The classical inversion transformation introduced by Kelvin is revisited. It is shown that it can be used to formulate the electrostatic image principle not only for the perfectly electrically conducting (PEC) sphere but also for the perfectly magnetically conducting (PMC) sphere and for the sphere with more general impedance boundary conditions. In the latter two cases the image of an electric point charge is seen to consist of electric point and line charges. More generally, it is shown that if the space is filled by the most general linear isotropic medium (bi-isotropic medium), the same method can be extended to form the corresponding image principle for the PEC, the PMC, and the impedance sphere. In these cases an electric point charge is seen to have an image composed, in general, of both electric and magnetic point and line charges. ¿ 2000 American Geophysical Union