Neutron elastic and inelastic scattering cross sections have been measured for 60.5 keV neutrons incident on /sup 187,188/Os. For /sup 187/Os the cross section for elastic scattering is 11 b and for inelastic scattering to the 9.75-keV level it is 1.13 b. These results and other scattering properties are represented in phase shift and scattering potential analyses, which then allow the prediction of neutron capture by /sup 187/Os nuclei in the 9.75-keV and ground levels. Capture rates thus provided are used in the Re-Os nucleochronology, and lead to a long galactic age, about 18 to 20 Gyr.