Mutual Impedance of Long Grounded Wires When the Conductivity of the Earth Varies Exponentially with Depth

This paper presents a formula for the mutual impedance of long grounded wires above the surface of the earth, on the assumption that the conductivity of the earth varies exponentially with depth according to the formula ${\mathrm{\gamma =\gamma }}_0{e}^{\mathrm{-bz}}$ . For b=0 the formula reduces to the known result for a uniformly conducting earth, while if b is allowed to become negatively infinite it reduces to the result for an earth consisting of a conducting layer at the surface only. For small values of b the first terms in the expansion of the impedance formula in powers of b are obtained, and curves are included of the real and imaginary parts of the coefficient of b.