  Recent deep blank field submillimeter surveys have revealed a population of
luminous high redshift galaxies that emit most of their energy in the
submillimeter. The results suggest that much of the star formation at high
redshift may be hidden to optical observations. In this paper we present
wide-area 850-micron SCUBA data on the Hawaii Survey Fields SSA13, SSA17, and
SSA22. Combining these new data with our previous deep field data, we establish
the 850-micron galaxy counts from 2 mJy to 10 mJy with a >3-sigma detection
limit. The area coverage is 104 square arcmin to 8 mJy and 7.7 square arcmin to
2.3 mJy. The differential 850-micron counts are well described by the function
n(S)=N_0/(a+S^3.2), where S is the flux in mJy, N_0=3.0 x 10^4 per square
degree per mJy, and a=0.4-1.0 is chosen to match the 850-micron extragalactic
background light. Between 20 to 30 per cent of the 850-micron background
resides in sources brighter than 2 mJy. Using an empirical fit to our >2 mJy
data constrained by the EBL at lower fluxes, we argue that the bulk of the
850-micron extragalactic background light resides in sources with fluxes near 1
mJy. The submillimeter sources are plausible progenitors of the present-day
spheroidal population.
