  High sensitivity (rms noise $\sim 0.5$ 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 $m_p \leq 18.0$ 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.
