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Suppose that dυ and dυ′ are two volume elements situated at points P and P′ respectively in a three-dimensional right circular cylinder, that y is the distance PP′, that z(y) is a given function of y, and that we wish to evaluate the sixfold integral
taken over all pairs of points P, P′ within the cylinder. We observe that z(y) is a function of y only; so that the sixfold integral can be expressed as a single integral
that is to say a weighted mean of z(y) over the relevant values of y, where the weight function is evidently given by
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