Variance apparent particle sizes for cylinders, prisms and hemispheres

Apparent particle sizes corresponding to the slope and intercept of the variance‐range curve are interpreted geometrically; the analytical results of Lele & Anantharaman for cylinders and certain prisms are confirmed. The slope apparent particle size is half the harmonic mean of h sec ϕ and b csc ϕ, where h is the height of the cylinder or prism, b is the breadth of a rectangle having an area equal to that of its top face and a width equal to that of its radiation shadow, and ϕ is the angle between its axis and the diffraction vector. For cylinders, but not in general for prisms, the intercept apparent particle size is 1/√2 times the geometric mean of the same quantities. For a hemisphere of diameter d the slope apparent particle size is given by d /(1 + cos ϕ), where ϕ is the angle between the diffraction vector and the normal to the plane face, and the intercept apparent particle size is the square root of π d 2 csc 2ϕ.