The principal magnetic properties of transformer core materials are generally expressed in terms of permeability and power loss per kilogramme. Another method, described in this paper, is to assign a complex value to the permeability (Sections 2 to 4). For many purposes this method possesses advantages; for example, very simple relations can be found (Sections 5 to 7) connecting the electrical characteristics of coils with the components of the vector permeability of their cores. Data for samples of nickel-iron and silicon-steel are given (Section 8) and, by way of an example of the use of the system, a simple method of securing the optimum design for a low-loss reactor is worked out (Section 9).