The molecular theory of the second light-scattering virial coefficient B(rho) is briefly reviewed, and tensor expressions for contributions to B(rho) of linear molecules, correct to the fourth power or the polarizability in the depolarized scattered intensity, are presented. These expressions are evaluated numerically by computer for nine gases and, where possible, compared with published experimental values. The results identify molecules which may be fruitfully investigated experimentally. The calculations also demonstrate the usefulness of an algebraic package (in this case Derive) in the accurate performance by computer of tedious manipulations often encountered in the theory of molecular interactions.