Abstract
SUMMARY: Aherne's method of estimating the number of components NV per unit volume in relatively thick sections is briefly described. Next, formulae are given which lead to an unbiased estimate of NV when the components are identical spheres. This is done for the situations (i) where there is perfect contrast and (ii) where there is contrast deficiency. Aherne's approximation for small objects is compared to the unbiased estimates, to give an idea of its accuracy. The results are used as a guide to the accuracy of Aherne's approximation in more general situations. A summary of recommendations to the experimenter, as to when it is satisfactory to use Aherne's method, is given.