In this paper we tabulate the various H-functions which occur in the solutions of transfer problems involving Rayleigh's phase function and Rayleigh scattering (including the state of polarization of the scattered radiation). The H-functions have been determined numerically as the solutions of the exact functional equations which they satisfy. The exact laws of darkening in the two states of polarization of the emergent radiation from an electron-scattering atmosphere are also tabulated in this paper.