  We present new constraints on the initial mass spectrum of the Galactic Old
Halo globular clusters. This has remained poorly-known so far, as both an
initial power-law mass spectrum and an initial lognormal mass function could
have evolved into the presently observed globular cluster mass distribution,
making the initial contribution of now lost low-mass objects ill-determined.
Our approach consists in comparing the evolution with time of both the radial
mass density profile and the number density profile of the globular cluster
system. Using the analytical expression established by Vesperini & Heggie for
the temporal evolution of the mass of a globular cluster on a circular orbit in
a stable Galactic potential, we evolve the mass and number density profiles of
many putative globular cluster systems, each starting with different initial
cluster mass spectrum and initial cluster space-density. We then compare the
modelled profiles with those of the Old Halo cluster system in order to
investigate which system(s) provide(s) the best consistency with the data.
(abridged)
