Measurements of charmless hadronic two-body B meson decays and the ratio $\mathcal{B}\left(\overrightarrow{B}DK\right)/\mathcal{B}\left(\overrightarrow{B}D\pi \right)$

We present final measurements of 13 charmless hadronic B decay modes from the CLEO experiment. The decay modes include the ten $\pi \pi ,$ $K\pi ,$ and KK final states and new limits on dibaryonic final states, $p\overline{p},$ $p\overline{\Lambda },$ and $\Lambda \overline{\Lambda },$ as well as a new determination of the ratio $\mathcal{B}\left(\overrightarrow{B}DK\right)/\mathcal{B}\left(\overrightarrow{B}D\pi \right).\mathrm{}$ The results are based on the full CLEO II and CLEO III data samples totalling $15.3{\mathrm{fb}}^{-1}$ at the ${\rm Y}\mathrm{}\left(4S\right),$ and supercede previously published results.