If a quarter section is further divided into quarters, what is the area of one of these smaller portions?

Rectangular Coordinate System: Sections, Squares, and Parts

The Rectangular Survey System, also known as the Public Land Survey System (PLSS) in the United States, is a systematic framework for dividing and identifying land areas on a large scale. This system relies on a grid of orthogonal lines, enabling precise and easy location identification and facilitating property transfer and registration. Understanding this system is crucial for engineers, surveyors, real estate appraisers, legal researchers, and anyone dealing with land and real estate.

The scientific significance of the Rectangular Survey System lies in providing a standard and organized reference framework for identifying geographic locations. This system contributes to: standardization of measurement, facilitating legal documentation, supporting urban planning, managing natural resources, enabling geospacial research, and facilitating GIS applications.

Rectangular Survey System: A system for dividing land based on a grid of perpendicular lines, creating squares and rectangles of specific sizes. It is used in the United States and Canada to define land ownership.

1. Basics of the Rectangular Survey System

• Base Line: A horizontal (east-west) imaginary line used as a reference for measuring distances north and south.
• Principal Meridian: A vertical (north-south) imaginary line used as a reference for measuring distances east and west.

The base line and principal meridian intersect at a reference point. "San Bernardino Base and Meridian" or "S.B.B. & M." is an example.

• Tier Lines: Imaginary lines parallel to the base line at regular intervals (usually 6 miles), dividing land into horizontal strips called "tiers."
• Range Lines: Imaginary lines parallel to the principal meridian at regular intervals (usually 6 miles), dividing land into vertical strips called "ranges."

2. Townships

A township is a square with sides of 6 miles, an area of 36 square miles, formed by the intersection of a tier and a range.

• Identification: Townships are identified based on their location relative to the base line and principal meridian, using the tier and range numbers.
  • Example: "Township 1 North, Range 3 East" or "T1N, R3E" is located in the first tier north of the base line and the third range east of the principal meridian.
• Calculations:
  • Area of a township = 6 miles x 6 miles = 36 square miles.
  • Area of a township = 36 square miles x 640 acres/square mile = 23,040 acres.

3. Sections

Each township is divided into 36 equal sections, each a square with sides of 1 mile. Each section has an area of 1 square mile or 640 acres.

• Numbering: Sections within a township are numbered from 1 to 36, starting in the northeast corner (Section 1) and continuing in a snake-like fashion to Section 36 in the southeast corner.

4. Partial Sections

Sections can be divided into smaller parts, such as quarters, and these quarters can be further divided into quarters or halves.

• Naming: Partial sections are named by specifying the sequence of divisions, from smallest to largest.
  • Example: "Southwest quarter of the Northeast quarter (SW 1/4 of NE 1/4)."
• Area Calculation:
  • Area of a quarter = 640 acres / 4 = 160 acres.
  • Area of a quarter of a quarter = 160 acres / 4 = 40 acres.

5. Adjustments & Government Lots

• Adjustments: Due to the Earth's curvature, range lines converge towards the poles. Adjustments are made every 24 miles (four townships) north and south of the base line. The township lines where adjustments are made are called "Correction Lines" or "Standard Parallels." Every fourth range line east and west of the principal meridian is called a "Guide Meridian."
• Government Lots: Irregularities occur on the northern and western boundaries of a township due to convergence or other factors. Quarter-sections on these boundaries are often irregular in size and shape. Irregular parcels can also result when land borders a body of water. An irregular parcel that is not a complete section or quarter-section is known as a "Government Lot," and it is identified by a government lot number.

6. Land Description

Land descriptions using the Rectangular Survey System follow a standard format, starting with the smallest part of the land and listing each larger part in sequence. The description must refer to the base line and principal meridian.

• Example: "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."
• Descriptions usually include the county and state.

7. Geodetic Survey System

The U.S. Geological Survey administers a Geodetic Survey System and publishes detailed topographic maps called "Quadrangles" showing base lines, principal meridians, section lines, and topographic features.

8. Lot, Block, and Tract System

Suitable for describing small parcels of land, such as building lots. Land is described by referring to an official map showing the boundaries of the parcel. This is also known as a subdivision map.

Each parcel in a subdivision map is identified by a number or letter. Once the map is recorded, a parcel can be described by referring to the lot number and the map.

• Example: "LOT 22 in BLOCK 21 of Short Line Beach Subdivision No. 2 as per map recorded in Book 4, Page 42 of Maps in the Office of the County Recorder of Los Angeles."

Reference Table:

• 1 acre = 43,560 square feet; 4,840 square yards.
• 1 square acre = 208.71 feet on each side (generally rounded to 209 feet).
• 1 mile = 5,280 feet.
• 1 square mile contains 640 acres.
• 1 section = 1 square mile, contains 640 acres.
• 1 township (standard) = six miles square (36 square miles).
• 1 commercial acre = 1 acre minus any required public dedications.
• 1 rod = 16.5 feet (5.5 yards). There are four rods, or 66 feet, in one chain, and 320 rods in one mile.

The rectangular survey system is a land division system used to accurately locate and describe properties, based on a network of perpendicular reference lines.

1. Principal Meridian and Base Line: The system uses two main reference lines: the Principal Meridian (north-south) and the Base Line (east-west), which are perpendicular. These lines are used to locate land within the system, relying on the "San Bernardino Base Line and Meridian."

2. Townships: Land is divided into Townships, which are 6 miles x 6 miles (36 square miles). Townships are formed by the intersection of Tier Lines (east-west, parallel to the Base Line) and Range Lines (north-south, parallel to the Principal Meridian). Each Township is located by its distance north or south of the Base Line and east or west of the Principal Meridian (e.g., T1N, R3E).

3. Sections: Each Township is divided into 36 Sections, each one square mile (640 acres). Sections are numbered 1 to 36, starting in the northeast corner and numbering in a serpentine fashion, ending with Section 36 in the southeast corner.

4. Partial Sections: Sections can be divided into smaller parts. Sections are divided into quarters, and quarters into quarters or halves. Parts are described from smallest to largest (e.g., SW 1/4 of NE 1/4).

5. Adjustments and Government Lots: Range Lines converge toward the poles due to the Earth's curvature. Adjustments are made to Range Lines periodically (every 24 miles) to compensate. County lines where adjustments occur are called correction lines. Convergence or water bodies can create irregular land parcels. Irregular parcels that are not a complete section or quarter section are "Government Lots."

6. Rectangular Survey System Descriptions: Land descriptions follow a standard format from smallest unit (part) to largest (Township). Descriptions must reference the Base Line and Principal Meridian. (e.g., NW 1/4 of the SW 1/4 of Sec. 33, T6S, R13W, S.B.B. & M.).

7. Geodetic Survey System: The U.S. Geological Survey manages a geodetic survey system and publishes detailed topographic maps called "Quadrangles." These maps include Base Lines, Principal Meridians, section lines, and major topographic features.