We report the results of linked theoretical and experimental studies of external infrared reflectivity by a Langmuir monolayer. The new feature in our analysis is the inclusion of the influence of the factor group splitting, arising from the presence of two molecules in the unit cell of a close packed two-dimensional monolayer lattice (CS phase), on the polarized reflection spectra of the monolayer. Our experimental study of the polarized reflection spectra of water supported Langmuir monolayers of tetracosanoic acid [H(CH2)(23)COOH] provide the first measurements of the factor group splittings of the CH2 symmetric and antisymmetric stretch vibrations in the CS phase of a monolayer. The existence of a nonzero factor group splitting is direct evidence for the presence of herringbonelike hydrocarbon chain packing in a two-dimensional crystalline phase of the monolayer. We also report values for the collective tilt angle in the tetracosanoic acid monolayer, as a function of surface area per molecule. The collective tilt angles for the unstrained I phase and the U phase of the tetracosanoic acid monolayer found in this work agree with those obtained from grazing incidence x-ray diffraction studies.