Land Division: Townships, Sections, and Descriptions

Land Division: Townships, Sections, and Descriptions
I. Introduction
This chapter delves into the intricacies of land division using the Rectangular Survey System (also known as the Public Land Survey System or PLSS). This system provides a structured method for dividing and describing land, particularly in the United States. Understanding this system is crucial for surveyors, appraisers, and anyone involved in real estate. We will examine the fundamental components of the system: townships, sections, and how they are used to create legal land descriptions.
II. The Rectangular Survey System: A Geometrical Framework
A. Fundamental Principles:
The Rectangular Survey System relies on a grid-based approach using a coordinate system that uses a principal meridian and a base line as the origin. The earth’s curvature introduces complexities that require adjustments to maintain accuracy.
1. Principal Meridian: An established north-south line used as a reference for surveys in a defined area. Each meridian has a unique name (e.g., San Bernardino Meridian).
2. Base Line: An established east-west line that intersects with the principal meridian, serving as the latitudinal reference.
3. Initial Point: The precise point where the principal meridian and base line intersect. This point has defined geodetic coordinates.
B. Tiers and Ranges: Defining the Grid
The grid is formed by lines running parallel to the principal meridian and the base line.
1. Tier Lines: East-west lines running parallel to the base line at six-mile intervals. These lines define tiers or township rows.
2. Range Lines: North-south lines running parallel to the principal meridian at six-mile intervals. These lines define ranges or township columns.
C. Townships: The Primary Unit
The intersection of a tier and a range creates a square of land called a township.
1. Dimensions: A standard township is nominally six miles by six miles, containing 36 square miles.
2. Area: The area of a township is calculated as:
Area = (6 miles) * (6 miles) = 36 square miles
Since 1 square mile = 640 acres, a township contains:
Area = 36 square miles * 640 acres/square mile = 23,040 acres
3. Designation: Townships are identified by their location relative to the principal meridian and base line. For example, “Township 1 North, Range 3 East” (T1N, R3E) refers to the township located in the first tier north of the base line and the third range east of the principal meridian.
4. Example: Calculate the area of T2S, R4W. The answer is 23,040 acres.
III. Sections: Dividing the Township
A. Section Lines:
Each township is further divided into 36 sections by lines spaced one mile apart, running north-south and east-west.
B. Section Numbering:
Sections are numbered sequentially from 1 to 36, starting in the northeast corner of the township and proceeding west to east, alternating direction in each row. This results in a serpentine numbering pattern.
C. Section Dimensions and Area:
Each section is nominally one mile by one mile, containing 640 acres. The area calculation is:
Area = (1 mile) * (1 mile) = 1 square mile
Area = 1 square mile * 640 acres/square mile = 640 acres
D. Quarter Sections and Finer Divisions:
Sections can be subdivided into smaller units, such as quarter sections (160 acres), quarter-quarter sections (40 acres), and so on. These divisions are described by their location within the larger section (e.g., “Northwest quarter of the Northeast quarter”).
E. Describing Partial Sections:
Descriptions of partial sections begin with the smallest division and progress to the largest. For instance, “Southwest quarter of the Northeast quarter (SW 1/4 of NE 1/4)” describes a 40-acre parcel.
IV. Accounting for Earth’s Curvature and Irregularities
A. Convergence of Meridians:
Due to the Earth’s curvature, meridians converge as they approach the poles. This means range lines that are intended to be parallel are not truly parallel, causing distortions in the rectangular grid.
B. Correction Lines and Guide Meridians:
To compensate for convergence, adjustments are made periodically.
1. Correction Lines (Standard Parallels): Township lines at intervals of 24 miles north and south of the base line where adjustments are made to range line spacing.
2. Guide Meridians: Range lines at intervals of 24 miles east and west of the principal meridian where adjustments are made to township line spacing.
C. Impact on Section Dimensions:
Convergence results in sections along the north and west boundaries of a township having irregular dimensions.
D. Government Lots:
Irregular parcels along bodies of water or due to convergence are designated as government lots and assigned a unique lot number. These lots do not conform to the standard section or quarter-section dimensions.
V. Rectangular Survey System Descriptions: Constructing Legal Descriptions
A. Standard Procedure:
Land descriptions using the Rectangular Survey System follow a specific format. They begin with the smallest division and progressively list larger divisions until the township, range, and principal meridian are specified.
B. Order of Elements:
A typical description includes the following elements, in order:
1. Subdivision of Section (e.g., NW 1/4 of the SW 1/4)
2. Section Number (e.g., Section 33)
3. Township Number and Direction (e.g., Township 6 South)
4. Range Number and Direction (e.g., Range 13 West)
5. Principal Meridian (e.g., San Bernardino Base and Meridian)
C. Example:
“The Northwest quarter of the Southwest quarter of Section 33, Township 6 South, Range 13 West, San Bernardino Base and Meridian.”
VI. Geodetic Survey System and Topographic Maps
A. Role of the U.S. Geological Survey (USGS):
The USGS maintains a geodetic survey system and publishes topographic maps, called quadrangles, which contain valuable information for land surveying and mapping.
B. Information on Quadrangles:
Quadrangles typically show:
1. Base lines and principal meridians
2. Section lines
3. Topographic features (e.g., towns, roads, water bodies)
4. Contour lines and elevations
VII. Practical Applications and Related Experiments
A. Field Exercise: Locating Sections and Townships Using Maps
1. Objective: To develop proficiency in locating specific sections and townships on a PLSS map.
2. Materials: USGS topographic maps or PLSS maps covering a specific area.
3. Procedure:
a. Select a random section designation (e.g., Section 15, T2N, R3E).
b. Using the map, locate the corresponding township (T2N, R3E).
c. Within the township, identify and locate the specified section (Section 15).
d. Repeat the exercise with multiple section and township designations to enhance familiarity.
B. Area Calculation Experiment: Comparing Theoretical and Actual Section Areas
1. Objective: To illustrate the impact of convergence on the actual area of sections.
2. Materials: A detailed PLSS map showing section dimensions, calculator, and measuring tools.
3. Procedure:
a. Select a township near a correction line and another further away.
b. Using the map, measure the dimensions of several sections in each township, particularly those along the north and west boundaries.
c. Calculate the area of each section using the measured dimensions.
d. Compare the calculated areas to the theoretical area of 640 acres.
e. Analyze the results to determine the impact of convergence on section area.
C. Developing Legal Descriptions from Field Data:
1. Objective: To practice constructing legal descriptions based on field observations.
2. Scenario: You are tasked with describing a specific parcel within a section. You have determined it to be the SE 1/4 of the NW 1/4 of the SW 1/4 of Section 9, T3N, R2W, Principal Meridian.
3. Task: Write the full legal description for the parcel using the appropriate terminology and format as outlined in the chapter.
4. Solution: The Southeast quarter of the Northwest quarter of the Southwest quarter of Section 9, Township 3 North, Range 2 West, Principal Meridian.
VIII. Mathematical Formulas and Equations
A. Area Calculations
1. Rectangle: Area = Length * Width (A = L * W)
2. Square: Area = Side * Side (A = S^2)
3. Township Area: Area = 6 miles * 6 miles = 36 sq miles = 23,040 acres
4. Section Area: Area = 1 mile * 1 mile = 1 sq mile = 640 acres
IX. Conclusion
The Rectangular Survey System provides a systematic method for dividing and describing land. While seemingly straightforward, the system incorporates complexities due to the Earth’s curvature and requires adjustments. A thorough understanding of townships, sections, legal descriptions, and the underlying principles is essential for accurate land surveying and property❓ management.
Chapter Summary
Land Division: Townships, Sections, and Descriptions - Scientific Summary
This chapter details the Rectangular Survey System (also known as the Public Land Survey System or PLSS), a standardized method for dividing and describing land, particularly in the United States. The system’s foundational elements are principal meridians (north-south lines) and base lines (east-west lines). Tier lines, parallel to the base line, create east-west strips called tiers, while range lines, parallel to the principal meridian, delineate north-south strips called ranges.
The intersection of a tier and a range defines a township, a square of land nominally six miles by six miles, containing 36 square miles. Townships are uniquely identified by their location relative to the principal meridian and base line (e.g., Township 1 North, Range 3 East). Each township is further subdivided into 36 sections, each approximately one mile square and containing 640 acres. Sections are numbered in a serpentine pattern, commencing in the northeast corner. Sections can be further divided into partial sections (e.g. quarter sections, quarter-quarter sections) for more precise land descriptions. Descriptions of partial sections list the divisions from smallest to largest (e.g., Southwest quarter of the Northeast quarter).
Due to the Earth’s curvature, range lines converge towards the poles. To compensate, adjustments are made every 24 miles north and south of the base line at Correction Lines (Standard Parallels). Guide Meridians are established every 24 miles east and west of the Principal Meridian. These adjustments lead to irregularities, primarily along the north and west boundaries of townships, resulting in irregular quarter sections. Parcels that don’t conform to standard section or quarter-section divisions, often due to natural features like bodies of water, are designated as Government Lots.
Rectangular survey descriptions are constructed by listing the smallest division to the largest, culminating in the township, range, and reference to the controlling Principal Meridian and Base Line.
The chapter also briefly references the geodetic survey system❓ maintained by the U.S. Geological Survey, which produces topographic maps (quadrangles) that include PLSS information alongside topographic features. Additionally, the Lot, Block, and Tract system, is introduced, which is used for the legal description of smaller parcels of land within subdivisions by reference to an official map.
The scientific implications of the Rectangular Survey System are its provision of a systematic and spatially referenced framework for land ownership, management, and resource allocation. Its inherent adjustments for the Earth’s curvature acknowledge geodetic principles. While simplifying land division, the system’s irregularities necessitate careful surveying and legal interpretation.