In parts I and II of this series, the dominant role of "primary" Raman moments of degree greater than one, to Raman intensities for molecules forming a uniform coating on pairs of spherical particles in close proximity, is demonstrated. In this paper, the effect of chain length, coverage, particle size, and separation, and the location of the particle in the chain on the intensity are explored for linear chains of coated particles. Intensity enhancements calculated for visible excitation are up to 30 times those for two particles, being approximately 4 X 10(6) for infinite chains of silver particles of radius 25-50 angstrom separated by the thickness of a layer of CO approximately 10(5) for platinum and approximately 10(4) for germanium chains. Furthermore, the enhancement for chains falls off appreciably more slowly with particle separation. Graphs of intensity vs coverage vary greatly in shape depending on particle size, molecular size, and polarizability.