The Sizes of Spheres from Profiles in a Thin Slice I. Opaque Spheres

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Abstract
Thin slices through specimens are made into slides for use in microscopy. If a specimen consists of opaque spherical particles in a transparent medium, there will be seen through the slice circular profiles of particles and sections through particles. For a random slice, the size distribution of these profiles can be related to the size distribution of the population of spheres. The extensive literature dealing with this relationship is surveyed.An important generalization of practical importance is made with the introduction of a resolution interval which excludes from observation those profiles that are too large or too small. How this affects the relationship between the profile and sphere size distributions is considered, and some special cases are used as illustrations.In Part II (COLEMAN, 1983) the corresponding results for the case of transparent spheres in an opaque specimen are given.