In this paper the problem of the evaluation of the grain-size distribution of a spherical granular material embedded in a matrix, upon the basis of the measured distribution of the sizes of the figures formed by the intersection of the grains with a random plane, is discussed and a solution, based upon matrix algebra, is developed.
There are no limitations on the method, with respect to the type of particle-size distribution function involved and, in theory, the grain-size distribution may be determined to any desired degree of accuracy by the use of a conversion table.
Conversion tables, which are sufficiently comprehensive to give results of worthwhile accuracy in most practical cases, are presented and the necessary calculations can be carried out, without recourse to complicated mathematics, by the use of a slide-rule or a desk calculating machine.
If the grain-size distribution must be divided into a number of classes greater than that covered by these tables, then extended tables must be prepared. This can be done, by application of the methods of the present work but evaluation upon a computer, by use of a standard fast-running routine, is then practically unavoidable.
The present treatment also leads directly to the number of particles of each size present in a unit volume of compact, this being a figure of technical importance which is not easily established by other methods.