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The matrix method of using Sayre relations, as applied to the solution of crystal structures by C ochran  and D ouglas , is briefly reviewed. The initial disadvantage of the method, that it requires electronic digital computers, is removed by the introduction of the concept of a constraint matrix, which leads to the selection of the so-called “basic permutation;” from this a set of desirable permutations is obtained by the use of a difference-card technique. The procedure is reviewed in steps suitable for practical application, and application to salicylic acid is illustrated.

The Constraint Matrix Method for Application of S ayre Relationships to the Solution of Crystal Structures