Chapter: What type of legal description uses a point of beginning and distances and directions to describe property boundaries? (EN)

Chapter: Metes and Bounds Legal Description

Defining Metes and Bounds

The type of legal description that employs a point of beginning (POB) and uses distances and directions to delineate property boundaries is called a Metes and Bounds description. This method relies on measurable dimensions (metes) and boundary directions (bounds) to create a closed perimeter encompassing the property. It’s a system rooted in surveying principles and geometric concepts.

Principles of Surveying and Geometry

• Planar Surveying: Metes and bounds descriptions are inherently linked to planar surveying, which assumes the Earth is flat for relatively small areas. This allows for the use of Euclidean geometry in calculating areas and determining boundary locations. While modern surveying increasingly employs geodetic surveying (accounting for Earth’s curvature), metes and bounds descriptions are based on the planar approximation.

• Angular Measurement: Directions are expressed as angles relative to a reference meridian, typically North or South. The angular unit is the degree (°), further divided into minutes (‘) and seconds (“). Examples:

  • N 45° E means 45 degrees East of North.
  • S 10° 30’ 15” W means 10 degrees, 30 minutes, and 15 seconds West of South.

• Linear Measurement: Distances are measured in linear units, most commonly feet or meters. These measurements are the “metes” of the description.

• Closure: A crucial aspect of a metes and bounds description is that it must “close.” This means that if one were to physically walk the boundaries as described, starting from the POB, they would end up back at the POB. Closure errors are unavoidable in practice due to measurement imperfections, but are typically minimized and adjusted mathematically.

Components of a Metes and Bounds Description

1. Point of Beginning (POB): A clearly identifiable, permanent landmark or monument. This could be a natural feature (e.g., a large rock, a river confluence), an artificial marker (e.g., a concrete monument, an iron pipe), or a point referenced to a coordinate system. The POB is the starting and ending point of the description.

2. Bearing and Distance Calls: A series of statements specifying the direction (bearing) and length (distance) of each boundary line. Each “call” describes a segment of the property’s perimeter. Example: “Thence North 45 degrees East, 100 feet.”

3. Adjoiners: Adjacent property owners or features along each boundary line. Identifying adjoiners helps to further clarify the location of the property lines. Example: “Thence North 45 degrees East, 100 feet along the Western boundary of Lot 2, Block A, Plat Book 10, Page 20.”

4. Natural Monuments and Artificial Monuments: Physical features used to define boundaries. Natural monuments are naturally occurring (rivers, trees), while artificial monuments are man-made (roads, fences). Monuments generally take precedence over bearings and distances if there is a discrepancy.

5. Closure Call: The final call of the description, which returns to the POB, ideally confirming the closure of the described area.

Mathematical Principles and Error Adjustment

• Coordinate Geometry: The conversion of bearings and distances into coordinate pairs (x, y) allows for precise calculations of area and perimeter. If the POB is assigned coordinates (0,0), subsequent points can be calculated using trigonometric functions:

  • x<sub>i+1</sub> = x<sub>i</sub> + d * sin(θ)
  • y<sub>i+1</sub> = y<sub>i</sub> + d * cos(θ)

  Where:
  * x<sub>i</sub>, y<sub>i</sub> are the coordinates of point i
  * d is the distance to point i+1
  * θ is the bearing angle to point i+1 (converted to radians)

• Area Calculation (Shoelace Formula): Once the coordinates of all boundary points are known, the area enclosed by the metes and bounds can be calculated using the shoelace formula:

  • Area = 0.5 * | Σ (x<sub>i</sub> * y<sub>i+1</sub> - x<sub>i+1</sub> * y<sub>i</sub>) | for i = 1 to n, where n is the number of points, and point n+1 is point 1 (the POB).

• Compass Rule (Bowditch Rule): A method for adjusting traverse closure errors. It distributes the error proportionally to the length of each course. The correction to the latitude (y-coordinate) or departure (x-coordinate) of a course is calculated as:

  • Correction<sub>latitude</sub> = -(Total Error<sub>latitude</sub> * Course Length / Total Traverse Length)
  • Correction<sub>departure</sub> = -(Total Error<sub>departure</sub> * Course Length / Total Traverse Length)

• Least Squares Adjustment: A more sophisticated method for adjusting traverse errors that considers the precision of the measurements. It minimizes the sum of the squares of the residuals (differences between observed and adjusted values).

Practical Applications and Related Experiments

1. Boundary Survey Exercise: Students can perform a simplified boundary survey using a tape measure and compass (or transit). They would measure the bearings and distances of a small, defined area, create a metes and bounds description, and then calculate the area using the shoelace formula. They would also experience the effects of measurement errors and attempt to adjust them using the compass rule.

2. Coordinate Geometry Simulation: A computer simulation where students input bearings and distances and observe the resulting polygon. They can experiment with different closure errors and observe how the area calculation is affected.

3. Historical Survey Reconstruction: Analyze historical metes and bounds descriptions and attempt to reconstruct the original boundaries using modern surveying tools and GIS software. This exercise highlights the challenges of interpreting older descriptions and the changes in land use over time.

Important Discoveries and Breakthroughs

• Development of the Transit and Theodolite: These instruments revolutionized surveying by allowing for precise angle measurements, leading to more accurate metes and bounds descriptions.

• Advancements in Distance Measurement: From chains and tapes to Electronic Distance Measurement (EDM) and Global Positioning System (GPS), advancements in distance measurement have significantly improved the accuracy of boundary surveys.

• Computer-Aided Design (CAD) and Geographic Information Systems (GIS): These technologies have streamlined the creation, analysis, and storage of metes and bounds descriptions. GIS allows for the integration of metes and bounds data with other spatial information, enabling powerful spatial analysis and visualization capabilities.

• Standardization of Surveying Practices: Professional surveying organizations and government agencies have developed standards for surveying practices, including error tolerance and documentation, which contribute to the reliability and consistency of metes and bounds descriptions.