High sensitivity (rms noise ~ 0.5 mJy) 21-cm HI line observations were made of
33 galaxies in the Virgo cluster, using the refurbished Arecibo telescope,
which resulted in the detection of 12 objects.
These data, combined with the measurements available from the literature, provide the first set of HI data that is complete
for all 355 late-type (Sa-Im-BCD) galaxies in the Virgo cluster with
m_p <= 18.0 mag.
The Virgo cluster \HI\ mass function (HIMF) that was derived for this optically selected galaxy sample is
in agreement with the HIMF derived for the Virgo cluster from the blind HIJASS HI survey
and is inconsistent with the Field HIMF.
This indicates that both in this rich cluster and in the general field, neutral hydrogen
is primarily associated with late-type galaxies, with marginal contributions
from early-type galaxies and isolated HI clouds. The inconsistency between the cluster and the field HIMF
derives primarily from the difference in the optical luminosity function of late-type galaxies in the two environments,
combined with the HI deficiency that is known to occur in galaxies in rich clusters.