P' is in each case called the image of P in the sphere S, and the charge －qa⧸f there supposed situated is the _electric image_ of the charge q at P. It will be seen that an electric image is a charge, or system of charges, on one side of an electrified surface which produces on the other side of that surface the same electrical field as is produced by the actual electrification of the surface. While by the theorem of replacement there is only one distribution over a surface which produces at all points on one side of a surface the same field as does a distribution D on the other side of the surface, this surface distribution may be equivalent to several different arrangements of D. Thus the point-charge at P' is only one of various image-distributions equivalent to the surface-distribution in the sense explained. For example, a uniform distribution over any spherical surface with centre at P' (Fig. 4) would do as well, provided this spherical surface were not large enough to extend beyond the surface S. In order to find the potential of the sphere (Fig. 4) when insulated with a charge Q upon it, in presence of the influencing charge q at the external point P, it is only necessary to imagine uniformly distributed over the sphere, already electrified in the manner just explained, the charge Q + aq⧸f. Then the whole charge will be Q, and the uniformity of distribution will be disturbed, as required by the action of the influencing point-charge. The potential will be Q⧸a + q⧸f. For a given potential V of the sphere, the total charge is aV － aq⧸f, that is the charge is aV over and above the induced charge. If instead of a single influencing point-charge at P there be a system of influencing point-charges at different external points, each of these has an image-charge to be found in amount and situation by the method just described, and the induced distribution is that obtained by superimposing all the surface distributions found for the different influencing points. The force of repulsion between the point-charge q and the sphere (with total charge Q) can be found at once by calculating the sum of the forces between q at P and the charges Q + aq⧸f at C and －aq⧸f at P'.