  We present the first results of a sub-millimeter survey of distant clusters
using the new Sub-mm Common-User Bolometer Array (SCUBA) on the James Clerk
Maxwell Telescope. We have mapped fields in two massive, concentrated clusters,
A370 at z=0.37 and Cl2244-02 at z=0.33, at wavelengths of 450 and 850-um. The
resulting continuum maps cover a total area of about 10 sq. arcmin to 1 sigma
noise levels less than 14 and 2 mJy per beam at the two wavelengths, 2-3 orders
of magnitude deeper than was previously possible. We have concentrated on
lensing clusters to exploit the amplification of all background sources by the
cluster, improving the sensitivity by a factor of 1.3--2 as compared with a
blank-field survey. A cumulative source surface density of (2.4+/-1.0) x 10^3
per sq. degree is found to a 50% completeness limit of ~4 mJy at 850-um. The
sub-mm spectral properties of these sources indicate that the majority lie at
high redshift, z>1. Without correcting for lens amplification, our observations
limit the blank-field counts at this depth. The surface density is 3 orders of
magnitude greater than the expectation of a non-evolving ber density of
strongly star-forming galaxies in the high-redshift Universe and suggest that
optical surveys may have substantial underestimated the star formation density
in the distant Universe. Deeper sub-mm surveys with SCUBA should detect large
numbers of star-forming galaxies at high redshift, and so provide strong
constraints on the formation of normal galaxies.
