The transmissions of neutrons through spherical shells of normal uranium, oralloy, and Pu239 are reported. One group of measurements was made using a pure fission neutron source produced by thermal neutrons. The other group of measurements was made using monoenergetic neutrons. From both groups of measurements, the inelastic scattering cross sections have been determined according to methods developed in Los Alamos Scientific Laboratory Report LA-1429 (Jaunary 1955)