A pedigree study shows close linkage of bipolar affective illness (manic depression) to the X-chromosome markers colour blindness and glucose-6-phosphate dehydrogenase deficiency. The maximum lod score ranges from 7.52 (assuming homogeneity) to 9.17 (assuming heterogeneity); that is, the odds in favour of linkage range between 3 X 10(7) to 1 and 10(9) to 1. These results provide confirmation that a major psychiatric disorder can be caused by a single genetic defect. As a possible first step in characterizing the primary genetic abnormality, this finding may have important implications for the aetiology, nosology, pathophysiology and, possibly, prevention and treatment of bipolar affective disorder. It also provides a means for identifying and characterizing homogeneous populations of patients and may help in clarifying aetiological heterogeneity.

A copositive quadratic form is a real form which is non-negative for non-negative arguments. A completely positive quadratic form is a real form which can be written as a sum of squares of non-negative real forms. The completely positive forms are basic in the study of block designs arising in combinatorial analysis (3). The copositive forms arise in the theory of inequalities and have been considered in a paper by Mordell (4) and two papers by Diananda(1, 2).

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