  Using the Ricci and scalar curvatures of the configuration manifold of
gravitational N-body systems, we study the exponential instability in their
trajectories. It is found that the exponentiation time-scale for isotropic
Plummer spheres varies very little with particle number if the softening is
small. Large softening on the other hand has a marked effect and, if large
enough, can cause the curvatures to become positive. This last result confirms
the previous observations for self gravitating sheets and suggests that the
qualitative behaviour of large-N and continuum systems may be different, and
that their equivalence is only obtained in the limit of infinite $N$ and finite
softening. It is also found that the presence of a large fraction of the
kinetic energy in rotational motion increases the exponentiation time-scales
significantly --- an effect that should be expected given the regular nature of
nearly circular motion. In the light of the results of this and of previous
studies, it is suggested that the exponential instability may arise from low
order resonances between the period of the variation of the gravitational field
due to distant encounters and the orbital period of a test particle. For
periods long compared to the exponentiation time but short compared to the
diffusion time-scales of the action variables, the standard picture of
collisionless dynamics may be valid in an averaged sense. Instead it is
suggested that, at least for systems with well defined final states, the
relaxation time should scale as $\sim N^{1/2}$.
