  We estimate the initial He content in about 30% of the Galactic globular
clusters (GGCs) from new star counts we have performed on the recently
published HST snapshot database of Colour Magnitude Diagrams (Piotto et al.
2002). More in detail, we use the so-called $R$-parameter and estimate the He
content from a calibration based on a recently updated set of stellar models.
We performed an accurate statistical analysis in order to assess whether GGCs
show a statistically significant spread in their initial He abundances, and
whether there is a correlation with the metallicity. We do not find any
significant dependence of the He abundance on the GC metallicity; this provides
an important constraint for models of Galaxy formation and evolution. Apart
from GGCs with the bluest HB morphology, the observed spread in the individual
He abundances is statistically compatible with the individual errors. This
means that either there is no intrinsic He spread among the GGCs, or that this
is masked by the errors. In the latter case we have estimated a firm 1$\sigma$
upper limit of 0.019 to the possible intrinsic spread. In case of the GGCs with
the bluest HB morphology we detect a significant spread towards higher
abundances inconsistent with the individual errors. In the hypothesis that the
intrinsic dispersion on the individual He abundances is zero, taking into
account the errors on the individual R-parameter estimates, as well as the
uncertainties on the GGC [M/H] scale and theoretical calibration, we have
determined an initial He abundance Y(GGC)=0.250\pm0.006 a value in perfect
agreement with current estimates based on CMB radiation analyses and
cosmological nucleosynthesis computations.
