Precise and general conditions for the validity of a comprehensive set of stereological fundamental formulae

SUMMARY The usual derivations of the well‐known fundamental formulae of stereology are unsatisfactory. Precise and general conditions for the validity of a comprehensive system of such formulae are given. They take the form of unbiased ratio estimators of stereological fractions. These estimators are defined for various types of ‘weighted’ random plane and line sections of the specimen. Thanks to certain probabilistic equivalences, these sections may in practice be implemented fairly easily. The system includes new formulae which allow the estimation of the mean lineal and areal projections of embedded features. The mean square errors of several alternative estimators of the same feature characteristics are compared.