The multiplication of neutrons by thin spherical shells of various materials surrounding a point source of 14-Mev neutrons has been measured. A special long counter was used whose energy response is independent of neutron energy over a range of energies from about 1 Mev to 14 Mev. The transmission of primary energy neutrons through the shells has been measured with a trans-stilbene detector and values of the inelastic collision cross sections have been derived. The quantity σn,2n+2σn,3n-σc is calculated, where σn,2n and σn,3n are the cross sections for (n, 2n) and (n, 3n) reactions and σc is the sum of the cross sections of all processes which destroy a neutron. Upper and lower limits are derived for σn,2n, σc, and σis (inelastic scattering) for all materials investigated. For a number of materials specific values for the cross sections are obtained.