## Weight of Sample Required

Gross Sample. Analyses are carried out on a sample extracted from the bulk, which, irrespective of the precautions taken, never represents the bulk exactly. The limiting (minimum) weight of the gross sample may be calculated, using a simple formula to give an error within predesignated limits, provided that the weight of the gross sample is much smaller than that of the bulk. The limiting weight is given by:

where Ms is the limiting weight in grams, Pis the powder density in g • cm"3, c7i is the variance of the tolerated sample error, w, is the fractional mass of the coarsest size class being sampled, and 1 is the arithmetic mean of the cubes of of the extreme diameter in the size class in cubic centimeters. This equation is applicable when the coarsest class covers a size range of not more than and vTT

1 and w1 is less than 50% of the total sample. Table 3 gives sample values.

 Upper sieve size, /■'m Lower sieve size, Pm Mass % in class (100w1) Sample weight required, g 600 420 0.1 37,500 420 300 2.5 474 300 212 19.2 14.9 212 150 35.6 1.32

Sample by Increments. For sampling a moving stream of powder, the gross sample is made up of increments. In this case the minimum incremental weight is given by:

where M1 is the average mass of the increment, C0 is the average rate of flow, w0 is the cutter width for a traversing cutter, and v0 is the cutter velocity. If w0 is too small, a biased sample deficient in coarse particles, results. For this reason w0 should be at least 3d, where d is the diameter of the largest particle present in the bulk.

ISO 3081 suggests a minimum incremental mass based on the maximum particle size in millimeters. These values are given in Table 4. Secondary samplers then reduce this to analytical quantities.

 Maximum particle size, mm Minimum mass of increment, kg 250-150 40.0 150-100 20.0 100-50 12.0 50-20 4.0 20-10 0.8 10-0 0.3

Gy (Ref 3) proposed an equation relating the standard deviation, which he calls the fundamental error C¥, to the sample size:

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