The polarized infrared reflectance of LaF3, CeF3, PrF3, and NdF3 has been measured from 40 to 500 cm-1 at 295, 78, and 7°K. Kramers-Kronig analyses of the reflectance spectra yield evidence for eleven infraredactive phonons in the polarization (Ec) and six in the polarization (Ec). These results, together with reported magnetic-resonance measurements, are consistent with a P3c1 magnetic space group. A theory and method for directly observing the longitudinal optical phonon frequencies of strongly anisotropic crystals in transmission are reported. © 1969 The American Physical Society.