The integrals appropriate to the classical second virial coefficient for a molecule obeying a spherical-shell central potential and including either a dipole moment or a quadrupole moment are calculated for a wide range of values of r0*, T*. The functions Hk(r0*, T*) are available for k=6, 10, 12, 15, 18, 20, and 24. The results are used to investigate the intermolecular forces in methyl chloride and benzene. In both cases a significant improvement in fit with experimental data is noted upon inclusion of multipolar forces. For benzene, treated as an axial molecule, a quadrupole moment Θ zz of ±15×10–26 esu is deduced.