In Transcontinental Triangulation and the American Arc of the Parallel, the 39th parallel is measured across the United States.

On Pages 869 to 871 the final analysis is done.

**For an arc of parallel**

C = length of arc as directly measured

D = astronomical difference of longitude (in seconds) of its terminal stations in latitude φᵢ

**For the 39th parallel**

C = 4,182,227 meters, measured

D = 173,807.83 arc seconds = 2896.7972 arc minutes = 48.279953 degrees

The circumference is a simple ratio: c = ( 360° / D ) * C

The total circumference of 39th parallel = ( 360° / 48.279953° ) * 4,182,227 meters

= 31,184,822 meters = 31,184.822 km

**Flat earth analysis**

If the earth is flat the circumference of all lines of latitude are easily found from this formula:

c = 2 * pi * r

Where “r” is the distance from the north pole to the line of latitude.

Per the Gleason’s Map, there are 60 Nautical miles per line of latitude. 39° north latitude is 51° from the north pole, or 3060 NM from the North Pole. This is 5667.12km. From the above formula for the circumference:

c = 2 * pi * 5667.12km = 35,607.57 km

Conclusion:

The flat earth prediction for the 39th latitude is 4422.75km off from measurement.

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