  We consider the Kolmogorov-Sinai entropy for dilute gases of $N$ hard disks
or spheres. This can be expanded in density as $h_{\mathrm{KS}} \propto n N
[\ln n a^d+ B + O(n a^d)+O(1/N)]$, with $a$ the diameter of the sphere or disk,
$n$ the density, and $d$ the dimensionality of the system. We estimate the
constant $B$ by solving a linear differential equation for the approximate
distribution of eigenvalues of the inverse radius of curvature tensor. We
compare the resulting values of $B$ both to previous estimates and to existing
simulation results, finding very good agreement with the latter. Also, we
compare the distribution of eigenvalues of the inverse radius of curvature
tensor resulting from our calculations to new simulation results. For most of
the spectrum the agreement between our calculations and the simulations again
is very good.
