A mathematical expression for oxygen-induced death of dehydrated bacteria is reported. Data in the literature for Serratia marcescens SUK were analysed and the expression describes viability changes over a range of lo4, oxygen concentration effects over a range of 400 and the effect of time up to 3 h. The expression should apply to the oxygen-induced death of other dehydrated bacteria.

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The expression 'contaminating particles' is used in the broadest sense: microorganisms, virus particles and mutants of a parent organism are examples from microbiology, but other sciences face a problem similar to that dealt with in this paper. According to the case, the 'medium' can be air, a culture medium, a suspension or any other material containing 'foreign' bodies. It is assumed that the contaminating particles are randomly distributed throughout the medium (i.e. that the probability of finding any individual particle in any one unit volume is constant and that the sampling procedure itself does not interfere with this assumption).Theoretically, the number of particles found in a random sample is an unbiased estimate of the density of the contaminant in the medium; but this is of little practical value, particularly where the sample drawn proves to be free from contaminants. The determination of an upper limit to the estimate of the density is often required and this upper limit is defined by a probability level previously fixed by the investigator. If, for instance, the 5 % upper limit of contamination of a medium is found to be six particles per litre (this is usually called the 5 % fiducial or confidence upper limit) the investigator concludes that the density of contamination is not higher, unless he is the victim of a 1 in 20 mischance of sampling. (Obviously the upper limit caters for sampling fluctuations only and the assumption of random distribution must hold good.)Four cases emerge and will be treated separately: (A) an uncontaminated sample drawn from an infinitely large medium; (B) an uncontaminated sample drawn from a medium of finite size; (C) a contaminated sample drawn from an infinitely large medium; (D) a contaminated sample drawn from a medium of finite size.(A) An uncontaminated sample drawn from an infinitely large medium 'Infinitely large' in this context means that the sample volume is negligible compared with the volume of the medium, e.g. samples of sterilized air. The numbers of contaminating particles in the separate units of volume will follow the Poisson distribution and therefore the upper limit n of its expectation is given by n = -log, P = (-logl0 P) x 2.3026, (1) where P stands for the selected probability level. This gives for instance n = 3 for P = 50/ and n = 4-6 for P = 1i%.It follows that the question 'How large (assuming it will turn out to be sterile)