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|The modern theory of sampling of particulate minerals essentially consists of a recent generalization of the procedures for applying and calibrating the formula usually known as ?Gy?s Formula? for sampling variance control, in which the central concept is a parameter called the liberation factor l. A model which can be experimentally adjusted was proposed by one of the authors several years ago, based on geostatistical considerations. This new model, which relates the liberation factor to the sizes of the fragments and mineral grains, solves the usual difficulties faced in the past, and permits predictions that are well verified in practice. Unfortunately, an older, arbitrary and less general formula is still widely used. The vast majority of today?s misapplications of Sampling Theory of Particulate Materials can be traced back to the use of this antiquated and generally incorrect model. Following a brief history of the models used for the liberation factor and a description of its main variable, the liberation size, and to illustrate the importance of proper modelling of l, this paper presents demonstrative calculations of the absurdity of the incorrect model using the particular case of gold mineralization as an example, followed by some more positive examples of application.|