We investigate the emission of sub-millimetre-wave radiation from galaxies in a 165 square arcminute region surrounding the Hubble Deep Field North. The data were obtained from dedicated observing runs from our group and others using the SCUBA camera on the James Clerk Maxwell Telescope, and combined using techniques specifically developed for low signal-to-noise source recovery. The resulting `Super-map is derived from about 60 shifts of JCMT time, taken in a variety of observing modes and chopping strategies, and combined here for the first time. At 850 micron we detect 19 sources at >4 sigma, including 5 not previously reported. We also list an additional 15 sources between 3.5 and 4.0 sigma (where 2 are expected by chance). The 450 micron map contains 5 sources at >4 sigma. We present a new estimate of the 850 micron and 450 micron source counts. The number of sub-mm galaxies we detect account for approximately 40% of the 850 micron sub-mm background, and we show that mild extrapolations can reproduce it entirely. A clustering analysis fails to detect any significant signal in this sample of SCUBA detected objects. A companion paper describes the multiwavelength properties of the sources.
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