PARTICLE SIZE AND SHAPE MEASURE>IENTS AND STATISTICS 



called the frequency (/»•), and the total num- 

 ber of particles measured is denoted by n. 

 The following table is a summary of the defi- 

 nitions of various means. 



The median and the mode are also often 

 used as a measure of central tendency. The 

 median is the middle value (or interpolated 

 middle value) of a set of measurements ar- 

 ranged in order of magnitude. The mode is 

 the measurement with the maximum fre- 

 quency. The mode is sometimes reported 

 with the arithmetic mean or the median to 

 give an indication of the skewness of the 

 distribution. 



Some quantitative indication of particle 

 shape is often desirable. Harold Heywood 

 has suggested the following method. The 

 particle is assumed to be resting on a plane 

 in the position of greatest stability. The 

 breadth (J5) is the distance between two 

 parallel lines tangent to the projection of the 



particle on the plane and placed so that the 

 distance between them is as small as possible. 

 The length (L) is the distance between 

 parallel lines tangent to the projection and 

 perpendicular to the lines defining the 

 breadth. The thickness (T) is the distance 

 between two planes parallel to the plane of 

 greatest stability and tangent to the surface 

 of the particle. Flakiness is defined as B/T 

 and elongation as L/B. 



The sizes of particles in a powder or other 

 particulate system may be represented by 

 some mean value, as indicated above. Usu- 

 ally some indication of size distribution or 

 spread is desirable and can be provided by 

 the standard deviation, 



/ 



-^{di- dYSi, 

 n 



or by means of quartiles if the median is 

 used as the measure of central tendency. 

 Quartiles are the values completing the first 

 25% and the first 75% of the values when 

 they are arranged according to increasing 

 order of magnitude. However, it is often 

 necessary to provide a more complete indica- 

 tion of the particle size distribution. Classi- 

 fied data can readily be represented by a bar 

 type of graph called a histogram. The posi- 

 tion of the bar locates the class interval and 

 the length of the bar corresponds to the fre- 

 quency. 



Suppose that in preparing the histogram 

 an infinite number of particles are measured 

 and the class intervals made to approach 

 zero. The ends of the bars would become a 

 smooth curve, called the size frequency 

 curve. The function describing the curve is 

 the distribution function. Probably the most 

 familiar distribution function is the normal 

 distribution, defined by the equation 



where s is the standard deviation. The stand- 

 ard deviation for particles which are dis- 

 tributed normally is such that the interval 



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