  This paper summarises a numerical investigation of the statistical properties
of orbits evolved in `frozen,' time-independent N-body realisations of smooth,
time-independent density distributions, allowing for 10^(2.5)<N<10^(5.5). Two
principal conclusions were reached: (1) In the limit of a nearly `unsoftened'
two-body kernel, the value of the largest Lyapunov exponent does NOT appear to
decrease systematically with increasing N. (2) Nevertheless, there is a clear
quantifiable sense in which, on the average, as N increases chaotic orbits in
the frozen-N systems come to more closely approximate characteristics in the
smooth potential. When viewed in configuration or velocity space, or as probed
by collisionless invariants like angular momentum, frozen-N orbits typically
diverge from smooth potential characteristics as a power law in time on a time
scale proportional to N^(1/2)t_D, with t_D a characteristic dynamical, or
crossing, time.
