We investigate the dynamical evolution of the Galactic globular cluste
r system in considerably greater detail than has been done hitherto, f
inding that destruction rates are significantly larger than given by p
revious estimates. The general scheme (but not the detailed implementa
tion) follows Aguilar Hut, & Ostriker. For the evolution of individual
clusters, we use a Fokker-Planck code including the most important ph
ysical processes governing the evolution: two-body relaxation, tidal t
runcation of clusters, compressive gravitational shocks while clusters
pass through the Galactic disk, and tidal shocks due to passage close
to the bulge. Gravitational shocks are treated comprehensively, using
a recent result by Kundic & Ostriker that the (Delta E(2)) shock-indu
ced relaxation term, driving an additional dispersion of energies, Is
generally more important than the usual energy shift term (Delta E). V
arious functional forms of the correction factor are adopted to allow
for the adiabatic conservation of stellar actions in a presence of tra
nsient gravitational perturbation. We use a recent compilation of the
globular cluster positional and structural parameters, and a collectio
n of radial velocity measurements. Two transverse to the line-of-sight
velocity components were assigned randomly according to the two kinem
atic models for the cluster system (following the method of Aguilar, H
ut, & Ostriker): one with an isotropic peculiar velocity distribution,
corresponding to the present-day cluster population, and the other wi
th the radially preferred peculiar velocities, similar to those of the
stellar halo. We use the Ostriker & Caldwell and the Bahcall, Schmidt
, & Soneira models for our Galaxy. For each cluster in our sample, we
calculated its orbits over a Hubble time, starting from the present ob
served positions and assumed velocities. Medians of the resulting set
of peri- and apogalactic distances and velocities are used then as an
input for the Fokker-Planck code. Evolution of the cluster is followed
up to its total dissolution due to a coherent action of all of tile d
estruction mechanisms. The rate of destruction is then obtained as a m
edian over all the cluster sample, in accord with Aguilar, Hut, & Ostr
iker. We find that the total destruction rate is much larger than that
given by Aguilar, Hut, & Ostriker with more than half of the present
clusters (52%-58% for the Ostriker & Caldwell model, and 75%-86% for t
he Bahcall, Schmidt, & Soneira model) destroyed in the next Hubble tim
e. Alternatively put, the typical time to destruction is comparable to
the typical age, a result that would follow from (but is not required
by) an initially power law distribution of destruction times. We disc
uss some implications for a past history of the globular cluster syste
m and the initial distribution of the destruction times, raising the p
ossibility that the current population is but a very small fraction of
the initial population with the remnants of the destroyed clusters co
nstituting presently a large fraction of the spheroid (bulge + halo) s
tellar population.