The determination of the change in the value of the earth potential of any part of an alternating-current system, when that part is earthed through an impedance of known value, is one of the primary aims of this paper. The author has already investigated the problem for systems in which the earth capacity currents can be safely neglected,† but, since this condition does not always hold even approximately in practice, it is hoped that the complete solution of the problem will prove more useful.The first part of the paper is devoted to the derivation of a simple equivalent network which represents the various leakage paths of the system, the method of solution being based on Kirchhoff's Law. The completeness of the theory in regard to its application under normal conditions of working is then demonstrated, and the effects due both to the presence of harmonics in the E.M.F. waves and to the voltage-drop, along the mains are fully considered.Following this there is a short description of methods to determine the values ofFandKwithout interrupting the supply to the consumers. Formulæ are given which enable the separate values off1f2andf3to be obtained in the case of three-wire three-phase systems:The last section contains a discussion of the Petersen coil method of earthing; special reference being made to transient current phenomena. The dangers attending the use of the coil are explained, and it is pointed out that this method of earthing would be expected to fulfil the same duties on any type of alternating-current system, irrespective of the form of its voltage diagram.