It is shown that any variable current method of electrical exploration must be interpreted in terms of a semi-infinite conducting medium underlying a semi-infinite insulator. The complete theoretical treatment for a homogeneous conductor is outlined, and the details of the solution for low frequencies are presented. These indicate that the measured field intensities are not in-phase with the exciting current as has previously been assumed. These out-of-phase components from a homogeneous earth complicate the desired interpretation in terms of resistivity discontinuities at depth. The results of this paper provide a means of suitably correcting for this factor. Secondly, the insulating (air) region is shown to have an influence on the electromagnetic fields within the conductor. Thus, when considering the image approximation, the images are influenced by the air region and cannot be assumed to behave as they would in an infinite conductor. The lack of validity of this earlier assumption is demonstrated and suitable correction factors are derived. Specific results for the two cases of most practical interest are presented in graphical form. These are compared with experimental data obtained from a laboratory scaled model composed of metallic plates.