By introducing heterogeneity indices, an empirical equation is proposed for characterizing the heterogeneity of non-isotropic fields. The formula is an extension of Fairfield Smith's (1938) empirical law describing heterogeneity in isotropic fields. Based on these indices, criteria are provided for choosing optimum plot shapes in terms of minimizing the sample variance and cost. Sample plots having their largest dimension in the direction with the largest index will give more accurate results (less variable) than plots with other shapes. Relations between the optimum plot size and relative cost versus variogram parameters are given for several variogram models. These relations indicate that variograms with small effective ranges have a very profound effect on the optimum plot sizes.

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