On integrating direct methods and isomorphous replacement techniques .2. The quartet invariant estimate

In a preceding paper [Giacovazzo & Siliqi (1996). Acta Cryst. A52, 133-142], the joint probability distribution of seven pairs of isomorphous structure factors was derived. Its complicated mathematical expressions are here simplified by introducing the assumption that isomorphism is due to heavy-atom addition to the native structure. The reliability of the conclusive formula for calculated error-free data perfectly agrees with expectations. The formula, however, is not robust against lack of isomorphism and errors in measurements: in the paper, theoretical reasons are given justifying this behaviour. The use of the prior information on the heavy-atom structure markedly improves the formula, which then proves suitable for practical applications.