Dilution Egg-Counts and the Poisson Series

Researches involving dilution egg-counts, recently carried out by members of the staff of this Institute, have shown that the error variance, i.e. that between parallel counts, approximates more or less closely to the mean count. The following examples illustrate this point:—The counts were all made by the same technique, and it is fair to total them in order to observe the average effect. This agreement between variance (or mean square) and mean is a feature of the Poisson distribution, and it has been assumed that dilution counts are in fact distributed according to the terms of that series, in all cases where the technique is adequate. Reasonable agreement between mean and error variance becomes, indeed, a criterion of the accuracy of the sampling technique. The purpose of the present note is to enquire a little further into the theoretical basis of this assumption, doubts having arisen as to whether high counts (say, up to 100) can be expected to conform to the Poisson series.The essence of the McMaster (Gordon & Whitlock) technique is that one counts the eggs lying under a centimetre square engraved on a coverglass which is supported 0·15 cm. above a slide, i.e. the eggs contained in 0·15 cc. of faecal suspension. Since the suspending liquid is a half-saturated solution of salt, the eggs float up into one optical plane immediately below the coverglass, this making for ease in counting.