  This paper details the solar neutrino analysis of the 385.17-day Phase-III
data set acquired by the Sudbury Neutrino Observatory (SNO). An array of $^3$He
proportional counters was installed in the heavy-water target to measure
precisely the rate of neutrino-deuteron neutral-current interactions. This
technique to determine the total active $^8$B solar neutrino flux was largely
independent of the methods employed in previous phases. The total flux of
active neutrinos was measured to be
$5.54^{+0.33}_{-0.31}(stat.)^{+0.36}_{-0.34}(syst.)\times 10^{6}$ cm$^{-2}$
s$^{-1}$, consistent with previous measurements and standard solar models. A
global analysis of solar and reactor neutrino mixing parameters yielded the
best-fit values of $\Delta m^2 = 7.59^{+0.19}_{-0.21}\times 10^{-5}{eV}^2$ and
$\theta = 34.4^{+1.3}_{-1.2}$ degrees.
