One often hears of government issues such as a state bill (in Indiana) proposed to change the value of π (pi), the ratio of the circumference to diameter of a circle. This was never actually tried, just proposed.

A more interesting example of how things need adjusted in the field is that of the Jefferson grid.

This page looks at surveying of the land. In particular, it looks at surveying the western United States in the 19th century in a very general overview.

Thomas Jefferson (1743-1826) established what is called the "Jefferson Grid" to layout the newly acquired Louisiana purchase in 1803 (from Napoleon in France) in one mile square grids (640 acres) since much of that land was flat plain land.

Napoleon took power and became emperor after the democracy of the French Revolution collapsed in ways predicted by the Founding Fathers of the United States and for which the Founding Fathers provided checks and balances (which have been in the process of being dismantled for some time now). Laying out the land in one mile squares seems simple until one gets into the field, starts to work, and realizes that the earth is not flat.

You can inspect this using, say, Google Earth (for 3D round earth perspective) or Google Maps (for 2D flat earth projections). The radius of the earth is about 3958.80 miles.

• The diameter of the earth is about 7917.60 miles.
• The circumference of the earth is about 24873.87 miles.

For this simple model, the earth will be assumed to be a perfect sphere.

Assume we are interested in 1.0 mile squares.

Assume we are at a latitude of 40.0000 degrees north (e.g., central Indiana, southern Iowa, northern Missouri).

At 0.0000 degrees latitude, the radius is 3958.80 miles.

At 40.0000 degrees latitude, the radius is 3032.62 miles.

At 40.0000 degrees latitude, a distance of 1.0 mile(s) east-west is 0.0188932 degrees longitude. Now go 1.0 mile(s) north. This is at latitude 40.0145 degrees north.

At 40.0145 degrees latitude, the radius is 3031.97 miles.

At 40.0145 degrees latitude, a distance of 1.0 mile(s) east-west is 0.0188972 degrees longitude.

The difference amounts to 1.119307 feet or 13.431685 inches per 1 mile(s).

This small discrepancy can add up.

This is why, in the mid-west where one mile squares were laid out, every so often an adjustment needed to be made to get everything back in line on the east-west and north-south lines so that a dog-leg was added.

The difference is not visible on east-west lines but is visible on north-south lines.
At the above latitude, about every 24 miles the cumulative error amounted to about 13.4 feet and an adjustment might be made.

Roads running north and south would need to have "doglegs" to not go through laid out one mile squares.

On actual satellite images, one can see that the surveyors did make small errors from time to time and place to place.