http://worldcat.org/entity/work/id/137056354

True average size of a fragment between any chosen limits

The object of this study was to develop a method for determining the correct average fragment size, between any chosen limits, of a range of sizes. Ordinarily, the arithmetic average of the lower and upper limits of a grouping is assumed to be the average fragment weight of that group. According to Mott's distribution, the smaller the fragment, the greater is the number of fragments. Therefore the arithmetic average of any grouping of fragment sizes would be larger than the true average. By writing an expression for the average size of a fragment in an interval between m and m delta m (where delta m is small), allowing delta m to approach a limit of zero, and substituting Mott's equation in the resulting differential and integrating, we get a generalized expression for the true average size of a fragment between any chosen limits. (Author).

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