Transformations in the Complex Plane

The most promising way of extending the engineering applications of field theory is to develop new coordinate systems. Section I listed the eleven systems whose coordinate surfaces are of the first or second degree. Klein [12] and Bôcher [4] extended this list to include a class of fourth-degree surfaces known as cyclides [13]. All possible systems of this class are treated by Bôcher. They include the eleven coordinates of Section I, as well as more complicated coordinates; but all are either simply separable or R-separable (Section IV).