Bottomley projection

The Bottomley map projection is an equal area map projection defined as:

where

and φ is the latitude, λ is the longitude from the central meridian, and φ₁ is the given parallel of the projection which determines its shape, all in radians.

Parallels (i.e. lines of latitude) are concentric elliptical arcs of constant eccentricity equal to cos φ₁, centred on the north pole. On the central meridian, shapes are not distorted, but elsewhere they are. Different projections can be produced by altering the eccentricity of the arcs, making it vary between the sinusoidal projection and the Werner projection.