  We use 772$\times 10^6$ $B \bar{B}$ meson pairs collected at the
$\Upsilon(4S)$ resonance with the Belle detector to measure the branching
fraction for $\bar{B} \rightarrow X_s \gamma$. Our measurement uses a
sum-of-exclusives approach in which 38 of the hadronic final states with
strangeness equal to $+1$, denoted by $X_s$, are reconstructed. The inclusive
branching fraction for $M_{X_s}<$ 2.8 GeV/$c^2$, which corresponds to a minimum
photon energy of 1.9 GeV, is measured to be ${\cal B}(\bar{B} \rightarrow X_s
\gamma)=(3.51\pm0.17\pm0.33)\times10^{-4}$, where the first uncertainty is
statistical and the second is systematic.
