A surface of rotation whose meridional section is defined by the equation r = a sech(b ( Ψ + c)), where a, b and c are constants, Ψ is the isometric latitude and r is the perpendicular distance from the axis of rotation to the surface. The constants are chosen to make the aposphere osculate the spheroid (with which it has a common axis or rotation) along some parallel that passes through the centre of the region for which a transformation is required.