We carry out a simple analysis of (n+3)-dimensional gravity in the context of
recent work on 'large' supplementary dimensions and deduce a formula for the
expected compactification radius for the n additional dimensions in the
universe, as a function of the Planck and the electro-weak scales. We argue
that the correspondingly modified gravitational force gives rise to effects
that might be within the detection range of dedicated neutron experiments. A
scattering analysis of the corresponding modified gravitational forces suggests
that slow neutron scattering off atomic nuclei with null spin may provide an
experimental test for these ideas.Comment: A revised version suggesting a specific neutron-scattering
experiment. Physics Letters B, accepted for publicatio