Derivation of is quite complicated in either Cartesian or spherical coordinates. It is, however, straightforward in prolate ellipsoidal coordinates defined by the variables and . Here and are the distances from the field point to charges and , respectively, and is the distance between the two charges. Expressed in the Cartesian coordinates of the graphic: , , . The equipotentials are given by . The function representing the orthogonal network of lines of force must then satisfy the equation . The solution , transformed back to Cartesian coordinates, is represented by the red contour plot shown in the graphic.