The electric field of a low frequency oscillator placed on the surface of a two layer earth is determined in two special cases, namely, the case in which the conductivities of the two layers are nearly equal, and the case in which the lower layer is a perfect insulator; in the latter case, only terms of zero and first order in frequency are considered. It is shown that, when the upper layer is sufficiently thin or is very thick, the mutual inductance of two wire elements on the surface of a two layer earth has the same value as for a homogeneous earth. In the case of an insulated layer, it is shown that the maximum departure of the value of mutual inductance of two collinear wire elements from the corresponding value on a homogeneous earth is 35%.