Numerical calculation of multiple reflections in diffuse cavities

The equivalence of the effective emissivity and effective absorptivity of an isothermal diffuse cavity is proved by mathematical induction. The effective emissivity, effective absorptivity, and difference between the effective reflectivity and unity, which are numerically computed for cylindrical cavities, agree with each other within computer round-off error. Error in the above three quantities arises mostly from the assumption of constant effective emissivities across subdivisions of the cavity surfaces. The precise determination of effective emissivities shows that the minimum emissivity on the base of a long cylinder does not necessarily occur at the center.