where s,? is the variance between different sampling locations in the field, s* is the variance between aliquots from the same field sample, c,; is the sampling cost per field sample, and K is the cost per aliquot. From Equation 3 we suppose s* = 2.5 wi9-92, Hence, Consequently, if we know the ratio of costs c,/K and have s,° from previous studies, then the above equation for n solved for different values of w. It's clear that no aliquot weight increases. Once n has been chosen?? Fhe of n' (number of different field gBiples) may be obtained an estimate of may be creases as optimum value by solving Cochran's cost equation (if the total study budget is considered fixed) or the appropriate variance equation (if the study must be designed to achieve a specified precision of the mean over all sample locations). The cost equation is given by Cochran (1977) on page 280. His Equation 10.15 (p. 278) gives the approximate variance equation. If interest centers on estimating the average Pu concentration for the sampled area, then, making use of Equation 9 we find that for NS-201 Specifying s;? and c, will allow us to choose an appropriate n by exam~ ining the solution of n for different values of w. Note that s,2 is now the variance of Pu eBicentrations between field sample locations. As was the case for Am discussed above, n'’ may be obtained by solving Cochran's cost or variance equation depending on whether cost or the variance of the overall area mean has been preassigned. EFFECTS OF CHANGING ALIQUOT SIZE ON MEDIANS AND GEOMETRIC MEANS We have seen from Figure 1 that the median and geometric mean Am concen- trations tend to increase with increasing aliquot size. Based on arguments by Michels (1977), we believe that this is not due to chance. Michels considers a hypothetical, large environmental air sample that has some true average arithemtic mean (expected value) concentration. He supposes that this sample is subsampled using aliquots of different volumes V; and V2, where Vy > V,. If the concentrations resulting from the use of both aliquot sizes are lognormally distributed, Michels shows that the ratio of the true geometric means for aliquot volumes V> and Vi is 420