ABSTRACT
This chapter outlines the general procedures to be followed in the transformation process for all of the projections which permit the differential geometry approach. It introduces the authalic sphere, a sphere with the same area as the spheroidal model of the Earth. The chapter considers two types of projections. The first type are those which are best applied to a local area of the Earth. These are the Albers with one or two standard parallels, the Bonne, and the azimuthal and cylindrical equal area. The second type are the world maps: the sinusoidal, the Mollweide, the parabolic, the Hammer-Aitoff, the Boggs eumorphic, and Eckert IV. Many of the equal area projections may be derived by applying the processes of differential geometry. This is done for the transformation to the authalic sphere and the derivation of the Albers with one standard parallel, the Bonne, the cylindrical, and the sinusoidal projections.
