The equation for the zero-sequence impedance of a three-phase transmission line with ground return and the equation for the electric intensity in the earth were derived following the method of Carson. The equation for the impedance was identical with the equations of Carson, however, the electric intensity equation derived included more terms than the equation of Carson. The additional terms were due to the two additional conductors in the three-phase line;A solution of the equation for the electric intensity could not be found and numerical solutions for three particular transmission line configurations were made. The results of these calculations are shown in Figures 2--12 inclusive;Numerical integrations were made of the power losses and the flux linkages established by the current flow in the earth. From these quantities the impedance was calculated for one of the line configurations. Comparison of this impedance with values obtained from Clark and Westinghouse are as follows: NumericalIntegration ClarkeWestinghouse 0.272+j2.000.272+j2.04 0.272+j2.04. The above comparison of impedances indicates that the reactance obtained by numerical integration is about two percent lower than that obtained by Clarke and Westinghouse.