Rectangular Survey System: Townships and Sections

Rectangular Survey System: Townships and Sections

Introduction
The Rectangular Survey System (also known as the Public Land Survey System or PLSS) is a method used in the United States to survey and designate land ownership. This system provides a standardized way to divide land into regular, easily describable parcels. The core components of the system are principal meridians, base lines, townships, and sections. This chapter will delve into the scientific and mathematical principles behind townships and sections, explaining how they are created and described.

A. Principal Meridians and Base Lines
The foundation of the Rectangular Survey System lies in two perpendicular reference lines:
1. Principal Meridian: A north-south line that serves as the primary longitudinal reference for a large area. Each principal meridian has its own designated name (e.g., San Bernardino Meridian).
2. Base Line: An east-west line that intersects the principal meridian and serves as the primary latitudinal reference.
These lines are established through astronomical observations and geodetic surveying techniques, ensuring accuracy in the initial framework. The determination of true north for the principal meridian involves finding the celestial pole using instruments like theodolites or total stations. The base line is then established perpendicular to the principal meridian, often by using precise leveling techniques to ensure a consistent elevation reference.

B. Townships
Each rectangular survey grid consists of a series of lines that run parallel to the principal meridian and the base line, at intervals of six miles. The east-west lines (running parallel to the base line) are called TIER LINES. The north-south lines (parallel to the principal meridian) are referred to as RANGE LINES.
Township lines divide the land into a series of east-west strips, called TIERS. Range lines divide the land into north-south strips called RANGES. Where a tier intersects with a range, the result is a six miles by six miles square of land known as a TOWNSHIP. Thus, each township contains 36 square miles. Townships are the main divisions of land in the rectangular survey system. Each township is identified according to its distance from the principal meridian and base line.

1. Tiers: East-west lines running parallel to the base line at six-mile intervals. Tiers are numbered consecutively north and south from the base line (e.g., Tier 1 North, Tier 2 South).
2. Ranges: North-south lines running parallel to the principal meridian at six-mile intervals. Ranges are numbered consecutively east and west from the principal meridian (e.g., Range 1 East, Range 2 West).
3. Township Designation: A township is identified by its tier and range designation. The format is "Township [Tier Number] [North/South], Range [Range Number] [East/West]" (e.g., Township 1 North, Range 3 East, or T1N, R3E).

Example: The township that is located at the intersection of the first township tier north of the base line, and the third range east of the principal meridian, is called: “Township 1 North, Range 3 East”, or “T1N, R3E”.

C. Sections
Each six-mile-square township is divided into an even smaller rectangular grid, with grid lines (called section lines) spaced one mile apart. The section lines run both north-south and east-west within the township. The result is that each township contains 36 sections, each SECTION measuring one mile on a side and containing 640 acres❓❓. The sections are numbered from 1 to 36, starting with Section 1 in the northeast corner of the township and continuing across and down in snake-like fashion to Section 36 in the southeast corner.

1. Section Definition: A section is a square parcel of land, approximately one mile on each side.
2. Section Area: One section is nominally 640 acres.
3. Section Numbering: Sections are numbered in a serpentine pattern, starting in the northeast corner and proceeding west, then east in the next row, and so on. This pattern ensures that adjacent sections have significantly different numbers.

Mathematical Relationship:
    * Area of a section = 1 mile * 1 mile = 1 square mile
    * 1 square mile = 640 acres

D. Partial Sections
Sections may be broken down into even smaller rectangular blocks. This is done by first dividing the section into quarters, and then progressively dividing the quarter sections into quarters or halves. Partial sections are described by simply listing the sequence of the divisions, starting with the smallest one and ending with the largest.

1. Quarter Sections: A section can be divided into four equal parts, each approximately 160 acres, designated as Northeast (NE), Northwest (NW), Southeast (SE), and Southwest (SW) quarters.
2. Further Subdivisions: Quarter sections can be further subdivided into quarter-quarter sections (40 acres), half-quarter sections (80 acres), etc.
3. Description Convention: Partial sections are described by starting with the smallest division and working up to the section level (e.g., "Southwest quarter of the Northeast quarter").

Example: The partial section that is highlighted in Figure 4-5 would be described as “Southwest quarter of the Northeast quarter (SW 1/4 of NE 1/4).”

Mathematical Relationships:
    * Area of a quarter section = 640 acres / 4 = 160 acres
    * Area of a quarter-quarter section = 160 acres / 4 = 40 acres

E. Adjustments and Government Lot❓❓s
The range lines in the rectangular survey are supposed to run true north and south. They are also supposed to be parallel, spaced six miles apart. Due to the fact that the earth is not flat, however, lines running north and south are not parallel to each other, they tend to converge (get closer together) as they approach the poles. To account for this convergence, the range lines in the rectangular survey must be adjusted.
To maintain an approximate distance of six miles between range lines, they are adjusted at intervals of every 24 miles (every fourth township line) north and south of the base line. The township lines where the adjustments are made are referred to as CORRECTION LINES or STANDARD PARALLELS. Similarly, every fourth range line east and west of the principle meridian is referred to as a GUIDE MERIDIAN.
Irregularities due to convergence or other factors are usually accounted for along the north and west boundaries of a township. For this reason, the quarter sections that lie along these boundaries are often somewhat irregular in size and shape. Irregular parcels in a township can also result when land abuts a body of water such as a river, lake or ocean. An irregular parcel that does not constitute a full section or quarter section is known as a GOVERNMENT LOT, and is identified by a special government lot number.

1. Convergence of Meridians: Due to the Earth's curvature, north-south lines converge as they approach the poles.
2. Correction Lines (Standard Parallels): East-west lines established every 24 miles north and south of the base line to correct for the convergence of meridians.
3. Guide Meridians: North-south lines established every 24 miles east and west of the principal meridian to further manage convergence and maintain the rectangular grid.
4. Government Lots: Irregular parcels of land, typically along the north and west sides of townships or adjacent to bodies of water, which are assigned specific lot numbers. These lots compensate for the irregularities caused by convergence or physical features.

The convergence can be approximated by the following formula, though this is a simplification:

* Convergence Angle (in degrees) ≈ (Longitude Difference) * sin(Latitude)

    * Where:
        * Longitude Difference is the difference in longitude between two range lines.
        * Latitude is the latitude at which the convergence is being calculated.

Because of this, sections along the north and west boundaries of a township often deviate from the ideal 640 acres. These discrepancies are accounted for by the establishment of Government Lots.

F. Rectangular Survey System Descriptions
Land descriptions using the rectangular survey system are relatively simple. The standard procedure is to begin with the smallest division that identifies the parcel, and then list each larger division in sequence. At the end, the description must refer to the base and meridian that is the reference for the grid.

1. Order of Description: The standard order for describing a parcel of land is from smallest to largest: quarter-quarter section, quarter section, section, township, range, and principal meridian.
2. Example Description: "The Northwest quarter of the Southwest quarter of Section 33, Township 6 South, Range 13 West, San Bernardino Base and Meridian."
3. Abbreviated Form: "The NW 1/4 of the SW 1/4 of Sec. 33, T6S, R13W, S.B.B. & M."
4. Completeness: Accurate and unambiguous descriptions must include the county and state to avoid confusion.

Example: A typical rectangular survey description might read “The Northwest quarter of the Southwest quarter of Section 33, Township 6 South, Range 13 West, San Bernardino Base and Meridian,” or “The NW 1/4 of the SW 1/4 of Sec. 33, T6S, R13W, S.B.B. & M.”
(Note: descriptions usually include county and state as well to avoid confusion.)

G. Geodetic Survey System
As part of the government survey system, the U. S. Department of the Interior Geological Survey maintains a geodetic survey system and publishes detailed topographic maps. These maps, called QUADRANGLES, ordinarily contain the base lines and principal meridians, section lines, and most major topographic features, including towns, roads, bodies of water, and contour lines and elevations of land.

1. USGS Quadrangle Maps: The United States Geological Survey (USGS) creates topographic maps called quadrangles that depict the terrain, cultural features, and PLSS information.
2. Map Content: Quadrangle maps include base lines, principal meridians, section lines, contour lines, roads, water bodies, and other relevant features.

These maps are created using advanced surveying and mapping techniques, including photogrammetry, remote sensing, and GPS technology. The accuracy of these maps is crucial for land management, resource exploration, and engineering projects.

Conclusion
The Rectangular Survey System provides a structured and efficient method for dividing and describing land. Understanding the principles of principal meridians, base lines, townships, and sections is essential for anyone involved in land surveying, real estate, or land management. The system’s mathematical basis and adjustment mechanisms ensure that land descriptions are as accurate and consistent as possible, despite the challenges posed by the Earth’s curvature.