Measurements have been made of the nonelastic cross sections of neutrons in Be, C, Al, Ti, Cr, Fe, Ni, Cu, Ag, Sn, Pb, and Bi. These cross sections include all processes except elastic scattering. The experiments have been carried out with monoenergetic neutrons of 3.5, 4.7, 7.1, 12.7, and 14.1 Mev. The neutrons were produced with a Van de Graaff accelerator using the nuclear reactions: ${\mathrm{T}}^{3}(p, n){\mathrm{He}}^{3}$, $\mathrm{D}(d, n){\mathrm{He}}^{3}$, and ${\mathrm{T}}^{3}(d, n){\mathrm{He}}^{4}$. Cross sections were determined from transmissions through spherical shells which were 3.8 cm in radius and 2 cm thick. A new type of neutron detector which gives energy information about neutrons and is insensitive to $\ensuremath{\gamma}$ radiation was placed at the center of the spherical shell and was used as a biased detector of neutrons. The results of these experiments show that the nonelastic neutron cross section for 12.7- and 14.1-Mev neutrons is nearly geometrical and is closely approximated by $\ensuremath{\sigma}=\ensuremath{\pi}{(R+\ensuremath{\lambda})}^{2}$, where $R=1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{A}^{\frac{1}{3}}$. The nonelastic cross sections are roughly constant in the energy range 5 to 14 Mev; below about 5 Mev the cross sections begin to decrease.The elastic cross sections can be obtained by subtracting the nonelastic cross sections from the total cross sections. The variations with energy of the nonelastic and elastic cross sections are quite different.Data with 12.7-Mev neutrons and low counter bias, give the relative number of $\ensuremath{\gamma}$ rays given off per inelastic collision of these neutrons. The number of $\ensuremath{\gamma}$ rays decreases rapidly with increasing atomic number and there are less than 5% as many $\ensuremath{\gamma}$ rays from Bi as from Al, Ti, Cr, and Fe.