The probability that a set of counts of particles transmitted over a measured path through a gas at a sequence of pressures can correspond to a particular value of the total cross section is calculated. From this, recipes are given for determining the best value of the cross section and of its mean square deviation, for evaluating the random and systematic errors in the cross section caused by random fluctuations in gas pressure and errors in the reading of gas pressure, and for prescribing the parameters of an experiment to achieve maximum precision in a given time of measurement.