Experimental measurements of the positions of the optical plasma resonance band for thin island films of noble metals agree closely with positions calculated from a simple equation with no disposable parameters. The equation includes the volume fraction of particles, the refractive index of the substrate, and the real part of the dielectric constant of the metal. This equation is derived from the Lorentz-Lorenz or Clausius-Mossotti conditions. The particles in the films are right cylinders, and have polarizabilities consistent with the equation. There is no need to assume fitting parameters involving particle shapes and sizes and their distributions.