The compensation theorem is often used to obtain the approximate effect of small changes in the elements of an electrical network. The paper describes an extension to a continuous system which includes, instead of a set of circuit elements, a boundary-surface exhibiting the property of surface impedance. The change in mutual impedance between two pairs of terminals situated outside this surface, due to a small change of surface impedance, is expressed as a surface integral. This result, which is deduced from an exact expression allied to Huygens's principle, simplifies the evaluation of the effect of imperfectly conducting ground upon the self-impedance of an aerial placed above it, and enables account to be taken of the presence of an earth system. The effect of the earth system upon radiation from an aerial carrying a given current may also be obtained. Two propagation problems are considered, reflection at a land/sea boundary, and reflection at a cliff. An intermediate result is used in the case of cliff reflection, to which the concept of surface impedance is not applicable.