We have imaged a $sim$6 arcminute$^2$ region in the Bootes Deep Field using the 350 $mu$m-optimised second generation Submillimeter High Angular Resolution Camera (SHARC II), achieving a peak 1$sigma$ sensitivity of $sim$5 mJy. We detect three sources above 3$sigma$, and determine a spurious source detection rate of 1.09 in our maps. In the absence of $5sigma$ detections, we rely on deep 24 $mu$m and 20 cm imaging to deduce which sources are most likely to be genuine, giving two real sources. From this we derive an integral source count of 0.84$^{+1.39}_{-0.61}$ sources arcmin$^{-2}$ at $S>13$ mJy, which is consistent with 350 $mu$m source count models that have an IR-luminous galaxy population evolving with redshift. We use these constraints to consider the future for ground-based short-submillimetre surveys.
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