The relation between infra-red dichroism of a band produced by co-valent linkages in a crystal, and the direction of the changing dipole moment is treated quantitatively. Observations of dichroism have been made in a crystalline layer of adipic acid, and in a single crystal of diketopiperazine. The results agree with the crystal structures of the materials as derived from X-ray spectra, when the usual assumptions as to valency angles are made in calculating NH, CH and OH bond directions. The stretching mode frequencies of NH in diketopiperazine consist of at least six peaks, all showing exactly the same dichroism. The breadth of the OH band in adipic acid can perhaps be explained as being due to rotation of the OH group around the single bond CO link.