Feret‘s Statistical Diameter as a Measure of Particle Size

Abstract

VARIOUS measures of the size of irregularly shaped particles as seen in profile under the microscope have been used, chosen according to their theoretical significance or practical ease of measurement. These include, using Heywood‘s notation^1,2 : (i) the diameter of the circle of equal area, d ; (ii) the diameter of the circle of equal perimeter, D ; (iii) the length of line bisecting the profile area (Martin‘s statistical diameter³), M ; and (iv) the perpendicular distance between parallel tangents touching opposite sides of the profile (Feret‘s statistical diameter⁴), F. M and F are determined for randomly oriented particles, thus giving an average value over all possible orientations. d is usually regarded as the ideal measure of particles seen in profile, but is somewhat difficult to determine experimentally with precision. It is, however, common practice when sizing very small particles to estimate d visually by comparing them with standard reference circles on a Patterson and Cawood or similar type of eyepiece graticule^5,6. M and F are convenient to measure in practice with aid of an eyepiece scale or filar micrometer, and have been extensively used by various Workers. D, or rather the ratio D/d, termed by Heywood¹ the ‘contour ratio', and its reciprocal called the ‘degree of circularity' by Wadell⁷, have been used in discussing the shape and hydrodynamical properties of particles. For these purposes D has usually been determined by direct perimeter measurement of the projected images of particles. It does not appear to have been adopted intentionally in any work known to me as a direct single measure of particle size.