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

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.     

The Sizes of Spheres from Profiles in a Thin Slice II. Transparent Spheres

Formulae are derived for obtaining the size distribution of transparent spherical particles which are embedded in an opaque material. The data are the sizes of the circular profiles made by particles in a random thin slice of a specimen when it is viewed orthogonally. The formulae incorporate resolution constraints which cause various profile size ranges to be unobservable. Approximate solutions are obtained under specific resolution constraints when the slice is very thin. The corresponding case of opaque spheres in a transparent material was the subject of Part I (Coleman, 1982).     

Morphological and architectural features of young Nothofagus pumilio (Poepp. & Endl.) Krasser (Fagaceae)

The morphology and architecture of young Nothofagus pumilio plants growing as understorey and in a cleared area were assessed. Length, number of internodes, presence of branches and apex condition were registered for each growth unit (GU) in the sampled plant. GUs were grouped according to branching order and age of the bearing axis. Understorey plants were seven years old and had a short trunk bearing 2–3 orders of branches; all of their most recent GUs were horizontal and of comparable size. Plants growing in the cleared area were 10–16 years old and had a vigorous vertical and dominant trunk bearing 4–5 orders of less vigorous, horizontal branches. Plants from the cleared area showed signs of having had comparable-size GUs in all of their axes at a younger stage of growth. N. pumilio plants appear to start their growth with the production of short GUs in all of their axes irrespective of the light conditions. In contrast, the development of a vertical, vigorous trunk, seems to be restricted to plants growing in open environments.     

A Simple Method for Fixing, Dehydrating and Embedding Pollen Tubes Cultivated in Vitro for Optical and Transmission Electron Microscopy

A simple method to cultivate pollen tubes in a gelatin medium is presented. After the growth of the pollen tubes in the culture medium, they are fixed, dehydrated, and embedded in resin for ultramicrotomy. The method is easy and does not require the purchase of special materials beyond those needed for the usual techniques for studying biological specimens under transmission electron microscopy.