Suppose that λ is the average density per unit volume in a suspension of infective particles such as virus particles. To estimate λ the usual method is to make up a series of inocula of various dilutions containing expected numbers of particles …λi−1, λi, λi+1,… which are known multiples of λ. Each of these is then tested by inoculation in a host such as an egg. We consider only the case where the dilution series is twofold (λi=λ2i, say) and the same number of eggs, N, is tested at each dilution. Then if we are sure that an egg is infected if and only if the inoculum contains at least one infective particle, the probability that the egg remains sterile is Pi=exp {− λ2i}. If each particle is not certainly infective but has a probability p of infecting the egg, the probability of sterility of an egg chosen at random is exp {− λp2i} provided that p does not vary from egg to egg. It is then only possible to estimate λp from the results.