Phase determination from new joint probability distribution: space group P1

New joint probability distributions of several normalized structure factors are obtained by fixing the crystal structure and allowing the indices to range uniformly but not independently over the vectors in reciprocal space. From these the expected values of the product of powers of several structure factors are found. A subsequent integrating process, together with an important identity, then yield greatly improved formulas for phase determination by means of which the phases of the structure factors are obtainable from the magnitudes of the structure factors alone. Owing to the greater power of these formulas the data are used more efficiently, and complex structures may be more readily analyzed than heretofore.