  We apply a simple linearization, well known in solid state physics, to
approximate the evolution at early times of cosmological N-body simulations of
gravity. In the limit that the initial perturbations, applied to an infinite
perfect lattice, are at wavelengths much greater than the lattice spacing $l$
the evolution is exactly that of a pressureless self-gravitating fluid treated
in the analagous (Lagrangian) linearization, with the Zeldovich approximation
as a sub-class of asymptotic solutions. Our less restricted approximation
allows one to trace the evolution of the discrete distribution until the time
when particles approach one another (i.e. ``shell crossing''). We calculate
modifications of the fluid evolution, explicitly dependent on $l$ i.e.
discreteness effects in the N body simulations. We note that these effects
become increasingly important as the initial red-shift is increased at fixed
$l$. The possible advantages of using a body centred cubic, rather than simple
cubic, lattice are pointed out.
