An appreciation of the chance of failing to detect small amounts of infectivity is the main consideration in the design of any test for non-infectivity. The absence of infectivity can never be proved, and many samples must be tested and found negative before there is reasonable assurance that a supposedly non-infective vaccine is safe to use.

The highest percentage, p, of samples likely to be infective for various numbers of negative observations, n, has been calculated from the expression (1−p)n = P for different levels of P, the chance of failure to detect a positive. For example, if 100 observations are made and found negative the percentage of infective samples would be unlikely (P = 0·05) to exceed 3·0 and highly unlikely (P = 0·01) to exceed 4·5. It is suggested that at least this number of observations be made.

The particular problem of detecting foot-and-mouth disease virus by inoculation of a susceptible host is considered in relation to the theoretical requirements of a test of sound design.

The multiple intradermal tongue inoculation of a number of cattle is the method that best meets these requirements. It is shown that this method is the most sensitive for the detection of foot-and-mouth disease virus, at least twenty observations can be provided by one animal, the presence of non-infective but antigenic material in the inoculum does not hinder the detection of a trace of active virus, and an estimate of the initial susceptibility of the tongue tissue of non-reactors can usually be obtained.

Although a much larger volume can be tested by subcutaneous inoculation, disadvantages of this route are shown to be that with some strains very large amounts of virus are required for infection, only one observation is provided by each animal, the presence of non-infective but antigenic material in the inoculum may mask the presence of active virus, and non-reactors to an immunizing dose of vaccine cannot subsequently be tested for a measure of their initial susceptibility relevant to this route of inoculation.

I am indebted to Dr J. O. Irwin, of the Statistical Research Unit, London School of Hygiene and Tropical Medicine, for advice on the use of the binomial distribution and for his helpful criticism of the manuscript; to Dr Ian A. Galloway, Director of this Institute for his interest and encouragement and to Mr W. J. Brownsea for technical assistance during the work described in this and the previous paper.