We have described a theory forU, the potential of mean torque of rigid solutes at infinite dilution in a uniaxial liquid crystal phase; this may be used to calculate (Sxx-Syy) andSzz, the principal elements of the Saupe ordering matrix. In its simplest formU(ω) contains only second-rank terms and the dependence of the biaxiality (Sxx-Syy) is determined by ω, a parameter which describes the departure of the potential of mean torque from cylindrical symmetry, and is predicted to be temperature independent. If dispersion forces are responsible for the magnitude of the orientational order parameter then ω should be independent of the solvent and depend only on the anisotropy in the electric polarizability of the solute. Indeed, this independence should result for any pair potential which can be factorized into a product of solute and solvent properties. These predictions are tested here by determining values ofSzzand (Sxx-Syy) for anthracene-d10as a solute in several liquid crystal solvents, from the quadrupolar splittings obtained from the deuteron N.M.R. spectra. It is found that ω has a strong dependence on the nature of the solvent, which demonstrates that the solute ordering cannot be determined primarily by dispersion forces, or by a factorizable potential. There is also a weaker temperature dependence of λ observed for each binary mixture, and we show how this might be caused by a dependence of ω on solvent ordering, or by the inclusion of a fourth-rank term inU(ω).