In this paper, exact vibration frequencies of circular, annular and sector membranes with a radial power law density are presented for the first time. It is found that in general, the sequence of modes may not correspond to increasing az-imuthal mode number n. The normalized frequency increases with the absolute value of the power index |ν|. For a circular membrane, the fundamental frequency occurs at n = 0 where n is the number of nodal diameters. For an annular membrane, the frequency increases with respect to the inner radius b. When b is close to one, the width 1 – b is the dominant factor and the differences in frequencies are small. For a sector membrane, n – 1 is the number of internal radial nodes and the fundamental frequency occurs at n = 1. Increased opening angle β increases the frequency.

The reverse flow pressure limiting aperture is a device that creates and sustains a substantial gas pressure difference between two chambers connected via an aperture. The aperture is surrounded by an annular orifice leading to a third chamber. The third chamber is maintained at a relatively high pressure that forces gas to flow through the annular aperture into the first of said two chambers. The ensuing gas flow develops into a supersonic annular gas jet, the core of which is coaxial with the central aperture. A pumping action is created at the core of the jet and any gas molecules leaking through the aperture from the second chamber are entrained and forced into the first chamber, thus creating a substantial pressure difference between the first and second chamber.

Recent collections of Sawdonia ornata have been made from the Strathmore Group which crops out in the Midland Valley of Scotland. The sediments are Lower Devonian, probably Emsian, in age. New morphological features discovered include planar branching of vegetative and fertile axes, abaxial emergences close to branch points and H branching. Well preserved cuticles have permitted reinterpretation of the structure of stornata, rosettes (hair bases), papillae and spines, and striated cuticle is identified as S. ornata. The morphology of sporangia and in situ spores is described. Pyritised axes have revealed details of xylem shape, maturation, changes in the vicinity of branching, tracheidal structure and the arrangement of xylem and cortex in deformed axes.