Relationships between the optical third-harmonic-generation susceptibility ${\ensuremath{\chi}}_{\mathrm{ijkl}}^{(3)}$(-3\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega}) and the nonvanishing order parameters 〈${P}_{2}$〉 and 〈${P}_{4}$〉 for a nematic-liquid-crystal phase are presented. Third-harmonic-generation experiments were performed on the nematic N-(p-methoxybenzylidene)-p-butylaniline (MBBA) using the wedge-maker fringe method as a function of polarization and temperature to demonstrate the simultaneous determination of 〈${P}_{2}$〉 and 〈${P}_{4}$〉. The results are in agreement with previous experimental results from nuclear magnetic resonance and Raman scattering studies. Local-field corrections are considered, and based on the data, local-field factors do not appear to depend on the long-range anisotropy of the macroscopic medium.