1.5 Historical Surveying Units, Instruments, and Practices

Historical Surveying Units, Instruments, and Practices

1. Historical Units of Length and Area

Understanding historical surveying units is essential for land boundary retracement. Survey technicians regularly encounter original deeds, colonial patents, and PLSS field notes recorded in historical linear and areal units created centuries ago.

Gunter's Chain

Designed by English mathematician Edmund Gunter in 1620, Gunter's chain became the standard measuring device for land boundary and PLSS surveys across North America.

• Chain Length: Exactly 66 feet long.
• Links: Divided into 100 metallic links connected by small oval rings.
• Link Length: Each link equals $66\text{ ft} \div 100 = \mathbf{0.66\text{ feet}} = \mathbf{7.92\text{ inches}}$.

Conversions Based on Gunter's Chain

1. Chains to Feet: $\text{Distance in feet} = \text{Chains} \times 66$
2. Chains to Miles: $80\text{ chains} = 1\text{ statute mile} = 5,280\text{ feet}$.
3. Square Chains to Acres: $10\text{ square chains} = 1\text{ acre} = 43,560\text{ square feet}$.
   • (Calculation: $1\text{ chain} \times 10\text{ chains} = 66\text{ ft} \times 660\text{ ft} = 43,560\text{ sq ft}$).

Rod, Perch, and Pole

The terms rod, perch, and pole are synonymous historical terms for a linear unit equal to 16.5 feet.

• $1\text{ rod} = 16.5\text{ feet} = 25\text{ links}$.
• $4\text{ rods} = 1\text{ chain} = 66\text{ feet}$.
• $320\text{ rods} = 1\text{ mile} = 5,280\text{ feet}$.
• $160\text{ square rods} = 1\text{ acre} = 43,560\text{ sq ft}$.

Spanish and Mexican Units: The Vara

In Southwestern states (such as Texas, New Mexico, Arizona, and California), historical land grants were surveyed in varas. The length of a vara varies by state statute:

• Texas Vara: Standardized by statute as $1\text{ vara} = 33.333\text{ inches} = 2.7778\text{ feet}$ (or 36 varas = 100 feet).
• California Vara: Historically recognized as approximately $33.372\text{ inches}$.

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2. Historical Surveying Instruments

Gunter's Chain Characteristics and Errors

Gunter's chains were made of heavy iron or steel wire. As a chain was dragged across rough ground during field operations, it was subject to two distinct physical systematic errors:

1. Chain Stretch (Wear): Friction at the contact surfaces of the 100 links and connecting rings caused micro-wear. Over time, accumulated joint wear caused the chain to physically stretch longer than 66 feet. Effect: A stretched chain measures ground distances long, causing reported field measurements to be shorter than actual ground distance.
2. Bent Links: Individual wire links could become bent by pulling against rocks or brush, making the chain physically shorter than 66 feet. Effect: Reports field measurements longer than actual ground distance.

Surveyor's Compass (Gunter's Compass)

Mounted on a single wooden staff (Jacob's staff) or tripod, the surveyor's compass measured magnetic bearings using a magnetized needle suspended over a 360-degree compass card. It featured open sighting vanes for targeting line-of-sight rods.

• Magnetic Declination: The angular difference between true astronomical north and magnetic north. Surveyors had to account for secular variation in declination over time.
• Local Attraction: Magnetic needle distortion caused by nearby iron ore deposits, steel fences, or iron mining tools.

Transit and Wye Level

• Surveyor's Transit: Known as the 'universal surveying instrument,' the transit combined a telescope with crosshairs and horizontal and vertical graduated metal limbs equipped with verniers for reading angles to minutes of arc ($1' = 1/60^\circ$).
• Wye (Y) Level: An early precision leveling instrument comprising a spirit level vial attached to a removable optical telescope resting in Y-shaped supports (wyes). Used with a target leveling rod to establish horizontal sight lines.

Plumb Bob and Gammon Reel

A pointed brass weight (plumb bob) suspended from a string was used to transfer ground points vertically up to instrument centers or raised measuring tapes. A spring-loaded gammon reel allowed quick adjustment of plumb line string length. Plumb bobs required shielding from wind deflection to maintain vertical precision.

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3. Worked Examples of Unit Conversions

Example 1: Converting Chains and Links to Feet

Convert a recorded deed distance of 12 chains 45 links into feet.

1. Total chains = $12.45\text{ chains}$.
2. Distance in feet = $12.45 \times 66\text{ ft} = \mathbf{821.70\text{ feet}}$.

Example 2: Calculating Acres from Chains

A field survey records a rectangular parcel measuring 15.00 chains by 8.00 chains. Calculate the area in acres.

1. Area in square chains = $15.00 \times 8.00 = 120.00\text{ sq chains}$.
2. Area in acres = $120.00 \div 10 = \mathbf{12.00\text{ acres}}$.