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Deltheil (1, pp. 114-120) has considered the distribution of distance in an n-dimensional hypersphere. In this paper I put his results (17) in a more compact form (16) ; and I investigate in greater detail the asymptotic form of the distribution for large n, for which the rather surprising result emerges that this distance is almost always nearly equal to the distance between the extremities of two orthogonal radii. I came to study this distribution by the need to compute a doubly-threefold integral, which measures the damage caused to plants by the presence of radioactive tracers in their fertilizers; for the distribution affords a method of evaluating numerically certain multiple integrals. I hope to describe elsewhere this application of the theory.
J. M. Hammersley (Fri,) studied this question.