  Recent submillimetre surveys have revealed a population of dusty, high
redshift sources of great cosmological significance for understanding
dust-enshrouded star formation in distant galaxies, and for determining the
origin of the far-IR background. In this paper, we analyze nine rich cluster
fields mapped at 850 and 450 microns with the SCUBA array on the James Clerk
Maxwell telescope. Lensing models of the clusters are developed in order to
derive accurate source counts for our sample. VLA maps of the same clusters are
used to help constrain the redshift distribution of our SCUBA detections.
Implications for high redshift galaxies and for the far-IR background are
discussed. We also provide limits on distributed dust produced by cooling flows
in these clusters.
