It is shown that many geophysical problems involving the induction of earth currents by external magnetic variations can be solved by a method of images in which the earth is replaced by the image of the inducing source located at some complex depth beneath the earth's surface. An expression for this complex depth in a horizontally stratified earth is derived, and the theory is developed in a general form that may be applied to any inducing magnetic field of external origin. The technique is applicable when the modulus of the image depth is somewhat less than a characteristic length of the field and also when it greatly exceeds the characteristic length. The theory is applied to dipole, line current, and elementary sources over a three-layer earth and compared with the exact solutions of previous authors. The magnitude of the error involved in the case of elementary sources is found to be nearly always less than 10%.