As the number of transuranic particles in the field sample increases and/or volume of individual particles decreases, the aliquots become This in turn will result in a reduction in aliquot to more homogeneous. Equation 4 of Grant and Pelton (1973) is a mathematity. aliquot variabil tation this phenomenon. of represen ical Aliquot size can also have an effect on the computed geometric mean and median of aliquot concentrations. Michels (1977) points out in the context of sampling air for particulates that the geometric mean concentration of a scarce contaminant will tend to increase with volume of His aliquot if aliquot concentrations are lognormally distributed. Figure 1 gives for the lognormal case the ratio of geometric means to be expected as a function of geometric standard deviation and the ratio of We are concerned here with the weight of soil aliquots aliquot volumes. rather than the volume of air passed through an air filter, but our Aitchison and Brown results discussed below show this same effect. (1969) give a comprehensive discussion of the lognormal distribution. It is important to note that on the average, the arithmetic mean should not increase with aliquot size. This is, the mathematical expected value of x is always the true mean concentration of the sample, regardless of aliquot size or the underlying distribution. As a consequence, estimates of transuranic inventory that are computed using x will not systematically change with aliquot size. Clearly, arithmetic means from different studies are more directly comparable than geometric means. We note that the variability studied here is between aliquots from a single location in the field. Taking larger size aliquots will reduce this within-sample variability, but it will not reduce the between-sample variability, i.e., the variability between soil samples collected at different locations. If between-sample variability is substantially greater than within-sample variability (resulting perhaps from a strong trend in concentration level with distance from ground zero), then use of larger aliquot sizes would not materially reduce the variance of a sample mean computed from all sampled locations. A study of the type discussed here, conducted before routine sampling starts, can give information on within-sample variability. This information, when combined with data on the variability between locations in the field, can be used to devise sampling plans for achieving a specified level of precision in concentration estimates or estimates of inventory. Cochran's (1977) approach to this problem is discussed in this paper. Wallace and Romney (1977) point out the problems of taking very small aliquots of soil for cleanup purposes when precise and accurate estimates of very low concentration levels may be required. The implications are that relatively large aliquots or many smaller aliquots will be required. SAMPLING AND SOIL PREPARATION METHODS This section is a summary of the complete field sampling and soil prepara-~ tion protocol given in Appendix A. 408