Estimation of linear properties of particle size distributions

This paper presents a general mathematical theory for quantitative investigation of the properties of a dilutely distributed particulate phase. If the process by which the specimen is sampled and the process by which particles in the sample are measured can be appropriately modelled, then this theory provides unbiased estimates of any linear property of the particle size cumulative frequency function under the assumption that particle centres are uniformly distributed within the specimen. Uniqueness of the estimate is discussed and variance formulae given. Some classical results on spherical particles and new results on cylindrical particles are presented as specific examples. The theory unifies a large body of current literature and also provides the basis for the inclusion of the effects of sample preparation and any anomalies encountered in the measurement process.