The general theory of slip flow established in the late 1960s is revisited. For a long time, the complete set of data of the slip and jump coefficients up to the second order of the small Knudsen number have been available only for the Bhatnagar-Gross-Krook model. The present paper provides the complete set of data of those coefficients for a hard-sphere gas on the diffuse reflection boundary. The data are obtained by using the general identities that have been deduced from recently developed symmetry arguments. A few simple application examples are also presented.