The generally accepted practices of biological assay, at least in so far as these are concerned with quantitative estimation, are contained within the concept of dilution assays (Finney [1964]; Jerne and Wood [1949]). In an analytical assay, each test preparation is regarded as a dilution of the standard preparation with a totally inert diluent. In a comparative assay, the preparations behave as though this dilution relation obtains, although it may no longer be a chemical fact. The design and analysis of an assay are directed at estimating the true or effective dilution factor, which represents the potency of a test preparation relative to the standard. Of course, a relative potency greater than unity is permissible, this corresponding to concentration instead of dilution. If the results of an assay experiment indicate that, for a particular test preparation, the dilution hypothesis is untenable, the assay is declared invalid. Whether this is attributed to contamination or some other experimental mishap, or whether the explanation appears to be some more serious inadequacy of a simple hypothesis, is not for discussion here; the answer must depend on experience and knowledge of the circumstances of the assay. What is clear is that the estimation of a single numerical value for relative potency is no longer practicable. Various writers, and most recently Cornfield [1964], have justifiably criticized a doctrinaire insistence that certain statistical criteria of validity be met before any assay is regarded as of practical value. Such an idealization may be scarcely relevant to the reality of many assay situations; if the preparations assayed are qualitatively dissimilar, the strict dilution requirements can scarcely be satisfied. The linear regressions of response on log dose may not be parallel, yet results of such comparative assays may still seem useful in giving some indications of 'relative potency'. Cornfield comments that 'If the slopes in such an assay do differ considerably, then there is no alternative than to treat relative potency