We have developed the method of images for the solution of two hyperspheres in d dimensions in a uniform field in order to study the O(c2) coefficient κ in the dielectric constant of the medium. The method employs extensions of image theory for classical charges and dipoles for dielectric spheres, which produce novel line charge and line dipole densities. Numerical results for κ with arbitrary integer d are consistent with our previous paper I (this issue), and demonstrate that the image method shows superior convergence properties. Although computationally less convenient, the procedure is, in principle, calculable term–by–term and leads to useful analytic results in the weak scattering limit. This work also produces a simple algebraic approximation that is useful everywhere.