A new formulation of the short-range anisotropic orientating potential experienced by a biaxial apolar particle dissolved in a uniaxial mesophase is given, where the interactions between the solute and the single molecules constituting the solvent are explicitly taken into account. To test the model, the order parameters of naphthalene have been calculated by using the Monte Carlo-Metropolis method and the results compared with H-1-NMR experimental data: the excellent agreement with the order parameters of the same molecule in the 'magic' nematic mixture 55 wt% ZLI1132 + EBBA seems to confirm once more that long-range orientational effects can be neglected for solutes dissolved in that phase.