Cassini projection

Its precise formulas were found through later analysis by Johann Georg von Soldner around 1810.

Considering the earth as a sphere, the projection is composed of the operations: where λ is the longitude from the central meridian and φ is the latitude.

Elsewhere, the distortion is largely in a north–south direction, and varies by the square of the distance from the central meridian.

Due to this, the Cassini projection works best for areas with greater north–south extent than east–west.

For example, Ordnance Survey maps of Great Britain used the Cassini projection from 1924 until the introduction of the National Grid.

Considering the earth as an ellipse, the projection is composed of these operations: and M is the meridional distance function.