Andersons of Colonial N. Carolina

I was curious how a Colonial surveyor might calculate the survey Metes and Bounds and turn those measurements into the total acreage.

Naturally, I asked Grok:

Calculating the Area (per Grok)

To calculate the total acres, colonial surveyors would follow a process that, while less precise than modern methods, was practical for the era. Here’s a detailed breakdown:

1. Plot the Parcel:
   • The surveyor would physically measure the distances and bearings in the field using a chain and compass, marking the corners with stakes or other monuments (e.g., trees, stones). They might also sketch a rough plat (map) on paper or a plane table to visualize the shape, as seen in historical plats like George Washington’s 1750 survey for John Lindsey, 223 acres in Frederick County, Va.
2. Divide into Simpler Shapes:
   • For irregular parcels, which were common in metes and bounds surveys, the surveyor would divide the land into simpler geometric shapes, such as triangles, trapezoids, or rectangles. For example, a quadrilateral could be split into two triangles by drawing a diagonal from the POB to the opposite corner.
3. Calculate the Area of Each Shape:
   • For Rectangles or Squares: If the parcel was roughly rectangular, they could use the formula:Area (in acres)=length (in chains)×width (in chains)10\text{Area (in acres)} = \frac{\text{length (in chains)} \times \text{width (in chains)}}{10}\text{Area (in acres)} = \frac{\text{length (in chains)} \times \text{width (in chains)}}{10}This worked because 1 acre = 10 square chains, a fact noted in historical surveying practices . For example, a parcel 10 chains by 10 chains would be (10 × 10) / 10 = 10 acres.
   • For Triangles: They would use the formula for the area of a triangle:Area=12×a×b×sin⁡(C)\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)where:
     • (a) and (b) are the lengths of two sides (in chains or poles, converted as needed).
     • (C) is the included angle between those sides, measured with a compass or estimated from the bearings. It was about here my eyes began to cross…
     • sin⁡(C)\sin(C)\sin(C) could be looked up in trigonometric tables, which were available by the 1700s, thanks to works like Edmund Gunter’s surveying manuals. For example, if a=38.25a = 38.25a = 38.25 chains, b=38.25b = 38.25b = 38.25 chains, and C=20°C = 20°C = 20°, with sin⁡(20°)≈0.342\sin(20°) \approx 0.342\sin(20°) \approx 0.342, the area would be 12×38.25×38.25×0.342≈245.14\frac{1}{2} \times 38.25 \times 38.25 \times 0.342 \approx 245.14\frac{1}{2} \times 38.25 \times 38.25 \times 0.342 \approx 245.14 square chains, then divided by 10 for acres.
     • For Trapezoids: They might use the average of the two parallel sides multiplied by the height, divided by 2, again converting to acres after calculating in square chains.
4. Sum the Areas:
   • If the parcel was divided into multiple shapes (e.g., two triangles), the areas of each shape would be calculated and summed to get the total area in square chains.
5. Convert to Acres:
   • The total area in square chains would be divided by 10 to get the area in acres, leveraging the relationship 1 acre = 10 square chains.

Grok’s answer did not satisfy me because, in my heart, I knew that a simple surveyor of 1753 would challenge you to a duel or thrash you unmercifully with a cane if you confronted him with that much unfathomable mathematics all at on time. Remember, none of these good folks even saw a need for middle names.

So I Googled, as any rational person would do… and found a good book that most surveyors had not read, because, well… many if not most could not read. Junior Colleges were scarce in Colonial North Carolina.

https://archive.org/details/b30505586/mode/2up

Grok can just, well, kiss my ass for lack of a better term.