" in older manuals), each containing 16 townships. Within each block, the township exteriors are surveyed in a systematic order.

Township Numbering#

Township and Range Designation

Each township is identified by two numbers:

• Township (T) -- the row number, counting north or south from the baseline.
• Range (R) -- the column number, counting east or west from the principal meridian.

The notation follows a standard format:

A complete township designation combines both: T3N, R4E means the township in the third row north of the baseline and the fourth column east of the principal meridian. The principal meridian must also be specified when the designation could be ambiguous (e.g., "T3N, R4E, San Bernardino Meridian").

Township Dimensions

A standard township is nominally 6 miles on each side, containing 36 square miles or 23,040 acres. In practice, no township is exactly 6 miles square because:

1. Convergence of meridians causes the north boundary to be shorter than the south boundary.
2. Measurement errors in the original survey may have produced lines longer or shorter than intended.
3. Topographic obstacles (rivers, mountains, reservation boundaries) may have prevented completion of the full grid.

The excess or deficiency in measurement is placed in specific locations by design. On meridional (north-south) lines, the excess or deficiency falls in the northernmost half-mile. On latitudinal (east-west) lines, it falls in the westernmost half-mile.

"Corners are established from east to west along the latitudinal curve connecting the 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 west half mile, and double sets of corners are avoided where unnecessary." -- BLM, Manual of Surveying Instructions (2009), Sec. 3-21

The Order of Survey#

The PLSS is surveyed in a specific order that reflects the precedence of different lines. This order matters for retracement because it determines which corners control which lines.

Hierarchy of Survey Lines

Surveying Township Exteriors

Township exteriors are surveyed by running lines in a specific sequence. The south and east boundaries of a township are established first (as parts of the adjacent township's subdivision or as parts of the standard parallel/guide meridian system). The north and west boundaries are then run as the survey proceeds.

The general rule for establishing corners on township boundaries is:

• On meridional lines (range lines running north-south): corners are established from south to north. The excess or deficiency in measurement is placed in the northernmost half-mile.
• On latitudinal lines (township lines running east-west): corners are established from east to west. The excess or deficiency is placed in the westernmost half-mile.

"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, and double sets of corners are avoided." -- BLM, Manual of Surveying Instructions (2009), Sec. 3-19

Closing Corners

When a line run during a later survey meets a previously established line, a closing corner is set at the point of intersection. The closing corner falls on the previously established line, and the distance from the closing corner to the nearest corner on that line (the "closing distance") represents the accumulated error.

Closing corners are important because they establish the legal terminus of the closing line. The closing distance -- the gap between the closing corner and the nearest standard corner -- is the measure of accuracy of the survey.

Convergence of Meridians#

The convergence of meridians is the fundamental geometric challenge of the PLSS. At the equator, one degree of longitude spans approximately 69.17 miles. At latitude 45 degrees North, one degree of longitude spans only about 49.0 miles -- a reduction of nearly 30 percent.

Calculating Convergence

The convergence between two meridians separated by a distance $d$ along a parallel at latitude $\phi$ can be approximated for PLSS purposes. Over a 6-mile township width, the convergence of the east and west range lines causes the north boundary to be shorter than the south boundary. The amount of convergence per mile of northward travel at latitude $\phi$ is approximately:

$\delta \approx \frac{d \cdot \tan(\phi)}{R}$

where $R$ is the radius of the Earth at that latitude and $d$ is the east-west distance. For practical PLSS work, the convergence across a 6-mile township at 45 degrees latitude is approximately 52 links (about 34 feet) per 6 miles of northing.

Effect on Township Shape

Without correction, a township at latitude 45 degrees North would have a north boundary roughly 34 feet shorter than its south boundary after 6 miles of meridional survey. After 24 miles (4 townships), the deficiency would be roughly 136 feet. Standard parallels reset this accumulation every 24 miles, confining the geometric distortion to manageable levels.

The following table illustrates the approximate convergence of range lines per township (6 miles) at various latitudes:

These values are approximate and vary with longitude and elevation. The precise convergence for any given survey depends on the geodetic parameters of the lines involved.

The sections in the north and west tiers of each township absorb the accumulated convergence and measurement errors. These are the "fractional" sections -- sections that may contain more or less than the standard 640 acres. The interior sections are intended to be standard.

Fractional Townships#

Not every township contains 36 complete sections. Fractional townships occur where:

• The survey encounters a water boundary (navigable river, lake, or ocean).
• The survey encounters a reservation boundary (Indian reservation, military reservation, national park).
• The survey encounters a state boundary.
• The survey encounters a prior grant (Spanish, Mexican, or French land grant).
• The survey encounters a previously established survey from a different initial point.

In fractional townships, the sections that are cut short are given lot numbers in addition to their section numbers, and the areas of these lots are computed individually.

Township Plats#

Every completed township survey produces a township plat -- the official map showing the boundaries, corners, section numbers, lot numbers, acreages, and topographic features within the township. The plat is part of the official record and, together with the field notes, defines the survey.

The plat shows:

• All section boundaries and their bearings and distances
• All corners and their types (section, quarter-section, meander, closing, etc.)
• All meander lines along navigable waters
• All lotting with computed acreages
• Topographic features noted in the survey
• The total area of the township and the area of each section and lot

The plat is filed with the BLM and becomes part of the permanent record. Original plats are available through the BLM's General Land Office Records at glorecords.blm.gov.

Defective Exteriors#

In some townships, the exterior boundaries were not established according to the standard plan. This may be because:

• The survey was interrupted by topographic obstacles.
• The survey closed on a prior survey with inconsistent corners.
• The township was invaded by a reservation, grant, or water body.
• The original survey was defective in measurement or procedure.

When township exteriors are defective, the subdivision of the interior must accommodate the deficiency. The BLM Manual provides specific guidance for handling defective exteriors, including procedures for offsetting section lines from the established boundaries and for creating amended monuments where necessary.

"A township invaded by a large meanderable body of water, impassable objects, or a State, reservation, or grant boundary may lack a full linear south or east boundary. This may require controlling section lines to be established as offsets from the township exteriors." -- BLM, Manual of Surveying Instructions (2009), Sec. 3-80

The Gunter's Chain and Distance Measurement#

Understanding the PLSS requires familiarity with the Gunter's chain, the unit of measurement used in virtually all original surveys. One Gunter's chain equals 66 feet (20.12 meters). The chain is divided into 100 links, each 0.66 feet (7.92 inches).

The key conversions for PLSS work:

Prior to 1900, most PLSS lines were measured with the Gunter's link chain -- a physical chain of 100 links. This chain was difficult to keep at standard length, and inaccuracies were common on steep slopes. Modern retracement surveyors must be aware that original measurements may differ from modern electronic measurements by significant amounts, and these differences must be resolved through proportionate measurement, not by assuming the modern measurement is correct.

Practical Example: Reading a Township Designation#

Consider the description: NW 1/4 of Section 14, T2N, R5W, Willamette Meridian.

This describes:

1. Willamette Meridian -- the principal meridian (governing Oregon and Washington).
2. T2N -- the second township north of the baseline.
3. R5W -- the fifth range west of the principal meridian.
4. Section 14 -- one of the 36 sections within that township.
5. NW 1/4 -- the northwest quarter of that section (160 acres, nominally).

To find this parcel on the ground, a surveyor would locate the township using the grid, find Section 14 within it, and then subdivide the section to identify the northwest quarter.

The Importance of the Official Record#

The official record of a township survey consists of the field notes and the plat. Both are essential to retracement. The field notes provide the detailed narrative of the survey -- distances, bearings, topographic features, corner descriptions, and monument markings. The plat provides the graphic depiction. Together, they form the legal record against which all subsequent surveys are measured.

"Since the Land Ordinance of 1785, it has been the continuous policy of the United States that land shall not leave Federal ownership until it has first been surveyed, and an approved plat of survey has been filed." -- BLM, Manual of Surveying Instructions (2009), Sec. 1-1

Every surveyor working in a PLSS state should know how to obtain and read original field notes and plats. The BLM's General Land Office Records (glorecords.blm.gov) provides public access to original survey records, including field notes, plats, and land patents.

Key Takeaways#

• The PLSS grid originates from an initial point where a principal meridian and baseline intersect. Townships are numbered north/south from the baseline; ranges are numbered east/west from the principal meridian.
• A standard township is nominally 6 miles square (36 square miles, 23,040 acres) and contains 36 sections.
• Standard parallels (correction lines) are run every 24 miles to correct for the convergence of meridians. Guide meridians are run every 24 miles in the east-west direction.
• Excess or deficiency in measurement is placed in the north half-mile of meridional lines and the west half-mile of latitudinal lines. The north and west tiers of sections absorb convergence errors.
• Closing corners are set where a later survey line meets a previously established line. The closing distance measures the accumulated error.
• Fractional townships occur where the survey encounters water, reservations, state boundaries, or prior grants.
• The township plat is the official map of the survey, filed with the BLM and forming part of the permanent public record.
• The order of survey (standard parallels before guide meridians before township exteriors before subdivision lines) establishes the hierarchy of control for retracement.

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. 3-1 through 3-50.
2. U.S. Department of the Interior, Bureau of Land Management. Restoration of Lost or Obliterated Corners and Subdivision of Sections. Manual Supplement.
3. White, C. Albert. A History of the Rectangular Survey System. U.S. Department of the Interior, Bureau of Land Management, 1983.
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: Sectionalized Land Surveys.