The Rayleigh identity, based on a multipole expansion theory, is extended to analyse the forces between particles
in an electrorheological system. The shear modulus for chains of particles arrayed on a square lattice is calculated. It
is found that the modulus increases linearly with the ratio of dielectric constants of the dispersed particles to that of
the continuous phase; as the ratio becomes larger, contrary to the expectations from a simple dipole approximation,
the modulus would saturate. In the case of conducting particles, the modulus varies with the frequency of the applied
field. In a limiting case of perfectly conducting particles, the conductivity is also considered. It is found that the
particle-particle forces are extremely sensitive to their separations from each other.