The use of the polarised mho distance relay for the protection of high-voltage lines has become widespread. Up to the present time, the relay has been thought to be of limited use in the protection of short lines, owing to its relatively small reach for arcing faults. However, recent practical tests have shown that the actual performance is considerably better than that predicted by theory. A new analysis is therefore developed in this paper which shows that the polarised mho relay has an offset characteristic, in the case of unbalanced faults, which encloses the origin and hence enhances the relay reach in the direction of the resistive axis. The degree of offset is a function of the source/line impedance ratio of the system to which the relay is connected. It is shown that the theory developed is in good agreement with results obtained in practice.It is shown in an Appendix that the theory also covers the cases of crosspolarised directional relays and polyphase impedance relays, both classes of relay having an offset characteristic. The paper concludes by discussing the implication of the results. It is noted that the polarised mho relay has most of the benefits of the reactance relay, while retaining the advantages of being inherently directional and insensitive to load currents and power swings. It is also noted that, by using this method of analysis, the reach for lines with series capacitance may be predicted.