Logarithmic divergence in the virial expansion of transport coefficients of hard spheres. I

The expansion of transport coefficients of gases in powers of the density makes a logarithmic divergence appear in the second-order correction to Boltzmann order term. This divergence arises from the sequences of four collisions among four isolated hard spheres. The number of distinct sequences may be reduced to 10 in the cases of the shear viscosity and the heat conductivity and to 9 for the self-diffusion coefficient. For these three transport coefficients the contributions of two sequences are computed in the first Enskog approximation and given in terms of elementary functions.