On the application of phase relationships to complex structures. IV. The coincidence method applied to general phases

For space groups with translational elements of symmetry it is possible to find relationships between the phases of pairs of reflexions which are of the same parity group. When the reflexions have one index in common then many indications for a given relationship may appear. A rigorous theory is described which enables the variance of the relationships to be derived although, in practice, a less rigorous approach is preferred which is more amenable to numerical work. The phase-coincidence procedure is being incorporated as an option in the MULTAN computer package for solving non-centrosymmetric structures.