to the standard deviation or coefficient of variation to be expected between aliquots. A summary of this information is given by Grant and Pelton (1973), whose reference list gives an introduction to the litera- ture. A simple mathematical expression relating aliquot size to aliquot variability would be a very useful tool for estimating the appropriate aliquot size te achieve a specified or required precision. In addition, if a cost equation were available to relate cost per analysis to aliquot size, this could be used in conjunction with the above aliquot size variability equation to estimate the number and size of aliquots for specified costs and desired precision in the mean of a field sample. In this section we begin by using the information from Figure 1 to estimate the relationship between aliquot size and variability for the particular location sampled at NS-201. This is then combined with a simple cost function to obtain estimates of the number and size of aliquots needed to achieve a desired precision for the mean Am concentration in a sample. Approximate results are also obtained for Pu by using the Pu/Am ratio believed to be appropriate for NS~201. Also discussed is a procedure given by Cochran (1977, pp. 280-283) for estimating the optimum number of field samples and aliquots per field sample when suitable information on costs as well as between sample and within sample variable is available. Results for Am Consider Figure 2 which is a log-log plot of the observed standard deviations s (from Figure 1) versus the corresponding aliquot sizes w to which these values of s apply. The correlation between log s and log w is 0.96, and the estimated linear regression is /\ log s = 0.20 - 0.46 log w. (2) Taking antilogarithms on both sides of Equation (2) gives -0.46 s=1.58 w (3) We note that the theoretical equation given by Grant and Pelton (their Equation 4) can be expressed as log s = 0.5 log f - 0.5 log w, (4) where f is a multiplicative function of the density, volume, and concentration of the particulate species of interest, and w is the aliquot weight. It is perhaps noteworthy that the last term of Equations 2 and 4 above are nearly identical. 414