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Linear Intercepts, Areas and Volumes



IN recent correspondence, Mr. P. A. P. Moran1 has suggested a simple method of finding the surface area of small objects from their average area of projection. Another simple method of finding the surface area and also the volume of small objects is based on the measurement of their average linear intercept (mean chord). Some years ago, while working on the determination of the grain-size of rocks, I derived two formulæ and discovered two theorems related to the average linear intercepts. The formulæ can be applied to the calculation of the average grain-size in granular aggregates in which the sizes and the shapes of grains are the same. The theorems, so far as I can see, have a purely academic interest, although their application to granular aggregates may be attempted.

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  1. 1

    Nature, 154, 490 (1944).

  2. 2

    Crofton, M. W., Proc. London Math. Soc., 8, 304 (1877).

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