  In an equilibrium system, the Kolmogorov-Sinai entropy, $h_{\mathrm{KS}}$,
equals the sum of the positive Lyapunov exponents, the exponential rates of
divergence of infinitesimal perturbations. Kinetic theory may be used to
calculate the Kolmogorov-Sinai entropy for dilute gases of many hard disks or
spheres in equilibrium at low number density $n$. The density expansion of
$h_{\mathrm{KS}}$ is $N \bar\nu A [\ln n + B + O(n)]$, where $\bar\nu$ is the
single-particle collision frequency. Previous calculations of $A$ were
succesful. Calculations of $B$, however, were unsatisfactory. In this paper, I
show how the probability distribution of the stretching factor can be
determined from a nonlinear differential equation by an iterative method. From
this the Kolmogorov-Sinai entropy follows as the average of the logarithm of
the stretching factor per unit time. I calculate approximate values of $B$ and
compare these to results from existing simulations. The agreement is good.
