It is now generally recognized that the " size " of a nonuniform particulate substance is not completely defined by a single mean value, such, for example, as the arithmetic mean diameter. On the contrary, several average diameters are necessary to a full mathematical description of the "size " of such materials. The significance of these size parameters was first pointed out by Perrott and Kinney (I) and has been discussed fully by Green (2) who also introduced the mathematical shape factors for defining the geometric shape of irregular particles. According to Green's definition, "an average diameter is the diameter of a hypothetical particle which in some way represents the total mass of particles" (lot. cit., p. 714).
Thus, we may have a series of parameters representing diameter, surface area, volume, specific surface, etc. The several average diameters necessary to a complete definition of particle size are presented in Table I, col. 3. These equations are general in form and may be employed regardless of the shape of the size-frequency distribution curve of the non-uniform material.
It will be observed that the parameters are functions of two factors: particle diameter and the numerical frequency of particles of a given diameter, d; hence, in order to calculate their respective values for a given sample, the size distribution data must be expressed in terms of frequency by count. This requirement is met when the distribution curve is obtained direct from the microscopic measurement of a large number of representative particles. There are several indirect means of classifying the particles into different size-groups * This diameter gives the specific surface for the sample as a whole; it should not be confused with d,, the diameter of the hypothetical particle having average specific surface.
Jan., 1933.1 SCREEN-ANALYSIS OF SUBSTANCES. 29
1929, PP. 369-387.
1 This value was obtained as follows: referring to Fig. 4, we see that 22 per cent. by weight of particles passing the 400 mesh screen were less than IO p in diameter and since 90.6 per cent. of the total sample passed the 400 mesh screen, this represents 20 per cent. of the original.
* 50 per cent. of 90.6 per cent.
3 Calibration sizes of the 400 and 325 mesh screens.