  We have carried out a fully sampled large area ($4^{\circ} \times 8^{\circ}$)
21cm \HI line survey of part of the Virgo cluster using the Jodrell Bank
multi-beam instrument. The survey has a sensitivity some 3 times better than
the standard HIJASS and HIPASS surveys. We detect 31 galaxies, 27 of which are
well known cluster members. The four new detections have been confirmed in the
HIPASS data and by follow up Jodrell Bank pointed observations. One object lies
behind M86, but the other 3 have no obvious optical counter parts upon
inspection of the digital sky survey fields. These 3 objects were mapped at
Arecibo with a smaller \am{3}{6} HPBW and a 4 times better sensitivity than the
Jodrell Bank data, which allow an improved determination of the dimensions and
location of two of the objects, but surprisingly failed to detect the third.
The two objects are resolved by the Arecibo beam giving them a size far larger
than any optical images in the nearby field. To our mass limit of $5 \times
10^{7}$ $\frac{\Delta v}{50 km s^{-1}}$ $M_{\odot}$ and column density limit of
$3 \times 10^{18}$ $\frac{\Delta v}{50 km s^{-1}}$ atoms cm$^{-2}$ these new
detections represent only about 2% of the cluster atomic hydrogen mass. Our
observations indicate that the \HI mass function of the cluster turns down at
the low mass end making it very different to the field galaxy \HI mass
function. This is quite different to the Virgo cluster optical luminosity
function which is much steeper than that in the general field. Many of the
sample galaxies are relatively gas poor compared to \HI selected samples of
field galaxies, confirming the 'anaemic spirals' view of Virgo cluster late
type galaxies.
