Basis for Lognormal Distribution Normal distributions are assumed to result from additive processes, while lognormal distributions are usually attributed to multiplicative processes. In the case of vegetation ingestion rates (I_), a normal distribution was apparently converted to a lognormal distribution by introduction of a normally varying reciprocal factor. Soil ingestion rates were assumed to be lognormally distributed because the three data points available (8.5, 57.3, and 278 g) approximate the power sequence (8, 64, 256, i.e., 23, 2©, 28) and because the coefficient of variation (s/x = 144/112) is greater than 1. Then it was demonstrated that the frequency distributions of plutonium concentrations in vegetation and soil samples from Area 13 (Tables 1 and 2) are also well described by assuming that they are lognormally distributed. An examination of the area data in Table 3 and the corrected piutonium inventory data published by Gilbert (1977) shows that the spatial distri- bution of plutonium in surface soils (0-5 cm depth) of Area 13 exhibits a logarithmic pattern and that this pattern probably accounts for the more or less lognormal distributions of plutonium concentrations in vegetation and soil samples. The log-log relationship which describes the spatial pattern of plutonium distribution has the general form y = ax , the linear form of which is where y ul In y= 1n a+b 1nx (3) the cumulative amount of plutonium, EPu, in the surface soils of sampling strata 6 through 1 in Area 13 (in curies), x = the cumulative area, LA, of sampling strata 6 through 1 and (in hectares), a is the y-intercept of the regression line, b is the slope of the regression line. The amount of plutonium in the surface soil of stratum j, calculated as follows: (Pu) j. where aC5 (Pu)j, was Mo Ay 10 -8 (Pu)j is the amount (curies) of plutonium in the surface soil of stratum j, C_. is the mean concentration (pci/g) of Pu in the surface soil of stratum j, M, is the weight of soil (0-5 cm depth) in g/m* (this is the bulk density soil sample. The mean bulk density was 1.13 + 0.03 g/cm3; so the average value of My is about 56,500 g/m?.), A, is the area (hectares) of stratum j, 494