``Think not thy own shadow longer than that of others.''
-- Sir Thomas Browne, Christian Morals. (1682)
Using this optimized algorithm, shadowing experiments were performed on
N-body systems in which M bodies move amongst N-M fixed ones.
For systems of 
with a variable-timestep
integrator and no softening, our results show that the length of time
an orbit is shadowable decreases with increasing M. However, it is
unclear whether this is owing to collective effects of interacting moving
particles, or whether each particle individually has a ``glitch rate'',
causing the global glitch rate to increase linearly with the number of
particles. However, for a system of N=65536,M=1 with softening and
integrating using constant timestep leapfrog, we were able to shadow
the moving particle for two dozen crossing times, which is
encouraging.