median also apply to the geometric mean since for the lognormal distribu- tion the estimated geometric mean is identical to the estimated median, i.e., exp(fi). CONCLUSIONS FOR ALIQUOT SIZE STUDY The variability with aliquot size study illustrates a number of features that should be considered at the design stages of an environmental study. The choice of aliquot size has been shown in this study to influence aliquot to aliquot variability as well as the expected value of the median and geometric mean. Between-aliquot variability was quite drastically reduced by using 100-g rather than l-or 10-g aliquots. This implies a larger number of l-g aliquots are required to estimate the true concentration of each field sample with specified accuracy and precision than would be the case if 25, 50; or 100-g aliquots were used. The shape of the distribution of aliquot concentrations, as determined by u and o, was observed to depend on aliquot size. This change in u and o is responsible for changes in the median and geometric mean with aliquot size. Aliquot size did not, however, have a systematic effect on the arithmetic mean. The rationale for these conclusions are illustrated for the lognormal distribution. The relative stability exp(u + 0*/2) suggests the arithmetic mean is preferred over the geometric mean and median for comparing studies that have used different aliquot sizes or other sampling techniques that tend to change the underlying skewed distribution shape of the data. A linear regression between the logarithms of aliquot standard deviation and aliquot size was found to fit the data. This was combined with cost functions to obtain an expression for the variance of the mean concentration as a function of analysis cost (or equivalently, the number of aliquots) and aliquot size. This variance expression decreases rapidly as aliquot size increases from 1 to 10 g. The rate of decline is much slower for aliquot sizes greater than 10 g. The question of determining the optimum number of field samples and number of aliquots per field sample is also discussed. A method by Cochran (1977) was cited that takes into account costs of collecting samples and analyzing aliquots. VARIABILITY WITH DISTANCE STUDY MOTIVATION AND BASIC CONCEPTS The purpose of this study was to obtain data that would be useful in determining the variogram (correlation structure) 423 for Am concentrations